diff --git a/LeanPool/SpherePacking/Conclusion.lean b/LeanPool/SpherePacking/Conclusion.lean
index 1e08e2269d..1874f57cfd 100644
--- a/LeanPool/SpherePacking/Conclusion.lean
+++ b/LeanPool/SpherePacking/Conclusion.lean
@@ -800,32 +800,15 @@ private theorem radialSchwartzParametric_iteratedFDeriv_integral
       rw [hprevious,
         (radialSchwartzParametric_hasFDerivAt_iteratedIntegral
           μ g C hmeas hbound n x).fderiv]
-      calc
-        (continuousMultilinearCurryLeftEquiv ℝ
-          (fun _ : Fin (n + 1) ↦ Ambient d) ℂ).symm
-            (∫ a : α, fderiv ℝ
-              (iteratedFDeriv ℝ n (g a : Ambient d → ℂ)) x ∂μ) =
-            ∫ a : α,
-              (continuousMultilinearCurryLeftEquiv ℝ
-                (fun _ : Fin (n + 1) ↦ Ambient d) ℂ).symm
-                  (fderiv ℝ
-                    (iteratedFDeriv ℝ n (g a : Ambient d → ℂ)) x)
-                  ∂μ := by
-              exact
-                (LinearIsometry.integral_comp_comm
-                  (𝕜 := ℝ)
-                  (LinearIsometryEquiv.toLinearIsometry
-                    ((continuousMultilinearCurryLeftEquiv ℝ
-                      (fun _ : Fin (n + 1) ↦ Ambient d) ℂ).symm))
-                  (fun a : α ↦ fderiv ℝ
-                    (iteratedFDeriv ℝ n
-                      (g a : Ambient d → ℂ)) x)).symm
-        _ = ∫ a : α, iteratedFDeriv ℝ (n + 1)
-              (g a : Ambient d → ℂ) x ∂μ := by
-              apply integral_congr_ae
-              filter_upwards [] with a
-              rw [iteratedFDeriv_succ_eq_comp_left]
-              rfl
+      simp_rw [iteratedFDeriv_succ_eq_comp_left, Function.comp_apply]
+      exact
+        (LinearIsometry.integral_comp_comm
+          (𝕜 := ℝ)
+          (LinearIsometryEquiv.toLinearIsometry
+            ((continuousMultilinearCurryLeftEquiv ℝ
+              (fun _ : Fin (n + 1) ↦ Ambient d) ℂ).symm))
+          (fun a : α ↦ fderiv ℝ
+            (iteratedFDeriv ℝ n (g a : Ambient d → ℂ)) x)).symm
 
 end ProbabilityAverage
 
diff --git a/LeanPool/SpherePacking/Foundations.lean b/LeanPool/SpherePacking/Foundations.lean
index bd29e766fa..730cd3c300 100644
--- a/LeanPool/SpherePacking/Foundations.lean
+++ b/LeanPool/SpherePacking/Foundations.lean
@@ -7,26 +7,20 @@ Authors: OpenAI, Sidharth Hariharan, Gareth Ma, Dean Cureton
 module
 
 public import Mathlib.Analysis.Distribution.SchwartzSpace.Basic
-import Mathlib.AlgebraicTopology.FundamentalGroupoid.SimplyConnected
 import Mathlib.Analysis.Complex.RemovableSingularity
-import Mathlib.Analysis.Convex.Contractible
 import Mathlib.Analysis.Convex.SpecificFunctions.Deriv
 import Mathlib.Analysis.Distribution.SchwartzSpace.Fourier
 import Mathlib.Analysis.InnerProductSpace.Calculus
 import Mathlib.Analysis.MellinInversion
 import Mathlib.Analysis.Meromorphic.Complex
 import Mathlib.Analysis.Real.Pi.Bounds
-import Mathlib.Analysis.SpecialFunctions.Complex.Arctan
 import Mathlib.Analysis.SpecialFunctions.Log.Base
 import Mathlib.Analysis.SpecialFunctions.Pow.Integral
 import Mathlib.Analysis.SpecialFunctions.Trigonometric.DerivHyp
 import Mathlib.MeasureTheory.Integral.Asymptotics
 import Mathlib.MeasureTheory.Measure.Lebesgue.VolumeOfBalls
 import Mathlib.Probability.Moments.ComplexMGF
-import Mathlib.RingTheory.SimpleRing.Principal
 import Mathlib.Tactic.NormNum.RealSqrt
-import Mathlib.Tactic.Polynomial.Basic
-import Mathlib.Tactic.ReduceModChar
 
 /-!
 # Foundations
@@ -153,7 +147,7 @@ private theorem plusPolynomial_imaginary_re_pos {ε u : ℝ}
     (hε : 0 < ε) (hu : -1 < u) :
     0 < (plusPolynomial ε (Complex.I * (u : ℂ))).re := by
   have hs : 0 ≤ (1 - u) ^ 2 * (1 + u) :=
-    mul_nonneg (sq_nonneg _) (by linarith)
+    mul_nonneg (sq_nonneg _) (by linear_combination hu)
   rw [plusPolynomial_imaginary, Complex.ofReal_re]
   exact add_pos_of_pos_of_nonneg (div_pos hε four_pos) hs
 
@@ -161,16 +155,16 @@ private theorem minusPolynomial_imaginary_re_neg {ε u : ℝ}
     (hε : 0 < ε) (hu : 1 + ε / 4 ≤ u) :
     (minusPolynomial ε (Complex.I * (u : ℂ))).re < 0 := by
   rw [minusPolynomial_imaginary, Complex.ofReal_re]
-  have huone : 1 ≤ u := by linarith
+  have huone : 1 ≤ u := by linarith only [hε, hu]
   have hs : (4 : ℝ) ≤ (1 + u) ^ 2 := by
-    linarith [sq_nonneg (u - 1)]
-  have ht : ε / 4 ≤ u - 1 := by linarith
+    linarith only [sq_nonneg (u - 1), hε, hu]
+  have ht : ε / 4 ≤ u - 1 := by linear_combination hu
   have hproduct : ε ≤ (u - 1) * (1 + u) ^ 2 := by
     calc
       ε = (ε / 4) * 4 := by ring
       _ ≤ (u - 1) * (1 + u) ^ 2 :=
-        mul_le_mul ht hs (by norm_num) (by linarith)
-  linarith
+        mul_le_mul ht hs (by norm_num) (by linarith only [hε, hu])
+  linarith only [hε, hproduct]
 
 end
 
@@ -239,7 +233,7 @@ private theorem integer_gamma_product (k : ℕ) {y : ℝ} (hy : y ≠ 0) :
     have him := congrArg Complex.im hj
     try dsimp [z] at him
     norm_num at him
-    exact hy (by linarith)
+    exact hy (by exact him)
   simpa only [add_comm] using! gamma_add_nat_eq_product z hz k
 
 private theorem half_integer_gamma_product (k : ℕ) (y : ℝ) :
@@ -255,8 +249,8 @@ private theorem half_integer_gamma_product (k : ℕ) (y : ℝ) :
     try dsimp [z] at hre
     norm_num at hre
     have hjnonneg : 0 ≤ (j : ℝ) := Nat.cast_nonneg j
-    linarith
-  simpa [z, add_comm, add_left_comm, add_assoc] using!
+    linarith only [hre]
+  simpa only [z, add_comm, add_left_comm, add_assoc] using!
     gamma_add_nat_eq_product z hz k
 
 end
@@ -373,7 +367,7 @@ private theorem antiFourierPart_nonneg_of_signs {d : ℕ}
     (x : Euclidean d) (hx : R ≤ ‖x‖) :
     0 ≤ (antiFourierPart f x).re := by
   change 0 ≤ ((𝓕 f) x).re - (f x).re
-  linarith [hfourier x, houtside x hx]
+  linarith only [hfourier x, houtside x hx, hfourier, houtside, hx]
 
 private structure AntiFourierWitness (d : ℕ) (R : ℝ) where
   function : TestFunction d
@@ -813,13 +807,13 @@ private theorem analytic_eq_zero_of_imaginary_ray
     refine ⟨z, ⟨?_, ?_⟩, ?_⟩
     · apply hvanish u
       try dsimp [u, t₀]
-      linarith
+      linarith only [hε]
     · intro hz
       have hu : u = t₀ := by
         have him := congrArg Complex.im hz
         simpa [z, z₀] using! him
       try dsimp [u] at hu
-      linarith
+      linarith only [hε, hu]
     · dsimp [z₀, z, u]
       rw [dist_eq_norm, ← sub_mul, ← Complex.ofReal_sub, norm_mul,
         Complex.norm_real, Complex.norm_I, mul_one, Real.norm_eq_abs]
@@ -839,6 +833,9 @@ private theorem nonnegative_compact_fourier_fixed_eq_zero {d : ℕ}
     (hcompact : HasCompactSupport (g : Euclidean d → ℂ))
     (hfixed : (𝓕 g : TestFunction d) = g) :
     g = 0 := by
+  let : NormedAddCommGroup (EuclideanSpace ℝ (Fin d)) := inferInstance
+  let : NormedSpace ℝ (EuclideanSpace ℝ (Fin d)) := inferInstance
+  let : MeasureSpace (EuclideanSpace ℝ (Fin d)) := inferInstance
   classical
   let : Nontrivial (Euclidean d) :=
     Module.nontrivial_of_finrank_pos (R := ℝ) (M := Euclidean d)
@@ -851,7 +848,7 @@ private theorem nonnegative_compact_fourier_fixed_eq_zero {d : ℕ}
     fun x => -2 * Real.pi * @inner ℝ (Euclidean d) _ x e
   have hX : Continuous X := by
     try dsimp [X]
-    fun_prop
+    exact Continuous.const_mul (Continuous.inner continuous_id' continuous_const) (-2 * Real.pi)
   let μ : Measure (Euclidean d) := nonnegativeSchwartzMeasure g hg
   let F : ℂ → ℂ := ProbabilityTheory.complexMGF X μ
   have hanalytic : AnalyticOnNhd ℂ F Set.univ := by
@@ -1101,6 +1098,7 @@ private theorem integral_radialProfile_mul {d : ℕ} (hd : 0 < d)
       radialSurfaceArea d •
         ∫ r : ℝ in Ioi 0,
           r ^ (d - 1) • (radialProfile hd f r * w r) := by
+  let : MeasureSpace (EuclideanSpace ℝ (Fin d)) := inferInstance
   let : Nonempty (Fin d) := Fin.pos_iff_nonempty.mp hd
   calc
     (∫ x : Euclidean d, f x * w ‖x‖) =
@@ -1303,6 +1301,9 @@ private theorem schwartz_mul_norm_cpow_integrable {d : ℕ}
   have hdim : 1 ≤ Module.finrank ℝ (Euclidean d) := by
     rw [finrank_euclideanSpace_fin]
     omega
+  let : NormedAddCommGroup (EuclideanSpace ℝ (Fin d)) := inferInstance
+  let : NormedSpace ℝ (EuclideanSpace ℝ (Fin d)) := inferInstance
+  let : MeasureSpace (EuclideanSpace ℝ (Fin d)) := inferInstance
   have hexponent :
       -z.re < (Module.finrank ℝ (Euclidean d) : ℝ) := by
     rw [finrank_euclideanSpace_fin]
@@ -1379,7 +1380,7 @@ private theorem gaussianMellinParameter_integrable
     simpa only [Real.rpow_one, neg_mul] using!
       (integrableOn_rpow_mul_exp_neg_mul_rpow
         (p := (1 : ℝ)) (s := b.re - 1) (b := r)
-        (by linarith) (by norm_num) hr)
+        (by linear_combination hb) (by norm_num) hr)
   apply (integrable_norm_iff hmeas).mp
   apply hreal.congr_fun _ measurableSet_Ioi
   intro a ha
@@ -1492,6 +1493,10 @@ private theorem gaussianMellinMixture_integrable {d : ℕ}
       (Function.uncurry (gaussianMellinMixture f b))
       ((volume : Measure (Euclidean d)).prod
         (volume.restrict (Ioi (0 : ℝ)))) := by
+  let : Nonempty (Euclidean d) := ⟨0⟩
+  let : NormedAddCommGroup (EuclideanSpace ℝ (Fin d)) := inferInstance
+  let : NormedSpace ℝ (EuclideanSpace ℝ (Fin d)) := inferInstance
+  let : MeasureSpace (EuclideanSpace ℝ (Fin d)) := inferInstance
   let : Nonempty (Fin d) := Fin.pos_iff_nonempty.mp hd
   have hpow : Measurable (fun a : ℝ => (a : ℂ) ^ (b - 1)) := by
     apply measurable_of_continuousOn_compl_singleton (0 : ℝ)
@@ -1645,6 +1650,7 @@ private theorem mellin_gaussianMellinPairingProfile {d : ℕ}
       Complex.Gamma b *
         (∫ x : Euclidean d,
           f x * (‖x‖ : ℂ) ^ (-(2 * b))) := by
+  let : MeasureSpace (EuclideanSpace ℝ (Fin d)) := inferInstance
   let : Nonempty (Fin d) := Fin.pos_iff_nonempty.mp hd
   unfold mellin
   simp only [smul_eq_mul]
@@ -1815,11 +1821,11 @@ private theorem fourier_riesz_pairing {d : ℕ}
                     (-(2 * ((d : ℂ) / 2 - b)))))) := by
   have hdual : 0 < (((d : ℂ) / 2 - b).re) := by
     norm_num
-    linarith
+    linarith only [hbd]
   have hdual_dimension :
       2 * (((d : ℂ) / 2 - b).re) < (d : ℝ) := by
     norm_num
-    linarith
+    linarith only [hb]
   calc
     Complex.Gamma b *
         (∫ ξ : Euclidean d,
@@ -1862,11 +1868,11 @@ private theorem fourier_riesz_pairing_strip {d : ℕ}
   have hb : 0 < b.re := by
     try dsimp [b]
     norm_num
-    linarith
+    exact hsd
   have hbd : 2 * b.re < (d : ℝ) := by
     try dsimp [b]
     norm_num
-    linarith
+    linear_combination hs
   have hleft : -(2 * b) = s - (d : ℂ) := by
     try dsimp [b]
     ring
@@ -1895,7 +1901,7 @@ private theorem radial_fourier_mellin_strip {d : ℕ}
             mellin (radialProfile hd f) ((d : ℂ) - s) := by
   have hdual : 0 < ((((d : ℂ) - s) / 2).re) := by
     norm_num
-    linarith
+    exact hsd
   have hgamma :
       Complex.Gamma (((d : ℂ) - s) / 2) ≠ 0 :=
     Complex.Gamma_ne_zero_of_re_pos hdual
@@ -2038,7 +2044,7 @@ private theorem shellOscillation_eq_sinc (B T : ℝ) :
       congr 2 <;> congr 1 <;> ring
     field_simp
     ring_nf at hsin ⊢
-    linarith
+    linarith only [hsin]
 
 private theorem cos_le_quartic {x : ℝ} (hx0 : 0 ≤ x) (hx1 : x ≤ 1) :
     Real.cos x ≤ 1 - x ^ 2 / 2 + x ^ 4 * (5 / 96 : ℝ) := by
@@ -2071,15 +2077,15 @@ private theorem sin_le_quintic {x : ℝ} (hx0 : 0 ≤ x) (hx1 : x ≤ 1) :
 private theorem sin_le_linear_sub_cubic {x : ℝ}
     (hx0 : 0 ≤ x) (hxhalf : x ≤ (1 / 2 : ℝ)) :
     Real.sin x ≤ x - (4 / 25 : ℝ) * x ^ 3 := by
-  have hx1 : x ≤ (1 : ℝ) := by linarith
+  have hx1 : x ≤ (1 : ℝ) := by linear_combination hxhalf
   have hsin := sin_le_quintic hx0 hx1
   have hsq : x ^ 2 ≤ (1 / 4 : ℝ) := by
     linarith only [mul_nonneg hx0 (sub_nonneg.mpr hxhalf), hxhalf]
   have hcub : 0 ≤ x ^ 3 := pow_nonneg hx0 _
   have hfifth : x ^ 5 ≤ x ^ 3 / 4 := by
     have hprod := mul_nonneg hcub (sub_nonneg.mpr hsq)
-    linarith [show x ^ 5 = x ^ 3 * x ^ 2 by ring]
-  linarith
+    linarith only [show x ^ 5 = x ^ 3 * x ^ 2 by ring, hprod]
+  linarith only [hsin, hcub, hfifth]
 
 private theorem sinc_abs (x : ℝ) : Real.sinc |x| = Real.sinc x := by
   rcases le_total 0 x with hx | hx
@@ -2100,13 +2106,13 @@ private theorem sinc_quadratic_gap_nonneg {x : ℝ}
   have hsin := sin_le_linear_sub_cubic hxpos.le hxhalf
   have hfrac : Real.sin x / x ≤ 1 - (4 / 25 : ℝ) * x ^ 2 := by
     apply (div_le_iff₀ hxpos).2
-    linarith
-  linarith
+    linear_combination hsin
+  linear_combination hfrac
 
 private theorem abs_sinc_le_twentyfour_twentyfive {x : ℝ}
     (hx : (1 / 2 : ℝ) ≤ x) :
     |Real.sinc x| ≤ (24 / 25 : ℝ) := by
-  have hxpos : 0 < x := by linarith
+  have hxpos : 0 < x := by linear_combination hx
   have hhalf : Real.sin (1 / 2 : ℝ) ≤ (12 / 25 : ℝ) := by
     have h := sin_le_quintic (x := (1 / 2 : ℝ)) (by norm_num) (by norm_num)
     norm_num at h ⊢
@@ -2125,7 +2131,7 @@ private theorem abs_sinc_le_twentyfour_twentyfive {x : ℝ}
     · have hslope := strictConcaveOn_sin_Icc.secant_strict_mono
         (a := (0 : ℝ)) (x := (1 / 2 : ℝ)) (y := x)
         ⟨le_rfl, Real.pi_pos.le⟩
-        ⟨by norm_num, by linarith [Real.pi_gt_three]⟩
+        ⟨by norm_num, by linarith only [Real.pi_gt_three, hxpi, hlt]⟩
         ⟨hxpos.le, hxpi⟩
         (by norm_num) hxpos.ne' hlt
       simp only [Real.sin_zero, sub_zero] at hslope
@@ -2144,12 +2150,12 @@ private theorem sinc_explicit (T : ℝ) :
     rw [← sinc_abs (T / 2)]
     simp only [abs_div, Nat.abs_ofNat]
   by_cases hsmall : |T| ≤ 1
-  · have hxhalf : |T| / 2 ≤ (1 / 2 : ℝ) := by linarith
+  · have hxhalf : |T| / 2 ≤ (1 / 2 : ℝ) := by linarith only [hsmall]
     have hgap := sinc_quadratic_gap_nonneg
       (x := |T| / 2) (by positivity) hxhalf
     have hsq : T ^ 2 ≤ (1 : ℝ) := by
       have habsq : |T| ^ 2 ≤ (1 : ℝ) := by
-        linarith [mul_nonneg (abs_nonneg T) (sub_nonneg.mpr hsmall)]
+        linarith only [mul_nonneg (abs_nonneg T) (sub_nonneg.mpr hsmall), hsmall]
       simpa only [sq_abs] using! habsq
     have hscaled :
         (4 / 25 : ℝ) * (|T| / 2) ^ 2 =
@@ -2161,12 +2167,12 @@ private theorem sinc_explicit (T : ℝ) :
   · have hlarge : 1 ≤ |T| := le_of_not_ge hsmall
     have hsq : (1 : ℝ) ≤ T ^ 2 := by
       have habsq : (1 : ℝ) ≤ |T| ^ 2 := by
-        linarith [sq_nonneg (|T| - 1)]
+        linarith only [sq_nonneg (|T| - 1), hsmall]
       simpa only [sq_abs] using! habsq
     have hgap := abs_sinc_le_twentyfour_twentyfive
-      (x := |T| / 2) (by linarith)
+      (x := |T| / 2) (by linarith only [hsmall])
     rw [min_eq_right hsq, hsinc]
-    linarith
+    linear_combination hgap
 
 private theorem shellOscillation_lower_bound (B T : ℝ) :
     (1 / 25 : ℝ) * min (T ^ 2) 1 ≤ shellOscillation B T := by
@@ -2182,7 +2188,7 @@ private theorem shellOscillation_lower_bound (B T : ℝ) :
         abs_mul _ _
       _ ≤ |Real.sinc (T / 2)| :=
         mul_le_of_le_one_right (abs_nonneg _) hcos
-  linarith [sinc_explicit T]
+  linarith only [sinc_explicit T, hprod]
 
 private theorem cosh_ratio_lower {a δ : ℝ} (ha : 0 ≤ a) (hδ : 0 ≤ δ) :
     Real.exp (δ * a) / 2 ≤
@@ -2191,7 +2197,7 @@ private theorem cosh_ratio_lower {a δ : ℝ} (ha : 0 ≤ a) (hδ : 0 ≤ δ) :
   rw [show (1 + δ) * a = a + δ * a by ring, Real.cosh_add]
   have hq : Real.exp (δ * a) / 2 ≤ Real.cosh (δ * a) := by
     rw [Real.cosh_eq]
-    linarith [Real.exp_pos (-(δ * a))]
+    linarith only [Real.exp_pos (-(δ * a))]
   calc
     Real.exp (δ * a) / 2 * Real.cosh a =
         Real.cosh a * (Real.exp (δ * a) / 2) := by ring
@@ -2254,7 +2260,7 @@ private theorem positiveShellDamping_lower_bound {ε ℓ δ T : ℝ}
       (fun a : ℝ => C * (1 - Real.cos (a * T))) :=
     continuous_const.mul hosc
   have hcosh : Continuous (fun a : ℝ => Real.cosh ((1 + δ) * a)) := by
-    fun_prop
+    exact Continuous.comp' Real.continuous_cosh (Continuous.const_mul continuous_id' (1 + δ))
   have hright : Continuous
       (fun a : ℝ => positiveShellDensity ε a *
         Real.cosh ((1 + δ) * a) * (1 - Real.cos (a * T))) :=
@@ -2273,7 +2279,9 @@ private theorem positiveShellDamping_lower_bound {ε ℓ δ T : ℝ}
       try dsimp [C, positiveShellDensity]
       calc
         shellWeight ε * Real.exp (δ * B) / 2
-          ≤ shellWeight ε * Real.exp (δ * a) / 2 := by gcongr
+          ≤ shellWeight ε * Real.exp (δ * a) / 2 := by
+            exact div_le_div_of_nonneg_right (mul_le_mul_of_nonneg_left he (le_of_lt hQ))
+                zero_le_two
         _ ≤ shellWeight ε *
             (Real.cosh ((1 + δ) * a) / Real.cosh a) := by
           calc
@@ -2287,7 +2295,7 @@ private theorem positiveShellDamping_lower_bound {ε ℓ δ T : ℝ}
     exact mul_le_mul_of_nonneg_right hbase
       (sub_nonneg.mpr (Real.cos_le_one _))
   have hmono := intervalIntegral.integral_mono_on
-    (μ := volume) (show B ≤ B + 1 by linarith)
+    (μ := volume) (show B ≤ B + 1 by linarith only [])
     (hleft.intervalIntegrable _ _)
     (hright.intervalIntegrable _ _) hpoint
   have hleftIntegral :
@@ -2307,12 +2315,17 @@ private theorem positiveShellDamping_lower_bound {ε ℓ δ T : ℝ}
         try dsimp [C]
         ring
     _ ≤ ℓ * (C * shellOscillation B T) := by
-      gcongr
+      refine mul_le_mul_of_nonneg_left
+          (mul_le_mul_of_nonneg_left ?_
+            (le_of_lt
+              (div_pos (mul_pos hQ (Real.exp_pos (δ * B)))
+                (zero_lt_two))))
+          hℓ
       exact shellOscillation_lower_bound B T
     _ ≤ ℓ * ∫ a in B..B + 1,
         positiveShellDensity ε a * Real.cosh ((1 + δ) * a) *
           (1 - Real.cos (a * T)) := by
-      gcongr
+      exact mul_le_mul_of_nonneg_left hmono hℓ
 
 private noncomputable def positiveShellRadiusContribution (ε : ℝ) : ℝ :=
   ∫ a in (ε⁻¹ ^ 3)..(ε⁻¹ ^ 3 + 1),
@@ -2342,7 +2355,7 @@ private theorem positiveShellRadiusContribution_bounds {ε : ℝ} (hε : 0 < ε)
       (fun a : ℝ => positiveShellDensity ε a * a *
         Real.sinh ((1 + δ) * a)) := by
     have hsinh : Continuous (fun a : ℝ => Real.sinh ((1 + δ) * a)) := by
-      fun_prop
+      exact Continuous.comp' Real.continuous_sinh (Continuous.const_mul continuous_id' (1 + δ))
     exact (hden.mul continuous_id).mul hsinh
   have hnonneg : ∀ a ∈ Set.Icc B (B + 1),
       0 ≤ positiveShellDensity ε a * a *
@@ -2354,7 +2367,7 @@ private theorem positiveShellRadiusContribution_bounds {ε : ℝ} (hε : 0 < ε)
       exact (div_pos hQ (Real.cosh_pos a)).le
     exact mul_nonneg (mul_nonneg hden0 ha0)
       (Real.sinh_nonneg_iff.mpr
-        (mul_nonneg (by linarith : 0 ≤ 1 + δ) ha0))
+        (mul_nonneg (by linear_combination hδ : 0 ≤ 1 + δ) ha0))
   have hpoint : ∀ a ∈ Set.Icc B (B + 1),
       positiveShellDensity ε a * a * Real.sinh ((1 + δ) * a) ≤ K := by
     intro a ha
@@ -2369,7 +2382,7 @@ private theorem positiveShellRadiusContribution_bounds {ε : ℝ} (hε : 0 < ε)
       positiveShellDensity ε a * a * Real.sinh ((1 + δ) * a)
         ≤ positiveShellDensity ε a * a *
           Real.cosh ((1 + δ) * a) := by
-            gcongr
+            refine mul_le_mul_of_nonneg_left ?_ (mul_nonneg hden0 ha0)
             exact (Real.sinh_lt_cosh (x := (1 + δ) * a)).le
       _ = shellWeight ε * a *
           (Real.cosh ((1 + δ) * a) / Real.cosh a) := by
@@ -2386,11 +2399,11 @@ private theorem positiveShellRadiusContribution_bounds {ε : ℝ} (hε : 0 < ε)
   constructor
   · change 0 ≤ ∫ a in B..B + 1,
         positiveShellDensity ε a * a * Real.sinh ((1 + δ) * a)
-    exact intervalIntegral.integral_nonneg (by linarith) hnonneg
+    exact intervalIntegral.integral_nonneg (by linarith only []) hnonneg
   · change (∫ a in B..B + 1,
         positiveShellDensity ε a * a * Real.sinh ((1 + δ) * a)) ≤ K
     have hmono := intervalIntegral.integral_mono_on (μ := volume)
-      (show B ≤ B + 1 by linarith)
+      (show B ≤ B + 1 by linarith only [])
       (hright.intervalIntegrable _ _)
       ((continuous_const : Continuous (fun _ : ℝ => K)).intervalIntegrable _ _)
       hpoint
@@ -2630,7 +2643,7 @@ private theorem positiveShellOscillatoryIntegral_continuous (ε : ℝ) :
     continuous_parametric_integral_of_continuous
       (μ := volume) hF isCompact_Icc
   have horder : (ε⁻¹ ^ 3) ≤ (ε⁻¹ ^ 3) + 1 := by
-    linarith
+    linarith only []
   have hident (t : ℝ) :
       (∫ a in (ε⁻¹ ^ 3)..(ε⁻¹ ^ 3 + 1),
         positiveShellDensity ε a * (Real.cos (a * t) - 1)) =
@@ -2699,7 +2712,7 @@ private theorem complexShellInterval_differentiable
       simpa only [id_eq, mul_one] using! (hasDerivAt_id z).const_mul (x : ℂ)
     have hcos := (Complex.hasDerivAt_cos
       ((x : ℂ) * z)).comp z hlinear
-    simpa [F, F', mul_assoc] using!
+    simpa only [F, F', mul_assoc] using!
       (hcos.sub_const (1 : ℂ)).const_mul (w x : ℂ)
   have hrewrite :
       (fun z : ℂ =>
@@ -2784,7 +2797,7 @@ private theorem mellinShellPhase_continuous {ε : ℝ}
     try dsimp [w]
     rw [max_eq_left ha.1]
   have hremote : (ε⁻¹ ^ 3) ≤ (ε⁻¹ ^ 3) + 1 := by
-    linarith
+    linarith only []
   have hpositive : Continuous (fun z : ℂ =>
       ∫ a in (ε⁻¹ ^ 3)..(ε⁻¹ ^ 3 + 1),
         (positiveShellDensity ε a : ℂ) *
@@ -2837,7 +2850,7 @@ private theorem mellinShellPhase_differentiable {ε : ℝ}
     rw [hshort_eq]
     exact complexShellInterval_differentiable w hw horder
   have hremote : (ε⁻¹ ^ 3) ≤ (ε⁻¹ ^ 3) + 1 := by
-    linarith
+    linarith only []
   have hpositive : Differentiable ℂ (fun z : ℂ =>
       ∫ a in (ε⁻¹ ^ 3)..(ε⁻¹ ^ 3 + 1),
         (positiveShellDensity ε a : ℂ) *
@@ -2868,8 +2881,8 @@ private theorem abs_realOscillatoryShellPhase_le {ε : ℝ}
   have hcos (a : ℝ) : |Real.cos (a * t) - 1| ≤ 2 := by
     apply (abs_le).2
     constructor
-    · linarith [Real.neg_one_le_cos (a * t)]
-    · linarith [Real.cos_le_one (a * t)]
+    · linarith only [Real.neg_one_le_cos (a * t)]
+    · linarith only [Real.cos_le_one (a * t)]
   have hosc : Continuous (fun a : ℝ => Real.cos (a * t) - 1) := by
     fun_prop
   have hs := shortShellDensity_intervalIntegrable hε horder
@@ -2899,7 +2912,7 @@ private theorem abs_realOscillatoryShellPhase_le {ε : ℝ}
                 |shortShellDensity ε a| *
                     |Real.cos (a * t) - 1|
                   ≤ |shortShellDensity ε a| * 2 := by
-                      gcongr
+                      refine mul_le_mul_of_nonneg_left ?_ (abs_nonneg (shortShellDensity ε a))
                       exact hcos a
                 _ = 2 * |shortShellDensity ε a| := by ring
       _ = 2 * ∫ a in (ε ^ 3)..(10 * Real.log (1 / ε)),
@@ -2928,7 +2941,7 @@ private theorem abs_realOscillatoryShellPhase_le {ε : ℝ}
                 |positiveShellDensity ε a| *
                     |Real.cos (a * t) - 1|
                   ≤ |positiveShellDensity ε a| * 2 := by
-                      gcongr
+                      refine mul_le_mul_of_nonneg_left ?_ (abs_nonneg (positiveShellDensity ε a))
                       exact hcos a
                 _ = 2 * |positiveShellDensity ε a| := by ring
       _ = 2 * ∫ a in (ε⁻¹ ^ 3)..(ε⁻¹ ^ 3 + 1),
@@ -2993,7 +3006,7 @@ private theorem saddleVerticalGamma_continuous {ℓ : ℝ} (hℓ : 0 < ℓ) :
     have hre := congrArg Complex.re hm
     norm_num at hre
     have hmnonneg : (0 : ℝ) ≤ (m : ℝ) := Nat.cast_nonneg m
-    linarith
+    linarith only [hz, hre]
   have harg : ContinuousAt
       (fun u : ℝ => ((ℓ : ℂ) - Complex.I * (u : ℂ)) / 2) t :=
     ((continuous_const.sub
@@ -3026,7 +3039,10 @@ private theorem saddleEnvelope_continuous {ε ℓ : ℝ}
   have hunit : Continuous (fun t : ℝ =>
       Complex.exp
         (Complex.I * (t : ℂ) * (Real.log Real.pi : ℂ) / 2)) := by
-    fun_prop
+    exact Continuous.cexp
+        (Continuous.comp' (Continuous.div_const continuous_id' 2)
+          (Continuous.comp' (continuous_mul_const ↑(Real.log Real.pi))
+            (Continuous.const_mul Complex.continuous_ofReal Complex.I)))
   have hgamma := saddleVerticalGamma_continuous hℓ
   have hphase : Continuous (fun t : ℝ =>
       Complex.exp ((ℓ : ℂ) *
@@ -3128,7 +3144,8 @@ private theorem saddleRegularMellinFactor_continuous {ε : ℝ}
     fun_prop
   have harg : Continuous (fun z : ℂ =>
       Complex.I * (z - (ℓ : ℂ)) / (ℓ : ℂ)) := by
-    fun_prop
+    exact Continuous.comp' (Continuous.div_const continuous_id' ↑ℓ)
+        (Continuous.const_mul (Continuous.fun_sub continuous_id' continuous_const) Complex.I)
   have hphase : Continuous (fun z : ℂ =>
       Complex.exp ((ℓ : ℂ) *
         mellinShellPhase ε
@@ -3148,7 +3165,8 @@ private theorem saddleRegularMellinFactor_differentiable {ε : ℝ}
     fun_prop
   have harg : Differentiable ℂ (fun z : ℂ =>
       Complex.I * (z - (ℓ : ℂ)) / (ℓ : ℂ)) := by
-    fun_prop
+    exact Differentiable.div_const
+        (Differentiable.const_mul (Differentiable.sub_const differentiable_id ↑ℓ) Complex.I) ↑ℓ
   have hphase : Differentiable ℂ (fun z : ℂ =>
       Complex.exp ((ℓ : ℂ) *
         mellinShellPhase ε
@@ -3202,7 +3220,7 @@ private theorem saddleMellinGamma_meromorphic :
   have hg : MeromorphicAt Complex.Gamma (z / 2) :=
     Meromorphic.Gamma (z / 2)
   have ha : AnalyticAt ℂ (fun u : ℂ => u / 2) z := by
-    fun_prop
+    exact AnalyticAt.div_const analyticAt_id
   simpa only [Function.comp_def] using!
     (MeromorphicAt.comp_analyticAt
       (g := fun u : ℂ => u / 2) (x := z) hg ha)
@@ -3676,7 +3694,7 @@ private theorem saddleNthGammaPoleNumerator_differentiableOn (n : ℕ) :
     change
       -(2 * ((n : ℝ) + 1)) < z.re ∧
         z.re < -(2 * (n : ℝ)) + 1 at hz
-    linarith [hz.1]
+    linarith only [hz.1, hz]
   have hgamma :
       DifferentiableAt ℂ Complex.Gamma
         (z / 2 + ((n + 1 : ℕ) : ℂ)) :=
@@ -4126,7 +4144,7 @@ private theorem saddlePoleCoordinate_ne_zero_at_other
   have hreal := congrArg Complex.re hzero
   norm_num [Nat.cast_mul, Complex.mul_re] at hreal
   have heq : (m : ℝ) = (n : ℝ) := by
-    linarith
+    linarith only [hreal]
   exact_mod_cast heq
 
 private noncomputable def plusSaddleFinitePoleRemaining
@@ -4157,7 +4175,7 @@ private theorem plusSaddleFinitePoleRemaining_differentiableAt_pole
       DifferentiableAt ℂ
         (fun _ : ℂ => plusSaddlePoleResidue ε ℓ m)
           (-((2 * n : ℕ) : ℂ)) := by
-    fun_prop
+    exact differentiableAt_const (plusSaddlePoleResidue ε ℓ m)
   have hdenominator :
       DifferentiableAt ℂ
         (fun z : ℂ => z + ((2 * m : ℕ) : ℂ))
@@ -4181,7 +4199,7 @@ private theorem minusSaddleFinitePoleRemaining_differentiableAt_pole
       DifferentiableAt ℂ
         (fun _ : ℂ => minusSaddlePoleResidue ε ℓ m)
           (-((2 * n : ℕ) : ℂ)) := by
-    fun_prop
+    exact differentiableAt_const (minusSaddlePoleResidue ε ℓ m)
   have hdenominator :
       DifferentiableAt ℂ
         (fun z : ℂ => z + ((2 * m : ℕ) : ℂ))
@@ -4210,7 +4228,7 @@ private theorem plusSaddleFinitePoleSubtraction_differentiableAt_of_not_pole
   have hconstant :
       DifferentiableAt ℂ
         (fun _ : ℂ => plusSaddlePoleResidue ε ℓ n) z := by
-    fun_prop
+    exact differentiableAt_const (plusSaddlePoleResidue ε ℓ n)
   have hdenominator :
       DifferentiableAt ℂ
         (fun w : ℂ => w + ((2 * n : ℕ) : ℂ)) z := by
@@ -4238,7 +4256,7 @@ private theorem minusSaddleFinitePoleSubtraction_differentiableAt_of_not_pole
   have hconstant :
       DifferentiableAt ℂ
         (fun _ : ℂ => minusSaddlePoleResidue ε ℓ n) z := by
-    fun_prop
+    exact differentiableAt_const (minusSaddlePoleResidue ε ℓ n)
   have hdenominator :
       DifferentiableAt ℂ
         (fun w : ℂ => w + ((2 * n : ℕ) : ℂ)) z := by
@@ -4599,7 +4617,8 @@ private theorem saddleMellinInversePower_differentiable
   change Differentiable ℂ
     (fun z : ℂ => (r : ℂ) ^ (-z))
   rw [hform]
-  fun_prop
+  exact Differentiable.cexp
+      (Differentiable.const_mul (Differentiable.fun_neg differentiable_id) (Complex.log ↑r))
 
 private noncomputable def saddleGaussianPoleSlope (z : ℂ) : ℂ :=
   dslope (fun w : ℂ => Complex.exp (w ^ 2)) 0 z
@@ -4609,7 +4628,7 @@ private theorem saddleGaussianPoleSlope_differentiable :
   have hgaussian :
       Differentiable ℂ
         (fun w : ℂ => Complex.exp (w ^ 2)) := by
-    fun_prop
+    exact Differentiable.cexp (Differentiable.fun_pow differentiable_id 2)
   unfold saddleGaussianPoleSlope
   exact differentiableOn_univ.mp
     ((Complex.differentiableOn_dslope
@@ -4683,7 +4702,7 @@ private theorem plusSaddleFiniteRapidPoleRegularPart_differentiableOn
   have hconstant : DifferentiableOn ℂ
       (fun _ : ℂ => plusSaddlePoleResidue ε ℓ n)
       (saddleFinitePoleHalfPlane N) := by
-    fun_prop
+    exact differentiableOn_const (plusSaddlePoleResidue ε ℓ n)
   have hslope : Differentiable ℂ
       (fun z : ℂ => saddleGaussianPoleSlope
         (z + ((2 * n : ℕ) : ℂ))) :=
@@ -4705,7 +4724,7 @@ private theorem minusSaddleFiniteRapidPoleRegularPart_differentiableOn
   have hconstant : DifferentiableOn ℂ
       (fun _ : ℂ => minusSaddlePoleResidue ε ℓ n)
       (saddleFinitePoleHalfPlane N) := by
-    fun_prop
+    exact differentiableOn_const (minusSaddlePoleResidue ε ℓ n)
   have hslope : Differentiable ℂ
       (fun z : ℂ => saddleGaussianPoleSlope
         (z + ((2 * n : ℕ) : ℂ))) :=
@@ -4999,9 +5018,9 @@ private theorem norm_plusPolynomial_le (ε : ℝ) (z : ℂ) :
         norm_add_le _ _
       _ = 1 + ‖z‖ ^ 2 := by simp only [norm_one, norm_pow]
   have hsq : 1 + ‖z‖ ^ 2 ≤ (1 + ‖z‖) ^ 2 := by
-    linarith
+    linarith only [hz]
   have hcube : (1 : ℝ) ≤ (1 + ‖z‖) ^ 3 :=
-    one_le_pow₀ (by linarith)
+    one_le_pow₀ (by linarith only [hz])
   unfold plusPolynomial
   calc
     ‖1 + z ^ 2 + ((ε / 4 : ℝ) : ℂ) +
@@ -5025,15 +5044,14 @@ private theorem norm_plusPolynomial_le (ε : ℝ) (z : ℂ) :
                 ‖Complex.I * z * (1 + z ^ 2)‖ ≤
                   ‖z‖ * (1 + ‖z‖ ^ 2) := by
               rw [norm_mul, norm_mul, Complex.norm_I, one_mul]
-              gcongr
+              exact mul_le_mul_of_nonneg_left hbase (norm_nonneg z)
             exact add_le_add hfirst hsecond
     _ ≤ (1 + ‖z‖) ^ 2 + |(ε / 4)| +
           ‖z‖ * (1 + ‖z‖) ^ 2 := by
             gcongr
     _ = (1 + ‖z‖) ^ 3 + |(ε / 4)| := by ring
     _ ≤ (1 + |(ε / 4)|) * (1 + ‖z‖) ^ 3 := by
-          linarith [mul_le_mul_of_nonneg_left hcube
-            (abs_nonneg (ε / 4))]
+          linarith only [mul_le_mul_of_nonneg_left hcube (abs_nonneg (ε / 4)), hcube]
 
 private theorem norm_minusPolynomial_le (ε : ℝ) (z : ℂ) :
     ‖minusPolynomial ε z‖ ≤
@@ -5074,7 +5092,7 @@ private theorem complexGamma_vertical_polynomial_bound {z : ℂ}
     have hre := congrArg Complex.re hzero
     norm_num at hre
     have hj : 0 ≤ (j : ℝ) := Nat.cast_nonneg j
-    linarith
+    linarith only [hz, hre]
   have hprod :
       |z.im| ^ k ≤
         ∏ j ∈ Finset.range k, ‖z + (j : ℂ)‖ := by
@@ -5094,7 +5112,7 @@ private theorem complexGamma_vertical_polynomial_bound {z : ℂ}
     |z.im| ^ k * ‖Complex.Gamma z‖ ≤
         (∏ j ∈ Finset.range k, ‖z + (j : ℂ)‖) *
           ‖Complex.Gamma z‖ := by
-            gcongr
+            exact mul_le_mul_of_nonneg_right hprod (norm_nonneg (Complex.Gamma z))
     _ = ‖Complex.Gamma z *
           ∏ j ∈ Finset.range k, (z + (j : ℂ))‖ := by
             rw [norm_mul, norm_prod]
@@ -5133,7 +5151,7 @@ private theorem complexGamma_shifted_vertical_polynomial_bound
     |z.im| ^ k * ‖Complex.Gamma z‖ ≤
         (∏ j ∈ Finset.range k, ‖z + (j : ℂ)‖) *
           ‖Complex.Gamma z‖ := by
-            gcongr
+            exact mul_le_mul_of_nonneg_right hprod (norm_nonneg (Complex.Gamma z))
     _ = ‖Complex.Gamma z *
           ∏ j ∈ Finset.range k, (z + (j : ℂ))‖ := by
             rw [norm_mul, norm_prod]
@@ -5187,7 +5205,7 @@ private theorem saddleGamma_shiftedLine_polynomial_bound
   calc
     |t| ^ m * ‖Complex.Gamma z‖ ≤
         |t| ^ (k + m) * ‖Complex.Gamma z‖ := by
-          gcongr
+          exact mul_le_mul_of_nonneg_right hpow (norm_nonneg (Complex.Gamma z))
     _ = (2 : ℝ) ^ (k + m) *
           ((|t| / 2) ^ (k + m) *
             ‖Complex.Gamma z‖) := by
@@ -5196,7 +5214,11 @@ private theorem saddleGamma_shiftedLine_polynomial_bound
     _ ≤ (2 : ℝ) ^ (k + m) *
           Real.Gamma
             (a / 2 + ((k + m : ℕ) : ℝ)) := by
-          gcongr
+          exact mul_le_mul_of_nonneg_left hgamma
+              (le_of_lt
+                (pow_pos
+                  (zero_lt_two)
+                  (k + m)))
 
 private theorem norm_complexCos_le_cosh_im (z : ℂ) :
     ‖Complex.cos z‖ ≤ Real.cosh z.im := by
@@ -5212,7 +5234,8 @@ private theorem norm_complexCos_le_cosh_im (z : ℂ) :
             norm_num
     _ ≤ (‖Complex.exp (z * Complex.I)‖ +
           ‖Complex.exp (-z * Complex.I)‖) / 2 := by
-            gcongr
+            refine div_le_div_of_nonneg_right ?_
+                zero_le_two
             exact norm_add_le _ _
     _ = Real.cosh z.im := by
           rw [Complex.norm_exp, Complex.norm_exp,
@@ -5236,10 +5259,10 @@ private theorem saddleHorizontalShellVariation_mono
   have hK : 0 ≤ K := hH.trans hHK
   have hcosH : Continuous
       (fun a : ℝ => Real.cosh (a * H) + 1) := by
-    fun_prop
+    exact Continuous.add_const (Continuous.comp' Real.continuous_cosh (continuous_mul_const H)) 1
   have hcosK : Continuous
       (fun a : ℝ => Real.cosh (a * K) + 1) := by
-    fun_prop
+    exact Continuous.add_const (Continuous.comp' Real.continuous_cosh (continuous_mul_const K)) 1
   have hcos (a : ℝ) :
       Real.cosh (a * H) ≤ Real.cosh (a * K) := by
     apply Real.cosh_le_cosh.mpr
@@ -5262,7 +5285,7 @@ private theorem saddleHorizontalShellVariation_mono
     gcongr
     exact hcos a
   have hB : (ε⁻¹ ^ 3) ≤ (ε⁻¹ ^ 3) + 1 := by
-    linarith
+    linarith only []
   have hp : IntervalIntegrable (positiveShellDensity ε) volume
       (ε⁻¹ ^ 3) ((ε⁻¹ ^ 3) + 1) :=
     (positiveShellDensity_continuous ε).intervalIntegrable
@@ -5295,7 +5318,7 @@ private theorem norm_mellinShellPhase_le_horizontalVariation
     positivity
   have hcosh : Continuous
       (fun a : ℝ => Real.cosh (a * H) + 1) := by
-    fun_prop
+    exact Continuous.add_const (Continuous.comp' Real.continuous_cosh (continuous_mul_const H)) 1
   have hcos (a : ℝ) (ha : 0 ≤ a) :
       ‖Complex.cos ((a : ℂ) * z) - 1‖ ≤
         Real.cosh (a * H) + 1 := by
@@ -5312,10 +5335,10 @@ private theorem norm_mellinShellPhase_le_horizontalVariation
       _ = ‖Complex.cos ((a : ℂ) * z)‖ + 1 := by
             norm_num
       _ ≤ Real.cosh ((a : ℂ) * z).im + 1 := by
-            gcongr
+            refine add_le_add ?_ (le_refl 1)
             exact norm_complexCos_le_cosh_im ((a : ℂ) * z)
       _ ≤ Real.cosh (a * H) + 1 := by
-            gcongr
+            refine add_le_add ?_ (le_refl 1)
             exact Real.cosh_le_cosh.mpr him
   have hshort :
       ‖∫ a in (ε ^ 3)..(10 * Real.log (1 / ε)),
@@ -5333,7 +5356,7 @@ private theorem norm_mellinShellPhase_le_horizontalVariation
     · exact (shortShellDensity_intervalIntegrable
         hε horder).abs.mul_continuousOn hcosh.continuousOn
   have hB : (ε⁻¹ ^ 3) ≤ (ε⁻¹ ^ 3) + 1 := by
-    linarith
+    linarith only []
   have hpositive :
       ‖∫ a in (ε⁻¹ ^ 3)..(ε⁻¹ ^ 3 + 1),
           (positiveShellDensity ε a : ℂ) *
@@ -5369,7 +5392,7 @@ private theorem norm_saddleShellExponential_horizontal_le
     _ = |ℓ| * ‖mellinShellPhase ε z‖ := by
           rw [norm_mul, Complex.norm_real, Real.norm_eq_abs]
     _ ≤ |ℓ| * saddleHorizontalShellVariation ε |z.im| := by
-          gcongr
+          refine mul_le_mul_of_nonneg_left ?_ (abs_nonneg ℓ)
           exact norm_mellinShellPhase_le_horizontalVariation
             hε horder (le_refl |z.im|)
 
@@ -5469,10 +5492,10 @@ private theorem saddleMellinShellArgument_shiftedLine_linear_le
     (abs_nonneg ((a - ℓ) / ℓ))
   calc
     _ ≤ 1 + (|t| / ℓ + |(a - ℓ) / ℓ|) := by
-      gcongr
+      exact add_le_add (le_refl 1) hargument
     _ ≤ |t| + |t| / ℓ +
           |(a - ℓ) / ℓ| * |t| := by
-      linarith
+      linear_combination ht + hoffset
     _ = _ := by
       rw [div_eq_mul_inv]
       ring
@@ -5760,11 +5783,11 @@ private theorem saddleShiftedGamma_continuousOn
   intro a ha
   change 0 < a / 2 + ((k + (m + 3) : ℕ) : ℝ)
   have ha' : A / 2 ≤ a / 2 := by
-    linarith [ha.1]
+    linarith only [ha.1, ha]
   rw [Nat.cast_add]
   have hm : (0 : ℝ) ≤ ((m + 3 : ℕ) : ℝ) :=
     Nat.cast_nonneg _
-  linarith
+  linarith only [hshift, ha']
 
 private theorem saddleFixedStripMajorant_continuousOn
     {A B : ℝ} (ε ℓ H : ℝ) (k m : ℕ)
@@ -5812,7 +5835,7 @@ private theorem plusSaddleMellinData_horizontalStrip_polynomial_bound
               ((a : ℂ) + (t : ℂ) * Complex.I)‖ ≤ C := by
   obtain ⟨k, hk⟩ := exists_nat_gt (-(A / 2))
   have hshiftA : 0 < A / 2 + (k : ℝ) := by
-    linarith
+    linear_combination hk
   let H : ℝ := saddleHorizontalStripHeight ℓ A B
   have hcont : ContinuousOn
       (fun a : ℝ => saddleFixedStripMajorant ε ℓ H a k m)
@@ -5860,7 +5883,7 @@ private theorem minusSaddleMellinData_horizontalStrip_polynomial_bound
               ((a : ℂ) + (t : ℂ) * Complex.I)‖ ≤ C := by
   obtain ⟨k, hk⟩ := exists_nat_gt (-(A / 2))
   have hshiftA : 0 < A / 2 + (k : ℝ) := by
-    linarith
+    linear_combination hk
   let H : ℝ := saddleHorizontalStripHeight ℓ A B
   have hcont : ContinuousOn
       (fun a : ℝ => saddleFixedStripMajorant ε ℓ H a k m)
@@ -5947,7 +5970,7 @@ private theorem norm_saddleShellExponential_le {ε ℓ : ℝ}
     _ = |ℓ| * |realOscillatoryShellPhase ε (t / ℓ)| :=
           abs_mul _ _
     _ ≤ |ℓ| * (2 * saddleShellTotalVariation ε) := by
-          gcongr
+          refine mul_le_mul_of_nonneg_left ?_ (abs_nonneg ℓ)
           exact abs_realOscillatoryShellPhase_le hε horder (t / ℓ)
     _ = 2 * |ℓ| * saddleShellTotalVariation ε := by ring
 
@@ -5980,7 +6003,11 @@ private theorem saddleEnvelope_vertical_polynomial_bound {ε ℓ : ℝ}
               rw [div_pow, div_mul_eq_mul_div, mul_div_assoc',
                 mul_div_cancel_left₀ _ (pow_ne_zero k two_ne_zero)]
       _ ≤ (2 : ℝ) ^ k * Real.Gamma (ℓ / 2 + k) := by
-              gcongr
+              exact mul_le_mul_of_nonneg_left hgamma
+                  (le_of_lt
+                    (pow_pos
+                      (zero_lt_two)
+                      k))
   have hunit :
       ‖Complex.exp
         (Complex.I * (t : ℂ) * (Real.log Real.pi : ℂ) / 2)‖ = 1 := by
@@ -6073,7 +6100,8 @@ private theorem saddleEnvelope_weighted_norm_le
             ring
     _ ≤ |t| ^ k * ‖saddleEnvelope ε ℓ t‖ *
           ((1 + |(ε / 4)|) * (1 + ℓ⁻¹) ^ 3 * |t| ^ 3) := by
-            gcongr
+            exact mul_le_mul_of_nonneg_left hpoly
+                (mul_nonneg (pow_nonneg (abs_nonneg t) k) (norm_nonneg (saddleEnvelope ε ℓ t)))
     _ = ((1 + |(ε / 4)|) * (1 + ℓ⁻¹) ^ 3) *
           (|t| ^ (k + 3) * ‖saddleEnvelope ε ℓ t‖) := by
             rw [pow_add]
@@ -6138,7 +6166,7 @@ private theorem integrable_of_continuous_polynomial_decay
   calc
     (|t| ^ k * ‖F t‖) * (1 + t ^ 2)
       ≤ (|t| ^ k * ‖F t‖) * (2 * t ^ 2) :=
-        mul_le_mul_of_nonneg_left (by linarith only [hsquare])
+        mul_le_mul_of_nonneg_left (by linear_combination hsquare)
           (mul_nonneg (pow_nonneg (abs_nonneg t) _) (norm_nonneg _))
     _ = 2 * (|t| ^ (k + 2) * ‖F t‖) := by rw [pow_add, sq_abs]; ring
     _ ≤ 2 * C := mul_le_mul_of_nonneg_left (htail t ht) (by norm_num)
@@ -6216,7 +6244,7 @@ private theorem plusSaddleMellinData_shiftedLine_moment_integrable
   intro m
   obtain ⟨k, hk⟩ := exists_nat_gt (-(a / 2))
   have hshift : 0 < a / 2 + (k : ℝ) := by
-    linarith
+    linear_combination hk
   refine ⟨saddleShiftedLineMajorant ε ℓ a k m,
     saddleShiftedLineMajorant_nonneg hℓ k m hshift, ?_⟩
   intro t ht
@@ -6237,7 +6265,7 @@ private theorem minusSaddleMellinData_shiftedLine_moment_integrable
   intro m
   obtain ⟨k, hk⟩ := exists_nat_gt (-(a / 2))
   have hshift : 0 < a / 2 + (k : ℝ) := by
-    linarith
+    linear_combination hk
   refine ⟨saddleShiftedLineMajorant ε ℓ a k m,
     saddleShiftedLineMajorant_nonneg hℓ k m hshift, ?_⟩
   intro t ht
@@ -6371,7 +6399,7 @@ private theorem saddleGaussianPoleRepresentative_shiftedLine_continuous
     have hre := congrArg Complex.re hzero
     norm_num [Complex.mul_re] at hre
     push_cast
-    linarith
+    linear_combination hre
   unfold saddleGaussianPoleRepresentative
   exact (Complex.continuous_exp.comp (hline.pow 2)).div
     hline hnonzero
@@ -6387,7 +6415,7 @@ private theorem saddleGaussianPoleRepresentative_shiftedLine_bound
   have hreal : a + ((2 * n : ℕ) : ℝ) ≠ 0 := by
     intro hzero
     apply ha
-    linarith
+    linear_combination hzero
   have habs : 0 < |a + ((2 * n : ℕ) : ℝ)| :=
     abs_pos.mpr hreal
   have hden :
@@ -7097,7 +7125,7 @@ private theorem saddleCauchyPolePrimitive_hasDerivAt
       (((a : ℂ) + (t : ℂ) * Complex.I)⁻¹) t := by
   have hden : a ^ 2 + t ^ 2 ≠ 0 := by
     have ha2 : 0 < a ^ 2 := sq_pos_of_ne_zero ha
-    linarith [sq_nonneg t]
+    linarith only [sq_nonneg t, ha2]
   have hatan : HasDerivAt
       (fun y : ℝ => Real.arctan (y / a))
       (a / (a ^ 2 + t ^ 2)) t := by
@@ -7164,7 +7192,7 @@ private theorem saddleCauchyPole_symmetric_intervalIntegral
     (fun t _ => saddleCauchyPolePrimitive_hasDerivAt ha t)
       hint]
   unfold saddleCauchyPolePrimitive
-  simp only [Complex.ofReal_arctan, Complex.ofReal_div, pow_two, Complex.ofReal_ofNat, neg_div,
+  simp only [Complex.ofReal_div, pow_two, Complex.ofReal_ofNat, neg_div,
     Real.arctan_neg,
     Complex.ofReal_neg, mul_neg, neg_mul, neg_neg, sub_sub_sub_cancel_right, sub_neg_eq_add,
       Complex.ofReal_mul]; ring
@@ -7474,10 +7502,10 @@ private theorem integrable_scaled_norm_moment
         (norm_nonneg _))]
     apply mul_le_mul_of_nonneg_right _ (norm_nonneg _)
     rw [abs_mul]
-    gcongr
+    refine pow_le_pow_left₀ (abs_nonneg y) ?_ k
     calc
       |y| = 1 * |y| := by ring
-      _ ≤ |c| * |y| := by gcongr
+      _ ≤ |c| * |y| := by exact mul_le_mul_of_nonneg_right hclarge (abs_nonneg y)
   simpa only [Real.norm_eq_abs] using! hresult
 
 private theorem plusSaddleFourierData_norm_moment_integrable {ε ℓ : ℝ}
@@ -7493,12 +7521,12 @@ private theorem plusSaddleFourierData_norm_moment_integrable {ε ℓ : ℝ}
   have hclarge : 1 ≤ |c| := by
     try dsimp [c]
     rw [abs_neg, abs_of_pos (mul_pos (by norm_num) Real.pi_pos)]
-    linarith [Real.pi_gt_three]
+    linarith only [Real.pi_gt_three]
   have h := integrable_scaled_norm_moment
     (plusSaddleSpectrum_continuous hε hℓ horder)
     (fun j => plusSaddleSpectrum_norm_moment_integrable
       hε hℓ horder j) hc hclarge k
-  simpa [plusSaddleFourierData, c, neg_mul, mul_assoc] using! h
+  simpa only [plusSaddleFourierData, c, neg_mul, mul_assoc] using! h
 
 private theorem minusSaddleFourierData_norm_moment_integrable {ε ℓ : ℝ}
     (hε : 0 < ε) (hℓ : 0 < ℓ)
@@ -7513,12 +7541,12 @@ private theorem minusSaddleFourierData_norm_moment_integrable {ε ℓ : ℝ}
   have hclarge : 1 ≤ |c| := by
     try dsimp [c]
     rw [abs_neg, abs_of_pos (mul_pos (by norm_num) Real.pi_pos)]
-    linarith [Real.pi_gt_three]
+    linarith only [Real.pi_gt_three]
   have h := integrable_scaled_norm_moment
     (minusSaddleSpectrum_continuous hε hℓ horder)
     (fun j => minusSaddleSpectrum_norm_moment_integrable
       hε hℓ horder j) hc hclarge k
-  simpa [minusSaddleFourierData, c, neg_mul, mul_assoc] using! h
+  simpa only [minusSaddleFourierData, c, neg_mul, mul_assoc] using! h
 
 private theorem plusSaddleFourierData_fourier_contDiff {ε ℓ : ℝ}
     (hε : 0 < ε) (hℓ : 0 < ℓ)
diff --git a/LeanPool/SpherePacking/GammaAnalysis.lean b/LeanPool/SpherePacking/GammaAnalysis.lean
index e91fe1ff81..63e4c7e327 100644
--- a/LeanPool/SpherePacking/GammaAnalysis.lean
+++ b/LeanPool/SpherePacking/GammaAnalysis.lean
@@ -58,7 +58,7 @@ private theorem complexFrullaniSegment_re_pos {z w : ℂ}
     have hfirst : 0 ≤ (1 - s) * z.re :=
       mul_nonneg (sub_nonneg.mpr hs.2) hz.le
     have hsecond : 0 < s * w.re := mul_pos hspos hw
-    linarith
+    linarith only [hfirst, hsecond]
 
 private noncomputable def complexFrullaniKernel (z w : ℂ) (x : ℝ) : ℂ :=
   (Complex.exp (-z * (x : ℂ)) -
@@ -97,7 +97,7 @@ private theorem intervalIntegral_complexLaplaceSegment
     have hinner :=
       (complexFrullaniSegment_hasDerivAt z w s).neg.mul_const
         (x : ℂ)
-    convert! hinner.cexp.neg.div_const (x : ℂ) using 1
+    convert hinner.cexp.neg.div_const (x : ℂ) using 1
     · simp only [Pi.neg_apply]
       field_simp [hxc]
   have hcontinuous :
@@ -137,7 +137,7 @@ private theorem complexFrullaniSegment_min_re_le
   have hsecond :
       0 ≤ s * (w.re - min z.re w.re) :=
     mul_nonneg hs.1 (sub_nonneg.mpr hwmin)
-  linarith
+  linarith only [hfirst, hsecond]
 
 private theorem complexFrullaniKernel_norm_le_exp
     (z w : ℂ) {x : ℝ} (hx : 0 < x) :
@@ -384,13 +384,13 @@ private theorem complexFrullaniShiftKernel_norm_le_exp
       _ ≤ ‖(1 : ℂ) - z‖ + 1 := by
         rw [Complex.norm_real, Real.norm_eq_abs,
           abs_of_nonneg hs.1]
-        linarith [hs.2]
+        linarith only [hs.2, hs]
   have hmin :
       min z.re 1 ≤
         min (z + (s : ℂ)).re (1 : ℂ).re := by
     apply le_min
     · simp only [Complex.add_re, Complex.ofReal_re]
-      linarith [min_le_left z.re (1 : ℝ), hs.1]
+      linarith only [min_le_left z.re (1 : ℝ), hs.1, hs]
     · exact min_le_right z.re (1 : ℝ)
   calc
     ‖complexFrullaniKernel (z + (s : ℂ)) 1 x‖ ≤
@@ -444,7 +444,7 @@ private theorem complexFrullaniShiftParameter_integrable
     rw [Set.uIoc_of_le (show (0 : ℝ) ≤ 1 by norm_num)] at hs
     have hspositive : 0 < (z + (s : ℂ)).re := by
       simp only [Complex.add_re, Complex.ofReal_re]
-      linarith [hs.1]
+      linarith only [hs.1, hz, hs]
     change
       IntegrableOn
         (complexFrullaniKernel (z + (s : ℂ)) 1)
@@ -467,7 +467,7 @@ private theorem complexFrullaniShiftParameter_integrable
       ⟨hs.1.le, hs.2⟩
     have hspositive : 0 < (z + (s : ℂ)).re := by
       simp only [Complex.add_re, Complex.ofReal_re]
-      linarith [hs.1]
+      linarith only [hs.1, hz, hs]
     have hkernel :=
       complexFrullaniKernel_integrable
         hspositive (by norm_num : 0 < (1 : ℂ).re)
@@ -517,7 +517,7 @@ private theorem intervalIntegral_complexFrullaniShift
       (∫ s in (0 : ℝ)..1,
         Complex.exp (-(z + (s : ℂ)) * (x : ℂ))) =
         complexFrullaniKernel z (z + 1) x := by
-    convert!
+    convert
       intervalIntegral_complexLaplaceSegment z (z + 1) hx
       using 1
     apply intervalIntegral.integral_congr
@@ -588,13 +588,13 @@ private theorem complexWallisLogPrimitive_hasDerivAt
   have hline := complexWallisTranslatedSegment_hasDerivAt z s
   have hpositive : 0 < (z + (s : ℂ)).re := by
     simp only [Complex.add_re, Complex.ofReal_re]
-    linarith [hs.1]
+    linarith only [hs.1, hz, hs]
   have hslit : z + (s : ℂ) ∈ Complex.slitPlane :=
     Complex.mem_slitPlane_iff.mpr (Or.inl hpositive)
   have hnonzero : z + (s : ℂ) ≠ 0 :=
     Complex.slitPlane_ne_zero hslit
   have hlog := hline.clog_real hslit
-  convert! (hline.mul hlog).sub hline using 1
+  convert (hline.mul hlog).sub hline using 1
   simp only [one_mul, div_eq_mul_inv, ne_eq, hnonzero, not_false_eq_true, mul_inv_cancel₀,
     add_sub_cancel_right]
 
@@ -605,7 +605,7 @@ private theorem intervalIntegral_complexWallisLog
       (z + 1) * Complex.log (z + 1) -
         z * Complex.log z - 1 := by
   have hline : Continuous (fun s : ℝ => z + (s : ℂ)) := by
-    fun_prop
+    exact Continuous.const_add Complex.continuous_ofReal z
   have hlog :
       ContinuousOn
         (fun s : ℝ => Complex.log (z + (s : ℂ)))
@@ -616,7 +616,7 @@ private theorem intervalIntegral_complexWallisLog
     apply Complex.mem_slitPlane_iff.mpr
     left
     simp only [Complex.add_re, Complex.ofReal_re]
-    linarith [hs.1]
+    linarith only [hs.1, hz, hs]
   rw [intervalIntegral.integral_eq_sub_of_hasDerivAt
     (fun s hs => by
       rw [Set.uIcc_of_le (show (0 : ℝ) ≤ 1 by norm_num)] at hs
@@ -652,7 +652,7 @@ private theorem integral_complexWallisPhaseKernel
       rw [Set.uIcc_of_le (show (0 : ℝ) ≤ 1 by norm_num)] at hs
       have hspositive : 0 < (z + (s : ℂ)).re := by
         simp only [Complex.add_re, Complex.ofReal_re]
-        linarith [hs.1]
+        linarith only [hs.1, hz, hs]
       change
         (∫ x : ℝ in Ioi 0,
           complexFrullaniKernel (z + (s : ℂ)) 1 x) =
@@ -714,7 +714,7 @@ private theorem stripNormalizedPoissonKernel_eq_extension
           (x := 0) (y := stripAngle σ)
           (by norm_num) hangle.2.le hangle.1
         simpa only [gt_iff_lt, Real.cos_zero] using! h
-      linarith [Real.one_le_cosh (Real.pi * T / 2)]
+      linarith only [Real.one_le_cosh (Real.pi * T / 2), hcos]
     rw [stripAngle_eq_pi_sub, Real.cos_pi_sub] at horiginal
     have hpositive :
         0 < Real.cosh (Real.pi * T / 2) +
@@ -731,7 +731,7 @@ private theorem stripNormalizedPoissonExtension_one (T : ℝ) :
     stripNormalizedPoissonExtension 1 T =
       limitingStripPoissonDensity T := by
   have hden : Real.cosh (Real.pi * T / 2) + 1 ≠ 0 := by
-    linarith [Real.one_le_cosh (Real.pi * T / 2)]
+    linarith only [Real.one_le_cosh (Real.pi * T / 2)]
   unfold stripNormalizedPoissonExtension limitingStripPoissonDensity
   simp only [sub_self, mul_zero, zero_div, Real.sinc_zero,
     Real.cos_zero, mul_one]
@@ -743,13 +743,14 @@ private theorem stripNormalizedPoissonExtension_continuousAt_one (T : ℝ) :
   unfold stripNormalizedPoissonExtension
   have hangle : Continuous
       (fun σ : ℝ => Real.pi * (1 - σ) / 2) := by
-    fun_prop
+    exact Continuous.comp' (Continuous.div_const continuous_id' 2)
+        (Continuous.const_mul (Continuous.fun_sub continuous_const continuous_id') Real.pi)
   have hden :
       Real.cosh (Real.pi * T / 2) +
         Real.cos (Real.pi * (1 - (1 : ℝ)) / 2) ≠ 0 := by
     simp only [sub_self, mul_zero, zero_div, Real.cos_zero]
     have hcosh := Real.one_le_cosh (Real.pi * T / 2)
-    linarith
+    linarith only [hcosh]
   exact
     ((continuous_const.mul
       (Real.continuous_sinc.comp hangle)).continuousAt.div
@@ -769,7 +770,7 @@ private theorem tendsto_stripNormalizedPoissonKernel (T : ℝ) :
         (fun σ : ℝ => stripNormalizedPoissonExtension σ T) := by
     filter_upwards [hpos, hlt] with σ hσpos hσlt
     exact stripNormalizedPoissonKernel_eq_extension
-      (by linarith) hσlt T
+      (by linarith only [hσpos, hσlt]) hσlt T
   have hext :
       Tendsto (fun σ : ℝ => stripNormalizedPoissonExtension σ T)
         (𝓝[<] 1) (𝓝 (limitingStripPoissonDensity T)) := by
@@ -793,7 +794,7 @@ private theorem inv_cosh_le_two_exp_neg_abs (u : ℝ) :
   have hhalf : Real.exp |u| / 2 ≤ Real.cosh u := by
     rw [← Real.cosh_abs, Real.cosh_eq]
     have hpositive := (Real.exp_pos (-|u|)).le
-    linarith
+    linarith only [hpositive]
   rw [← one_div, div_le_iff₀ (Real.cosh_pos u)]
   calc
     (1 : ℝ) =
@@ -817,15 +818,15 @@ private theorem stripNormalizedPoissonExtension_le_majorant
   have hqzero : 0 ≤ q := by
     try dsimp [q]
     exact div_nonneg (mul_nonneg Real.pi_pos.le (sub_nonneg.mpr hone))
-      (by norm_num)
+      (by norm_num1)
   have hqlarge : q ≤ Real.pi / 2 := by
     try dsimp [q]
-    linarith [mul_nonneg Real.pi_pos.le hzero]
+    linarith only [mul_nonneg Real.pi_pos.le hzero, hzero]
   have hqpi : q ≤ Real.pi := by
-    linarith [Real.pi_pos]
+    linarith only [Real.pi_pos, hqzero, hqlarge]
   have hcos : 0 ≤ Real.cos q :=
     Real.cos_nonneg_of_mem_Icc
-      ⟨by linarith [Real.pi_pos], hqlarge⟩
+      ⟨by linarith only [Real.pi_pos, hqzero, hqlarge], hqlarge⟩
   have hsinc : 0 ≤ Real.sinc q := by
     by_cases hq : q = 0
     · simp only [hq, Real.sinc_zero, zero_le_one]
@@ -835,11 +836,11 @@ private theorem stripNormalizedPoissonExtension_le_majorant
   have hden : 0 < Real.cosh u + Real.cos q :=
     add_pos_of_pos_of_nonneg (Real.cosh_pos u) hcos
   have hcoefficient : 0 < Real.pi / 4 :=
-    div_pos Real.pi_pos (by norm_num)
+    div_pos Real.pi_pos (by norm_num1)
   have habsu : |u| = (Real.pi / 2) * |T| := by
     try dsimp [u]
     rw [abs_div, abs_mul, abs_of_pos Real.pi_pos]
-    norm_num
+    norm_num1
     ring
   constructor
   · unfold stripNormalizedPoissonExtension
@@ -989,7 +990,7 @@ private theorem poissonLogistic_image_univ :
     constructor
     · positivity
     · apply (div_lt_one (by positivity)).2
-      linarith
+      linarith only []
   · intro hx
     have hratio : 0 < x / (1 - x) :=
       div_pos hx.1 (sub_pos.mpr hx.2)
@@ -1024,7 +1025,7 @@ private theorem poissonLogistic_injective :
   have hexp :
       Real.exp (Real.pi * u) = Real.exp (Real.pi * v) := by
     apply (div_eq_div_iff heu hev).mp at huv
-    linarith
+    linear_combination huv
   have harg : Real.pi * u = Real.pi * v :=
     Real.exp_injective hexp
   exact mul_left_cancel₀ Real.pi_ne_zero harg
@@ -1158,53 +1159,18 @@ private theorem gamma_one_add_imaginary_mul_gamma_one_sub
     Complex.Gamma (1 + Complex.I * (x : ℂ)) *
         Complex.Gamma (1 - Complex.I * (x : ℂ)) =
       ((Real.pi * x / Real.sinh (Real.pi * x) : ℝ) : ℂ) := by
-  let z : ℂ := Complex.I * (x : ℂ)
-  have hz : z ≠ 0 := by
-    try dsimp [z]
-    exact mul_ne_zero Complex.I_ne_zero
-      (Complex.ofReal_ne_zero.mpr hx)
-  have hnegz : -z ≠ 0 := neg_ne_zero.mpr hz
-  have hplus :
-      Complex.Gamma (1 + z) = z * Complex.Gamma z := by
-    convert! Complex.Gamma_add_one z hz using 1; ring_nf
-  have hminus :
-      Complex.Gamma (1 - z) =
-        (-z) * Complex.Gamma (-z) := by
-    convert! Complex.Gamma_add_one (-z) hnegz using 1; ring_nf
-  have hconjarg : -z = starRingEnd ℂ z := by
-    try dsimp [z]
-    simp only [map_mul, Complex.conj_I, Complex.conj_ofReal]
-    ring
-  have hgammaprod :
-      Complex.Gamma z * Complex.Gamma (-z) =
-        (‖Complex.Gamma z‖ ^ 2 : ℝ) := by
-    rw [hconjarg, Complex.Gamma_conj, mul_comm,
-      ← Complex.normSq_eq_conj_mul_self,
-      Complex.normSq_eq_norm_sq]
-  have hsinh : Real.sinh (Real.pi * x) ≠ 0 :=
-    Real.sinh_ne_zero.mpr
-      (mul_ne_zero Real.pi_ne_zero hx)
-  change Complex.Gamma (1 + z) *
-    Complex.Gamma (1 - z) = _
-  rw [hplus, hminus]
-  calc
-    (z * Complex.Gamma z) *
-        ((-z) * Complex.Gamma (-z)) =
-      ((x ^ 2 : ℝ) : ℂ) *
-        (Complex.Gamma z * Complex.Gamma (-z)) := by
-          try dsimp [z]
-          ring_nf
-          simp only [Complex.I_sq, neg_mul, one_mul, neg_neg, Complex.ofReal_pow]
-          ring
-    _ = ((x ^ 2 * ‖Complex.Gamma z‖ ^ 2 : ℝ) : ℂ) := by
-      rw [hgammaprod]
-      push_cast
-      ring
-    _ = ((Real.pi * x / Real.sinh (Real.pi * x) : ℝ) : ℂ) := by
-      try dsimp [z]
-      rw [norm_gamma_imaginary_sq hx]
-      congr 1
-      field_simp [hx, hsinh]
+  have hz : Complex.I * (x : ℂ) ≠ 0 :=
+    mul_ne_zero Complex.I_ne_zero (Complex.ofReal_ne_zero.mpr hx)
+  have hsin :
+      Complex.sin ((Real.pi : ℂ) * (Complex.I * (x : ℂ))) =
+        (Real.sinh (Real.pi * x) : ℂ) * Complex.I := by
+    rw [show (Real.pi : ℂ) * (Complex.I * (x : ℂ)) =
+      ((Real.pi * x : ℝ) : ℂ) * Complex.I by push_cast; ring,
+      Complex.sin_mul_I, ← Complex.ofReal_sinh]
+  rw [add_comm (1 : ℂ), Complex.Gamma_add_one _ hz,
+    mul_assoc, Complex.Gamma_mul_Gamma_one_sub, hsin]
+  push_cast
+  field_simp [Complex.I_ne_zero]
 
 private theorem poissonLogistic_characteristic_of_ne_zero
     {t : ℝ} (ht : t ≠ 0) :
@@ -1294,7 +1260,7 @@ private theorem poissonLogistic_characteristic_integrable (t : ℝ) :
       Continuous (fun u : ℝ =>
         Complex.exp
           (Complex.I * (t : ℂ) * (u : ℂ))) := by
-    fun_prop
+    exact Continuous.cexp (Continuous.const_mul Complex.continuous_ofReal (Complex.I * ↑t))
   apply poissonLogisticDensity_integrable.mono'
     (poissonLogisticDensity_integrable.ofReal.aestronglyMeasurable.mul
       hcontinuous.aestronglyMeasurable)
@@ -1363,7 +1329,8 @@ private theorem lowerEndpointPhase_continuous :
       positivity)
   have hfirst : Continuous
       (fun T : ℝ => -Real.pi * |T| / 4) := by
-    fun_prop
+    exact Continuous.comp' (Continuous.div_const continuous_id' 4)
+        (Continuous.const_mul (Continuous.abs continuous_id') (-Real.pi))
   have hsecond : Continuous
       (fun T : ℝ =>
         (1 / 2 : ℝ) * Real.log (1 + T ^ 2 / 4)) :=
@@ -1380,12 +1347,12 @@ private theorem abs_lowerEndpointPhase_le (T : ℝ) :
     |lowerEndpointPhase T| ≤ Real.pi * |T| + T ^ 2 := by
   have hnonneg : 0 ≤ T ^ 2 / 4 := by positivity
   have hlogzero : 0 ≤ Real.log (1 + T ^ 2 / 4) :=
-    Real.log_nonneg (by linarith)
+    Real.log_nonneg (by linear_combination hnonneg)
   have hlogupper :
       Real.log (1 + T ^ 2 / 4) ≤ T ^ 2 / 4 := by
     have h := Real.log_le_sub_one_of_pos
       (show 0 < 1 + T ^ 2 / 4 by positivity)
-    linarith
+    linear_combination h
   have hatanzero : 0 ≤ Real.arctan (|T| / 2) :=
     Real.arctan_nonneg.mpr (by positivity)
   have hatanupper : Real.arctan (|T| / 2) ≤ Real.pi / 2 :=
@@ -1402,8 +1369,8 @@ private theorem abs_lowerEndpointPhase_le (T : ℝ) :
   unfold lowerEndpointPhase
   apply (abs_le).2
   constructor
-  · linarith [sq_nonneg T]
-  · linarith [sq_nonneg T]
+  · linarith only [sq_nonneg T, hnonneg, hlogupper, hmulzero, hmulupper]
+  · linarith only [sq_nonneg T, hnonneg, hlogzero, hmulzero, hmulupper]
 
 private theorem stripPoissonExponentialMajorant_mul_lowerEndpointPhase_integrable :
     Integrable
@@ -1485,11 +1452,11 @@ private theorem tendsto_integral_stripNormalizedPoissonKernel_mul
   · filter_upwards [hpos, hlt] with σ hσpos hσlt
     exact
       (stripNormalizedPoissonKernel_integrable
-        (by linarith) hσlt).aestronglyMeasurable.mul hf
+        (by linarith only [hσpos, hσlt]) hσlt).aestronglyMeasurable.mul hf
   · filter_upwards [hpos, hlt] with σ hσpos hσlt
     filter_upwards [] with T
     have hext := stripNormalizedPoissonKernel_eq_extension
-      (by linarith : -1 < σ) hσlt T
+      (by linarith only [hσpos, hσlt] : -1 < σ) hσlt T
     have hbound := stripNormalizedPoissonExtension_le_majorant
       hσpos.le hσlt.le T
     rw [norm_mul, Real.norm_eq_abs, hext,
@@ -1522,7 +1489,7 @@ private theorem poissonLogistic_cosine_integrable (t : ℝ) :
         poissonLogisticDensity u * Real.cos (t * u)) := by
   have hcontinuous :
       Continuous (fun u : ℝ => Real.cos (t * u)) := by
-    fun_prop
+    exact Continuous.comp' Real.continuous_cos (Continuous.const_mul continuous_id' t)
   apply poissonLogisticDensity_integrable.mono'
     (poissonLogisticDensity_integrable.aestronglyMeasurable.mul
       hcontinuous.aestronglyMeasurable)
@@ -1594,12 +1561,12 @@ private theorem lowerWallisPhaseKernel_abs_le_moment
     positivity
   have hqone : q ≤ 1 := by
     try dsimp [q]
-    exact Real.exp_le_one_iff.mpr (by linarith)
+    exact Real.exp_le_one_iff.mpr (by linear_combination ht)
   have hone : 0 ≤ 1 - q := by
-    linarith
+    linear_combination hqone
   have hone_le : 1 - q ≤ t := by
     try dsimp [q]
-    linarith [Real.add_one_le_exp (-t)]
+    linarith only [Real.add_one_le_exp (-t)]
   have hcos :
       |Real.cos (u * t) - 1| ≤ |u| * t := by
     have h := Real.abs_cos_sub_cos_le (u * t) 0
@@ -1614,11 +1581,11 @@ private theorem lowerWallisPhaseKernel_abs_le_moment
         rw [← Real.exp_add]
         simp only [add_neg_cancel, Real.exp_zero]
   have hcancel_nonneg : 0 ≤ 1 - q - t * q := by
-    linarith
+    linear_combination hqproduct
   have hcancel_upper : 1 - q - t * q ≤ t ^ 2 := by
     calc
       1 - q - t * q ≤ t * (1 - q) := by
-        linarith [hone_le]
+        linear_combination hone_le
       _ ≤ t * t :=
         mul_le_mul_of_nonneg_left hone_le ht.le
       _ = t ^ 2 := by
@@ -1650,8 +1617,11 @@ private theorem lowerWallisPhaseKernel_abs_le_moment
         (mul_le_mul_of_nonneg_left hcos hone)
         hcancel_upper
     _ ≤ t * (|u| * t) + t ^ 2 := by
-      linarith [mul_le_mul_of_nonneg_right hone_le
-        (mul_nonneg (abs_nonneg u) ht.le)]
+      linarith only [
+        mul_le_mul_of_nonneg_right hone_le (mul_nonneg (abs_nonneg u) ht.le),
+        ht,
+        hone_le
+      ]
     _ = (|u| + 1) * t ^ 2 := by
       ring
 
@@ -1666,11 +1636,11 @@ private theorem lowerWallisPhaseKernel_abs_le_tail
     positivity
   have hqone : q ≤ 1 := by
     try dsimp [q]
-    exact Real.exp_le_one_iff.mpr (by linarith)
+    exact Real.exp_le_one_iff.mpr (by linear_combination ht)
   have hone : 0 ≤ 1 - q := by
-    linarith
+    linear_combination hqone
   have hone_upper : 1 - q ≤ 1 := by
-    linarith
+    linear_combination hqpos
   have ht_sq : t ≤ t ^ 2 := by
     nlinarith
   have hsq : 0 < t ^ 2 := sq_pos_of_pos htpos
@@ -1698,10 +1668,9 @@ private theorem lowerWallisPhaseKernel_abs_le_tail
             mul_le_mul_of_nonneg_left hcos hone
           _ ≤ 1 := by
             simpa only [mul_one, tsub_le_iff_right, le_add_iff_nonneg_right] using! hone_upper
-      linarith
+      linear_combination hfactor
     _ ≤ 1 + q * t ^ 2 := by
-      linarith [mul_nonneg hqpos.le
-        (sub_nonneg.mpr ht_sq)]
+      linarith only [mul_nonneg hqpos.le (sub_nonneg.mpr ht_sq), hqpos, ht_sq]
     _ = (1 / t ^ 2 + q) * t ^ 2 := by
       field_simp [htpos.ne']
 
@@ -1922,7 +1891,7 @@ private theorem integral_poissonLogistic_mul_lowerWallisPhaseKernel
         rw [← Real.exp_add]
         simp only [add_neg_cancel, Real.exp_zero]
       unfold wallisLaplaceKernel
-      field_simp [htne, hpositive, hdiff, hden]; linarith [hexp]
+      field_simp [htne, hpositive, hdiff, hden]; linarith only [hexp]
 
 private noncomputable def lowerWallisRegularizedPhaseKernel (a u t : ℝ) : ℝ :=
   ((1 - Real.exp (-t)) * Real.exp (-a * t) *
@@ -1965,25 +1934,25 @@ private theorem lowerWallisRegularizedPhaseKernel_abs_le_moment
     positivity
   have hqone : q ≤ 1 := by
     try dsimp [q]
-    exact Real.exp_le_one_iff.mpr (by linarith)
+    exact Real.exp_le_one_iff.mpr (by linear_combination ht)
   have hrpos : 0 < r := by
     try dsimp [r]
     positivity
   have hrone : r ≤ 1 := by
     try dsimp [r]
     apply Real.exp_le_one_iff.mpr
-    linarith [mul_nonneg hazero ht.le]
-  have hqnonneg : 0 ≤ 1 - q := by linarith
-  have hrnonneg : 0 ≤ 1 - r := by linarith
+    linarith only [mul_nonneg hazero ht.le, hazero, ht]
+  have hqnonneg : 0 ≤ 1 - q := by linear_combination hqone
+  have hrnonneg : 0 ≤ 1 - r := by linear_combination hrone
   have hqbound : 1 - q ≤ t := by
     try dsimp [q]
-    linarith [Real.add_one_le_exp (-t)]
+    linarith only [Real.add_one_le_exp (-t)]
   have hrbound : 1 - r ≤ t := by
     have hfirst : 1 - r ≤ a * t := by
       try dsimp [r]
-      linarith [Real.add_one_le_exp (-a * t)]
+      linarith only [Real.add_one_le_exp (-a * t)]
     have hsecond : a * t ≤ t := by
-      linarith [mul_nonneg (sub_nonneg.mpr haone) ht.le]
+      linarith only [mul_nonneg (sub_nonneg.mpr haone) ht.le, haone, ht]
     exact hfirst.trans hsecond
   have hsq : 0 < t ^ 2 := sq_pos_of_pos ht
   have hcorrection :
@@ -1991,7 +1960,7 @@ private theorem lowerWallisRegularizedPhaseKernel_abs_le_moment
           t ^ 2| ≤ 1 := by
     rw [abs_div, abs_of_pos hsq, abs_mul, abs_mul,
       abs_of_nonneg hqnonneg,
-      abs_of_nonpos (show r - 1 ≤ 0 by linarith)]
+      abs_of_nonpos (show r - 1 ≤ 0 by linear_combination hrone)]
     apply (div_le_iff₀ hsq).2
     have hcos := Real.abs_cos_le_one (u * t)
     calc
@@ -1999,7 +1968,7 @@ private theorem lowerWallisRegularizedPhaseKernel_abs_le_moment
           (1 - q) * (1 - r) := by
         have hfactor : 0 ≤ (1 - q) * (1 - r) :=
           mul_nonneg hqnonneg hrnonneg
-        linarith [mul_le_mul_of_nonneg_left hcos hfactor]
+        linarith only [mul_le_mul_of_nonneg_left hcos hfactor, hcos, hfactor]
       _ ≤ t * t :=
         mul_le_mul hqbound hrbound hrnonneg ht.le
       _ = 1 * t ^ 2 := by ring
@@ -2032,15 +2001,15 @@ private theorem lowerWallisRegularizedPhaseKernel_abs_le_tail
     positivity
   have hqone : q ≤ 1 := by
     try dsimp [q]
-    exact Real.exp_le_one_iff.mpr (by linarith)
+    exact Real.exp_le_one_iff.mpr (by linear_combination ht)
   have hrpos : 0 < r := by
     try dsimp [r]
     positivity
   have hrone : r ≤ 1 := by
     try dsimp [r]
     apply Real.exp_le_one_iff.mpr
-    linarith [mul_nonneg hazero htpos.le]
-  have hqnonneg : 0 ≤ 1 - q := by linarith
+    linarith only [mul_nonneg hazero htpos.le, hazero, htpos]
+  have hqnonneg : 0 ≤ 1 - q := by linear_combination hqone
   have hsq : 0 < t ^ 2 := sq_pos_of_pos htpos
   have htsq : t ≤ t ^ 2 := by nlinarith
   unfold lowerWallisRegularizedPhaseKernel
@@ -2063,12 +2032,12 @@ private theorem lowerWallisRegularizedPhaseKernel_abs_le_tail
         calc
           (1 - q) * r ≤ (1 - q) * 1 :=
             mul_le_mul_of_nonneg_left hrone hqnonneg
-          _ ≤ 1 := by linarith
+          _ ≤ 1 := by linear_combination hqpos
       have hfactor : 0 ≤ (1 - q) * r :=
         mul_nonneg hqnonneg hrpos.le
-      linarith [mul_le_mul_of_nonneg_left hcos hfactor]
+      linarith only [mul_le_mul_of_nonneg_left hcos hfactor, hcos, hfirst, hfactor]
     _ ≤ 1 + q * t ^ 2 := by
-      linarith [mul_nonneg hqpos.le (sub_nonneg.mpr htsq)]
+      linarith only [mul_nonneg hqpos.le (sub_nonneg.mpr htsq), hqpos, htsq]
     _ = (1 / t ^ 2 + q) * t ^ 2 := by
       field_simp [htpos.ne']
 
@@ -2126,7 +2095,7 @@ private theorem tendsto_integral_lowerWallisRegularizedPhaseKernel
     have haone : 1 / ((n : ℝ) + 1) ≤ 1 := by
       apply (div_le_iff₀ (show 0 < (n : ℝ) + 1 by positivity)).2
       have hn : 0 ≤ (n : ℝ) := Nat.cast_nonneg n
-      linarith
+      linarith only []
     rw [Real.norm_eq_abs]
     by_cases htone : t ≤ 1
     · simp only [lowerWallisRegularizedPhaseMajorant,
@@ -2330,7 +2299,7 @@ private theorem lowerWallisComplexLogPhase_ofReal
     rfl
   have hnorm : ‖(a : ℂ) + 1‖ = a + 1 := by
     rw [hcast, Complex.norm_real, Real.norm_eq_abs,
-      abs_of_nonneg (show 0 ≤ a + 1 by linarith)]
+      abs_of_nonneg (show 0 ≤ a + 1 by linear_combination ha)]
   unfold lowerWallisComplexLogPhase
   simp only [Complex.sub_re, Complex.add_re, Complex.one_re, Complex.mul_re, Complex.ofReal_re,
     Complex.log_re,
@@ -2357,7 +2326,7 @@ private theorem tendsto_lowerWallisComplexLogPhase_regularized (u : ℝ) :
             1 + a * Real.log a -
               (a + 1) * Real.log (a + 1)) := by
       have hshift : Continuous (fun a : ℝ => a + 1) := by
-        fun_prop
+        exact Continuous.add_const continuous_id' 1
       exact
         (continuous_const.add Real.continuous_mul_log).sub
           (Real.continuous_mul_log.comp hshift)
@@ -2567,7 +2536,7 @@ private theorem integral_poissonLogistic_lowerEndpointPhase :
   have hwallis :=
     integral_poissonLogistic_one_add_lowerEndpointPhase
   rw [hsplit, integral_poissonLogisticDensity] at hwallis
-  linarith
+  linear_combination hwallis
 
 private theorem limitingPoissonEndpointExpectation_eq_log_pi_div_two_sub_one :
     limitingPoissonEndpointExpectation =
@@ -2606,7 +2575,7 @@ private theorem limitingPoissonEndpointExpectation_eq_log_pi_div_two_sub_one :
             lowerEndpointPhase (2 * u)) := by
         rw [integral_const_mul]
   have hphase := integral_poissonLogistic_lowerEndpointPhase
-  linarith
+  linarith only [hscale, hlogistic, hphase]
 
 private theorem lowerPoissonEndpointSharpCoefficient_eq
     {c : ℝ} (hc : 0 < c) :
@@ -2649,15 +2618,15 @@ private theorem lowerPoissonEndpointSharpCoefficient_neg
     have hdiv : c < 1 / Real.pi := by
       simpa only [one_div] using! hsharp
     have h := (lt_div_iff₀ Real.pi_pos).mp hdiv
-    linarith
+    linear_combination h
   have hpositive : 0 < Real.pi * c :=
     mul_pos Real.pi_pos hc
   have hbelow : Real.pi ^ 2 * c ^ 2 < 1 := by
     have hfactor :
         0 < (1 - Real.pi * c) *
           (1 + Real.pi * c) :=
-      mul_pos (sub_pos.mpr hproduct) (by linarith)
-    linarith
+      mul_pos (sub_pos.mpr hproduct) (by linarith only [hproduct, hpositive])
+    linear_combination hfactor
   exact Real.log_neg (by positivity) hbelow
 
 private theorem tendsto_lowerPoissonEndpointSharpCoefficient
@@ -2696,19 +2665,19 @@ private theorem saddle_one_add_abs_cube_le (T : ℝ) :
   have hfactor : 0 ≤
       (|T| - 1) ^ 2 * (|T| + 1) :=
     mul_nonneg (sq_nonneg _) (by positivity)
-  linarith
+  linarith only [hfactor]
 
 private theorem plusPolynomial_imaginary_norm_ge_beta
     {ε u : ℝ} (hε : 0 < ε) (hu : -1 ≤ u) :
     (ε / 4) ≤ ‖plusPolynomial ε (Complex.I * (u : ℂ))‖ := by
   have hb : 0 < (ε / 4) := div_pos hε four_pos
   have hterm : 0 ≤ (1 - u) ^ 2 * (1 + u) :=
-    mul_nonneg (sq_nonneg _) (by linarith)
+    mul_nonneg (sq_nonneg _) (by linear_combination hu)
   have hvalue : 0 < (ε / 4) + (1 - u) ^ 2 * (1 + u) :=
     add_pos_of_pos_of_nonneg hb hterm
   rw [plusPolynomial_imaginary, Complex.norm_real,
     Real.norm_eq_abs, abs_of_pos hvalue]
-  linarith
+  linear_combination hterm
 
 private theorem plusPolynomial_imaginary_cubic_growth_le
     {ε u : ℝ} (hε : 0 < ε) (hu : -1 ≤ u) :
@@ -2716,62 +2685,38 @@ private theorem plusPolynomial_imaginary_cubic_growth_le
       (27 / (ε / 4) + 9) *
         ‖plusPolynomial ε (Complex.I * (u : ℂ))‖ := by
   have hb : 0 < (ε / 4) := div_pos hε four_pos
-  have hnorm :
-      (ε / 4) ≤ ‖plusPolynomial ε (Complex.I * (u : ℂ))‖ :=
-    plusPolynomial_imaginary_norm_ge_beta hε hu
+  have hterm : 0 ≤ (1 - u) ^ 2 * (1 + u) :=
+    mul_nonneg (sq_nonneg _) (by linear_combination hu)
+  have hvalue : ‖plusPolynomial ε (Complex.I * (u : ℂ))‖ =
+      (ε / 4) + (1 - u) ^ 2 * (1 + u) := by
+    rw [plusPolynomial_imaginary, Complex.norm_real, Real.norm_eq_abs]
+    exact abs_of_pos (add_pos_of_pos_of_nonneg hb hterm)
+  rw [hvalue]
   by_cases hbounded : u ≤ 2
-  · have habs : |u| ≤ 2 := by
-      exact (abs_le).mpr ⟨by linarith only [hu], hbounded⟩
-    have hcube : (1 + |u|) ^ 3 ≤ 27 := by
-      have hbase : 1 + |u| ≤ (3 : ℝ) := by linarith only [habs]
-      exact (pow_le_pow_left₀ (by positivity) hbase 3).trans_eq (by norm_num)
+  · have habs : |u| ≤ 2 := abs_le.mpr ⟨by linear_combination hu, hbounded⟩
+    have hcube : (1 + |u|) ^ 3 ≤ 27 :=
+      (pow_le_pow_left₀ (by positivity)
+        (show 1 + |u| ≤ (3 : ℝ) by linear_combination habs) 3).trans_eq (by norm_num)
     calc
       (1 + |u|) ^ 3 ≤ 27 := hcube
       _ = (27 / (ε / 4)) * (ε / 4) := (div_mul_cancel₀ _ hb.ne').symm
-      _ ≤ (27 / (ε / 4)) *
-          ‖plusPolynomial ε (Complex.I * (u : ℂ))‖ :=
-        mul_le_mul_of_nonneg_left hnorm (by positivity)
-      _ ≤ (27 / (ε / 4) + 9) *
-          ‖plusPolynomial ε (Complex.I * (u : ℂ))‖ := by
-        have hnonnegative :=
-          norm_nonneg (plusPolynomial ε (Complex.I * (u : ℂ)))
-        linarith only [hnonnegative]
+      _ ≤ (27 / (ε / 4) + 9) * ((ε / 4) + (1 - u) ^ 2 * (1 + u)) :=
+        mul_le_mul (le_add_of_nonneg_right (by norm_num))
+          (le_add_of_nonneg_right hterm) hb.le (by positivity)
   · have hlarge : 2 < u := lt_of_not_ge hbounded
-    have habs : |u| = u := abs_of_pos (by linarith only [hlarge])
-    have hvalue :
-        ‖plusPolynomial ε (Complex.I * (u : ℂ))‖ =
-          (ε / 4) + (1 - u) ^ 2 * (1 + u) := by
-      rw [plusPolynomial_imaginary, Complex.norm_real,
-        Real.norm_eq_abs]
-      apply abs_of_pos
-      exact add_pos_of_pos_of_nonneg hb
-        (mul_nonneg (sq_nonneg _) (by linarith only [hlarge]))
-    have hsq :
-        (1 + u) ^ 2 ≤ 9 * (1 - u) ^ 2 := by
-      have hfactor : 0 ≤ (2 * u - 1) * (u - 2) :=
-        mul_nonneg (by linarith only [hlarge]) (by linarith only [hlarge])
+    have hsquare : (1 + u) ^ 2 ≤ 9 * (1 - u) ^ 2 := by
+      have hfactor := mul_nonneg
+        (show 0 ≤ 2 * u - 1 by linarith only [hlarge])
+        (show 0 ≤ u - 2 by linear_combination hlarge)
       linarith only [hfactor]
-    have hcube :
-        (1 + u) ^ 3 ≤
-          9 * ((1 - u) ^ 2 * (1 + u)) := by
-      have hproduct := mul_le_mul_of_nonneg_right
-        hsq (show 0 ≤ 1 + u by linarith only [hlarge])
-      linarith only [hproduct]
-    rw [habs]
-    calc
-      (1 + u) ^ 3 ≤
-          9 * ((1 - u) ^ 2 * (1 + u)) := hcube
-      _ ≤ 9 * ‖plusPolynomial ε
-          (Complex.I * (u : ℂ))‖ := by
-        rw [hvalue]
-        linarith only [hb]
-      _ ≤ (27 / (ε / 4) + 9) *
-          ‖plusPolynomial ε (Complex.I * (u : ℂ))‖ := by
-        have hnonnegative :=
-          norm_nonneg (plusPolynomial ε (Complex.I * (u : ℂ)))
-        have hcoefficient : 0 ≤ 27 / (ε / 4) := by
-          positivity
-        linarith only [mul_nonneg hcoefficient hnonnegative]
+    have hcubic : (1 + u) ^ 3 ≤ 9 * ((1 - u) ^ 2 * (1 + u)) := by
+      have hproduct := mul_le_mul_of_nonneg_right hsquare
+        (show 0 ≤ 1 + u by linear_combination hlarge)
+      linear_combination hproduct
+    rw [abs_of_pos (show 0 < u by linear_combination hlarge)]
+    exact hcubic.trans
+      (mul_le_mul (le_add_of_nonneg_left (div_nonneg (by norm_num) hb.le))
+        (le_add_of_nonneg_left hb.le) hterm (by positivity))
 
 private theorem minusPolynomial_imaginary_norm_ge_three_beta
     {ε u : ℝ} (hε : 0 < ε)
@@ -2779,17 +2724,17 @@ private theorem minusPolynomial_imaginary_norm_ge_three_beta
     3 * (ε / 4) ≤
       ‖minusPolynomial ε (Complex.I * (u : ℂ))‖ := by
   have hb : 0 < (ε / 4) := div_pos hε four_pos
-  have hone : 1 ≤ u := by linarith
+  have hone : 1 ≤ u := by linarith only [hε, hu]
   have hbeta : (ε / 4) ≤ u - 1 := by
-    linarith
+    linear_combination hu
   have hsquare : (4 : ℝ) ≤ (1 + u) ^ 2 := by
-    linarith [sq_nonneg (u - 1)]
+    linarith only [sq_nonneg (u - 1), hε, hu]
   have hproduct :
       4 * (ε / 4) ≤ (u - 1) * (1 + u) ^ 2 := by
     calc
       4 * (ε / 4) = (ε / 4) * 4 := by ring
       _ ≤ (u - 1) * (1 + u) ^ 2 :=
-        mul_le_mul hbeta hsquare (by norm_num) (by linarith)
+        mul_le_mul hbeta hsquare (by norm_num) (by linarith only [hε, hu])
   have hnegative := minusPolynomial_imaginary_re_neg hε hu
   rw [minusPolynomial_imaginary, Complex.norm_real,
     Real.norm_eq_abs]
@@ -2798,7 +2743,7 @@ private theorem minusPolynomial_imaginary_norm_ge_three_beta
       at hnegative
     exact hnegative
   rw [abs_of_neg harg]
-  linarith
+  linear_combination hproduct
 
 private theorem minusPolynomial_imaginary_cubic_growth_le
     {ε u : ℝ} (hε : 0 < ε)
@@ -2807,78 +2752,43 @@ private theorem minusPolynomial_imaginary_cubic_growth_le
       (9 / (ε / 4) + 6) *
         ‖minusPolynomial ε (Complex.I * (u : ℂ))‖ := by
   have hb : 0 < (ε / 4) := div_pos hε four_pos
-  have hone : 1 ≤ u := by linarith only [hu, hb]
-  have hbeta : (ε / 4) ≤ u - 1 := by
-    linarith only [hu]
-  have habs : |u| = u := abs_of_pos (zero_lt_one.trans_le hone)
-  have hnorm := minusPolynomial_imaginary_norm_ge_three_beta
-    hε hu
+  have hone : 1 ≤ u := by linear_combination hb + hu
+  have hnegative := minusPolynomial_imaginary_re_neg hε hu
+  have hvalue : ‖minusPolynomial ε (Complex.I * (u : ℂ))‖ =
+      (u - 1) * (1 + u) ^ 2 - (ε / 4) := by
+    rw [minusPolynomial_imaginary, Complex.norm_real, Real.norm_eq_abs]
+    rw [minusPolynomial_imaginary, Complex.ofReal_re] at hnegative
+    rw [abs_of_neg hnegative]
+    ring
+  have hnorm := minusPolynomial_imaginary_norm_ge_three_beta hε hu
+  rw [hvalue] at hnorm ⊢
+  have hpositive : 0 < (u - 1) * (1 + u) ^ 2 - (ε / 4) :=
+    (mul_pos (by norm_num : (0 : ℝ) < 3) hb).trans_le hnorm
+  rw [abs_of_pos (zero_lt_one.trans_le hone)]
   by_cases hbounded : u ≤ 2
-  · have hcube : (1 + |u|) ^ 3 ≤ 27 := by
-      have hbase : 1 + |u| ≤ (3 : ℝ) := by
-        rw [habs]
-        linarith only [hbounded]
-      exact (pow_le_pow_left₀ (by positivity) hbase 3).trans_eq (by norm_num)
+  · have hcube : (1 + u) ^ 3 ≤ 27 :=
+      (pow_le_pow_left₀ (by linear_combination hone)
+        (show 1 + u ≤ (3 : ℝ) by linear_combination hbounded) 3).trans_eq (by norm_num)
     calc
-      (1 + |u|) ^ 3 ≤ 27 := hcube
+      (1 + u) ^ 3 ≤ 27 := hcube
       _ = (9 / (ε / 4)) * (3 * (ε / 4)) := by
-        rw [div_mul_eq_mul_div, mul_div_assoc, mul_div_cancel_right₀ _ hb.ne']
+        rw [mul_left_comm (9 / (ε / 4)), div_mul_cancel₀ _ hb.ne']
         norm_num
-      _ ≤ (9 / (ε / 4)) *
-          ‖minusPolynomial ε (Complex.I * (u : ℂ))‖ :=
-        mul_le_mul_of_nonneg_left hnorm (by positivity)
-      _ ≤ (9 / (ε / 4) + 6) *
-          ‖minusPolynomial ε (Complex.I * (u : ℂ))‖ := by
-        have hnonnegative :=
-          norm_nonneg (minusPolynomial ε
-            (Complex.I * (u : ℂ)))
-        linarith only [hnonnegative]
+      _ ≤ (9 / (ε / 4) + 6) * ((u - 1) * (1 + u) ^ 2 - (ε / 4)) :=
+        mul_le_mul (le_add_of_nonneg_right (by norm_num)) hnorm
+          (by positivity) (by positivity)
   · have hlarge : 2 < u := lt_of_not_ge hbounded
-    have hnegative := minusPolynomial_imaginary_re_neg hε hu
-    have hvalue :
-        ‖minusPolynomial ε (Complex.I * (u : ℂ))‖ =
-          (u - 1) * (1 + u) ^ 2 - (ε / 4) := by
-      rw [minusPolynomial_imaginary, Complex.norm_real,
-        Real.norm_eq_abs]
-      have harg : (ε / 4) + (1 - u) * (1 + u) ^ 2 < 0 := by
-        rw [minusPolynomial_imaginary, Complex.ofReal_re]
-          at hnegative
-        exact hnegative
-      rw [abs_of_neg harg]
-      ring
-    have hsquare : (4 : ℝ) ≤ (1 + u) ^ 2 := by
-      linarith only [sq_nonneg (u - 1), hlarge]
-    have hterm :
-        2 * (ε / 4) ≤ (u - 1) * (1 + u) ^ 2 := by
-      calc
-        2 * (ε / 4) ≤ 4 * (ε / 4) := by linarith only [hb]
-        _ = (ε / 4) * 4 := by ring
-        _ ≤ (u - 1) * (1 + u) ^ 2 :=
-          mul_le_mul hbeta hsquare (by norm_num) (by linarith only [hone])
-    have hlinear : 1 + u ≤ 3 * (u - 1) := by
-      linarith only [hlarge]
-    have hcubic :
-        (1 + u) ^ 3 ≤
-          3 * ((u - 1) * (1 + u) ^ 2) := by
-      have hproduct :=
-        mul_le_mul_of_nonneg_right hlinear (sq_nonneg (1 + u))
-      linarith only [hproduct]
-    rw [habs]
+    have hlinear : 1 + u ≤ 3 * (u - 1) := by linarith only [hlarge]
+    have hcubic : (1 + u) ^ 3 ≤ 3 * ((u - 1) * (1 + u) ^ 2) := by
+      have hproduct := mul_le_mul_of_nonneg_right hlinear (sq_nonneg (1 + u))
+      linear_combination hproduct
     calc
-      (1 + u) ^ 3 ≤
-          3 * ((u - 1) * (1 + u) ^ 2) := hcubic
-      _ ≤ 6 * ‖minusPolynomial ε
-          (Complex.I * (u : ℂ))‖ := by
-        rw [hvalue]
-        linarith only [hterm]
-      _ ≤ (9 / (ε / 4) + 6) *
-          ‖minusPolynomial ε (Complex.I * (u : ℂ))‖ := by
-        have hnonnegative :=
-          norm_nonneg (minusPolynomial ε
-            (Complex.I * (u : ℂ)))
-        have hcoefficient : 0 ≤ 9 / (ε / 4) := by
-          positivity
-        linarith only [mul_nonneg hcoefficient hnonnegative]
+      (1 + u) ^ 3 ≤ 3 * ((u - 1) * (1 + u) ^ 2) := hcubic
+      _ ≤ 6 * ((u - 1) * (1 + u) ^ 2 - (ε / 4)) := by
+        linarith only [hb, hnorm]
+      _ ≤ (9 / (ε / 4) + 6) * ((u - 1) * (1 + u) ^ 2 - (ε / 4)) :=
+        mul_le_mul_of_nonneg_right
+          (le_add_of_nonneg_left (div_nonneg (by norm_num) hb.le)) hpositive.le
 
 private theorem saddle_complex_frequency_norm_le (T u : ℝ) :
     ‖(T : ℂ) + Complex.I * (u : ℂ)‖ ≤ |T| + |u| := by
@@ -2889,6 +2799,37 @@ private theorem saddle_complex_frequency_norm_le (T u : ℝ) :
     _ = |T| + |u| := by
       simp only [Complex.norm_real, Real.norm_eq_abs, Complex.norm_mul, Complex.norm_I, one_mul]
 
+private theorem polynomial_uniform_frequency_ratio_le
+    (P : ℂ → ℂ) {B H u : ℝ} (hB : 0 ≤ B)
+    (hD : 0 < ‖P (Complex.I * (u : ℂ))‖)
+    (hbase : ∀ z : ℂ, ‖P z‖ ≤ B * (1 + ‖z‖) ^ 3)
+    (hheight : (1 + |u|) ^ 3 ≤ H * ‖P (Complex.I * (u : ℂ))‖)
+    (T : ℝ) :
+    ‖P ((T : ℂ) + Complex.I * (u : ℂ))‖ /
+        ‖P (Complex.I * (u : ℂ))‖ ≤
+      (4 * B * H) * (1 + |T| ^ 3) := by
+  have htriangle :
+      1 + ‖(T : ℂ) + Complex.I * (u : ℂ)‖ ≤
+        (1 + |T|) * (1 + |u|) := by
+    linarith only [saddle_complex_frequency_norm_le T u,
+      mul_nonneg (abs_nonneg T) (abs_nonneg u)]
+  have hfrequency := saddle_one_add_abs_cube_le T
+  apply (div_le_iff₀ hD).2
+  calc
+    ‖P ((T : ℂ) + Complex.I * (u : ℂ))‖ ≤
+        B * (1 + ‖(T : ℂ) + Complex.I * (u : ℂ)‖) ^ 3 := hbase _
+    _ ≤ B * ((1 + |T|) * (1 + |u|)) ^ 3 :=
+      mul_le_mul_of_nonneg_left
+        (pow_le_pow_left₀ (by positivity) htriangle 3) hB
+    _ = (B * (1 + |T|) ^ 3) * (1 + |u|) ^ 3 := by ring
+    _ ≤ (B * (4 * (1 + |T| ^ 3))) *
+        (H * ‖P (Complex.I * (u : ℂ))‖) :=
+      mul_le_mul (mul_le_mul_of_nonneg_left hfrequency hB)
+        hheight (pow_nonneg (by positivity) 3)
+        (mul_nonneg hB ((pow_nonneg (by positivity) 3).trans hfrequency))
+    _ = ((4 * B * H) * (1 + |T| ^ 3)) *
+        ‖P (Complex.I * (u : ℂ))‖ := by ring
+
 private theorem exists_plusPolynomial_uniform_norm_ratio
     {ε : ℝ} (hε : 0 < ε) :
     ∃ C : ℝ, 0 < C ∧
@@ -2898,47 +2839,13 @@ private theorem exists_plusPolynomial_uniform_norm_ratio
           ‖plusPolynomial ε (Complex.I * (u : ℂ))‖ ≤
             C * (1 + |T| ^ 3) := by
   have hb : 0 < (ε / 4) := div_pos hε four_pos
-  refine ⟨4 * (1 + (ε / 4)) * (27 / (ε / 4) + 9),
-    by positivity, ?_⟩
+  refine ⟨4 * (1 + (ε / 4)) * (27 / (ε / 4) + 9), by positivity, ?_⟩
   intro u hu T
-  let z : ℂ := (T : ℂ) + Complex.I * (u : ℂ)
-  let D : ℝ := ‖plusPolynomial ε (Complex.I * (u : ℂ))‖
-  have hD : 0 < D :=
-    lt_of_lt_of_le hb (plusPolynomial_imaginary_norm_ge_beta hε hu)
-  have htriangle :
-      1 + ‖z‖ ≤ (1 + |T|) * (1 + |u|) := by
-    have hz := saddle_complex_frequency_norm_le T u
-    change ‖z‖ ≤ |T| + |u| at hz
-    linarith [mul_nonneg (abs_nonneg T) (abs_nonneg u)]
-  have hpower :
-      (1 + ‖z‖) ^ 3 ≤
-        ((1 + |T|) * (1 + |u|)) ^ 3 :=
-    pow_le_pow_left₀ (by positivity) htriangle 3
-  have hbase := norm_plusPolynomial_le ε z
-  rw [abs_of_pos hb] at hbase
-  have hfrequency := saddle_one_add_abs_cube_le T
-  have hheight := plusPolynomial_imaginary_cubic_growth_le
-    hε hu
-  change ‖plusPolynomial ε z‖ / D ≤
-    (4 * (1 + (ε / 4)) * (27 / (ε / 4) + 9)) *
-      (1 + |T| ^ 3)
-  apply (div_le_iff₀ hD).2
-  calc
-    ‖plusPolynomial ε z‖ ≤
-        (1 + (ε / 4)) * (1 + ‖z‖) ^ 3 := hbase
-    _ ≤ (1 + (ε / 4)) *
-        ((1 + |T|) * (1 + |u|)) ^ 3 := by
-      gcongr
-    _ = (1 + (ε / 4)) * (1 + |T|) ^ 3 *
-        (1 + |u|) ^ 3 := by
-      ring
-    _ ≤ (1 + (ε / 4)) *
-        (4 * (1 + |T| ^ 3)) *
-          ((27 / (ε / 4) + 9) * D) := by
-      gcongr
-    _ = ((4 * (1 + (ε / 4)) * (27 / (ε / 4) + 9)) *
-        (1 + |T| ^ 3)) * D := by
-      ring
+  have hD := hb.trans_le (plusPolynomial_imaginary_norm_ge_beta hε hu)
+  apply polynomial_uniform_frequency_ratio_le (plusPolynomial ε)
+    (by positivity) hD (fun z => ?_)
+    (plusPolynomial_imaginary_cubic_growth_le hε hu) T
+  simpa only [abs_of_pos hb] using norm_plusPolynomial_le ε z
 
 private theorem exists_minusPolynomial_uniform_norm_ratio
     {ε : ℝ} (hε : 0 < ε) :
@@ -2949,50 +2856,15 @@ private theorem exists_minusPolynomial_uniform_norm_ratio
           ‖minusPolynomial ε (Complex.I * (u : ℂ))‖ ≤
             C * (1 + |T| ^ 3) := by
   have hb : 0 < (ε / 4) := div_pos hε four_pos
-  refine ⟨4 * (1 + (ε / 4)) * (9 / (ε / 4) + 6),
-    by positivity, ?_⟩
+  refine ⟨4 * (1 + (ε / 4)) * (9 / (ε / 4) + 6), by positivity, ?_⟩
   intro u hu T
-  let z : ℂ := (T : ℂ) + Complex.I * (u : ℂ)
-  let D : ℝ := ‖minusPolynomial ε (Complex.I * (u : ℂ))‖
-  have hD : 0 < D := by
-    have h := minusPolynomial_imaginary_norm_ge_three_beta
-      hε hu
-    change 3 * (ε / 4) ≤ D at h
-    linarith
-  have htriangle :
-      1 + ‖z‖ ≤ (1 + |T|) * (1 + |u|) := by
-    have hz := saddle_complex_frequency_norm_le T u
-    change ‖z‖ ≤ |T| + |u| at hz
-    linarith [mul_nonneg (abs_nonneg T) (abs_nonneg u)]
-  have hpower :
-      (1 + ‖z‖) ^ 3 ≤
-        ((1 + |T|) * (1 + |u|)) ^ 3 :=
-    pow_le_pow_left₀ (by positivity) htriangle 3
-  have hbase := norm_minusPolynomial_le ε z
-  rw [abs_of_pos hb] at hbase
-  have hfrequency := saddle_one_add_abs_cube_le T
-  have hheight := minusPolynomial_imaginary_cubic_growth_le
-    hε hu
-  change ‖minusPolynomial ε z‖ / D ≤
-    (4 * (1 + (ε / 4)) * (9 / (ε / 4) + 6)) *
-      (1 + |T| ^ 3)
-  apply (div_le_iff₀ hD).2
-  calc
-    ‖minusPolynomial ε z‖ ≤
-        (1 + (ε / 4)) * (1 + ‖z‖) ^ 3 := hbase
-    _ ≤ (1 + (ε / 4)) *
-        ((1 + |T|) * (1 + |u|)) ^ 3 := by
-      gcongr
-    _ = (1 + (ε / 4)) * (1 + |T|) ^ 3 *
-        (1 + |u|) ^ 3 := by
-      ring
-    _ ≤ (1 + (ε / 4)) *
-        (4 * (1 + |T| ^ 3)) *
-          ((9 / (ε / 4) + 6) * D) := by
-      gcongr
-    _ = ((4 * (1 + (ε / 4)) * (9 / (ε / 4) + 6)) *
-        (1 + |T| ^ 3)) * D := by
-      ring
+  have hD : 0 < ‖minusPolynomial ε (Complex.I * (u : ℂ))‖ := by
+    have h := minusPolynomial_imaginary_norm_ge_three_beta hε hu
+    linarith only [hb, h]
+  apply polynomial_uniform_frequency_ratio_le (minusPolynomial ε)
+    (by positivity) hD (fun z => ?_)
+    (minusPolynomial_imaginary_cubic_growth_le hε hu) T
+  simpa only [abs_of_pos hb] using norm_minusPolynomial_le ε z
 
 private theorem plusPolynomial_add_sub (ε : ℝ) (z w : ℂ) :
     plusPolynomial ε (z + w) - plusPolynomial ε z =
@@ -3029,9 +2901,9 @@ private theorem plusSaddleLinearCoefficient_norm_le (z : ℂ) :
     _ = 2 * ‖z‖ + ‖(1 : ℂ) + 3 * z ^ 2‖ := by
       simp only [Complex.norm_mul, Complex.norm_ofNat, Complex.norm_I, one_mul]
     _ ≤ 2 * ‖z‖ + (1 + 3 * ‖z‖ ^ 2) := by
-      gcongr
+      exact add_le_add (le_refl (2 * ‖z‖)) hinner
     _ ≤ 3 * (1 + ‖z‖) ^ 2 := by
-      linarith [norm_nonneg z]
+      linarith only [norm_nonneg z]
 
 private theorem minusSaddleLinearCoefficient_norm_le (z : ℂ) :
     ‖2 * z - Complex.I * (1 + 3 * z ^ 2)‖ ≤
@@ -3052,9 +2924,9 @@ private theorem minusSaddleLinearCoefficient_norm_le (z : ℂ) :
     _ = 2 * ‖z‖ + ‖(1 : ℂ) + 3 * z ^ 2‖ := by
       simp only [Complex.norm_mul, Complex.norm_ofNat, Complex.norm_I, one_mul]
     _ ≤ 2 * ‖z‖ + (1 + 3 * ‖z‖ ^ 2) := by
-      gcongr
+      exact add_le_add (le_refl (2 * ‖z‖)) hinner
     _ ≤ 3 * (1 + ‖z‖) ^ 2 := by
-      linarith [norm_nonneg z]
+      linarith only [norm_nonneg z]
 
 private theorem plusSaddleQuadraticCoefficient_norm_le (z : ℂ) :
     ‖1 + 3 * Complex.I * z‖ ≤
@@ -3066,7 +2938,7 @@ private theorem plusSaddleQuadraticCoefficient_norm_le (z : ℂ) :
     _ = 1 + 3 * ‖z‖ := by
       simp only [norm_one, Complex.norm_mul, Complex.norm_ofNat, Complex.norm_I, mul_one]
     _ ≤ 3 * (1 + ‖z‖) ^ 2 := by
-      linarith [norm_nonneg z, sq_nonneg ‖z‖]
+      linarith only [norm_nonneg z, sq_nonneg ‖z‖]
 
 private theorem minusSaddleQuadraticCoefficient_norm_le (z : ℂ) :
     ‖1 - 3 * Complex.I * z‖ ≤
@@ -3078,14 +2950,14 @@ private theorem minusSaddleQuadraticCoefficient_norm_le (z : ℂ) :
     _ = 1 + 3 * ‖z‖ := by
       simp only [norm_one, Complex.norm_mul, Complex.norm_ofNat, Complex.norm_I, mul_one]
     _ ≤ 3 * (1 + ‖z‖) ^ 2 := by
-      linarith [norm_nonneg z, sq_nonneg ‖z‖]
+      linarith only [norm_nonneg z, sq_nonneg ‖z‖]
 
 private theorem saddle_abs_sq_le_add_cube (T : ℝ) :
     |T| ^ 2 ≤ |T| + |T| ^ 3 := by
   have hfactor :
       0 ≤ |T| * (|T| - (1 / 2 : ℝ)) ^ 2 :=
     mul_nonneg (abs_nonneg T) (sq_nonneg _)
-  linarith [abs_nonneg T]
+  linarith only [abs_nonneg T, hfactor]
 
 private theorem saddle_cubic_translation_norm_le
     (u T : ℝ) (A B C : ℂ)
@@ -3099,18 +2971,18 @@ private theorem saddle_cubic_translation_norm_le
   let S : ℝ := |T| + |T| ^ 3
   have hH : 1 ≤ H := by
     try dsimp [H]
-    linarith [abs_nonneg u, sq_nonneg |u|]
+    linarith only [abs_nonneg u, sq_nonneg |u|]
   have hS : 0 ≤ S := by
     try dsimp [S]
     positivity
   have hT : |T| ≤ S := by
     try dsimp [S]
-    linarith [pow_nonneg (abs_nonneg T) 3]
+    linarith only [pow_nonneg (abs_nonneg T) 3]
   have hT2 : |T| ^ 2 ≤ S := by
     exact saddle_abs_sq_le_add_cube T
   have hT3 : |T| ^ 3 ≤ S := by
     try dsimp [S]
-    linarith [abs_nonneg T]
+    linarith only [abs_nonneg T]
   have hfirst :
       ‖(T : ℂ) * A‖ ≤ |T| * (3 * H) := by
     rw [norm_mul, Complex.norm_real, Real.norm_eq_abs]
@@ -3125,17 +2997,14 @@ private theorem saddle_cubic_translation_norm_le
       ‖C * (T : ℂ) ^ 3‖ ≤ |T| ^ 3 := by
     rw [norm_mul, norm_pow, Complex.norm_real,
       Real.norm_eq_abs]
-    linarith [mul_le_mul_of_nonneg_right hC
-      (pow_nonneg (abs_nonneg T) 3)]
+    linarith only [mul_le_mul_of_nonneg_right hC (pow_nonneg (abs_nonneg T) 3), hC]
   have hfirst' : |T| * (3 * H) ≤ 3 * H * S := by
-    linarith [mul_le_mul_of_nonneg_left hT
-      (show 0 ≤ 3 * H by positivity)]
+    linarith only [mul_le_mul_of_nonneg_left hT (show 0 ≤ 3 * H by positivity), hT]
   have hsecond' : |T| ^ 2 * (3 * H) ≤ 3 * H * S := by
-    linarith [mul_le_mul_of_nonneg_left hT2
-      (show 0 ≤ 3 * H by positivity)]
+    linarith only [mul_le_mul_of_nonneg_left hT2 (show 0 ≤ 3 * H by positivity), hT2]
   have hthird' : |T| ^ 3 ≤ H * S := by
     have hraise : S ≤ H * S := by
-      linarith [mul_nonneg (sub_nonneg.mpr hH) hS]
+      linarith only [mul_nonneg (sub_nonneg.mpr hH) hS, hH, hS]
     exact hT3.trans hraise
   calc
     ‖(T : ℂ) * A + (T : ℂ) ^ 2 * B +
@@ -3145,13 +3014,13 @@ private theorem saddle_cubic_translation_norm_le
       norm_add_le _ _
     _ ≤ (‖(T : ℂ) * A‖ + ‖(T : ℂ) ^ 2 * B‖) +
         ‖C * (T : ℂ) ^ 3‖ := by
-      gcongr
+      refine add_le_add ?_ (le_refl ‖C * ↑T ^ 3‖)
       exact norm_add_le _ _
     _ ≤ (|T| * (3 * H) + |T| ^ 2 * (3 * H)) +
         |T| ^ 3 := by
-      gcongr
+      exact add_le_add (add_le_add hfirst hsecond) hthird
     _ ≤ 9 * H * S := by
-      linarith [mul_nonneg (show 0 ≤ H by positivity) hS]
+      linarith only [mul_nonneg (show 0 ≤ H by positivity) hS, hT, hfirst', hsecond', hthird']
     _ = 9 * (1 + |u|) ^ 2 * (|T| + |T| ^ 3) := by
       rfl
 
@@ -3247,7 +3116,7 @@ private theorem exists_plusPolynomial_uniform_difference_ratio
     have hfactor :
         0 ≤ |u| * (1 + |u|) ^ 2 :=
       mul_nonneg (abs_nonneg u) (sq_nonneg _)
-    linarith
+    linear_combination hfactor
   have hgrowth := plusPolynomial_imaginary_cubic_growth_le
     hε hu
   have hquadratic :
@@ -3266,7 +3135,11 @@ private theorem exists_plusPolynomial_uniform_difference_ratio
       9 * (1 + |u|) ^ 2 * S :=
         plusPolynomial_translation_norm_le ε u T
     _ ≤ 9 * ((27 / (ε / 4) + 9) * D) * S := by
-      gcongr
+      exact mul_le_mul_of_nonneg_right
+          (mul_le_mul_of_nonneg_left hquadratic
+            (le_of_lt
+              ((by norm_num))))
+          (add_nonneg (abs_nonneg T) (pow_nonneg (abs_nonneg T) 3))
     _ = ((9 * (27 / (ε / 4) + 9)) * S) * D := by
       ring
 
@@ -3288,7 +3161,7 @@ private theorem exists_minusPolynomial_uniform_difference_ratio
     have h := minusPolynomial_imaginary_norm_ge_three_beta
       hε hu
     change 3 * (ε / 4) ≤ D at h
-    linarith
+    linarith only [hε, h]
   have hS : 0 ≤ S := by
     try dsimp [S]
     positivity
@@ -3296,7 +3169,7 @@ private theorem exists_minusPolynomial_uniform_difference_ratio
     have hfactor :
         0 ≤ |u| * (1 + |u|) ^ 2 :=
       mul_nonneg (abs_nonneg u) (sq_nonneg _)
-    linarith
+    linarith only [hfactor]
   have hgrowth := minusPolynomial_imaginary_cubic_growth_le
     hε hu
   have hquadratic :
@@ -3315,7 +3188,11 @@ private theorem exists_minusPolynomial_uniform_difference_ratio
       9 * (1 + |u|) ^ 2 * S :=
         minusPolynomial_translation_norm_le ε u T
     _ ≤ 9 * ((9 / (ε / 4) + 6) * D) * S := by
-      gcongr
+      exact mul_le_mul_of_nonneg_right
+          (mul_le_mul_of_nonneg_left hquadratic
+            (le_of_lt
+              ((by norm_num))))
+          (add_nonneg (abs_nonneg T) (pow_nonneg (abs_nonneg T) 3))
     _ = ((9 * (9 / (ε / 4) + 6)) * S) * D := by
       ring
 
@@ -3338,7 +3215,7 @@ private theorem upperNegativeHalfGammaArgument_ne_zero
       sub_self, sub_zero,
     Complex.zero_re] at hre
   have hN : 0 ≤ (N : ℝ) := Nat.cast_nonneg N
-  linarith
+  linarith only [hre]
 
 private theorem upperNegativeHalfGammaArgument_succ_add_one
     (N : ℕ) (s : ℝ) :
@@ -3355,7 +3232,7 @@ private theorem tendsto_upper_shortEndpoint_scaled :
     (by norm_num : (0 : ℝ) < 1)
   simp only [Real.rpow_one] at hlog
   have hscaled := hlog.const_mul (-10 : ℝ)
-  convert! hscaled using 1
+  convert hscaled using 1
   · ext ε
     rw [one_div, Real.log_inv]
     ring
@@ -3367,7 +3244,7 @@ private theorem tendsto_upper_one_add_shortEndpoint_scaled :
   have hid : Tendsto (fun ε : ℝ => ε)
       (𝓝[>] (0 : ℝ)) (𝓝 (0 : ℝ)) :=
     tendsto_id.mono_left nhdsWithin_le_nhds
-  convert! hid.add tendsto_upper_shortEndpoint_scaled using 1
+  convert hid.add tendsto_upper_shortEndpoint_scaled using 1
   · ext ε
     ring
   · norm_num
@@ -3380,7 +3257,7 @@ private theorem eventually_upper_shortMargin_positive :
       Tendsto (fun ε : ℝ =>
         10 * (ε * (1 + (10 * Real.log (1 / ε)))))
         (𝓝[>] (0 : ℝ)) (𝓝 (0 : ℝ)) := by
-    convert! tendsto_upper_one_add_shortEndpoint_scaled.const_mul
+    convert tendsto_upper_one_add_shortEndpoint_scaled.const_mul
       (10 : ℝ) using 1; norm_num
   have hsmall := hscaled.eventually
     (Iio_mem_nhds (by norm_num : (0 : ℝ) < 1 / 2))
@@ -3389,10 +3266,10 @@ private theorem eventually_upper_shortMargin_positive :
   change 0 < ε at hε
   have hcompare :
       ε * (1 + a) ≤ ε * (1 + (10 * Real.log (1 / ε))) :=
-    mul_le_mul_of_nonneg_left (by linarith [ha.2]) hε.le
+    mul_le_mul_of_nonneg_left (by linarith only [ha.2, ha]) hε.le
   change 10 * (ε * (1 + (10 * Real.log (1 / ε)))) < 1 / 2
     at hbound
-  linarith
+  linarith only [hcompare, hbound]
 
 private theorem eventually_upper_shellLocation_gt_shortEndpoint :
     ∀ᶠ ε : ℝ in 𝓝[>] (0 : ℝ),
@@ -3415,7 +3292,7 @@ private theorem eventually_upper_shellLocation_gt_shortEndpoint :
     filter_upwards [hevent] with ε hε
     change ε ^ 2 * (ε * (1 + (10 * Real.log (1 / ε)))) < 1
       at hε
-    linarith
+    linear_combination hε
   filter_upwards [self_mem_nhdsWithin, hsmall]
     with ε hε hbound
   change 0 < ε at hε
@@ -3500,18 +3377,18 @@ private theorem tendsto_upper_log_cubic_gaussian_atTop :
   · filter_upwards [eventually_ge_atTop (1 : ℝ)] with x hx
     have hlog : 0 ≤ Real.log x := Real.log_nonneg hx
     have hcube : 0 ≤ x ^ 3 := by positivity
-    exact mul_nonneg (by linarith) (Real.exp_pos _).le
+    exact mul_nonneg (by linarith only [hlog, hcube]) (Real.exp_pos _).le
   · filter_upwards [eventually_ge_atTop (1 : ℝ)] with x hx
-    have hxpos : 0 < x := by linarith
+    have hxpos : 0 < x := by linear_combination hx
     have hlog := Real.log_le_sub_one_of_pos hxpos
     have hsquare : 0 ≤ x ^ 2 - 1 := by
-      linarith [sq_nonneg (x - 1)]
+      linarith only [sq_nonneg (x - 1), hx]
     have hcube : x ≤ x ^ 3 := by
-      linarith [mul_nonneg hxpos.le hsquare]
+      linarith only [mul_nonneg hxpos.le hsquare, hxpos, hsquare]
     have hfactor :
         10 * Real.log x + x ^ 3 ≤
           11 * (x ^ 3 + 1) := by
-      linarith
+      linarith only [hlog, hcube]
     calc
       (10 * Real.log x + x ^ 3) *
           Real.exp (-(x ^ 2) / 8) ≤
@@ -3534,7 +3411,7 @@ private theorem tendsto_upper_shell_log_correction_atTop :
   have hscaled : Tendsto (fun x : ℝ =>
       5 * Real.log x / x)
       atTop (𝓝 (0 : ℝ)) := by
-    convert! hlog.const_mul (5 : ℝ) using 1
+    convert hlog.const_mul (5 : ℝ) using 1
     · ext x
       ring
     · norm_num
@@ -3579,13 +3456,13 @@ private theorem eventually_upper_shell_parameter_margin :
           shellWeight ε *
             Real.exp ((ε / 2) * (ε⁻¹ ^ 3)) := by
     exact (div_lt_one hden).mp hε
-  linarith
+  linarith only [hscaled]
 
 private theorem upper_one_sub_cos_le_min (x : ℝ) :
     1 - Real.cos x ≤ min (x ^ 2 / 2) 2 := by
   apply le_min
-  · linarith [Real.one_sub_sq_div_two_le_cos (x := x)]
-  · linarith [Real.neg_one_le_cos x]
+  · linarith only [Real.one_sub_sq_div_two_le_cos (x := x)]
+  · linarith only [Real.neg_one_le_cos x]
 
 private theorem upper_min_frequency_inverse_sq_le
     {a : ℝ} (ha : 0 < a) (T : ℝ) :
@@ -3595,10 +3472,10 @@ private theorem upper_min_frequency_inverse_sq_le
   by_cases hsmall : T ^ 2 ≤ 1
   · rw [min_eq_left hsmall]
     have hmin := min_le_left (T ^ 2) ((a ^ 2)⁻¹)
-    linarith [mul_nonneg (sq_nonneg T) hinv]
+    linarith only [mul_nonneg (sq_nonneg T) hinv, hinv, hmin]
   · rw [min_eq_right (le_of_not_ge hsmall)]
     have hmin := min_le_right (T ^ 2) ((a ^ 2)⁻¹)
-    linarith
+    linear_combination hmin
 
 private noncomputable def upperShortShellDamping (ε ℓ δ T : ℝ) : ℝ :=
   ℓ * ∫ a in (ε ^ 3)..(10 * Real.log (1 / ε)),
@@ -3642,9 +3519,9 @@ private theorem upper_shortShellDensity_damping_le
       Real.exp (δ * A) * min (T ^ 2) 1 *
         (1 + (a ^ 2)⁻¹) := by
   have hmarginone : (1 - 10 * ε * (1 + a)) ≤ 1 := by
-    linarith [mul_nonneg hε.le (show 0 ≤ 1 + a by linarith)]
+    linarith only [mul_nonneg hε.le (show 0 ≤ 1 + a by linarith), hε, ha]
   have hnegativeexp : Real.exp (-2 * a) ≤ 1 := by
-    exact Real.exp_le_one_iff.mpr (by linarith)
+    exact Real.exp_le_one_iff.mpr (by linarith only [ha])
   have hratio :
       Real.cosh ((1 + δ) * a) / Real.cosh a ≤
         Real.exp (δ * A) := by
@@ -3758,7 +3635,7 @@ private theorem upperShortShellDamping_global_bound
         (Real.cosh_pos a)).ne'
   have hcosh : Continuous
       (fun a : ℝ => Real.cosh ((1 + δ) * a)) := by
-    fun_prop
+    exact Continuous.comp' Real.continuous_cosh (Continuous.const_mul continuous_id' (1 + δ))
   have hosc : Continuous
       (fun a : ℝ => 1 - Real.cos (a * T)) := by
     fun_prop
@@ -3807,7 +3684,7 @@ private theorem upperShortShellDamping_global_bound
   have hcoefficient :
       A - a₀ + a₀⁻¹ - A⁻¹ ≤ A + a₀⁻¹ := by
     have hAinv : 0 ≤ A⁻¹ := (inv_pos.mpr hA).le
-    linarith
+    linear_combination ha₀ + hAinv
   change
     ℓ * (∫ a in a₀..A,
       (-shortShellDensity ε a) *
@@ -3838,7 +3715,7 @@ private theorem eventually_upper_shortCutoff_le_shortEndpoint :
   have hupper := tendsto_shortEndpoint.eventually_ge_atTop
     (1 : ℝ)
   filter_upwards [hlower, hupper] with ε hl hu
-  linarith
+  linear_combination hl + hu
 
 private theorem upper_shell_parameter_margin_propagate
     {ε δ : ℝ}
@@ -3856,7 +3733,7 @@ private theorem upper_shell_parameter_margin_propagate
   let q : ℝ := δ - ε / 2
   have hq : 0 ≤ q := by
     try dsimp [q]
-    linarith
+    linear_combination hδ
   have hexp :
       Real.exp (q * (10 * Real.log (1 / ε))) ≤
         Real.exp (q * (ε⁻¹ ^ 3)) :=
@@ -3912,7 +3789,7 @@ private theorem eventually_upper_shortShell_domination :
   change 0 < ε at hε
   intro ℓ hℓ δ hδ T
   have hδnonneg : 0 ≤ δ := by
-    linarith
+    linarith only [hε, hδ]
   have hshort :
       upperShortShellDamping ε ℓ δ T ≤
         ℓ * upperShellShortCoefficient ε *
@@ -3922,10 +3799,10 @@ private theorem eventually_upper_shortShell_domination :
       hε hℓ hδnonneg horder
       (fun a ha => by
         have h := hshortmargin a ha
-        linarith)
+        linear_combination h)
   have hpropagate :=
     upper_shell_parameter_margin_propagate hδ
-      (le_of_lt (by linarith [hseparation])) hmargin
+      (le_of_lt (by linear_combination hseparation)) hmargin
   have hpositive :=
     positiveShellDamping_lower_bound
       (ε := ε) (ℓ := ℓ) (δ := δ) (T := T)
@@ -3940,7 +3817,7 @@ private theorem eventually_upper_shortShell_domination :
     _ ≤ ℓ * ((1 / 5000 : ℝ) * shellWeight ε *
           Real.exp (δ * (ε⁻¹ ^ 3))) *
             min (T ^ 2) 1 := by
-      convert! mul_le_mul_of_nonneg_right
+      convert mul_le_mul_of_nonneg_right
         (mul_le_mul_of_nonneg_left hpropagate hℓ)
           hfreq using 1; ring
     _ = (1 / 100 : ℝ) *
@@ -3977,7 +3854,7 @@ private theorem upperPositiveShellVariance_bounds
     try dsimp [B]
     positivity
   have hQ : 0 < shellWeight ε := shellWeight_pos ε
-  have horder : B ≤ B + 1 := by linarith
+  have horder : B ≤ B + 1 := by linarith only []
   have hcont : Continuous (fun a : ℝ =>
       positiveShellDensity ε a * a ^ 2 *
         Real.cosh ((1 + δ) * a)) := by
@@ -4012,7 +3889,11 @@ private theorem upperPositiveShellVariance_bounds
       _ ≤ shellWeight ε * a ^ 2 *
           (Real.cosh ((1 + δ) * a) /
             Real.cosh a) := by
-        gcongr
+        exact mul_le_mul (mul_le_mul_of_nonneg_left hsquare (le_of_lt hQ)) hratio
+            (le_of_lt
+              (div_pos (Real.exp_pos (δ * B))
+                (zero_lt_two)))
+            (mul_nonneg (le_of_lt hQ) (Even.pow_nonneg (even_two_mul 1) a))
       _ = positiveShellDensity ε a * a ^ 2 *
           Real.cosh ((1 + δ) * a) := by
         unfold positiveShellDensity
@@ -4081,10 +3962,9 @@ private theorem upper_shortShellDensity_variance_le
         Real.cosh ((1 + δ) * a) ≤
       (1 / 2 : ℝ) * Real.exp (δ * A) := by
   have hmargin : (1 - 10 * ε * (1 + a)) ≤ 1 := by
-    linarith [mul_nonneg hε.le
-      (show 0 ≤ 1 + a by linarith)]
+    linarith only [mul_nonneg hε.le (show 0 ≤ 1 + a by linarith), hε, ha]
   have hexp : Real.exp (-2 * a) ≤ 1 :=
-    Real.exp_le_one_iff.mpr (by linarith)
+    Real.exp_le_one_iff.mpr (by linarith only [ha])
   have hratio :
       Real.cosh ((1 + δ) * a) / Real.cosh a ≤
         Real.exp (δ * A) :=
@@ -4144,7 +4024,7 @@ private theorem upperShortShellVariance_global_bound
     positivity
   have hcosh : Continuous
       (fun a : ℝ => Real.cosh ((1 + δ) * a)) := by
-    fun_prop
+    exact Continuous.comp' Real.continuous_cosh (Continuous.const_mul continuous_id' (1 + δ))
   have hleft : ContinuousOn
       (fun a : ℝ =>
         (-shortShellDensity ε a) * a ^ 2 *
@@ -4182,7 +4062,7 @@ private theorem upperShortShellVariance_global_bound
           smul_eq_mul] using! hmono
     _ ≤ (A + a₀⁻¹) * K := by
       apply mul_le_mul_of_nonneg_right _ hK
-      linarith
+      linear_combination ha₀ + hinv
     _ = (1 / 2 : ℝ) * upperShellShortCoefficient ε *
         Real.exp (δ * A) := by
       unfold upperShellShortCoefficient
@@ -4218,7 +4098,7 @@ private theorem upper_shellLocation_one_le
     1 ≤ (ε⁻¹ ^ 3) := by
   have hinv : 1 ≤ ε⁻¹ :=
     (one_le_inv₀ hε).mpr hεone
-  convert! pow_le_pow_left₀
+  convert pow_le_pow_left₀
     (show (0 : ℝ) ≤ 1 by norm_num) hinv 3 using 1; norm_num
 
 private theorem eventually_upper_shortShellVariance_domination :
@@ -4244,10 +4124,10 @@ private theorem eventually_upper_shortShellVariance_domination :
   have hB : 1 ≤ (ε⁻¹ ^ 3) :=
     upper_shellLocation_one_le hε hεone.le
   have hBsq : 1 ≤ (ε⁻¹ ^ 3) ^ 2 := by
-    linarith [sq_nonneg ((ε⁻¹ ^ 3) - 1)]
+    linarith only [sq_nonneg ((ε⁻¹ ^ 3) - 1), hB]
   have hpropagate :=
     upper_shell_parameter_margin_propagate
-      hδ (by linarith [hseparation]) hmargin
+      hδ (by linear_combination hseparation + hεone + hε) hmargin
   have hvariance :=
     upperShortShellVariance_global_bound
       hε hδnonneg horder
@@ -4265,7 +4145,7 @@ private theorem eventually_upper_shortShellVariance_domination :
     _ ≤ (1 / 2 : ℝ) *
         ((1 / 5000 : ℝ) * shellWeight ε *
           Real.exp (δ * (ε⁻¹ ^ 3))) := by
-      convert! mul_le_mul_of_nonneg_left
+      convert mul_le_mul_of_nonneg_left
         hpropagate (by norm_num : (0 : ℝ) ≤ 1 / 2)
         using 1; ring
     _ ≤ (1 / 100 : ℝ) *
@@ -4274,7 +4154,7 @@ private theorem eventually_upper_shortShellVariance_domination :
             Real.exp (δ * (ε⁻¹ ^ 3))) := by
       have hscaled :=
         mul_le_mul_of_nonneg_right hBsq hqexp
-      linarith
+      linarith only [hqexp, hscaled]
     _ ≤ (1 / 100 : ℝ) *
         upperPositiveShellVariance ε δ :=
       mul_le_mul_of_nonneg_left hpositive
@@ -4304,7 +4184,7 @@ private theorem eventually_upper_netShellVariance_bounds :
     (δ := δ) hε horder
     (fun a ha => by
       have h := hmargin a ha
-      linarith)
+      linear_combination h)
   have hupper := hdom δ hδ
   unfold upperNetShellVariance
   constructor <;> linarith
@@ -4324,7 +4204,7 @@ private theorem upperPositiveShellThirdMoment_le
     try dsimp [B]
     positivity
   have horder : B ≤ B + 1 := by
-    linarith
+    linarith only []
   have hdensity := positiveShellDensity_continuous ε
   have hbase : Continuous (fun a : ℝ =>
       positiveShellDensity ε a * a ^ 2 *
@@ -4408,7 +4288,7 @@ private theorem upperShortShellThirdMoment_le
     positivity
   have hcosh : Continuous
       (fun a : ℝ => Real.cosh ((1 + δ) * a)) := by
-    fun_prop
+    exact Continuous.comp' Real.continuous_cosh (Continuous.const_mul continuous_id' (1 + δ))
   have hbase : ContinuousOn (fun a : ℝ =>
       (-shortShellDensity ε a) * a ^ 2 *
         Real.cosh ((1 + δ) * a)) (Set.Icc a₀ A) :=
@@ -4490,7 +4370,7 @@ private theorem eventually_upper_shortShellThirdMoment_domination :
     (δ := δ) hε horder
     (fun a ha => by
       have h := hmargin a ha
-      linarith)
+      linear_combination h)
   calc
     upperShortShellThirdMoment ε δ ≤
       (10 * Real.log (1 / ε)) * upperShortShellVariance ε δ := hthird
@@ -4522,7 +4402,7 @@ private theorem eventually_upper_netShellThirdMoment_bound :
     (δ := δ) hε
   have hnegative := hshort δ hδ
   unfold upperNetShellThirdMoment
-  linarith
+  linear_combination hpositive + hnegative
 
 private theorem upper_inv_one_sub_exp_neg_bounds
     {x : ℝ} (hx : 0 < x) :
@@ -4530,16 +4410,16 @@ private theorem upper_inv_one_sub_exp_neg_bounds
       (1 - Real.exp (-x))⁻¹ ≤ 1 + x⁻¹ := by
   have hden : 0 < 1 - Real.exp (-x) := by
     have he : Real.exp (-x) < 1 :=
-      Real.exp_lt_one_iff.mpr (by linarith)
-    linarith
+      Real.exp_lt_one_iff.mpr (by linear_combination hx)
+    linear_combination he
   have hlower : 1 - Real.exp (-x) ≤ x := by
-    linarith [Real.add_one_le_exp (-x)]
+    linarith only [Real.add_one_le_exp (-x)]
   have hplus : 0 < 1 + x := by
-    linarith
+    linear_combination hx
   have hexp : Real.exp (-x) ≤ (1 + x)⁻¹ := by
     rw [Real.exp_neg]
     apply (inv_le_inv₀ (Real.exp_pos x) hplus).2
-    linarith [Real.add_one_le_exp x]
+    linarith only [Real.add_one_le_exp x]
   constructor
   · exact (inv_le_inv₀ hx hden).2 hlower
   · have hgoal :
@@ -4620,8 +4500,8 @@ private theorem upperGammaVarianceDensity_pointwise_bounds
   have hkernel := upper_inv_one_sub_exp_neg_bounds hx
   have hden : 0 < 1 - Real.exp (-x) := by
     have he : Real.exp (-x) < 1 :=
-      Real.exp_lt_one_iff.mpr (by linarith)
-    linarith
+      Real.exp_lt_one_iff.mpr (by linear_combination hx)
+    linear_combination he
   have hfactor : 0 ≤ a * Real.exp (-η * a) := by
     positivity
   have hidentity :
@@ -5337,7 +5217,7 @@ private theorem realHyperbolicShellPhase_hasDerivAt
     exact realHyperbolicShellInterval_hasDerivAt
       w hw horder u
   have hremote : (ε⁻¹ ^ 3) ≤ (ε⁻¹ ^ 3) + 1 := by
-    linarith
+    linarith only []
   have hpositive := realHyperbolicShellInterval_hasDerivAt
     (positiveShellDensity ε)
     (positiveShellDensity_continuous ε) hremote u
@@ -5481,9 +5361,11 @@ private theorem plusSaddleSmallRadiusPolynomial_error
     try dsimp [s]
     exact (div_le_iff₀ hℓ).mpr (by simpa only [one_mul] using! hn)
   have hsquare : (2 + s) ^ 2 ≤ 9 := by
-    linarith [mul_nonneg
-      (show 0 ≤ 3 - (2 + s) by linarith)
-      (show 0 ≤ 3 + (2 + s) by linarith)]
+    linarith only [
+      mul_nonneg (show 0 ≤ 3 - (2 + s) by linarith) (show 0 ≤ 3 + (2 + s) by linarith),
+      hs,
+      hsone
+    ]
   have hnumerator : 0 ≤ s * (2 + s) ^ 2 :=
     mul_nonneg hs (sq_nonneg _)
   change |((ε / 4) - s * (2 + s) ^ 2) /
@@ -5517,7 +5399,7 @@ private theorem abs_exp_sub_one_le_abs_mul_exp_abs (t : ℝ) :
       rw [← Real.exp_add]
       simp only [add_neg_cancel, Real.exp_zero]
     rw [hcancel] at hmul
-    linarith
+    linear_combination hmul
   · have hexp : Real.exp t ≤ 1 := by
       simpa only [Real.exp_le_one_iff, Real.exp_zero] using! Real.exp_le_exp.mpr ht
     have hnegt : 0 ≤ -t := neg_nonneg.mpr ht
@@ -5528,13 +5410,12 @@ private theorem abs_exp_sub_one_le_abs_mul_exp_abs (t : ℝ) :
       abs_of_nonpos ht]
     have hsupport := Real.add_one_le_exp t
     have hlinear : 1 - Real.exp t ≤ -t := by
-      linarith
+      linear_combination hsupport
     calc
       -(Real.exp t - 1) = 1 - Real.exp t := by ring
       _ ≤ -t := hlinear
       _ ≤ -t * Real.exp (-t) := by
-        linarith [mul_nonneg hnegt
-          (sub_nonneg.mpr hexpneg)]
+        linarith only [mul_nonneg hnegt (sub_nonneg.mpr hexpneg), hnegt, hexpneg]
 
 private theorem plusSaddleSmallRadiusCoefficient_error_of_phase
     {ε ℓ : ℝ}
@@ -5629,8 +5510,7 @@ private theorem exists_plusSaddleSmallRadiusCoefficient_error
         (C * (n : ℝ) ^ 2 + K * (n : ℝ)) / ℓ by
           ring]
     apply (div_le_div_iff_of_pos_right hℓ).mpr
-    linarith [mul_nonneg hC hnreal,
-      mul_nonneg hK (sq_nonneg (n : ℝ))]
+    linarith only [mul_nonneg hC hnreal, mul_nonneg hK (sq_nonneg (n : ℝ)), hC, hK, hnreal]
   have hq :
       C * (n : ℝ) ^ 2 / ℓ ≤
         (C + K) * (n : ℝ) ^ 2 / ℓ := by
@@ -5723,7 +5603,7 @@ private theorem saddleExpSeries_polynomialMoment_hasSum (y : ℝ) :
   have hsecond :=
     saddleExpSeries_secondFallingMoment_hasSum y
   have hcombined := hfirst.add hsecond
-  convert! hcombined using 1
+  convert hcombined using 1
   · funext n
     ring
   · ring
@@ -5907,7 +5787,7 @@ private theorem saddleExpSeries_alternating_tail_bound
   have hidentity : Real.exp (-y) -
       (∑ n ∈ Finset.range m, f n) =
         ∑' n : ℕ, f (n + m) := by
-    linarith
+    linarith only [hdecomp]
   calc
     |Real.exp (-y) -
         (∑ n ∈ Finset.range m, f n)| =
@@ -5955,7 +5835,7 @@ private theorem exists_plusSaddleSmallRadius_finiteResidue_error
   have htail := saddleExpSeries_alternating_tail_bound
     hy (N + 1) (by
       push_cast
-      linarith)
+      linear_combination hyratio)
   have hsplit :
       (∑ n ∈ Finset.range (N + 1),
         ((-y) ^ n / (n.factorial : ℝ)) *
@@ -6088,8 +5968,8 @@ private theorem upperGammaMeasureDensity_pos
     0 < upperGammaMeasureDensity ℓ η a := by
   have hx : 0 < 2 * a / ℓ := by positivity
   have hden : 0 < 1 - Real.exp (-(2 * a / ℓ)) := by
-    have he := Real.exp_lt_one_iff.mpr (show -(2 * a / ℓ) < 0 by linarith)
-    linarith
+    have he := Real.exp_lt_one_iff.mpr (show -(2 * a / ℓ) < 0 by linear_combination hx)
+    linear_combination he
   unfold upperGammaMeasureDensity
   exact div_pos (Real.exp_pos _) (mul_pos ha hden)
 
@@ -6149,8 +6029,7 @@ private theorem upperGammaDampingIntegrand_integrable
     sub_nonneg.mpr (Real.cos_le_one _)
   have hquad :
       1 - Real.cos (a * T) ≤ (a * T) ^ 2 / 2 := by
-    linarith [Real.one_sub_sq_div_two_le_cos
-      (x := a * T)]
+    linarith only [Real.one_sub_sq_div_two_le_cos (x := a * T)]
   unfold upperGammaDampingIntegrand
   rw [Real.norm_eq_abs,
     abs_of_nonneg (mul_nonneg hcos hdensity.le)]
@@ -6200,7 +6079,7 @@ private theorem upperGammaDampingIntegrand_lower_on_window
   have hexp : (Real.exp 1)⁻¹ ≤
       Real.exp (-η * a) := by
     rw [← Real.exp_neg]
-    exact Real.exp_le_exp.mpr (by linarith)
+    exact Real.exp_le_exp.mpr (by linear_combination heta)
   have hvariance :=
     (upperGammaVarianceDensity_pointwise_bounds
       (η := η) hℓ ha).1
@@ -6216,7 +6095,14 @@ private theorem upperGammaDampingIntegrand_lower_on_window
       ring
     _ ≤ (T ^ 2 / 4) *
           ((ℓ / 2) * Real.exp (-η * a)) := by
-      gcongr
+      exact mul_le_mul_of_nonneg_left
+          (mul_le_mul_of_nonneg_left hexp
+            (le_of_lt
+              (div_pos hℓ
+                (zero_lt_two))))
+          (le_of_lt
+            (div_pos (lt_of_le_of_ne' (Even.pow_nonneg (even_two_mul 1) T) (pow_ne_zero 2 hT))
+              ((by norm_num))))
     _ ≤ (T ^ 2 / 4) *
           (a ^ 2 * upperGammaMeasureDensity ℓ η a) :=
       mul_le_mul_of_nonneg_left hvariance hquarter
@@ -6291,7 +6177,7 @@ private theorem upperGammaDamping_lower_bound
       change ((volume : Measure ℝ)
         (Ioc (0 : ℝ) q)).toReal = q
       rw [Real.volume_Ioc,
-        ENNReal.toReal_ofReal (by linarith)]
+        ENNReal.toReal_ofReal (by linarith only [hq])]
       simp only [sub_zero]
     have hconstintegral :
         (∫ a : ℝ in Ioc (0 : ℝ) q, c) = q * c := by
@@ -6353,7 +6239,7 @@ private theorem eventually_upperSaddleDamping_gamma_add_shell
   intro ℓ hℓ δ hδ T
   have hshort := hdom ℓ hℓ.le δ hδ T
   unfold upperSaddleDamping
-  linarith
+  linear_combination hshort
 
 private theorem eventually_upperSaddleVariance_bounds
     : ∀ᶠ ε : ℝ in 𝓝[>] (0 : ℝ),
@@ -6373,7 +6259,7 @@ private theorem eventually_upperSaddleVariance_bounds
   change 0 < ε at hε
   intro ℓ hℓ δ hδ
   have hη : 0 < 2 + δ := by
-    linarith
+    linarith only [hε, hδ]
   obtain ⟨hγlow, hγhigh⟩ :=
     upperGammaVariance_bounds hℓ hη
   obtain ⟨hslow, hshigh⟩ :=
@@ -6413,9 +6299,9 @@ private theorem eventually_upperSaddleVariance_pos
   change 0 < ε at hε
   intro ℓ hℓ δ hδ
   have hδnonnegative : 0 ≤ δ := by
-    linarith
+    linarith only [hε, hδ]
   have hη : 0 < 2 + δ := by
-    linarith
+    linarith only [hε, hδ]
   have hshell :=
     upperPositiveShellVariance_pos hε hδnonnegative
   have hpositive :
@@ -6430,8 +6316,8 @@ private theorem upperGammaThirdMoment_le_two_mul_variance
     {ℓ η : ℝ} (hℓ : 1 ≤ ℓ) (hη : 2 ≤ η) :
     upperGammaThirdMoment ℓ η ≤
       2 * upperGammaVariance ℓ η := by
-  have hℓpositive : 0 < ℓ := by linarith
-  have hηpositive : 0 < η := by linarith
+  have hℓpositive : 0 < ℓ := by linear_combination hℓ
+  have hηpositive : 0 < η := by linear_combination hη
   have hγthird :=
     (upperGammaThirdMoment_bounds hℓpositive hηpositive).2
   have hγvariance :=
@@ -6441,17 +6327,14 @@ private theorem upperGammaThirdMoment_le_two_mul_variance
     apply (div_le_div_iff₀
       (show 0 < 2 * η ^ 2 by positivity)
       (show 0 < 2 * η by positivity)).2
-    linarith [mul_nonneg hηpositive.le
-      (show 0 ≤ η - 1 by linarith)]
+    linarith only [mul_nonneg hηpositive.le (show 0 ≤ η - 1 by linarith), hη, hηpositive]
   have hηsquare : 4 ≤ η ^ 2 := by
-    linarith [sq_nonneg (η - 2)]
+    linarith only [sq_nonneg (η - 2), hη]
   have hsquare : 4 ≤ ℓ * η ^ 2 := by
     calc
       (4 : ℝ) ≤ η ^ 2 := hηsquare
       _ ≤ ℓ * η ^ 2 := by
-        linarith [mul_nonneg
-          (show 0 ≤ ℓ - 1 by linarith)
-          (sq_nonneg η)]
+        linarith only [mul_nonneg (show 0 ≤ ℓ - 1 by linarith) (sq_nonneg η), hℓ]
   have hsecond :
       2 / (ℓ * η ^ 3) ≤ 1 / (2 * η) := by
     apply (div_le_div_iff₀
@@ -6459,15 +6342,15 @@ private theorem upperGammaThirdMoment_le_two_mul_variance
       (show 0 < 2 * η by positivity)).2
     have hscaled :=
       mul_le_mul_of_nonneg_right hsquare hηpositive.le
-    linarith
+    linear_combination hscaled
   calc
     upperGammaThirdMoment ℓ η ≤
         1 / (2 * η ^ 2) +
           2 / (ℓ * η ^ 3) := hγthird
     _ ≤ 2 * (1 / (2 * η)) := by
-      linarith
+      linear_combination hfirst + hsecond
     _ ≤ 2 * upperGammaVariance ℓ η := by
-      linarith
+      linarith only [hγvariance]
 
 private noncomputable def upperSaddleShellThirdCoefficient (ε : ℝ) : ℝ :=
   (ε⁻¹ ^ 3) + 1 + (10 * Real.log (1 / ε)) / 100
@@ -6487,13 +6370,13 @@ private theorem eventually_upperSaddleThirdMoment_le_variance
     with ε hε horder hnet hthird
   change 0 < ε at hε
   intro ℓ hℓ δ hδ
-  have hℓpositive : 0 < ℓ := by linarith
+  have hℓpositive : 0 < ℓ := by linarith only [hℓ]
   have hδnonnegative : 0 ≤ δ := by
-    linarith
+    linarith only [hε, hδ]
   have hη : 2 ≤ 2 + δ := by
-    linarith
+    linarith only [hε, hδ]
   have hηpositive : 0 < 2 + δ := by
-    linarith
+    linarith only [hε, hδ]
   have hgamma :=
     upperGammaThirdMoment_le_two_mul_variance
       hℓ hη
@@ -6503,7 +6386,7 @@ private theorem eventually_upperSaddleThirdMoment_le_variance
     upperPositiveShellVariance_pos hε hδnonnegative
   have hnetnonnegative :
       0 ≤ upperNetShellVariance ε δ := by
-    linarith
+    linarith only [hnetlower, hpositiveShell]
   have hgammavariance :
       0 ≤ upperGammaVariance ℓ (2 + δ) := by
     have h := (upperGammaVariance_bounds
@@ -6524,7 +6407,7 @@ private theorem eventually_upperSaddleThirdMoment_le_variance
       upperPositiveShellVariance ε δ ≤
         (100 / 99 : ℝ) *
           upperNetShellVariance ε δ := by
-    linarith
+    linarith only [hnetlower]
   have hthirdshell :
       upperNetShellThirdMoment ε δ ≤
         (100 / 99 : ℝ) *
@@ -6544,8 +6427,16 @@ private theorem eventually_upperSaddleThirdMoment_le_variance
             upperNetShellVariance ε δ := by
         ring
   unfold upperSaddleThirdMoment upperSaddleVariance
-  linarith [mul_nonneg hC hgammavariance,
-    mul_nonneg hC hnetnonnegative]
+  linarith only [
+    mul_nonneg hC hgammavariance,
+    mul_nonneg hC hnetnonnegative,
+    hgamma,
+    hnetlower,
+    hpositiveShell,
+    hgammavariance,
+    hC,
+    hthirdshell
+  ]
 
 private theorem upperShortMargin_mul_exp_antitone
     {ε : ℝ} (hε : 0 < ε) :
@@ -6589,11 +6480,10 @@ private theorem upperShortMargin_mul_exp_antitone
       have h := interior_subset ha
       exact h
     have hmargin : (1 - 10 * ε * (1 + a)) ≤ 1 := by
-      linarith [mul_nonneg hε.le
-        (show 0 ≤ 1 + a by linarith)]
+      linarith only [mul_nonneg hε.le (show 0 ≤ 1 + a by linarith), hε, ha0]
     exact mul_nonpos_of_nonneg_of_nonpos
       (mul_nonneg hε.le (Real.exp_pos _).le)
-      (by linarith)
+      (by linear_combination hmargin)
 
 private theorem upperShortMargin_mul_exp_le_zero_value
     {ε a : ℝ} (hε : 0 < ε) (ha : 0 ≤ a) :
@@ -6616,7 +6506,7 @@ private theorem upperFirstBranch_shortRatio_le
       1 - 4 * ε := by
   have hmarginupper :
       (1 - 10 * ε * (1 + a)) ≤ 1 - 10 * ε := by
-    linarith [mul_nonneg hε.le ha]
+    linarith only [mul_nonneg hε.le ha, hε, ha]
   by_cases hubounded : u ≤ 1
   · have huexp :
         Real.exp ((u - 1) * a) ≤ 1 := by
@@ -6641,21 +6531,19 @@ private theorem upperFirstBranch_shortRatio_le
           gcongr
       _ = (1 - 10 * ε * (1 + a)) := by ring
       _ ≤ 1 - 10 * ε := hmarginupper
-      _ ≤ 1 - 4 * ε := by linarith
+      _ ≤ 1 - 4 * ε := by linarith only [hε]
   · have hugreater : 1 ≤ u :=
       (le_of_not_ge hubounded)
-    have hδ : 0 ≤ u - 1 := by linarith
+    have hδ : 0 ≤ u - 1 := by linarith only [hubounded]
     have hratio :
         Real.cosh (u * a) / Real.cosh a ≤
           Real.exp ((u - 1) * a) := by
-      convert! cosh_ratio_upper ha hδ using 1; ring_nf
+      convert cosh_ratio_upper ha hδ using 1; ring_nf
     have hdouble :
         Real.exp (2 * (u - 1) * a) ≤
           Real.exp (ε * a) := by
       apply Real.exp_le_exp.mpr
-      linarith [mul_nonneg
-        (show 0 ≤ ε - 2 * (u - 1) by linarith)
-        ha]
+      linarith only [mul_nonneg (show 0 ≤ ε - 2 * (u - 1) by linarith) ha, ha, huupper]
     calc
       (1 - 10 * ε * (1 + a)) *
           Real.exp ((u - 1) * a) *
@@ -6675,7 +6563,7 @@ private theorem upperFirstBranch_shortRatio_le
       _ ≤ 1 - 10 * ε :=
         upperShortMargin_mul_exp_le_zero_value
           hε ha
-      _ ≤ 1 - 4 * ε := by linarith
+      _ ≤ 1 - 4 * ε := by linarith only [huupper, hubounded]
 
 private theorem upperFirstBranch_shortMeasure_pointwise
     {ε ℓ u a : ℝ}
@@ -6688,7 +6576,7 @@ private theorem upperFirstBranch_shortMeasure_pointwise
       (1 - 4 * ε) *
         upperGammaMeasureDensity ℓ (1 + u) a := by
   have hfactor : 0 ≤ 1 - 4 * ε := by
-    linarith
+    linarith only [hεsmall]
   have hratio := upperFirstBranch_shortRatio_le
     hε ha.le hulower huupper hmargin
   have hvariance :=
@@ -6700,7 +6588,7 @@ private theorem upperFirstBranch_shortMeasure_pointwise
         upperGammaMeasureDensity ℓ (1 + u) a := by
     apply (div_le_iff₀
       (sq_pos_of_pos ha)).2
-    linarith
+    linear_combination hvariance
   have hbasepositive :
       0 ≤ (ℓ / 2) *
         Real.exp (-(1 + u) * a) / a ^ 2 := by
@@ -6756,12 +6644,12 @@ private theorem upperFirstBranch_shortDamping_le_gamma
   let η : ℝ := 1 + u
   have hη : 0 < η := by
     try dsimp [η]
-    linarith
+    linarith only [hulower]
   have ha₀ : 0 < a₀ := by
     try dsimp [a₀]
     positivity
   have hfactor : 0 ≤ 1 - 4 * ε := by
-    linarith
+    linarith only [hεsmall]
   have hsubset : Ioc a₀ A ⊆ Ioi (0 : ℝ) := by
     intro a ha
     exact ha₀.trans ha.1
@@ -6779,7 +6667,7 @@ private theorem upperFirstBranch_shortDamping_le_gamma
   have hs := shortShellDensity_intervalIntegrable hε horder
   have hcosh : Continuous
       (fun a : ℝ => Real.cosh (u * a)) := by
-    fun_prop
+    exact Continuous.comp' Real.continuous_cosh (Continuous.const_mul continuous_id' u)
   have hosc : Continuous
       (fun a : ℝ => 1 - Real.cos (a * T)) := by
     fun_prop
@@ -6881,7 +6769,7 @@ private theorem positiveShellDamping_nonneg
   unfold positiveShellDamping
   apply mul_nonneg hℓ
   apply intervalIntegral.integral_nonneg
-    (show (ε⁻¹ ^ 3) ≤ (ε⁻¹ ^ 3) + 1 by linarith)
+    (show (ε⁻¹ ^ 3) ≤ (ε⁻¹ ^ 3) + 1 by linarith only [])
   intro a ha
   unfold positiveShellDensity
   exact mul_nonneg
@@ -6914,7 +6802,7 @@ private theorem upperFirstBranchSaddleDamping_lower_bound
   have hpositive := positiveShellDamping_nonneg
     (ε := ε) (δ := u - 1) (T := T) hℓ.le
   unfold upperFirstBranchSaddleDamping
-  linarith
+  linarith only [hshort, hpositive]
 
 private theorem saddle_shifted_complexCos_re
     (a T u : ℝ) :
@@ -6963,7 +6851,10 @@ private theorem saddle_complexShellInterval_re
         Complex.cos
           ((x : ℂ) *
             ((T : ℂ) + Complex.I * (u : ℂ))) - 1) := by
-    fun_prop
+    exact Continuous.fun_sub
+        (Continuous.comp' Complex.continuous_cos
+          (Continuous.comp' (continuous_mul_const (↑T + Complex.I * ↑u)) Complex.continuous_ofReal))
+        continuous_const
   have hF : IntervalIntegrable F volume a b := by
     exact (hwcomplex.mul hkernel.continuousOn).intervalIntegrable_of_Icc
       hab
@@ -7028,7 +6919,7 @@ private theorem mellinShellPhase_shifted_re
   · exact saddle_complexShellInterval_re
       (positiveShellDensity ε)
       (show (ε⁻¹ ^ 3) ≤ (ε⁻¹ ^ 3) + 1 by
-        linarith)
+        linarith only [])
       (positiveShellDensity_continuous ε).continuousOn T u
 
 private theorem saddle_shellInterval_hyperbolic_sub_oscillatory
@@ -7086,7 +6977,7 @@ private theorem saddleShellPhase_damping_identity
     saddle_shellInterval_hyperbolic_sub_oscillatory
       (positiveShellDensity ε)
       (show (ε⁻¹ ^ 3) ≤ (ε⁻¹ ^ 3) + 1 by
-        linarith)
+        linarith only [])
       (positiveShellDensity_continuous ε).continuousOn T u
   rw [mellinShellPhase_shifted_re hε horder T u]
   unfold realHyperbolicShellPhase
@@ -7397,7 +7288,7 @@ private theorem radialMellinFrequency_injective {d : ℕ}
     have h := hfrequency (-(2 * Real.pi * ξ))
     rw [radialMellinFrequency_eq_criticalLogFourier,
       radialMellinFrequency_eq_criticalLogFourier] at h
-    convert! h using 1 <;> field_simp [Real.pi_ne_zero]
+    convert h using 1 <;> field_simp [Real.pi_ne_zero]
   have hlog : radialCriticalLogProfile hd f =
       radialCriticalLogProfile hd g := by
     funext u
@@ -7708,20 +7599,20 @@ private theorem saddleLogGamma_differentiableAt {x : ℝ} (hx : 0 < x) :
   exact (Real.differentiableAt_Gamma
     (fun n => ne_of_gt (by
       have hn : 0 ≤ (n : ℝ) := Nat.cast_nonneg n
-      linarith))).log (Real.Gamma_pos_of_pos hx).ne'
+      linarith only [hx]))).log (Real.Gamma_pos_of_pos hx).ne'
 
 private theorem saddleDigamma_bounds {x : ℝ} (hx : 1 < x) :
     Real.log (x - 1) ≤ saddleDigamma x ∧
       saddleDigamma x ≤ Real.log x := by
-  have hxpositive : 0 < x := by linarith
-  have hxprevious : 0 < x - 1 := by linarith
-  have hnext : 0 < x + 1 := by linarith
+  have hxpositive : 0 < x := by linear_combination hx
+  have hxprevious : 0 < x - 1 := by linear_combination hx
+  have hnext : 0 < x + 1 := by linear_combination hx
   have hdiff := saddleLogGamma_differentiableAt hxpositive
   constructor
   · have hconv := Real.convexOn_log_Gamma.slope_le_deriv
       (show x - 1 ∈ Ioi (0 : ℝ) from hxprevious)
       (show x ∈ Ioi (0 : ℝ) from hxpositive)
-      (show x - 1 < x by linarith) hdiff
+      (show x - 1 < x by linarith only []) hdiff
     have hrec := saddleLogGamma_add_one hxprevious
     have hshift : (x - 1) + 1 = x := by ring
     rw [hshift] at hrec
@@ -7733,7 +7624,7 @@ private theorem saddleDigamma_bounds {x : ℝ} (hx : 1 < x) :
   · have hconv := Real.convexOn_log_Gamma.deriv_le_slope
       (show x ∈ Ioi (0 : ℝ) from hxpositive)
       (show x + 1 ∈ Ioi (0 : ℝ) from hnext)
-      (show x < x + 1 by linarith) hdiff
+      (show x < x + 1 by linarith only []) hdiff
     have hrec := saddleLogGamma_add_one hxpositive
     unfold saddleDigamma
     rw [slope_def_field] at hconv
@@ -7760,8 +7651,8 @@ private theorem tendsto_saddleDigamma_sub_log :
       atTop (𝓝 (0 : ℝ)) := by
     refine hlog.congr' ?_
     filter_upwards [eventually_gt_atTop (1 : ℝ)] with x hx
-    have hxzero : x ≠ 0 := by linarith
-    have hxprevious : x - 1 ≠ 0 := by linarith
+    have hxzero : x ≠ 0 := by linarith only [hx]
+    have hxprevious : x - 1 ≠ 0 := by linarith only [hx]
     rw [← Real.log_div hxprevious hxzero]
     congr 1
     field_simp
diff --git a/LeanPool/SpherePacking/HarmonicAnalysis.lean b/LeanPool/SpherePacking/HarmonicAnalysis.lean
index f62b27f847..4af5d3ce8c 100644
--- a/LeanPool/SpherePacking/HarmonicAnalysis.lean
+++ b/LeanPool/SpherePacking/HarmonicAnalysis.lean
@@ -68,7 +68,7 @@ private theorem tendsto_saddleEulerHarmonicCorrection
         atTop atTop := by
     have h := hcast.atTop_add
       (tendsto_const_nhds (x := m + 1))
-    convert! h using 1
+    convert h using 1
     funext n
     ring
   have hdigamma :=
@@ -140,7 +140,7 @@ private theorem tendsto_saddleEulerHarmonicCorrection
   push_cast at hrec
   rw [show m + ((n : ℝ) + 1) =
     m + (n : ℝ) + 1 by ring] at hrec
-  linarith
+  linarith only [hrec]
 
 private noncomputable def upperCenteredLaplaceKernel
     (c T a : ℝ) : ℂ :=
@@ -284,11 +284,11 @@ private theorem upperGammaCenteredGeometricLimit_eq_kernel
     upperCenteredLaplaceKernel η T a *
         (((1 - Real.exp (-(2 * a / ℓ)))⁻¹ : ℝ) : ℂ) =
       upperGammaCenteredKernel ℓ η T a := by
-  simp only [upperCenteredLaplaceKernel, mul_comm, Complex.ofReal_mul, mul_neg, div_eq_mul_inv,
-    Complex.ofReal_inv, Complex.ofReal_exp, Complex.ofReal_neg, mul_assoc, mul_left_comm,
-      Complex.ofReal_sub,
+  simp only [upperCenteredLaplaceKernel, Complex.ofReal_mul, div_eq_mul_inv,
+    Complex.ofReal_inv, Complex.ofReal_exp, Complex.ofReal_neg, Complex.ofReal_sub,
     Complex.ofReal_one, Complex.ofReal_ofNat, upperGammaCenteredKernel,
-      upperGammaMeasureDensity, mul_inv_rev]
+    upperGammaMeasureDensity, mul_inv_rev]
+  ring
 
 private theorem tendsto_integral_upperGammaCenteredTruncatedKernel
     {ℓ η : ℝ} (hℓ : 0 < ℓ) (hη : 0 < η) (T : ℝ) :
@@ -315,7 +315,7 @@ private theorem tendsto_integral_upperGammaCenteredTruncatedKernel
       apply Real.exp_lt_one_iff.mpr
       have hp : 0 < 2 * a / ℓ :=
         div_pos (mul_pos (by norm_num) ha) hℓ
-      linarith
+      linear_combination hp
     have hsum :
         (∑ k ∈ Finset.range (n + 1),
           Real.exp (-(2 * a / ℓ)) ^ k) ≤
@@ -349,7 +349,7 @@ private theorem tendsto_integral_upperGammaCenteredTruncatedKernel
       apply Real.exp_lt_one_iff.mpr
       have hp : 0 < 2 * a / ℓ :=
         div_pos (mul_pos (by norm_num) ha) hℓ
-      linarith
+      linear_combination hp
     have hgeo :=
       (hasSum_geometric_of_lt_one hq0 hq1).tendsto_sum_nat
     have hshift := hgeo.comp (tendsto_add_atTop_nat 1)
@@ -647,7 +647,7 @@ private theorem exp_integral_upperGammaCenteredTruncatedKernel
               (((b *
                 (∑ k ∈ Finset.range (n + 1),
                   (m + (k : ℝ))⁻¹) : ℝ) : ℂ))) := by
-    simpa [m, b] using!
+    simpa only [m, b, Complex.ofReal_add, Complex.ofReal_natCast] using!
       exp_integral_upperGammaCenteredTruncatedKernel_eq_product
         hℓ hη T n
   have hphase :
@@ -796,7 +796,7 @@ private theorem exp_upperGammaCenteredPhase
                     (m + (k : ℝ))⁻¹) : ℝ) : ℂ)))) := by
     filter_upwards [eventually_gt_atTop (0 : ℕ)]
       with n hn
-    simpa [m, b] using!
+    simpa only [m, b] using!
       exp_integral_upperGammaCenteredTruncatedKernel
         hℓ hη T hn
   have hmatch :=
@@ -844,7 +844,7 @@ private theorem saddleSourceCenteredPhase_cubic_remainder_norm_le
           T ^ 2 : ℝ) : ℂ)‖ ≤
       (ℓ * upperSaddleThirdMoment ε ℓ (u - 1) / 6) *
         |T| ^ 3 := by
-  have hη : 0 < 1 + u := by linarith
+  have hη : 0 < 1 + u := by linear_combination hu
   have hgamma :=
     upperGammaCenteredPhase_cubic_remainder_norm_le
       hℓ hη T
@@ -946,7 +946,7 @@ private theorem saddleSourceCenteredEnvelope_eq_gamma_shell
           ((ℓ * T * Real.log Real.pi / 2 : ℝ) : ℂ)) *
         Complex.exp
           (Complex.I * ((ℓ * T * v : ℝ) : ℂ))) := by
-  have hη : 0 < 1 + u := by linarith
+  have hη : 0 < 1 + u := by linarith only [hu]
   have hm : 0 < ℓ * (1 + u) / 2 := by positivity
   have hG :
       (Real.Gamma (ℓ * (1 + u) / 2) : ℂ) ≠ 0 := by
@@ -1015,7 +1015,7 @@ private theorem saddleSourceCenteredEnvelope_stationary_eq_exp_phase
     saddleSourceCenteredEnvelope ε ℓ u
         (saddleSourceStationaryLogRadius ε ℓ u) T =
       Complex.exp (saddleSourceCenteredPhase ε ℓ u T) := by
-  have hη : 0 < 1 + u := by linarith
+  have hη : 0 < 1 + u := by linear_combination hu
   rw [saddleSourceCenteredEnvelope_eq_gamma_shell
     hℓ hu]
   rw [saddleSourceStationaryFrequencyPhase_eq]
@@ -1099,7 +1099,10 @@ private theorem saddleSourceCenteredEnvelope_stationary_gaussian_error_le
         (Complex.norm_exp_sub_one_le hRone) hg.le
     _ ≤ saddleSourceGaussianKernel ε ℓ u T *
         (2 * q) := by
-      gcongr
+      exact mul_le_mul_of_nonneg_left
+          (mul_le_mul_of_nonneg_left hR
+            zero_le_two)
+          (le_of_lt hg)
     _ = 2 * saddleSourceGaussianKernel ε ℓ u T * q := by
       ring
 
@@ -1204,7 +1207,7 @@ private theorem saddleSourceCenteredPolynomial_centralGaussianError_le
         _ ≤ ‖P ((T : ℂ) + z) - P z‖ + ‖P z‖ :=
           norm_add_le _ _
         _ ≤ p * ‖P z‖ + ‖P z‖ := by
-          gcongr
+          exact add_le_add hpolyT (le_refl ‖P z‖)
         _ = (1 + p) * ‖P z‖ := by ring
     have hg : 0 ≤ saddleSourceGaussianKernel ε ℓ u T := by
       unfold saddleSourceGaussianKernel
@@ -1248,7 +1251,14 @@ private theorem saddleSourceCenteredPolynomial_centralGaussianError_le
             ((1 + p) * ‖P z‖) +
           saddleSourceGaussianKernel ε ℓ u T *
             (p * ‖P z‖) := by
-          gcongr
+          exact add_le_add
+              (mul_le_mul henvq hpolynorm (norm_nonneg (P (↑T + z)))
+                (mul_nonneg
+                  (mul_nonneg
+                    zero_le_two
+                    hg)
+                  hq))
+              (mul_le_mul_of_nonneg_left hpolyT hg)
       _ = c * saddleSourceGaussianKernel ε ℓ u T := by
         try dsimp [c]
         ring
@@ -1388,7 +1398,7 @@ private theorem saddle_abs_le_exp_sq (T : ℝ) :
   have hsquare : (|T| - 1) ^ 2 ≥ 0 := sq_nonneg _
   have habs : |T| ^ 2 = T ^ 2 := sq_abs T
   have hlinear : |T| ≤ 1 + T ^ 2 := by
-    linarith [abs_nonneg T, sq_nonneg T]
+    linarith only [abs_nonneg T, sq_nonneg T, hsquare, habs]
   exact hlinear.trans (by
     simpa only [add_comm] using! Real.add_one_le_exp (T ^ 2))
 
@@ -1406,14 +1416,14 @@ private theorem saddleGaussianTailWeight_le_two_exp_three_sq (T : ℝ) :
     exact (Real.one_le_exp_iff).mpr (by positivity)
   unfold saddleGaussianTailWeight
   rw [hexpcube] at hcube
-  linarith
+  linarith only [hcube, hone]
 
 private theorem saddleGaussianTailWeight_le_two_exp_three_abs (T : ℝ) :
     saddleGaussianTailWeight T ≤
       2 * Real.exp (3 * |T|) := by
   have hlinear : |T| ≤ Real.exp |T| := by
     calc
-      |T| ≤ 1 + |T| := by linarith
+      |T| ≤ 1 + |T| := by linarith only []
       _ ≤ Real.exp |T| := by
         simpa only [add_comm] using! Real.add_one_le_exp |T|
   have hcube : |T| ^ 3 ≤ (Real.exp |T|) ^ 3 :=
@@ -1426,7 +1436,7 @@ private theorem saddleGaussianTailWeight_le_two_exp_three_abs (T : ℝ) :
     exact (Real.one_le_exp_iff).mpr (by positivity)
   unfold saddleGaussianTailWeight
   rw [hexpcube] at hcube
-  linarith
+  linarith only [hcube, hone]
 
 private theorem saddle_integral_exp_neg_mul_abs
     {a : ℝ} (ha : 0 < a) :
@@ -1491,7 +1501,7 @@ private theorem saddleGaussian_cubic_tail_integral_le
         Real.exp (-k * T ^ 2)) ≤
       2 * Real.exp (-(k / 4) * R ^ 2) *
         Real.sqrt (Real.pi / (k / 4)) := by
-  have hkpos : 0 < k := by linarith
+  have hkpos : 0 < k := by linear_combination hk
   have hquarter : 0 < k / 4 := by positivity
   let c : ℝ := 2 * Real.exp (-(k / 4) * R ^ 2)
   have hc : 0 ≤ c := by
@@ -1515,16 +1525,17 @@ private theorem saddleGaussian_cubic_tail_integral_le
         3 * T ^ 2 + (-k * T ^ 2) ≤
           (-(k / 4) * R ^ 2) +
             (-(k / 4) * T ^ 2) := by
-      linarith [
-        mul_nonneg (show 0 ≤ k - 6 by linarith)
-          (sq_nonneg T),
-        mul_nonneg (show 0 ≤ k by linarith)
-          (show 0 ≤ T ^ 2 - R ^ 2 by linarith)]
+      linarith only [
+        mul_nonneg (show 0 ≤ k - 6 by linarith) (sq_nonneg T),
+        mul_nonneg (show 0 ≤ k by linarith) (show 0 ≤ T ^ 2 - R ^ 2 by linarith),
+        hk,
+        hsq
+      ]
     calc
       saddleGaussianTailWeight T * Real.exp (-k * T ^ 2) ≤
           (2 * Real.exp (3 * T ^ 2)) *
             Real.exp (-k * T ^ 2) := by
-              gcongr
+              refine mul_le_mul_of_nonneg_right ?_ (le_of_lt (Real.exp_pos (-k * T ^ 2)))
               exact saddleGaussianTailWeight_le_two_exp_three_sq T
       _ = 2 * Real.exp
           (3 * T ^ 2 + (-k * T ^ 2)) := by
@@ -1533,7 +1544,8 @@ private theorem saddleGaussian_cubic_tail_integral_le
       _ ≤ 2 * Real.exp
           (-(k / 4) * R ^ 2 +
             (-(k / 4) * T ^ 2)) := by
-              gcongr
+              exact mul_le_mul_of_nonneg_left (Real.exp_monotone hexponent)
+                  zero_le_two
       _ = c * Real.exp (-(k / 4) * T ^ 2) := by
             try dsimp [c]
             rw [Real.exp_add]
@@ -1566,7 +1578,7 @@ private theorem saddleExponential_cubic_tail_integral_le
         Real.exp (-k * |T|)) ≤
       2 * Real.exp (-(k / 4) * R) *
         (2 / (k / 4)) := by
-  have hkpos : 0 < k := by linarith
+  have hkpos : 0 < k := by linear_combination hk
   have hquarter : 0 < k / 4 := by positivity
   let c : ℝ := 2 * Real.exp (-(k / 4) * R)
   have hc : 0 ≤ c := by
@@ -1587,16 +1599,18 @@ private theorem saddleExponential_cubic_tail_integral_le
     have hexponent :
         3 * |T| + (-k * |T|) ≤
           (-(k / 4) * R) + (-(k / 4) * |T|) := by
-      linarith [
-        mul_nonneg (show 0 ≤ k - 6 by linarith)
-          hTabs,
-        mul_nonneg (show 0 ≤ k by linarith)
-          (show 0 ≤ |T| - R by linarith)]
+      linarith only [
+        mul_nonneg (show 0 ≤ k - 6 by linarith) hTabs,
+        mul_nonneg (show 0 ≤ k by linarith) (show 0 ≤ |T| - R by linarith),
+        hk,
+        hT,
+        hTabs
+      ]
     calc
       saddleGaussianTailWeight T * Real.exp (-k * |T|) ≤
           (2 * Real.exp (3 * |T|)) *
             Real.exp (-k * |T|) := by
-              gcongr
+              refine mul_le_mul_of_nonneg_right ?_ (le_of_lt (Real.exp_pos (-k * |T|)))
               exact saddleGaussianTailWeight_le_two_exp_three_abs T
       _ = 2 * Real.exp
           (3 * |T| + (-k * |T|)) := by
@@ -1604,7 +1618,8 @@ private theorem saddleExponential_cubic_tail_integral_le
             ring
       _ ≤ 2 * Real.exp
           (-(k / 4) * R + (-(k / 4) * |T|)) := by
-              gcongr
+              exact mul_le_mul_of_nonneg_left (Real.exp_monotone hexponent)
+                  zero_le_two
       _ = c * Real.exp (-(k / 4) * |T|) := by
             try dsimp [c]
             rw [Real.exp_add]
@@ -1648,7 +1663,7 @@ private theorem saddleGaussianOuterPhi_le_endpointBarrier
         c * ℓ * Q * Real.exp (B * δ₀) := by
   have hδnonneg : 0 ≤ δ := hδ₀.trans hδ
   have hlog := Real.log_le_sub_one_of_pos
-    (show 0 < 2 + δ by linarith)
+    (show 0 < 2 + δ by linear_combination hδ₀ + hδ)
   have hexpstep :
       Real.exp (B * δ₀) *
           (1 + B * (δ - δ₀)) ≤
@@ -1658,7 +1673,7 @@ private theorem saddleGaussianOuterPhi_le_endpointBarrier
           (1 + B * (δ - δ₀)) ≤
         Real.exp (B * δ₀) *
           Real.exp (B * (δ - δ₀)) := by
-            gcongr
+            refine mul_le_mul_of_nonneg_left ?_ (le_of_lt (Real.exp_pos (B * δ₀)))
             simpa only [add_comm] using!
               Real.add_one_le_exp (B * (δ - δ₀))
       _ = Real.exp (B * δ) := by
@@ -1668,7 +1683,7 @@ private theorem saddleGaussianOuterPhi_le_endpointBarrier
   have hdifference :
       Real.exp (B * δ₀) * (B * (δ - δ₀)) ≤
         Real.exp (B * δ) - Real.exp (B * δ₀) := by
-    linarith
+    linear_combination hexpstep
   have hcoefficient : 0 ≤ c * ℓ * Q := by
     apply (mul_nonneg_iff_of_pos_right hB).mp
     exact mul_nonneg
@@ -1677,9 +1692,9 @@ private theorem saddleGaussianOuterPhi_le_endpointBarrier
     mul_le_mul_of_nonneg_left hdifference hcoefficient
   have hlinearscaled :=
     mul_le_mul_of_nonneg_right hscale
-      (show 0 ≤ δ - δ₀ by linarith)
+      (show 0 ≤ δ - δ₀ by linear_combination hδ)
   unfold saddleGaussianOuterPhi
-  linarith
+  linarith only [hlog, hexpscaled, hlinearscaled]
 
 private theorem eventually_saddleGaussianOuterPhi_uniform
     {B Q c δ₀ : ℝ}
@@ -1707,7 +1722,7 @@ private theorem eventually_saddleGaussianOuterPhi_uniform
           Real.exp (A * δ₀ + 4) *
             (ℓ ^ (1 / 2 : ℝ) * Real.exp (-s * ℓ)))
         atTop (𝓝 (0 : ℝ)) := by
-      convert!
+      convert
         (tendsto_const_nhds
           (x := Real.exp (A * δ₀ + 4))).mul hbase using 1; simp only [mul_zero]
     apply hscaled.congr'
@@ -1737,7 +1752,7 @@ private theorem eventually_saddleGaussianOuterPhi_uniform
         (A / (c * Q * B * Real.exp (B * δ₀)))]
       with ℓ hℓ
     apply (div_le_iff₀ hfactor).mp at hℓ
-    linarith
+    linear_combination hℓ
   filter_upwards [eventually_ge_atTop (0 : ℝ),
     hthreshold, hsmall] with ℓ hℓ hscale hbound
   intro δ hδ
@@ -1751,7 +1766,7 @@ private theorem eventually_saddleGaussianOuterPhi_uniform
     apply mul_le_mul_of_nonneg_left _ (Real.sqrt_nonneg ℓ)
     apply Real.exp_le_exp.mpr
     try dsimp [A, s]
-    linarith
+    linear_combination hphi
   exact hcompare.trans_lt hbound
 
 private theorem upperPositiveShellVariance_firstBranch_le
@@ -1764,7 +1779,7 @@ private theorem upperPositiveShellVariance_firstBranch_le
   have hB : 0 ≤ B := by
     try dsimp [B]
     positivity
-  have horder : B ≤ B + 1 := by linarith
+  have horder : B ≤ B + 1 := by linarith only []
   have huabs : |u| ≤ 1 + ε / 2 := by
     apply (abs_le).mpr
     constructor <;> linarith
@@ -1817,10 +1832,10 @@ private theorem upperFirstBranch_saddleSourceGaussianVariance_upper_bound
   let η : ℝ := 1 + u
   have hη : 0 < η := by
     try dsimp [η]
-    linarith
+    linear_combination hulower
   have hηupper : η ≤ 2 + ε / 2 := by
     try dsimp [η]
-    linarith
+    linear_combination huupper
   have hgammabound :=
     (upperGammaVariance_bounds hℓ hη).2
   have hsmallterm : 1 / (ℓ * η ^ 2) ≤ 1 / η := by
@@ -1832,7 +1847,7 @@ private theorem upperFirstBranch_saddleSourceGaussianVariance_upper_bound
     calc
       upperGammaVariance ℓ η ≤
           1 / (2 * η) + 1 / (ℓ * η ^ 2) := hgammabound
-      _ ≤ 1 / (2 * η) + 1 / η := by gcongr
+      _ ≤ 1 / (2 * η) + 1 / η := by exact add_le_add (le_refl (1 / (2 * η))) hsmallterm
       _ = (3 / 2 : ℝ) / η := by ring_nf
   have hshort := upperShortShellVariance_nonneg
     (δ := u - 1) hε horder hmargin
@@ -1850,7 +1865,7 @@ private theorem upperFirstBranch_saddleSourceGaussianVariance_upper_bound
       try dsimp [η]
       ring
     rw [hargument]
-    linarith
+    linear_combination hgamma + hshort + hremote
   calc
     saddleSourceGaussianVariance ε ℓ u ≤
       (3 / 2 : ℝ) / η +
@@ -1876,10 +1891,10 @@ private theorem saddle_exp_neg_mul_min_le_add
     rcases le_total x y with hxy | hyx
     · rw [min_eq_left hxy, max_eq_left]
       apply Real.exp_le_exp.mpr
-      linarith [mul_nonneg ha (sub_nonneg.mpr hxy)]
+      linarith only [mul_nonneg ha (sub_nonneg.mpr hxy), ha, hxy]
     · rw [min_eq_right hyx, max_eq_right]
       apply Real.exp_le_exp.mpr
-      linarith [mul_nonneg ha (sub_nonneg.mpr hyx)]
+      linarith only [mul_nonneg ha (sub_nonneg.mpr hyx), ha, hyx]
   rw [hmax]
   exact max_le_add_of_nonneg
     (Real.exp_pos (-a * x)).le (Real.exp_pos (-a * y)).le
@@ -1906,7 +1921,7 @@ private theorem saddleSourceNormalizedEnvelope_continuous
         Complex.ofReal_re, Complex.add_re, Complex.one_re, Complex.ofReal_im, Complex.add_im,
           Complex.one_im, add_zero,
         mul_zero, sub_zero, Complex.I_re, zero_mul, Complex.I_im, Complex.mul_im, sub_self]
-      linarith [mul_pos hℓ (show 0 < 1 + u by linarith)]
+      linarith only [mul_pos hℓ (show 0 < 1 + u by linarith), hℓ, hu]
     exact (saddleMellinGamma_differentiableAt_of_re_pos
       hre).continuousAt.comp_of_eq harg.continuousAt (by rfl)
   have hregular : Continuous
@@ -1957,7 +1972,8 @@ private theorem saddleSourceTailIntegrand_continuous
           Real.exp (-saddleSourceContourDamping ε ℓ u T)) := by
   have hweight : Continuous saddleGaussianTailWeight := by
     unfold saddleGaussianTailWeight
-    fun_prop
+    exact Continuous.const_add
+        (Continuous.comp' (Continuous.fun_pow continuous_id' 3) (Continuous.abs continuous_id')) 1
   exact hweight.mul
     (saddleSourceDampingExponential_continuous
       hε hℓ hu horder)
@@ -1975,7 +1991,7 @@ private theorem saddleSourceContourDamping_firstBranch_min_lower_bound
     (ε * ℓ / (2 * Real.exp 1)) *
         min (T ^ 2 / (1 + u)) |T| ≤
       saddleSourceContourDamping ε ℓ u T := by
-  have hη : 0 < 1 + u := by linarith
+  have hη : 0 < 1 + u := by linear_combination hulower
   have hgamma := upperGammaDamping_lower_bound
     hℓ hη T
   have hfirst := upperFirstBranchSaddleDamping_lower_bound
@@ -2008,7 +2024,7 @@ private theorem saddleSource_firstBranch_weighted_integrable
   let a : ℝ := ε * ℓ / (2 * Real.exp 1)
   have hη : 0 < η := by
     try dsimp [η]
-    linarith
+    linear_combination hulower
   have ha : 0 < a := by
     try dsimp [a]
     positivity
@@ -2053,8 +2069,7 @@ private theorem saddleSource_firstBranch_weighted_integrable
       -a * (T ^ 2 / η) = -(a / η) * T ^ 2 := by
     ring
   rw [hrearrange] at hexp
-  linarith [mul_le_mul_of_nonneg_left hexp
-    (saddleGaussianTailWeight_nonneg T)]
+  linarith only [mul_le_mul_of_nonneg_left hexp (saddleGaussianTailWeight_nonneg T), hexp]
 
 private theorem saddleSource_firstBranch_weighted_tail_le
     {ε ℓ u R : ℝ}
@@ -2086,7 +2101,7 @@ private theorem saddleSource_firstBranch_weighted_tail_le
   let a : ℝ := ε * ℓ / (2 * Real.exp 1)
   have hη : 0 < η := by
     try dsimp [η]
-    linarith
+    linarith only [hulower]
   have ha : 0 < a := by
     try dsimp [a]
     positivity
@@ -2129,8 +2144,7 @@ private theorem saddleSource_firstBranch_weighted_tail_le
               -a * (T ^ 2 / η) = -(a / η) * T ^ 2 := by
             ring
           rw [hrearrange]
-    linarith [mul_le_mul_of_nonneg_left hexp
-      (saddleGaussianTailWeight_nonneg T)]
+    linarith only [mul_le_mul_of_nonneg_left hexp (saddleGaussianTailWeight_nonneg T), hexp]
   have hcompare := setIntegral_mono_on
     hsource.integrableOn hmajor.integrableOn
     (saddleGaussianTailSet_measurable R) hpoint
@@ -2167,7 +2181,7 @@ private theorem saddleSource_firstBranch_weighted_tail_le
             Real.sqrt (Real.pi / (a / η / 4)) +
           2 * Real.exp (-(a / 4) * R) *
             (2 / (a / 4)) := by
-      gcongr
+      refine add_le_add ?_ ?_
       · apply saddleGaussian_cubic_tail_integral_le
         · exact hquadratic
         · exact hR
@@ -2192,7 +2206,13 @@ private theorem saddleFirstBranch_normalizedGaussian_prefactor_le
           4 * Real.pi * (η * V) / c := by
             field_simp [hc.ne', hℓ.ne', hη.ne']
       _ ≤ 4 * Real.pi * C / c := by
-        gcongr
+        exact div_le_div_of_nonneg_right
+            (mul_le_mul_of_nonneg_left hupper
+              (le_of_lt
+                (mul_pos
+                  ((by norm_num))
+                  Real.pi_pos)))
+            (le_of_lt hc)
       _ = 4 * (Real.pi * C / c) := by ring
   rw [← Real.sqrt_mul (mul_nonneg hℓ.le hV.le)]
   calc
@@ -2242,7 +2262,7 @@ private theorem saddleFirstBranch_normalizedLinear_prefactor_le
     apply (div_le_div_iff₀ hℓ (mul_pos hℓ hη)).mpr
     have hscaled :=
       mul_le_mul_of_nonneg_left hupper hℓ.le
-    linarith
+    linear_combination hscaled
   have hidentity :
       Real.sqrt (ℓ * V) / ℓ = Real.sqrt (V / ℓ) := by
     calc
@@ -2293,7 +2313,7 @@ private theorem saddleSource_firstBranch_normalized_tail_bound
   let R : ℝ := z / Real.sqrt (ℓ * V)
   have hη : 0 < η := by
     try dsimp [η]
-    linarith
+    linarith only [hulower]
   have hc : 0 < c := by
     try dsimp [c]
     positivity
@@ -2417,8 +2437,7 @@ private theorem saddleSourceFirstBranchVarianceCoefficient_pos
   have hshell :=
     saddleSourcePositiveShellVariance_nonneg ε (ε / 2)
   unfold saddleSourceFirstBranchVarianceCoefficient
-  linarith [mul_nonneg
-    (show 0 ≤ 2 + ε / 2 by positivity) hshell]
+  linarith only [mul_nonneg (show 0 ≤ 2 + ε / 2 by positivity) hshell, hε, hshell]
 
 private noncomputable def saddleFirstBranchTailLogMajorant
     (c C ℓ : ℝ) : ℝ :=
@@ -2450,7 +2469,7 @@ private theorem tendsto_saddleFirstBranchTailLogMajorant
         -(c / (4 * C)) *
           (Real.log ℓ / 4) ^ (1 / 6 : ℝ))
       atTop atBot :=
-    hpower.const_mul_atTop_of_neg (by linarith)
+    hpower.const_mul_atTop_of_neg (by linear_combination hrate)
   have hexp : Tendsto
       (fun ℓ : ℝ =>
         Real.exp
@@ -2466,7 +2485,7 @@ private theorem tendsto_saddleFirstBranchTailLogMajorant
       (fun ℓ : ℝ =>
         Real.sqrt (C / (Real.log ℓ / 4)))
       atTop (𝓝 (0 : ℝ)) := by
-    convert! hratio.sqrt using 1; simp only [Real.sqrt_zero]
+    convert hratio.sqrt using 1; simp only [Real.sqrt_zero]
   have hfirst := hexp.const_mul
     (4 * Real.sqrt (Real.pi * C / c))
   have hsecond := hsqrt.const_mul (16 / c)
@@ -2548,10 +2567,10 @@ private theorem eventually_saddleSource_firstBranch_uniform_tail :
   let z : ℝ := (ℓ * η) ^ (1 / 12 : ℝ)
   have hη : 0 < η := by
     try dsimp [η]
-    linarith
+    linear_combination hulower
   have hηU : η ≤ U := by
     try dsimp [η, U]
-    linarith
+    linear_combination huupper
   have hscale : 1 ≤ ℓ * η :=
     hlogoneℓ.trans hlogscale
   have hV : 0 < V := by
@@ -2562,7 +2581,7 @@ private theorem eventually_saddleSource_firstBranch_uniform_tail :
         0 ≤ (1 - 10 * ε * (1 + a)) := by
     intro a ha
     have h := hmargin a ha
-    linarith
+    linear_combination hεsmall + hε + h
   have hvariance :=
     upperFirstBranch_saddleSourceGaussianVariance_upper_bound
       hε hℓ hulower huupper horder hmargin' hscale
@@ -2575,12 +2594,11 @@ private theorem eventually_saddleSource_firstBranch_uniform_tail :
       _ = C := by field_simp [hη.ne']
   have hlinear : 6 ≤ c * ℓ := by
     have h := (div_le_iff₀ hc).mp hlinbase
-    linarith
+    linear_combination h
   have hquadratic : 6 ≤ (c * ℓ) / η := by
     apply (le_div_iff₀ hη).mpr
     have h := (div_le_iff₀ hc).mp hquadbase
-    linarith [mul_le_mul_of_nonneg_left hηU
-      (by norm_num : (0 : ℝ) ≤ 6)]
+    linarith only [mul_le_mul_of_nonneg_left hηU (by norm_num : (0 : ℝ) ≤ 6), hηU, h]
   have hz : 0 ≤ z := by
     try dsimp [z]
     positivity
@@ -2588,8 +2606,8 @@ private theorem eventually_saddleSource_firstBranch_uniform_tail :
     (z := z) (C := C)
     hε hεsmall hℓ hulower huupper horder hmargin'
     hV hC hupper hz (by
-      convert! hquadratic using 1; dsimp [c, η]; ring) (by
-      convert! hlinear using 1; dsimp [c]; ring)
+      convert hquadratic using 1; dsimp [c, η]; ring) (by
+      convert hlinear using 1; dsimp [c]; ring)
   have hlognonneg : 0 ≤ Real.log ℓ / 4 := zero_le_one.trans hlogoneℓ
   have hpower :
       (Real.log ℓ / 4) ^ (1 / 6 : ℝ) ≤ z ^ 2 := by
@@ -2666,7 +2684,7 @@ private theorem eventually_saddleGaussianOuterPhi_uniform_polynomial
     filter_upwards [hlimit] with ℓ hℓ
     intro δ hδ
     have hδnonnegative : 0 ≤ δ := hδ₀.trans hδ
-    have hη : 0 < 2 + δ := by linarith
+    have hη : 0 < 2 + δ := by linear_combination hδ₀ + hδ
     have hpower :
         (2 + δ) ^ 4 =
           Real.exp (4 * Real.log (2 + δ)) := by
@@ -2736,7 +2754,7 @@ private theorem saddleSourcePositiveShellThirdMoment_nonneg
   have hB : 0 ≤ (ε⁻¹ ^ 3) := by
     positivity
   unfold upperPositiveShellThirdMoment
-  apply intervalIntegral.integral_nonneg (by linarith)
+  apply intervalIntegral.integral_nonneg (by linarith only [])
   intro a ha
   have ha : 0 ≤ a := hB.trans ha.1
   have hdensity : 0 ≤ positiveShellDensity ε a := by
@@ -2757,7 +2775,7 @@ private theorem upperPositiveShellThirdMoment_firstBranch_le
   have hB : 0 ≤ B := by
     try dsimp [B]
     positivity
-  have horder : B ≤ B + 1 := by linarith
+  have horder : B ≤ B + 1 := by linarith only []
   have huabs : |u| ≤ 1 + ε / 2 := by
     apply (abs_le).mpr
     constructor <;> linarith
@@ -2806,7 +2824,7 @@ private theorem upperGammaVariance_firstBranch_scaled_le
         (upperGammaVariance_bounds hℓ hη).2 hη.le
     _ = 1 / 2 + 1 / (ℓ * η) := by
       field_simp [hℓ.ne', hη.ne']
-    _ ≤ (3 / 2 : ℝ) := by linarith
+    _ ≤ (3 / 2 : ℝ) := by linear_combination hone
 
 private theorem upperGammaThirdMoment_firstBranch_scaled_le
     {ℓ η : ℝ} (hℓ : 0 < ℓ) (hη : 0 < η)
@@ -2818,7 +2836,9 @@ private theorem upperGammaThirdMoment_firstBranch_scaled_le
   have htwo : 2 / (ℓ * η) ≤ (2 : ℝ) := by
     calc
       2 / (ℓ * η) = 2 * (1 / (ℓ * η)) := by ring
-      _ ≤ 2 * (1 : ℝ) := by gcongr
+      _ ≤ 2 * (1 : ℝ) := by
+        exact mul_le_mul_of_nonneg_left hone
+            zero_le_two
       _ = 2 := by ring
   calc
     η ^ 2 * upperGammaThirdMoment ℓ η ≤
@@ -2829,7 +2849,7 @@ private theorem upperGammaThirdMoment_firstBranch_scaled_le
         (sq_nonneg η)
     _ = 1 / 2 + 2 / (ℓ * η) := by
       field_simp [hℓ.ne', hη.ne']
-    _ ≤ (5 / 2 : ℝ) := by linarith
+    _ ≤ (5 / 2 : ℝ) := by linear_combination htwo
 
 private noncomputable def saddleSourceFirstBranchThirdMomentCoefficient
     (ε : ℝ) : ℝ :=
@@ -2854,13 +2874,13 @@ private theorem upperFirstBranch_saddleSourceThirdMoment_scaled_le
   let U : ℝ := 2 + ε / 2
   have hη : 0 < η := by
     try dsimp [η]
-    linarith
+    linear_combination hulower
   have hU : 0 < U := by
     try dsimp [U]
     positivity
   have hηU : η ≤ U := by
     try dsimp [η, U]
-    linarith
+    linear_combination huupper
   have hA : 0 ≤ (10 * Real.log (1 / ε)) := by
     have hcut : 0 < (ε ^ 3) := by
       positivity
@@ -2879,7 +2899,7 @@ private theorem upperFirstBranch_saddleSourceThirdMoment_scaled_le
       upperShortShellVariance ε (u - 1) ≤
         upperGammaVariance ℓ η := by
     try dsimp [η]
-    linarith [mul_nonneg hε.le hgammanonneg]
+    linarith only [mul_nonneg hε.le hgammanonneg, hε, hgammanonneg, hshortvariance]
   have hshortthird := upperShortShellThirdMoment_le
     (δ := u - 1) hε horder hmargin
   have hshort :
@@ -2897,9 +2917,13 @@ private theorem upperFirstBranch_saddleSourceThirdMoment_scaled_le
       _ = (10 * Real.log (1 / ε)) * η *
           (η * upperGammaVariance ℓ η) := by ring
       _ ≤ (10 * Real.log (1 / ε)) * η * (3 / 2 : ℝ) := by
-        gcongr
+        exact mul_le_mul_of_nonneg_left hgamma (mul_nonneg hA (le_of_lt hη))
       _ ≤ (10 * Real.log (1 / ε)) * U * (3 / 2 : ℝ) := by
-        gcongr
+        exact mul_le_mul_of_nonneg_right (mul_le_mul_of_nonneg_left hηU hA)
+            (le_of_lt
+              (div_pos
+                ((by norm_num))
+                (zero_lt_two)))
       _ = (3 / 2 : ℝ) * (10 * Real.log (1 / ε)) * U := by
         ring
   have hremote :=
@@ -2916,7 +2940,7 @@ private theorem upperFirstBranch_saddleSourceThirdMoment_scaled_le
           η ^ 2 * upperPositiveShellThirdMoment ε (ε / 2) :=
         mul_le_mul_of_nonneg_left hremote (sq_nonneg η)
       _ ≤ U ^ 2 * upperPositiveShellThirdMoment ε (ε / 2) := by
-        gcongr
+        exact mul_le_mul_of_nonneg_right (pow_le_pow_left₀ (le_of_lt hη) hηU 2) hremote0
   unfold saddleSourceFirstBranchThirdMomentCoefficient
   unfold upperSaddleThirdMoment upperNetShellThirdMoment
   have hargument : 2 + (u - 1) = η := by
@@ -2930,7 +2954,7 @@ private theorem upperFirstBranch_saddleSourceThirdMoment_scaled_le
     (5 / 2 : ℝ) +
       (3 / 2 : ℝ) * (10 * Real.log (1 / ε)) * U +
       U ^ 2 * upperPositiveShellThirdMoment ε (ε / 2)
-  linarith only [hthirdgamma, hshort, hremoteScaled]
+  linear_combination hthirdgamma + hshort + hremoteScaled
 
 private noncomputable def saddleSourceSecondBranchVarianceFloor (ε : ℝ) : ℝ :=
   (99 / 200 : ℝ) * (ε⁻¹ ^ 3) ^ 2 *
@@ -2955,7 +2979,7 @@ private theorem eventually_saddleSourceGaussianVariance_secondBranch_floor :
     with ε hε hvariance
   change 0 < ε at hε
   intro ℓ hℓ δ hδ
-  have hδ0 : 0 ≤ δ := by linarith
+  have hδ0 : 0 ≤ δ := by linarith only [hε, hδ]
   have hB : 0 ≤ (ε⁻¹ ^ 3) := by
     positivity
   have hfactor :
@@ -2989,17 +3013,25 @@ private theorem eventually_saddleSourceGaussianVariance_secondBranch_floor :
               (ε⁻¹ ^ 3) ^ 2 *
                 shellWeight ε *
                   Real.exp (δ * (ε⁻¹ ^ 3))) := by
-        gcongr
+        exact mul_le_mul_of_nonneg_left (mul_le_mul_of_nonneg_left hmono hfactor)
+            (le_of_lt
+              (div_pos
+                ((by norm_num))
+                ((by norm_num))))
       _ ≤ (99 / 100 : ℝ) *
             upperPositiveShellVariance ε δ := by
-        gcongr
-  have hη : 0 < 2 + δ := by linarith
+        exact mul_le_mul_of_nonneg_left hpositive
+            (le_of_lt
+              (div_pos
+                ((by norm_num))
+                ((by norm_num))))
+  have hη : 0 < 2 + δ := by linarith only [hε, hδ]
   have hgamma : 0 ≤ 1 / (2 * (2 + δ)) := by
     positivity
   unfold saddleSourceGaussianVariance
   have hargument : 1 + δ - 1 = δ := by ring
   rw [hargument]
-  linarith
+  linear_combination hfull + hfloor + hgamma
 
 private theorem saddleSource_cubic_window_le
     {ℓ V M C z T : ℝ}
@@ -3015,7 +3047,11 @@ private theorem saddleSource_cubic_window_le
   calc
     (ℓ * M / 6) * |T| ^ 3 ≤
         (ℓ * (C * V) / 6) * |T| ^ 3 := by
-      gcongr
+      exact mul_le_mul_of_nonneg_right
+          (div_le_div_of_nonneg_right (mul_le_mul_of_nonneg_left hM (le_of_lt hℓ))
+            (le_of_lt
+              ((by norm_num))))
+          (pow_nonneg (abs_nonneg T) 3)
     _ ≤ (ℓ * (C * V) / 6) *
         (z / Real.sqrt (ℓ * V)) ^ 3 := by
       gcongr
@@ -3147,11 +3183,11 @@ private theorem exists_polynomial_uniform_central_window
       exact mul_nonneg
         (mul_nonneg (abs_nonneg T) (sub_nonneg.mpr hTunit))
         (by positivity)
-    linarith
+    linarith only [hfactor]
   have hscale : 2 * C * R ≤ κ := by
     have hmin : R ≤ κ / (2 * C) := min_le_right _ _
     have hfactor : 0 < 2 * C := by positivity
-    linarith [(le_div_iff₀ hfactor).mp hmin]
+    linarith only [(le_div_iff₀ hfactor).mp hmin, hmin, hfactor]
   calc
     ‖P ((T : ℂ) + Complex.I * (u : ℂ)) - P (Complex.I * (u : ℂ))‖ ≤
       C * (|T| + |T| ^ 3) * ‖P (Complex.I * (u : ℂ))‖ :=
@@ -3161,7 +3197,7 @@ private theorem exists_polynomial_uniform_central_window
       calc
         C * (|T| + |T| ^ 3) ≤ C * (2 * R) := by
           apply mul_le_mul_of_nonneg_left _ hC.le
-          linarith
+          linarith only [hT, hcube]
         _ = 2 * C * R := by ring
     _ ≤ κ * ‖P (Complex.I * (u : ℂ))‖ := by
       exact mul_le_mul_of_nonneg_right hscale (norm_nonneg _)
@@ -3239,7 +3275,7 @@ private theorem saddleSource_scaled_cubic_window_le
       (K / (6 * c * Real.sqrt c)) *
         (z ^ 3 / Real.sqrt (ℓ * η)) := by
   have hV : 0 < V := by
-    nlinarith [hvariance, mul_pos hη hc]
+    exact pos_of_mul_pos_right (hc.trans_le hvariance) hη.le
   have hs : 0 < Real.sqrt (ℓ * V) :=
     Real.sqrt_pos.2 (mul_pos hℓ hV)
   have ht : 0 < Real.sqrt (ℓ * η) :=
@@ -3250,7 +3286,7 @@ private theorem saddleSource_scaled_cubic_window_le
     Real.sqrt_pos.2 hc
   have hm : M ≤ K / η ^ 2 := by
     apply (le_div_iff₀ (sq_pos_of_pos hη)).2
-    linarith
+    linarith only [hmoment]
   have hcross :
       Real.sqrt (ℓ * V) * η =
         Real.sqrt (ℓ * η) * Real.sqrt (η * V) := by
@@ -3292,7 +3328,13 @@ private theorem saddleSource_scaled_cubic_window_le
     (ℓ * M / 6) * |T| ^ 3 ≤
         (ℓ * (K / η ^ 2) / 6) *
           (z / Real.sqrt (ℓ * V)) ^ 3 := by
-      gcongr
+      refine mul_le_mul
+        (div_le_div_of_nonneg_right
+          (mul_le_mul_of_nonneg_left hm hℓ.le) (by norm_num))
+        (pow_le_pow_left₀ (abs_nonneg T) hT 3)
+        (pow_nonneg (abs_nonneg T) 3) ?_
+      exact div_nonneg
+        (mul_nonneg hℓ.le (div_nonneg hK (sq_nonneg η))) (by norm_num)
     _ = (K / 6) * z ^ 3 /
         (Real.sqrt (ℓ * η) *
           (Real.sqrt (η * V)) ^ 3) := by
@@ -3311,7 +3353,11 @@ private theorem saddleSource_scaled_cubic_window_le
     _ ≤ (K / 6) * z ^ 3 /
         (Real.sqrt (ℓ * η) *
           (Real.sqrt c) ^ 3) := by
-      gcongr
+      exact div_le_div_of_nonneg_left
+        (mul_nonneg (div_nonneg hK (by norm_num)) (pow_nonneg hz 3))
+        (mul_pos ht (pow_pos hcroot 3))
+        (mul_le_mul_of_nonneg_left
+          (pow_le_pow_left₀ hcroot.le hwlower 3) ht.le)
     _ = (K / (6 * c * Real.sqrt c)) *
         (z ^ 3 / Real.sqrt (ℓ * η)) := by
       have hcsquare : (Real.sqrt c) ^ 2 = c :=
@@ -3330,7 +3376,7 @@ private theorem upperFirstBranch_saddleSourceGaussianVariance_scaled_lower_bound
       (10 * Real.log (1 / ε)), 0 ≤ (1 - 10 * ε * (1 + a))) :
     2 * ε ≤ (1 + u) *
       saddleSourceGaussianVariance ε ℓ u := by
-  have hη : 0 < 1 + u := by linarith
+  have hη : 0 < 1 + u := by linear_combination hulower
   have hgamma := (upperGammaVariance_bounds hℓ hη).1
   have hsource :=
     upperFirstBranch_saddleSourceGaussianVariance_lower_bound
@@ -3342,10 +3388,16 @@ private theorem upperFirstBranch_saddleSourceGaussianVariance_scaled_lower_bound
       norm_num
     _ ≤ (1 + u) *
         (4 * ε * upperGammaVariance ℓ (1 + u)) := by
-      gcongr
+      exact mul_le_mul_of_nonneg_left
+          (mul_le_mul_of_nonneg_left hgamma
+            (le_of_lt
+              (mul_pos
+                ((by norm_num))
+                hε)))
+          (le_of_lt hη)
     _ ≤ (1 + u) *
         saddleSourceGaussianVariance ε ℓ u := by
-      gcongr
+      exact mul_le_mul_of_nonneg_left hsource (le_of_lt hη)
 
 private theorem saddleSourceFirstBranchThirdMomentCoefficient_pos
     {ε : ℝ} (hε : 0 < ε)
@@ -3376,7 +3428,7 @@ private theorem saddleSourceFirstBranch_cubic_central_window_le
       (saddleSourceFirstBranchThirdMomentCoefficient ε /
         (12 * ε * Real.sqrt (2 * ε))) *
           (ℓ * (1 + u)) ^ (-(1 / 4 : ℝ)) := by
-  have hη : 0 < 1 + u := by linarith
+  have hη : 0 < 1 + u := by linear_combination hulower
   have hx : 0 < ℓ * (1 + u) := mul_pos hℓ hη
   have hK :=
     saddleSourceFirstBranchThirdMomentCoefficient_pos hε horder
@@ -3430,7 +3482,7 @@ private theorem eventually_saddleSourceSecondBranch_cubic_central_window_le :
     with ε hε horder hfloor hmoment
   change 0 < ε at hε
   intro ℓ hℓ δ hδ T hT
-  have hℓpositive : 0 < ℓ := by linarith
+  have hℓpositive : 0 < ℓ := by linear_combination hℓ
   have hfloorpositive :=
     saddleSourceSecondBranchVarianceFloor_pos hε
   have hvariance := hfloor ℓ hℓpositive δ hδ
@@ -3537,7 +3589,9 @@ private theorem saddleSource_scaled_central_radius_le
         _ = z * Real.sqrt (ℓ * V) * η := by ring
     _ ≤ U * z /
         (Real.sqrt (ℓ * η) * Real.sqrt c) := by
-      gcongr
+      exact div_le_div₀ (mul_nonneg hU hz) (mul_le_mul_of_nonneg_right hηU hz)
+          (mul_pos (Real.sqrt_pos_of_pos (mul_pos hℓ hη)) (Real.sqrt_pos_of_pos hc))
+          (mul_le_mul_of_nonneg_left hwlower (le_of_lt (Real.sqrt_pos_of_pos (mul_pos hℓ hη))))
     _ = (U / Real.sqrt c) *
         (z / Real.sqrt (ℓ * η)) := by
       ring
@@ -3554,7 +3608,7 @@ private theorem saddleSourceFirstBranch_central_radius_le
     saddleSourceFirstBranchCentralRadius ε ℓ u ≤
       ((2 + ε / 2) / Real.sqrt (2 * ε)) *
         (ℓ * (1 + u)) ^ (-(5 / 12 : ℝ)) := by
-  have hη : 0 < 1 + u := by linarith
+  have hη : 0 < 1 + u := by linear_combination hulower
   have hx : 0 < ℓ * (1 + u) := mul_pos hℓ hη
   have hvariance :=
     upperFirstBranch_saddleSourceGaussianVariance_scaled_lower_bound
@@ -3564,7 +3618,7 @@ private theorem saddleSourceFirstBranch_central_radius_le
     (V := saddleSourceGaussianVariance ε ℓ u)
     (c := 2 * ε) (U := 2 + ε / 2)
     (z := (ℓ * (1 + u)) ^ (1 / 12 : ℝ))
-    hℓ hη (by positivity) (by linarith)
+    hℓ hη (by positivity) (by linear_combination huupper)
     (Real.rpow_nonneg hx.le _) hvariance
   calc
     saddleSourceFirstBranchCentralRadius ε ℓ u ≤
@@ -3637,14 +3691,14 @@ private theorem eventually_saddleSourceFirstBranch_cubic_window :
       (10 * Real.log (1 / ε)), 0 ≤ (1 - 10 * ε * (1 + a)) := by
     intro a ha
     have h := hmargin a ha
-    linarith
+    linear_combination h
   intro κ hκ
   let A : ℝ := saddleSourceFirstBranchThirdMomentCoefficient ε /
     (12 * ε * Real.sqrt (2 * ε))
   have htendsto :
       Tendsto (fun x : ℝ => A * x ^ (-(1 / 4 : ℝ)))
         atTop (𝓝 (0 : ℝ)) := by
-    convert! tendsto_const_nhds.mul
+    convert tendsto_const_nhds.mul
       (tendsto_rpow_neg_atTop
         (by norm_num : (0 : ℝ) < 1 / 4)) using 1
     all_goals simp only [mul_zero]
@@ -3656,9 +3710,9 @@ private theorem eventually_saddleSourceFirstBranch_cubic_window :
     with ℓ hℓ hlog hlogone
   intro u hu huupper hstar T hT
   have hxN : N ≤ ℓ * (1 + u) := by
-    linarith
+    linarith only [hlog, hstar]
   have hxone : 1 ≤ ℓ * (1 + u) := by
-    linarith
+    linarith only [hlogone, hstar]
   have hbound := saddleSourceFirstBranch_cubic_central_window_le
     hε hεsmall hℓ hu huupper horder hmargin'
     hxone hT
@@ -3686,7 +3740,7 @@ private theorem eventually_saddleSourceSecondBranch_cubic_window :
   have htendsto :
       Tendsto (fun ℓ : ℝ => A * ℓ ^ (-(1 / 4 : ℝ)))
         atTop (𝓝 (0 : ℝ)) := by
-    convert! tendsto_const_nhds.mul
+    convert tendsto_const_nhds.mul
       (tendsto_rpow_neg_atTop
         (by norm_num : (0 : ℝ) < 1 / 4)) using 1
     all_goals simp only [mul_zero]
@@ -3720,13 +3774,13 @@ private theorem eventually_saddleSourceFirstBranch_central_radius_lt :
       (10 * Real.log (1 / ε)), 0 ≤ (1 - 10 * ε * (1 + a)) := by
     intro a ha
     have h := hmargin a ha
-    linarith
+    linear_combination h
   intro κ hκ
   let A : ℝ := (2 + ε / 2) / Real.sqrt (2 * ε)
   have htendsto :
       Tendsto (fun x : ℝ => A * x ^ (-(5 / 12 : ℝ)))
         atTop (𝓝 (0 : ℝ)) := by
-    convert! tendsto_const_nhds.mul
+    convert tendsto_const_nhds.mul
       (tendsto_rpow_neg_atTop
         (by norm_num : (0 : ℝ) < 5 / 12)) using 1
     all_goals simp only [mul_zero]
@@ -3737,7 +3791,7 @@ private theorem eventually_saddleSourceFirstBranch_central_radius_lt :
     with ℓ hℓ hlog
   intro u hu huupper hstar
   have hxN : N ≤ ℓ * (1 + u) := by
-    linarith
+    linarith only [hlog, hstar]
   exact (saddleSourceFirstBranch_central_radius_le
     hε hεsmall hℓ hu huupper horder hmargin').trans_lt
       (hN (ℓ * (1 + u)) hxN)
@@ -3760,7 +3814,7 @@ private theorem eventually_saddleSourceSecondBranch_central_radius_lt :
   have htendsto :
       Tendsto (fun ℓ : ℝ => A * ℓ ^ (-(5 / 12 : ℝ)))
         atTop (𝓝 (0 : ℝ)) := by
-    convert! tendsto_const_nhds.mul
+    convert tendsto_const_nhds.mul
       (tendsto_rpow_neg_atTop
         (by norm_num : (0 : ℝ) < 5 / 12)) using 1
     all_goals simp only [mul_zero]
@@ -3781,9 +3835,8 @@ private theorem exists_saddleSource_central_error_tolerance
     positivity
   have hquarter : q ≤ (1 / 4 : ℝ) := min_le_left _ _
   have hk : q ≤ κ / 8 := min_le_right _ _
-  refine ⟨q, hq, by linarith, ?_⟩
-  linarith [mul_nonneg hq.le
-    (sub_nonneg.mpr hquarter)]
+  refine ⟨q, hq, by linarith only [hq, hquarter], ?_⟩
+  linarith only [mul_nonneg hq.le (sub_nonneg.mpr hquarter), hq, hquarter, hk]
 
 private theorem eventually_saddleSourceFirstBranch_centralGaussianErrors :
     ∀ᶠ ε : ℝ in 𝓝[>] (0 : ℝ),
@@ -3820,7 +3873,7 @@ private theorem eventually_saddleSourceFirstBranch_centralGaussianErrors :
       (10 * Real.log (1 / ε)), 0 ≤ (1 - 10 * ε * (1 + a)) := by
     intro a ha
     have h := hmargin a ha
-    linarith
+    linear_combination h
   intro κ hκ
   obtain ⟨q, hq, hqone, hfactor⟩ :=
     exists_saddleSource_central_error_tolerance hκ
@@ -3837,7 +3890,7 @@ private theorem eventually_saddleSourceFirstBranch_centralGaussianErrors :
   let R : ℝ := saddleSourceFirstBranchCentralRadius ε ℓ u
   have hV := hvariance ℓ hℓ u hu huupper
   have hR : 0 ≤ R := by
-    have hη : 0 ≤ 1 + u := by linarith
+    have hη : 0 ≤ 1 + u := by linear_combination hu
     try dsimp [R, saddleSourceFirstBranchCentralRadius]
     exact div_nonneg
       (Real.rpow_nonneg (mul_nonneg hℓ.le hη) _)
@@ -3878,7 +3931,7 @@ private theorem eventually_saddleSourceFirstBranch_centralGaussianErrors :
         hcentral
       _ < κ * ‖plusPolynomial ε (Complex.I * (u : ℂ))‖ *
           (∫ T : ℝ, saddleSourceGaussianKernel ε ℓ u T) := by
-        gcongr
+        exact mul_lt_mul_of_pos_right (mul_lt_mul_of_pos_right hfactor hden) hG
   · intro huminus
     have hpoly : ∀ T : ℝ, |T| ≤ R →
         ‖minusPolynomial ε
@@ -3894,7 +3947,7 @@ private theorem eventually_saddleSourceFirstBranch_centralGaussianErrors :
       have hbound :=
         minusPolynomial_imaginary_norm_ge_three_beta
           hε huminus
-      linarith
+      linarith only [hε, hbound]
     have hcentral :=
       saddleSourceCenteredMinusIntegrand_centralGaussianError_le
         hε hℓ hu horder hmargin' hV hR hq.le hqone hq.le
@@ -3910,7 +3963,7 @@ private theorem eventually_saddleSourceFirstBranch_centralGaussianErrors :
         hcentral
       _ < κ * ‖minusPolynomial ε (Complex.I * (u : ℂ))‖ *
           (∫ T : ℝ, saddleSourceGaussianKernel ε ℓ u T) := by
-        gcongr
+        exact mul_lt_mul_of_pos_right (mul_lt_mul_of_pos_right hfactor hden) hG
 
 private theorem eventually_saddleSourceSecondBranch_centralGaussianErrors :
     ∀ᶠ ε : ℝ in 𝓝[>] (0 : ℝ),
@@ -3955,7 +4008,7 @@ private theorem eventually_saddleSourceSecondBranch_centralGaussianErrors :
       (10 * Real.log (1 / ε)), 0 ≤ (1 - 10 * ε * (1 + a)) := by
     intro a ha
     have h := hmargin a ha
-    linarith
+    linear_combination h
   intro κ hκ
   obtain ⟨q, hq, hqone, hfactor⟩ :=
     exists_saddleSource_central_error_tolerance hκ
@@ -3971,13 +4024,13 @@ private theorem eventually_saddleSourceSecondBranch_centralGaussianErrors :
   intro δ hδ
   let u : ℝ := 1 + δ
   let R : ℝ := saddleSourceSecondBranchCentralRadius ε ℓ u
-  have hδzero : 0 ≤ δ := by linarith
+  have hδzero : 0 ≤ δ := by linarith only [hε, hδ]
   have hu : -1 < u := by
     try dsimp [u]
-    linarith
+    linarith only [hε, hδ]
   have huminus : 1 + ε / 4 ≤ u := by
     try dsimp [u]
-    linarith
+    linarith only [hε, hδ]
   have hV : 0 < saddleSourceGaussianVariance ε ℓ u := by
     try dsimp [u]
     exact hvariance ℓ hℓ δ hδ
@@ -4021,7 +4074,8 @@ private theorem eventually_saddleSourceSecondBranch_centralGaussianErrors :
             saddleSourceGaussianPlusIntegrand ε ℓ u T)‖ <
         κ * ‖plusPolynomial ε (Complex.I * (u : ℂ))‖ *
           (∫ T : ℝ, saddleSourceGaussianKernel ε ℓ u T)
-    exact hcentral.trans_lt (by gcongr)
+    exact hcentral.trans_lt
+      (mul_lt_mul_of_pos_right (mul_lt_mul_of_pos_right hfactor hden) hG)
   · have hpoly : ∀ T : ℝ, |T| ≤ R →
         ‖minusPolynomial ε
             ((T : ℂ) + Complex.I * (u : ℂ)) -
@@ -4036,7 +4090,7 @@ private theorem eventually_saddleSourceSecondBranch_centralGaussianErrors :
       have hbound :=
         minusPolynomial_imaginary_norm_ge_three_beta
           hε huminus
-      linarith
+      linarith only [hε, hbound]
     have hcentral :=
       saddleSourceCenteredMinusIntegrand_centralGaussianError_le
         hε hℓ hu horder hmargin' hV hR hq.le hqone hq.le
@@ -4048,7 +4102,8 @@ private theorem eventually_saddleSourceSecondBranch_centralGaussianErrors :
             saddleSourceGaussianMinusIntegrand ε ℓ u T)‖ <
         κ * ‖minusPolynomial ε (Complex.I * (u : ℂ))‖ *
           (∫ T : ℝ, saddleSourceGaussianKernel ε ℓ u T)
-    exact hcentral.trans_lt (by gcongr)
+    exact hcentral.trans_lt
+      (mul_lt_mul_of_pos_right (mul_lt_mul_of_pos_right hfactor hden) hG)
 
 private theorem upperPositiveShellDamping_local_variance_lower
     {ε ℓ δ T : ℝ}
@@ -4060,13 +4115,13 @@ private theorem upperPositiveShellDamping_local_variance_lower
   have hB : 0 ≤ B := by
     try dsimp [B]
     positivity
-  have hB1 : 0 < B + 1 := by linarith
-  have horder : B ≤ B + 1 := by linarith
+  have hB1 : 0 < B + 1 := by linear_combination hB
+  have horder : B ≤ B + 1 := by linarith only []
   have hwindow : (B + 1) * |T| ≤ 1 / 2 := by
     calc
       (B + 1) * |T| ≤
           (B + 1) * (1 / (2 * (B + 1))) := by
-            apply mul_le_mul_of_nonneg_left _ (by linarith)
+            apply mul_le_mul_of_nonneg_left _ (by linear_combination hB)
             simpa only [one_div, mul_inv_rev, B] using! hT
       _ = 1 / 2 := by
         field_simp [hB1.ne']
@@ -4074,7 +4129,7 @@ private theorem upperPositiveShellDamping_local_variance_lower
     positiveShellDensity_continuous ε
   have hcosh : Continuous
       (fun a : ℝ => Real.cosh ((1 + δ) * a)) := by
-    fun_prop
+    exact Continuous.comp' Real.continuous_cosh (Continuous.const_mul continuous_id' (1 + δ))
   have hosc : Continuous
       (fun a : ℝ => 1 - Real.cos (a * T)) := by
     fun_prop
@@ -4163,10 +4218,10 @@ private theorem upperGammaVarianceDensity_laplace_linear_lower
     positivity
   have hden : 0 < 1 - Real.exp (-x) := by
     have h := Real.exp_lt_one_iff.mpr
-      (show -x < 0 by linarith)
-    linarith
+      (show -x < 0 by linear_combination hx)
+    linear_combination h
   have hdenone : 1 - Real.exp (-x) ≤ 1 := by
-    linarith [Real.exp_pos (-x)]
+    linarith only [Real.exp_pos (-x)]
   have hinv : 1 ≤ (1 - Real.exp (-x))⁻¹ := by
     rw [inv_eq_one_div]
     apply (le_div_iff₀ hden).2
@@ -4206,7 +4261,7 @@ private theorem upperGammaDamping_local_variance_lower
     calc
       1 / (2 * η) = (1 / η) / 2 := by ring
       _ ≤ 1 / η := by
-        linarith [inv_pos.mpr hη]
+        linarith only [inv_pos.mpr hη, hq]
   have hsubset : Ioc p q ⊆ Ioi (0 : ℝ) := by
     intro a ha
     exact hp.trans ha.1
@@ -4223,13 +4278,15 @@ private theorem upperGammaDamping_local_variance_lower
     intro a ha
     have ha0 : 0 < a := hp.trans ha.1
     have halower : 1 / (2 * η) ≤ a := by
-      simpa [p] using! ha.1.le
+      simpa only [p] using! ha.1.le
     have haupper : a ≤ 1 / η := by
-      simpa [q] using! ha.2
+      simpa only [q] using! ha.2
     have hquarter : 1 / (4 * η) ≤ a / 2 := by
       calc
         1 / (4 * η) = (1 / (2 * η)) / 2 := by ring
-        _ ≤ a / 2 := by gcongr
+        _ ≤ a / 2 := by
+          exact div_le_div_of_nonneg_right halower
+              zero_le_two
     have heta : η * a ≤ 1 := by
       calc
         η * a ≤ η * (1 / η) :=
@@ -4239,7 +4296,7 @@ private theorem upperGammaDamping_local_variance_lower
         Real.exp (-η * a) := by
       rw [← Real.exp_neg]
       apply Real.exp_le_exp.mpr
-      linarith
+      linarith only [heta]
     have hmoment :
         (ℓ / 4 + 1 / (4 * η)) *
             (Real.exp 1)⁻¹ ≤
@@ -4262,7 +4319,7 @@ private theorem upperGammaDamping_local_variance_lower
             Real.exp (-η * a) := by
           gcongr
         _ ≤ a ^ 2 * upperGammaMeasureDensity ℓ η a := by
-          linarith
+          linarith only [hgamma, hlinear]
     have haT : |a * T| ≤ 1 := by
       rw [abs_mul, abs_of_pos ha0]
       calc
@@ -4327,8 +4384,8 @@ private theorem upperGammaDamping_local_variance_lower
       _ = ℓ / (2 * η) + 1 / η ^ 2 := by
         field_simp [hℓ.ne', hη.ne']
       _ ≤ ℓ / η + 1 / η ^ 2 := by
-        gcongr
-        linarith
+        refine add_le_add (div_le_div₀ (le_of_lt hℓ) (le_refl ℓ) hη ?_) (le_refl (1 / η ^ 2))
+        linarith only [hη]
   have hidentity :
       (q - p) * C =
         ((ℓ / η + 1 / η ^ 2) /
@@ -4343,7 +4400,13 @@ private theorem upperGammaDamping_local_variance_lower
           ring
     _ ≤ ((ℓ / η + 1 / η ^ 2) /
         (32 * Real.exp 1)) * T ^ 2 := by
-          gcongr
+          exact mul_le_mul_of_nonneg_right
+              (div_le_div_of_nonneg_right hscaled
+                (le_of_lt
+                  (mul_pos
+                    ((by norm_num))
+                    (Real.exp_pos 1))))
+              (Even.pow_nonneg (even_two_mul 1) T)
     _ = (q - p) * C := hidentity.symm
     _ = ∫ a : ℝ in Ioc p q, C :=
       hconstintegral.symm
@@ -4371,9 +4434,9 @@ private theorem eventually_saddleSourceContourDamping_secondBranch_local_coerciv
   change 0 < ε at hε
   intro ℓ hℓ δ hδ T hT
   have hδnonnegative : 0 ≤ δ := by
-    linarith
+    linarith only [hε, hδ]
   have hη : 0 < 2 + δ := by
-    linarith
+    linarith only [hε, hδ]
   have hB : 0 ≤ (ε⁻¹ ^ 3) := by
     positivity
   have hhalf :
@@ -4381,10 +4444,10 @@ private theorem eventually_saddleSourceContourDamping_secondBranch_local_coerciv
     have hb : 0 < 2 * ((ε⁻¹ ^ 3) + 1) := by
       positivity
     apply (div_le_iff₀ hb).2
-    linarith
+    linear_combination hB
   have hTgamma : |T| ≤ 2 + δ := by
     have hsmall := hT.trans hhalf
-    linarith
+    linarith only [hε, hδ, hT, hhalf]
   have hgamma := upperGammaDamping_local_variance_lower
     hℓ hη hTgamma
   have hshell := upperPositiveShellDamping_local_variance_lower
@@ -4414,7 +4477,7 @@ private theorem eventually_saddleSourceContourDamping_secondBranch_local_coerciv
           upperGammaVariance ℓ (2 + δ) * T ^ 2 ≤
         (ℓ / (32 * Real.exp 1)) *
           upperGammaVariance ℓ (2 + δ) * T ^ 2 := by
-            convert! mul_le_mul_of_nonneg_right
+            convert mul_le_mul_of_nonneg_right
               hγcoefficient hγbase using 1 <;> ring
       _ ≤ upperGammaDamping ℓ (2 + δ) T := hgamma
   have heone : 1 ≤ Real.exp 1 :=
@@ -4426,7 +4489,7 @@ private theorem eventually_saddleSourceContourDamping_secondBranch_local_coerciv
       (1 / (100 * Real.exp 1) : ℝ) ≤ 1 / 100 := by
         apply (div_le_iff₀ (by positivity :
           (0 : ℝ) < 100 * Real.exp 1)).2
-        linarith
+        linear_combination heone
       _ ≤ (99 / 100 : ℝ) * (1 / 4) := by
         norm_num
   have hsbase :
@@ -4443,7 +4506,7 @@ private theorem eventually_saddleSourceContourDamping_secondBranch_local_coerciv
         (99 / 100 : ℝ) *
           ((ℓ / 4) *
             upperPositiveShellVariance ε δ * T ^ 2) := by
-            convert! mul_le_mul_of_nonneg_right
+            convert mul_le_mul_of_nonneg_right
               hscoefficient hsbase using 1 <;> ring
       _ ≤ (99 / 100 : ℝ) *
           positiveShellDamping ε ℓ δ T :=
@@ -4453,7 +4516,7 @@ private theorem eventually_saddleSourceContourDamping_secondBranch_local_coerciv
         upperGammaVariance ℓ (2 + δ) +
           upperPositiveShellVariance ε δ := by
     unfold upperSaddleVariance
-    linarith [(hnet δ hδ).2]
+    linarith only [(hnet δ hδ).2, hnet, hδ]
   have hfactor : 0 ≤
       (ℓ / (100 * Real.exp 1)) * T ^ 2 := by
     positivity
@@ -4468,7 +4531,7 @@ private theorem eventually_saddleSourceContourDamping_secondBranch_local_coerciv
           upperGammaVariance ℓ (2 + δ) * T ^ 2 +
         (ℓ / (100 * Real.exp 1)) *
           upperPositiveShellVariance ε δ * T ^ 2 := by
-          convert! mul_le_mul_of_nonneg_left
+          convert mul_le_mul_of_nonneg_left
             hvariance hfactor using 1 <;> ring
     _ ≤ upperGammaDamping ℓ (2 + δ) T +
         (99 / 100 : ℝ) *
@@ -4493,8 +4556,8 @@ private theorem eventually_saddleSourceContourDamping_secondBranch_min_lower_bou
     with ε hε hdom
   change 0 < ε at hε
   intro ℓ hℓ δ hδ T
-  have hδ0 : 0 ≤ δ := by linarith
-  have hη : 0 < 2 + δ := by linarith
+  have hδ0 : 0 ≤ δ := by linarith only [hε, hδ]
+  have hη : 0 < 2 + δ := by linarith only [hε, hδ]
   have hgamma := upperGammaDamping_lower_bound
     hℓ hη T
   have hshell : 0 ≤ (99 / 100 : ℝ) *
@@ -4502,7 +4565,7 @@ private theorem eventually_saddleSourceContourDamping_secondBranch_min_lower_bou
     positivity [positiveShellDamping_nonneg
       (ε := ε) (δ := δ) (T := T) hℓ.le]
   rw [saddleSourceContourDamping_eq_secondBranch]
-  linarith [hdom ℓ hℓ δ hδ T]
+  linarith only [hdom ℓ hℓ δ hδ T, hdom, hℓ, hδ, hgamma, hshell]
 
 private theorem eventually_saddleSource_secondBranch_weighted_integrable :
     ∀ᶠ ε : ℝ in 𝓝[>] (0 : ℝ),
@@ -4523,14 +4586,14 @@ private theorem eventually_saddleSource_secondBranch_weighted_integrable :
   intro ℓ hℓ δ hδ
   let η : ℝ := 2 + δ
   let a : ℝ := ℓ / (8 * Real.exp 1)
-  have hδ0 : 0 ≤ δ := by linarith
+  have hδ0 : 0 ≤ δ := by linarith only [hε, hδ]
   have hη : 0 < η := by
     try dsimp [η]
-    linarith
+    linarith only [hε, hδ]
   have ha : 0 < a := by
     try dsimp [a]
     positivity
-  have hu : -1 < 1 + δ := by linarith
+  have hu : -1 < 1 + δ := by linarith only [hε, hδ]
   have hgaussian :=
     saddleGaussianTailWeight_mul_gaussian_integrable
       (div_pos ha hη)
@@ -4574,8 +4637,7 @@ private theorem eventually_saddleSource_secondBranch_weighted_integrable :
           Real.exp (-(a / η) * T ^ 2) +
         saddleGaussianTailWeight T *
           Real.exp (-a * |T|)
-  linarith [mul_le_mul_of_nonneg_left hexp
-    (saddleGaussianTailWeight_nonneg T)]
+  linarith only [mul_le_mul_of_nonneg_left hexp (saddleGaussianTailWeight_nonneg T), hexp]
 
 private theorem saddleGaussian_weighted_integral_le_rescaled
     {k : ℝ} (hk : 0 < k) :
@@ -4613,7 +4675,7 @@ private theorem saddleGaussian_weighted_integral_le_rescaled
     have hcube : 0 ≤ |T| ^ 3 := by positivity
     have hscaled := mul_le_mul_of_nonneg_right
       hCproduct hcube
-    linarith
+    linarith only [hCone, hscaled]
   have hpoint (T : ℝ) :
       saddleGaussianTailWeight T *
           Real.exp (-k * T ^ 2) ≤
@@ -4695,7 +4757,7 @@ private theorem saddleExponential_weighted_integral_le_rescaled
     have hcube : 0 ≤ |T| ^ 3 := by positivity
     have hscaled := mul_le_mul_of_nonneg_right
       hCproduct hcube
-    linarith
+    linarith only [hCone, hscaled]
   have hpoint (T : ℝ) :
       saddleGaussianTailWeight T *
           Real.exp (-k * |T|) ≤
@@ -4803,10 +4865,10 @@ private theorem eventually_saddleSource_secondBranch_pointwise_gaussian_plus_out
   let t₀ : ℝ := saddleSourceSecondBranchLocalFrequency ε
   let a : ℝ := ℓ / (8 * Real.exp 1)
   let η : ℝ := 2 + δ
-  have hδ0 : 0 ≤ δ := by linarith
+  have hδ0 : 0 ≤ δ := by linarith only [hε, hδ]
   have hη : 0 < η := by
     try dsimp [η]
-    linarith
+    linarith only [hε, hδ]
   have ha : 0 < a := by
     try dsimp [a]
     positivity
@@ -4820,7 +4882,7 @@ private theorem eventually_saddleSource_secondBranch_pointwise_gaussian_plus_out
     apply (div_le_iff₀
       (show (0 : ℝ) < 2 * ((ε⁻¹ ^ 3) + 1) by
         positivity)).2
-    linarith
+    linarith only [hB]
   have hw : 0 ≤ saddleGaussianTailWeight T :=
     saddleGaussianTailWeight_nonneg T
   by_cases hinside : |T| ≤ t₀
@@ -4836,7 +4898,7 @@ private theorem eventually_saddleSource_secondBranch_pointwise_gaussian_plus_out
               ε ℓ δ * T ^ 2) := by
       apply Real.exp_le_exp.mpr
       unfold saddleSourceSecondBranchGaussianRate
-      linarith
+      linear_combination hquadratic
     have hfirst := mul_le_mul_of_nonneg_left hlocalexp hw
     have houter : 0 ≤
         Real.exp
@@ -4850,7 +4912,7 @@ private theorem eventually_saddleSource_secondBranch_pointwise_gaussian_plus_out
                 (-saddleSourceSecondBranchGammaLinearRate
                   ℓ * |T|)) := by
       positivity
-    linarith
+    linear_combination hfirst + houter
   · have houtside : t₀ ≤ |T| :=
       le_of_not_ge hinside
     have hsquare : t₀ ^ 2 ≤ T ^ 2 := by
@@ -4894,7 +4956,7 @@ private theorem eventually_saddleSource_secondBranch_pointwise_gaussian_plus_out
       rw [saddleSourceContourDamping_eq_secondBranch]
       have hfull := hdom ℓ hℓ δ hδ T
       try dsimp [a, η] at hgamma ⊢
-      linarith
+      linear_combination hbarrier + hgamma + hfull
     have hmin := saddle_exp_neg_mul_min_le_add
       (a := a) (x := T ^ 2 / η) (y := |T|) ha.le
     have hexp :
@@ -4917,7 +4979,7 @@ private theorem eventually_saddleSource_secondBranch_pointwise_gaussian_plus_out
             (-(saddleSourceSecondBranchOuterBarrier ε ℓ δ +
               a * min (T ^ 2 / η) |T|)) := by
             apply Real.exp_le_exp.mpr
-            linarith
+            linear_combination hcombined
         _ = Real.exp
               (-saddleSourceSecondBranchOuterBarrier ε ℓ δ) *
             Real.exp
@@ -4950,7 +5012,7 @@ private theorem eventually_saddleSource_secondBranch_pointwise_gaussian_plus_out
             (-saddleSourceSecondBranchGaussianRate
               ε ℓ δ * T ^ 2) := by
       positivity
-    linarith
+    linear_combination hweighted + hfirst
 
 private theorem eventually_saddleSource_secondBranch_weighted_tail_explicit :
     ∀ᶠ ε : ℝ in 𝓝[>] (0 : ℝ),
@@ -4999,8 +5061,8 @@ private theorem eventually_saddleSource_secondBranch_weighted_tail_explicit :
   let q : ℝ := saddleSourceSecondBranchGammaGaussianRate ℓ δ
   let a : ℝ := saddleSourceSecondBranchGammaLinearRate ℓ
   let b : ℝ := saddleSourceSecondBranchOuterBarrier ε ℓ δ
-  have hδ0 : 0 ≤ δ := by linarith
-  have hη : 0 < 2 + δ := by linarith
+  have hδ0 : 0 ≤ δ := by linarith only [hε, hδ]
+  have hη : 0 < 2 + δ := by linarith only [hε, hδ]
   have hV := hvariance ℓ hℓ δ hδ
   have hkpos : 0 < k := by
     try dsimp [k, saddleSourceSecondBranchGaussianRate]
@@ -5294,8 +5356,8 @@ private theorem saddle_sqrt_le_one_add
     Real.sqrt x ≤ 1 + x := by
   apply Real.sqrt_le_iff.mpr
   constructor
-  · linarith
-  · linarith [sq_nonneg x]
+  · linear_combination hx
+  · linarith only [sq_nonneg x, hx]
 
 private theorem saddle_inverse_sqrt_cube_le
     {q : ℝ} (hq : 0 < q) :
@@ -5313,12 +5375,12 @@ private theorem saddle_inverse_sqrt_cube_le
   have hidentity :
       ((s ^ 3)⁻¹) ^ 2 = (6 / q) ^ 3 := by
     field_simp [hq.ne', hs.ne']
-    linarith [hcubed]
+    linarith only [hcubed]
   have hnonnegative : 0 ≤ (s ^ 3)⁻¹ := by
     positivity
   change (s ^ 3)⁻¹ ≤ 1 + (6 / q) ^ 3
   rw [← hidentity]
-  linarith [sq_nonneg ((s ^ 3)⁻¹ - (1 / 2 : ℝ))]
+  linarith only [sq_nonneg ((s ^ 3)⁻¹ - (1 / 2 : ℝ))]
 
 private theorem saddleSecondBranch_gammaWeightedCoefficient_le
     {q η C : ℝ}
@@ -5331,7 +5393,7 @@ private theorem saddleSecondBranch_gammaWeightedCoefficient_le
       Real.sqrt (Real.pi / (q / 2)) ≤
         (2 * (1 + (6 * C) ^ 3) *
           (1 + 2 * Real.pi * C)) * η ^ 4 := by
-  have hη0 : 0 ≤ η := by linarith
+  have hη0 : 0 ≤ η := by linear_combination hη
   have hηthree : 1 ≤ η ^ 3 := by
     simpa only [one_pow] using!
       (pow_le_pow_left₀
@@ -5342,12 +5404,15 @@ private theorem saddleSecondBranch_gammaWeightedCoefficient_le
         1 + (6 / q) ^ 3 := by
     apply max_le
     · have : 0 ≤ (6 / q) ^ 3 := by positivity
-      linarith
+      linear_combination this
     · exact hinverse
   have hqscaled : 6 / q ≤ 6 * C * η := by
     calc
       6 / q = 6 * (1 / q) := by ring
-      _ ≤ 6 * (C * η) := by gcongr
+      _ ≤ 6 * (C * η) := by
+        exact mul_le_mul_of_nonneg_left hrate
+            (le_of_lt
+              ((by norm_num)))
       _ = 6 * C * η := by ring
   have hmaxpoly :
       max (1 : ℝ) ((Real.sqrt (q / 6) ^ 3)⁻¹) ≤
@@ -5356,11 +5421,18 @@ private theorem saddleSecondBranch_gammaWeightedCoefficient_le
       max (1 : ℝ) ((Real.sqrt (q / 6) ^ 3)⁻¹) ≤
           1 + (6 / q) ^ 3 := hmax
       _ ≤ 1 + (6 * C * η) ^ 3 := by
-        gcongr
+        exact add_le_add (le_refl 1)
+            (pow_le_pow_left₀
+              (le_of_lt
+                (div_pos
+                  ((by norm_num))
+                  hq))
+              hqscaled 3)
       _ ≤ (1 + (6 * C) ^ 3) * η ^ 3 := by
-        linarith [mul_nonneg
-          (show 0 ≤ (6 * C) ^ 3 by positivity)
-          (show 0 ≤ η ^ 3 - 1 by linarith)]
+        linarith only [
+          mul_nonneg (show 0 ≤ (6 * C) ^ 3 by positivity) (show 0 ≤ η ^ 3 - 1 by linarith),
+          hηthree
+        ]
   have hpiscaled :
       Real.pi / (q / 2) ≤
         2 * Real.pi * C * η := by
@@ -5369,7 +5441,11 @@ private theorem saddleSecondBranch_gammaWeightedCoefficient_le
           (2 * Real.pi) * (1 / q) := by
         field_simp [hq.ne']
       _ ≤ (2 * Real.pi) * (C * η) := by
-        gcongr
+        exact mul_le_mul_of_nonneg_left hrate
+            (le_of_lt
+              (mul_pos
+                (zero_lt_two)
+                Real.pi_pos))
       _ = 2 * Real.pi * C * η := by ring
   have hsqrt :
       Real.sqrt (Real.pi / (q / 2)) ≤
@@ -5379,9 +5455,9 @@ private theorem saddleSecondBranch_gammaWeightedCoefficient_le
           1 + Real.pi / (q / 2) :=
         saddle_sqrt_le_one_add (by positivity)
       _ ≤ 1 + 2 * Real.pi * C * η := by
-        linarith
+        linear_combination hpiscaled
       _ ≤ (1 + 2 * Real.pi * C) * η := by
-        linarith
+        linear_combination hη
   calc
     2 * max (1 : ℝ)
         ((Real.sqrt (q / 6) ^ 3)⁻¹) *
@@ -5412,22 +5488,33 @@ private theorem saddleSecondBranch_linearWeightedCoefficient_le
   have hbase : 6 / a ≤ 6 * C := by
     calc
       6 / a = 6 * (1 / a) := by ring
-      _ ≤ 6 * C := by gcongr
+      _ ≤ 6 * C := by
+        exact mul_le_mul_of_nonneg_left hrate
+            (le_of_lt
+              ((by norm_num)))
   have hmax :
       max (1 : ℝ) (((a / 6) ^ 3)⁻¹) ≤
         1 + (6 * C) ^ 3 := by
     rw [hidentity]
     apply max_le
     · have : 0 ≤ (6 * C) ^ 3 := by positivity
-      linarith
+      linear_combination this
     · have hcubes : (6 / a) ^ 3 ≤ (6 * C) ^ 3 := by
-        gcongr
-      linarith
+        exact pow_le_pow_left₀
+            (le_of_lt
+              (div_pos
+                ((by norm_num))
+                ha))
+            hbase 3
+      linear_combination hcubes
   have hlinear : 2 / (a / 2) ≤ 4 * C := by
     calc
       2 / (a / 2) = 4 * (1 / a) := by
         field_simp [ha.ne']; ring
-      _ ≤ 4 * C := by gcongr
+      _ ≤ 4 * C := by
+        exact mul_le_mul_of_nonneg_left hrate
+            (le_of_lt
+              ((by norm_num)))
   calc
     2 * max (1 : ℝ) (((a / 6) ^ 3)⁻¹) *
         (2 / (a / 2)) ≤
@@ -5437,8 +5524,7 @@ private theorem saddleSecondBranch_linearWeightedCoefficient_le
       have hcoefficient :
           0 ≤ 8 * C * (1 + (6 * C) ^ 3) := by
         positivity
-      linarith [mul_le_mul_of_nonneg_left
-        hηfour hcoefficient]
+      linarith only [mul_le_mul_of_nonneg_left hηfour hcoefficient, hηfour, hcoefficient]
 
 private noncomputable def saddleSourceSecondBranchMomentCoefficient : ℝ :=
   let C : ℝ := 8 * Real.exp 1
@@ -5494,9 +5580,12 @@ private theorem saddleSourceSecondBranch_outerMoment_le
           (Real.exp_pos 1).ne', hηpositive.ne']
       _ ≤ C * η := by
         apply (div_le_iff₀ hℓpositive).2
-        linarith [mul_nonneg
-          (mul_nonneg hC.le hηpositive.le)
-          (show 0 ≤ ℓ - 1 by linarith)]
+        linarith only [
+          mul_nonneg (mul_nonneg hC.le hηpositive.le) (show 0 ≤ ℓ - 1 by linarith),
+          hℓ,
+          hηpositive,
+          hC
+        ]
   have harate : 1 / a ≤ C := by
     calc
       1 / a = C / ℓ := by
@@ -5506,8 +5595,7 @@ private theorem saddleSourceSecondBranch_outerMoment_le
           (Real.exp_pos 1).ne']
       _ ≤ C := by
         apply (div_le_iff₀ hℓpositive).2
-        linarith [mul_nonneg hC.le
-          (show 0 ≤ ℓ - 1 by linarith)]
+        linarith only [mul_nonneg hC.le (show 0 ≤ ℓ - 1 by linarith), hℓ, hC]
   have hgamma := saddleSecondBranch_gammaWeightedCoefficient_le
     hq hη hC hqrate
   have hlinear := saddleSecondBranch_linearWeightedCoefficient_le
@@ -5527,7 +5615,7 @@ private theorem saddleSourceSecondBranch_outerMoment_le
       (2 * (1 + (6 * C) ^ 3) *
           (1 + 2 * Real.pi * C) +
         8 * C * (1 + (6 * C) ^ 3)) * η ^ 4
-  linarith
+  linear_combination hgamma + hlinear
 
 private noncomputable def saddleSourceSecondBranchVarianceCoefficient (ε : ℝ) : ℝ :=
   2 + ((ε⁻¹ ^ 3) + 1) ^ 2 * shellWeight ε
@@ -5551,13 +5639,13 @@ private theorem eventually_saddleSourceGaussianVariance_secondBranch_upper :
     with ε hε hvariance
   change 0 < ε at hε
   intro ℓ hℓ δ hδ
-  have hℓpositive : 0 < ℓ := by linarith
-  have hδ0 : 0 ≤ δ := by linarith
+  have hℓpositive : 0 < ℓ := by linarith only [hℓ]
+  have hδ0 : 0 ≤ δ := by linarith only [hε, hδ]
   let η : ℝ := 2 + δ
   have hηtwo : 2 ≤ η := by
     try dsimp [η]
-    linarith
-  have hη : 0 < η := by linarith
+    linarith only [hε, hδ]
+  have hη : 0 < η := by linarith only [hε, hδ]
   have hB : 0 ≤ (ε⁻¹ ^ 3) := by
     positivity
   have hexp : 1 ≤
@@ -5567,15 +5655,15 @@ private theorem eventually_saddleSourceGaussianVariance_secondBranch_upper :
   have hfirst : 1 / (2 * η) ≤ (1 : ℝ) := by
     apply (div_le_iff₀
       (show 0 < 2 * η by positivity)).2
-    linarith
+    linarith only [hε, hδ]
   have hden : 0 < ℓ * η ^ 2 := by positivity
   have hsecond : 1 / (ℓ * η ^ 2) ≤ (1 : ℝ) := by
     apply (div_le_iff₀ hden).2
     have hηsquare : 1 ≤ η ^ 2 := by
-      linarith [sq_nonneg (η - 1)]
+      linarith only [sq_nonneg (η - 1), hε, hδ]
     have hscaled := mul_le_mul_of_nonneg_right
       hℓ (sq_nonneg η)
-    linarith
+    linarith only [hηsquare, hscaled]
   have hshell :=
     (upperPositiveShellVariance_bounds hε hδ0).2
   have hfull := (hvariance ℓ hℓpositive δ hδ).2
@@ -5590,9 +5678,9 @@ private theorem eventually_saddleSourceGaussianVariance_secondBranch_upper :
         ((ε⁻¹ ^ 3) + 1) ^ 2 *
           shellWeight ε *
             Real.exp (((ε⁻¹ ^ 3) + 1) * δ) := by
-    convert! hshell using 1; ring_nf
+    convert hshell using 1; ring_nf
   unfold saddleSourceSecondBranchVarianceCoefficient
-  linarith
+  linarith only [hexp, hfirst, hsecond, hsource, hshell']
 
 private theorem eventually_saddleSource_secondBranch_sqrtVariance_le :
     ∀ᶠ ε : ℝ in 𝓝[>] (0 : ℝ),
@@ -5613,7 +5701,7 @@ private theorem eventually_saddleSource_secondBranch_sqrtVariance_le :
   let C : ℝ := saddleSourceSecondBranchVarianceCoefficient ε
   have hC : 0 < C :=
     saddleSourceSecondBranchVarianceCoefficient_pos ε
-  have hℓpositive : 0 < ℓ := by linarith
+  have hℓpositive : 0 < ℓ := by linear_combination hℓ
   have hsource := hupper ℓ hℓ δ hδ
   have hscaled := mul_le_mul_of_nonneg_left
     hsource hℓpositive.le
@@ -5662,7 +5750,7 @@ theorem tendsto_saddleSourceSecondBranchLocalTailMajorant :
   have hexp := Real.tendsto_exp_atBot.comp hnegative
   have hscaled := hexp.const_mul
     (2 * Real.sqrt (400 * Real.exp 1 * Real.pi))
-  convert! hscaled using 1
+  convert hscaled using 1
   · funext ℓ
     congr 2
     ring
@@ -5741,11 +5829,11 @@ private theorem eventually_saddleSource_secondBranch_uniform_tail :
   let V : ℝ := saddleSourceGaussianVariance ε ℓ (1 + δ)
   let z : ℝ := ℓ ^ (1 / 12 : ℝ)
   let η : ℝ := 2 + δ
-  have hℓpositive : 0 < ℓ := by linarith
-  have hδ0 : 0 ≤ δ := by linarith
+  have hℓpositive : 0 < ℓ := by linear_combination hℓ
+  have hδ0 : 0 ≤ δ := by linarith only [hε, hδ]
   have hη : 1 ≤ η := by
     try dsimp [η]
-    linarith
+    linarith only [hε, hδ]
   have hVfloor : V₀ ≤ V := by
     try dsimp [V₀, V]
     exact hfloor ℓ hℓpositive δ hδ
@@ -5755,11 +5843,11 @@ private theorem eventually_saddleSource_secondBranch_uniform_tail :
     positivity
   have hscale : 600 * Real.exp 1 ≤ ℓ * V₀ := by
     have h := (div_le_iff₀ hV₀).mp hone
-    linarith
+    exact h
   have hfullscale : 600 * Real.exp 1 ≤ ℓ * V := by
     have h := mul_le_mul_of_nonneg_left
       hVfloor hℓpositive.le
-    linarith
+    linear_combination hscale + h
   have hk :
       6 ≤ saddleSourceSecondBranchGaussianRate ε ℓ δ := by
     unfold saddleSourceSecondBranchGaussianRate
@@ -5769,8 +5857,8 @@ private theorem eventually_saddleSource_secondBranch_uniform_tail :
     have hgoal :
         (6 : ℝ) ≤ (ℓ * V) / (100 * Real.exp 1) := by
       apply (le_div_iff₀ hden).2
-      linarith
-    convert! hgoal using 1; ring
+      linear_combination hfullscale
+    convert hgoal using 1; ring
   have hsource := htail ℓ hℓpositive δ hδ z hz hk
   have hpower : z ^ 2 = ℓ ^ (1 / 6 : ℝ) := by
     try dsimp [z]
@@ -5860,7 +5948,7 @@ private theorem eventually_saddleSource_secondBranch_uniform_tail :
             (-saddleSourceContourDamping
               ε ℓ (1 + δ) T)) ≤ _ at hsource
   dsimp only [M] at houterterm
-  linarith
+  linear_combination hlocalterm + houterterm + hsource
 
 end
 
@@ -5947,7 +6035,7 @@ private theorem saddleGaussian_fullLine_error_le_central_add_tails
     _ ≤ ‖∫ T : ℝ in s, (F T - G T)‖ +
           ((∫ T : ℝ in tail, ‖F T‖) +
             (∫ T : ℝ in tail, ‖G T‖)) := by
-          gcongr
+          exact add_le_add (le_refl ‖∫ (T : ℝ) in s, F T - G T‖) htailbound
     _ = ‖∫ T : ℝ in Icc (-R) R, (F T - G T)‖ +
         (∫ T : ℝ in saddleGaussianTailSet R, ‖F T‖) +
         (∫ T : ℝ in saddleGaussianTailSet R, ‖G T‖) := by
@@ -5993,12 +6081,12 @@ private theorem saddleSource_scaled_tail_lt_relative_gaussian
         Real.sqrt (2 * Real.pi) /
           Real.sqrt (ℓ * saddleSourceGaussianVariance ε ℓ u) := by
     apply (eq_div_iff hs.ne').mpr
-    linarith
+    linear_combination hmass
   have hW :
       W < κ /
         Real.sqrt (ℓ * saddleSourceGaussianVariance ε ℓ u) := by
     apply (lt_div_iff₀ hs).mpr
-    linarith
+    linear_combination hnormalized
   calc
     X ≤ C * A * W := hbound
     _ < C * A *
@@ -6102,7 +6190,7 @@ private theorem exists_saddleSourceCenteredMinusIntegrand_weighted_tail_integral
   obtain ⟨C, hC, hpoly⟩ := exists_minusPolynomial_uniform_weighted_bound hε
   exact ⟨C, hC, fun ℓ hℓ u hu v R hweighted =>
     SaddleSign.centeredIntegrand_weighted_tail_integral_le .minus
-      hε hℓ (by linarith) horder (hpoly u hu) v R hweighted⟩
+      hε hℓ (by linarith only [hε, hu]) horder (hpoly u hu) v R hweighted⟩
 
 private theorem SaddleSign.gaussianIntegrand_tail_norm_eq (s : SaddleSign)
     (ε ℓ u R : ℝ) :
@@ -6230,8 +6318,8 @@ private theorem saddleSourceGaussianKernel_normalized_tail_le
     positivity
   have hk : 6 ≤ k := by
     try dsimp [k, V]
-    linarith
-  have hkpos : 0 < k := by linarith
+    linarith only [hlarge]
+  have hkpos : 0 < k := by linear_combination hk
   have hR : 0 ≤ R := by
     try dsimp [R]
     positivity
@@ -6244,12 +6332,11 @@ private theorem saddleSourceGaussianKernel_normalized_tail_le
     intro T hT
     have hw : 1 ≤ saddleGaussianTailWeight T := by
       unfold saddleGaussianTailWeight
-      linarith [pow_nonneg (abs_nonneg T) 3]
+      linarith only [pow_nonneg (abs_nonneg T) 3]
     unfold saddleSourceGaussianKernel
     change Real.exp (-k * T ^ 2) ≤
       saddleGaussianTailWeight T * Real.exp (-k * T ^ 2)
-    linarith [mul_le_mul_of_nonneg_right hw
-      (Real.exp_pos (-k * T ^ 2)).le]
+    linarith only [mul_le_mul_of_nonneg_right hw (Real.exp_pos (-k * T ^ 2)).le, hw]
   have hcompare := setIntegral_mono_on
     hgaussian.integrableOn hweighted.integrableOn
       (saddleGaussianTailSet_measurable R) hpoint
@@ -6329,7 +6416,7 @@ private theorem tendsto_saddleSourceGaussianNormalizedTailMajorant :
       atTop atBot := by
     have h := hpower.const_mul_atTop_of_neg
       (by norm_num : -(1 / 8 : ℝ) < 0)
-    convert! h using 1
+    convert h using 1
     funext x
     ring
   have hexp := Real.tendsto_exp_atBot.comp hnegative
@@ -6390,10 +6477,10 @@ private theorem eventually_saddleSource_firstBranch_uniform_gaussian_tail :
   let z : ℝ := (ℓ * η) ^ (1 / 12 : ℝ)
   have hη : 0 < η := by
     try dsimp [η]
-    linarith
+    linear_combination hulower
   have hηupper : η ≤ U := by
     try dsimp [η, U]
-    linarith
+    linear_combination huupper
   have hV : 0 < V :=
     hvariance ℓ hℓ u hulower huupper
   have hmargin' :
@@ -6401,7 +6488,7 @@ private theorem eventually_saddleSource_firstBranch_uniform_gaussian_tail :
         0 ≤ (1 - 10 * ε * (1 + a)) := by
     intro a ha
     have h := hmargin a ha
-    linarith
+    linear_combination hεsmall + hε + h
   have hvar :=
     upperFirstBranch_saddleSourceGaussianVariance_scaled_lower_bound
       hε hεsmall hℓ hulower huupper horder hmargin'
@@ -6412,16 +6499,16 @@ private theorem eventually_saddleSource_firstBranch_uniform_gaussian_tail :
     exact hvar.trans hproduct
   have hthreshold' : 6 * U ≤ ℓ * ε := by
     have h := (div_le_iff₀ hε).mp hthreshold
-    linarith
+    exact h
   have hlarge : 12 ≤ ℓ * V := by
     have hproduct := mul_le_mul_of_nonneg_left
       hvarupper hℓ.le
     have hmain : U * 12 ≤ U * (ℓ * V) := by
-      linarith
+      linarith only [hthreshold', hproduct]
     by_contra hnot
     have hlt : ℓ * V < 12 := lt_of_not_ge hnot
     have hcontradiction := mul_lt_mul_of_pos_left hlt hU
-    linarith
+    linarith only [hthreshold', hproduct, hcontradiction]
   have hz : 0 ≤ z := by
     try dsimp [z]
     exact Real.rpow_nonneg
@@ -6490,7 +6577,7 @@ private theorem eventually_saddleSource_secondBranch_uniform_gaussian_tail :
   have hlarge : 12 ≤ ℓ * V := by
     have hbase := (div_le_iff₀ hV₀).mp hthreshold
     calc
-      12 ≤ ℓ * V₀ := by linarith
+      12 ≤ ℓ * V₀ := by exact hbase
       _ ≤ ℓ * V :=
         mul_le_mul_of_nonneg_left hVlower hℓ.le
   have hz : 0 ≤ z := by
@@ -6569,7 +6656,7 @@ private theorem eventually_saddleSourceFirstBranch_sourceL1Tails :
       (10 * Real.log (1 / ε)), 0 ≤ (1 - 10 * ε * (1 + a)) := by
     intro a ha
     have h := hmargin a ha
-    linarith
+    linear_combination hεsmall + hε + h
   obtain ⟨Cp, hCp, hplus⟩ :=
     exists_saddleSourceCenteredPlusIntegrand_weighted_tail_integral_bound
       hε horder
@@ -6595,14 +6682,14 @@ private theorem eventually_saddleSourceFirstBranch_sourceL1Tails :
           saddleGaussianTailWeight T *
             Real.exp (-saddleSourceContourDamping ε ℓ u T)) <
           κ / Cp := by
-    simpa [R, V, saddleSourceFirstBranchCentralRadius] using! hp u hu huupper hstar
+    simpa only [R, V, saddleSourceFirstBranchCentralRadius] using! hp u hu huupper hstar
   have hmnormal :
       Real.sqrt (ℓ * V) *
         (∫ T : ℝ in saddleGaussianTailSet R,
           saddleGaussianTailWeight T *
             Real.exp (-saddleSourceContourDamping ε ℓ u T)) <
           κ / Cm := by
-    simpa [R, V, saddleSourceFirstBranchCentralRadius] using! hm u hu huupper hstar
+    simpa only [R, V, saddleSourceFirstBranchCentralRadius] using! hm u hu huupper hstar
   constructor
   · have hden : 0 <
         ‖plusPolynomial ε (Complex.I * (u : ℂ))‖ :=
@@ -6623,7 +6710,7 @@ private theorem eventually_saddleSourceFirstBranch_sourceL1Tails :
             (∫ T : ℝ in saddleGaussianTailSet R,
               saddleGaussianTailWeight T *
                 Real.exp (-saddleSourceContourDamping ε ℓ u T))) := by
-          gcongr
+          exact mul_le_mul_of_nonneg_left hbound (le_of_lt (Real.sqrt_pos_of_pos (mul_pos hℓ hV)))
       _ = Cp * ‖plusPolynomial ε (Complex.I * (u : ℂ))‖ *
           (Real.sqrt (ℓ * V) *
             (∫ T : ℝ in saddleGaussianTailSet R,
@@ -6632,7 +6719,7 @@ private theorem eventually_saddleSourceFirstBranch_sourceL1Tails :
           ring
       _ < Cp * ‖plusPolynomial ε (Complex.I * (u : ℂ))‖ *
           (κ / Cp) := by
-          gcongr
+          exact mul_lt_mul_of_pos_left hpnormal (mul_pos hCp hden)
       _ = κ * ‖plusPolynomial ε (Complex.I * (u : ℂ))‖ := by
           field_simp [hCp.ne']
   · intro huminus
@@ -6642,7 +6729,7 @@ private theorem eventually_saddleSourceFirstBranch_sourceL1Tails :
       have hnorm :=
         minusPolynomial_imaginary_norm_ge_three_beta
           hε huminus
-      linarith
+      linarith only [hε, hnorm]
     have hbound := hminus ℓ hℓ u huminus v R hweighted
     change
       Real.sqrt (ℓ * V) *
@@ -6658,7 +6745,7 @@ private theorem eventually_saddleSourceFirstBranch_sourceL1Tails :
             (∫ T : ℝ in saddleGaussianTailSet R,
               saddleGaussianTailWeight T *
                 Real.exp (-saddleSourceContourDamping ε ℓ u T))) := by
-          gcongr
+          exact mul_le_mul_of_nonneg_left hbound (le_of_lt (Real.sqrt_pos_of_pos (mul_pos hℓ hV)))
       _ = Cm * ‖minusPolynomial ε (Complex.I * (u : ℂ))‖ *
           (Real.sqrt (ℓ * V) *
             (∫ T : ℝ in saddleGaussianTailSet R,
@@ -6667,7 +6754,7 @@ private theorem eventually_saddleSourceFirstBranch_sourceL1Tails :
           ring
       _ < Cm * ‖minusPolynomial ε (Complex.I * (u : ℂ))‖ *
           (κ / Cm) := by
-          gcongr
+          exact mul_lt_mul_of_pos_left hmnormal (mul_pos hCm hden)
       _ = κ * ‖minusPolynomial ε (Complex.I * (u : ℂ))‖ := by
           field_simp [hCm.ne']
 
@@ -6706,7 +6793,7 @@ private theorem eventually_saddleSourceFirstBranch_gaussianL1Tails :
   have hkernel :
       s * (∫ T : ℝ in saddleGaussianTailSet R,
         saddleSourceGaussianKernel ε ℓ u T) < κ := by
-    simpa [s, R, saddleSourceFirstBranchCentralRadius] using! hℓ u hu huupper hstar
+    simpa only [s, R, saddleSourceFirstBranchCentralRadius] using! hℓ u hu huupper hstar
   constructor
   · have hden : 0 <
         ‖plusPolynomial ε (Complex.I * (u : ℂ))‖ :=
@@ -6717,7 +6804,7 @@ private theorem eventually_saddleSourceFirstBranch_gaussianL1Tails :
         ‖saddleSourceGaussianPlusIntegrand ε ℓ u T‖) <
       κ * ‖plusPolynomial ε (Complex.I * (u : ℂ))‖
     rw [saddleSourceGaussianPlusIntegrand_tail_norm_eq]
-    linarith [mul_lt_mul_of_pos_left hkernel hden]
+    linarith only [mul_lt_mul_of_pos_left hkernel hden, hkernel, hden]
   · intro huminus
     have hden : 0 <
         ‖minusPolynomial ε (Complex.I * (u : ℂ))‖ := by
@@ -6725,13 +6812,13 @@ private theorem eventually_saddleSourceFirstBranch_gaussianL1Tails :
       have hnorm :=
         minusPolynomial_imaginary_norm_ge_three_beta
           hε huminus
-      linarith
+      linarith only [hε, hnorm]
     change s *
       (∫ T : ℝ in saddleGaussianTailSet R,
         ‖saddleSourceGaussianMinusIntegrand ε ℓ u T‖) <
       κ * ‖minusPolynomial ε (Complex.I * (u : ℂ))‖
     rw [saddleSourceGaussianMinusIntegrand_tail_norm_eq]
-    linarith [mul_lt_mul_of_pos_left hkernel hden]
+    linarith only [mul_lt_mul_of_pos_left hkernel hden, hkernel, hden]
 
 private theorem eventually_saddleSourceFirstBranch_fullGaussianErrors :
     ∀ᶠ ε : ℝ in 𝓝[>] (0 : ℝ),
@@ -6817,7 +6904,7 @@ private theorem eventually_saddleSourceFirstBranch_fullGaussianErrors :
       _ < ‖plusPolynomial ε (Complex.I * (u : ℂ))‖ *
           (∫ T : ℝ,
             saddleSourceGaussianKernel ε ℓ u T) := by
-        linarith [mul_pos hden hG]
+        linarith only [mul_pos hden hG, hG, hden]
   · intro huminus
     have hden : 0 <
         ‖minusPolynomial ε (Complex.I * (u : ℂ))‖ := by
@@ -6825,7 +6912,7 @@ private theorem eventually_saddleSourceFirstBranch_fullGaussianErrors :
       have hnorm :=
         minusPolynomial_imaginary_norm_ge_three_beta
           hε huminus
-      linarith
+      linarith only [hε, hnorm]
     have hfull :=
       saddleGaussian_fullLine_error_lt_of_central_and_normalized_tails
         (ε := ε) (ℓ := ℓ) (u := u) (R := R)
@@ -6859,7 +6946,7 @@ private theorem eventually_saddleSourceFirstBranch_fullGaussianErrors :
       _ < ‖minusPolynomial ε (Complex.I * (u : ℂ))‖ *
           (∫ T : ℝ,
             saddleSourceGaussianKernel ε ℓ u T) := by
-        linarith [mul_pos hden hG]
+        linarith only [mul_pos hden hG, hG, hden]
 
 private theorem eventually_saddleSourceSecondBranch_sourceL1Tails_of_uniform_tail
     (hweighted :
@@ -6935,10 +7022,10 @@ private theorem eventually_saddleSourceSecondBranch_sourceL1Tails_of_uniform_tai
   let V : ℝ := saddleSourceGaussianVariance ε ℓ u
   have hu : -1 < u := by
     try dsimp [u]
-    linarith
+    linarith only [hε, hδ]
   have huminus : 1 + ε / 4 ≤ u := by
     try dsimp [u]
-    linarith
+    linarith only [hε, hδ]
   have hV : 0 < V := by
     try dsimp [V, u]
     exact hvariance ℓ hℓ δ hδ
@@ -6978,7 +7065,7 @@ private theorem eventually_saddleSourceSecondBranch_sourceL1Tails_of_uniform_tai
             (∫ T : ℝ in saddleGaussianTailSet R,
               saddleGaussianTailWeight T *
                 Real.exp (-saddleSourceContourDamping ε ℓ u T))) := by
-          gcongr
+          exact mul_le_mul_of_nonneg_left hbound (le_of_lt (Real.sqrt_pos_of_pos (mul_pos hℓ hV)))
       _ = Cp * ‖plusPolynomial ε (Complex.I * (u : ℂ))‖ *
           (Real.sqrt (ℓ * V) *
             (∫ T : ℝ in saddleGaussianTailSet R,
@@ -6987,7 +7074,7 @@ private theorem eventually_saddleSourceSecondBranch_sourceL1Tails_of_uniform_tai
           ring
       _ < Cp * ‖plusPolynomial ε (Complex.I * (u : ℂ))‖ *
           (κ / Cp) := by
-          gcongr
+          exact mul_lt_mul_of_pos_left hpnormal (mul_pos hCp hden)
       _ = κ * ‖plusPolynomial ε (Complex.I * (u : ℂ))‖ := by
           field_simp [hCp.ne']
   · have hden : 0 <
@@ -6996,7 +7083,7 @@ private theorem eventually_saddleSourceSecondBranch_sourceL1Tails_of_uniform_tai
       have hnorm :=
         minusPolynomial_imaginary_norm_ge_three_beta
           hε huminus
-      linarith
+      linarith only [hε, hnorm]
     have hbound := hminus ℓ hℓ u huminus v R hweighted'
     change
       Real.sqrt (ℓ * V) *
@@ -7012,7 +7099,7 @@ private theorem eventually_saddleSourceSecondBranch_sourceL1Tails_of_uniform_tai
             (∫ T : ℝ in saddleGaussianTailSet R,
               saddleGaussianTailWeight T *
                 Real.exp (-saddleSourceContourDamping ε ℓ u T))) := by
-          gcongr
+          exact mul_le_mul_of_nonneg_left hbound (le_of_lt (Real.sqrt_pos_of_pos (mul_pos hℓ hV)))
       _ = Cm * ‖minusPolynomial ε (Complex.I * (u : ℂ))‖ *
           (Real.sqrt (ℓ * V) *
             (∫ T : ℝ in saddleGaussianTailSet R,
@@ -7021,7 +7108,7 @@ private theorem eventually_saddleSourceSecondBranch_sourceL1Tails_of_uniform_tai
           ring
       _ < Cm * ‖minusPolynomial ε (Complex.I * (u : ℂ))‖ *
           (κ / Cm) := by
-          gcongr
+          exact mul_lt_mul_of_pos_left hmnormal (mul_pos hCm hden)
       _ = κ * ‖minusPolynomial ε (Complex.I * (u : ℂ))‖ := by
           field_simp [hCm.ne']
 
@@ -7062,14 +7149,14 @@ private theorem eventually_saddleSourceSecondBranch_gaussianL1Tails :
     Real.sqrt (ℓ * saddleSourceGaussianVariance ε ℓ u)
   have hu : -1 < u := by
     try dsimp [u]
-    linarith
+    linarith only [hε, hδ]
   have huminus : 1 + ε / 4 ≤ u := by
     try dsimp [u]
-    linarith
+    linarith only [hε, hδ]
   have hkernel :
       s * (∫ T : ℝ in saddleGaussianTailSet R,
         saddleSourceGaussianKernel ε ℓ u T) < κ := by
-    simpa [s, R, u, saddleSourceSecondBranchCentralRadius] using! hℓ δ hδ
+    simpa only [s, R, u, saddleSourceSecondBranchCentralRadius] using! hℓ δ hδ
   constructor
   · have hden : 0 <
         ‖plusPolynomial ε (Complex.I * (u : ℂ))‖ :=
@@ -7080,20 +7167,20 @@ private theorem eventually_saddleSourceSecondBranch_gaussianL1Tails :
         ‖saddleSourceGaussianPlusIntegrand ε ℓ u T‖) <
       κ * ‖plusPolynomial ε (Complex.I * (u : ℂ))‖
     rw [saddleSourceGaussianPlusIntegrand_tail_norm_eq]
-    linarith [mul_lt_mul_of_pos_left hkernel hden]
+    linarith only [mul_lt_mul_of_pos_left hkernel hden, hkernel, hden]
   · have hden : 0 <
         ‖minusPolynomial ε (Complex.I * (u : ℂ))‖ := by
       have hb := div_pos hε four_pos
       have hnorm :=
         minusPolynomial_imaginary_norm_ge_three_beta
           hε huminus
-      linarith
+      linarith only [hε, hnorm]
     change s *
       (∫ T : ℝ in saddleGaussianTailSet R,
         ‖saddleSourceGaussianMinusIntegrand ε ℓ u T‖) <
       κ * ‖minusPolynomial ε (Complex.I * (u : ℂ))‖
     rw [saddleSourceGaussianMinusIntegrand_tail_norm_eq]
-    linarith [mul_lt_mul_of_pos_left hkernel hden]
+    linarith only [mul_lt_mul_of_pos_left hkernel hden, hkernel, hden]
 
 private theorem eventually_saddleSourceSecondBranch_fullGaussianErrors_of_sourceL1
     (hsource :
@@ -7168,10 +7255,10 @@ private theorem eventually_saddleSourceSecondBranch_fullGaussianErrors_of_source
   let v : ℝ := saddleSourceStationaryLogRadius ε ℓ u
   have hu : -1 < u := by
     try dsimp [u]
-    linarith
+    linarith only [hε, hδ]
   have huminus : 1 + ε / 4 ≤ u := by
     try dsimp [u]
-    linarith
+    linarith only [hε, hδ]
   have hV : 0 < saddleSourceGaussianVariance ε ℓ u := by
     try dsimp [u]
     exact hvariance ℓ hℓ δ hδ
@@ -7225,14 +7312,14 @@ private theorem eventually_saddleSourceSecondBranch_fullGaussianErrors_of_source
       _ < ‖plusPolynomial ε (Complex.I * (u : ℂ))‖ *
           (∫ T : ℝ,
             saddleSourceGaussianKernel ε ℓ u T) := by
-        linarith [mul_pos hden hG]
+        linarith only [mul_pos hden hG, hG, hden]
   · have hden : 0 <
         ‖minusPolynomial ε (Complex.I * (u : ℂ))‖ := by
       have hb := div_pos hε four_pos
       have hnorm :=
         minusPolynomial_imaginary_norm_ge_three_beta
           hε huminus
-      linarith
+      linarith only [hε, hnorm]
     have hfull :=
       saddleGaussian_fullLine_error_lt_of_central_and_normalized_tails
         (ε := ε) (ℓ := ℓ) (u := u) (R := R)
@@ -7273,7 +7360,7 @@ private theorem eventually_saddleSourceSecondBranch_fullGaussianErrors_of_source
       _ < ‖minusPolynomial ε (Complex.I * (u : ℂ))‖ *
           (∫ T : ℝ,
             saddleSourceGaussianKernel ε ℓ u T) := by
-        linarith [mul_pos hden hG]
+        linarith only [mul_pos hden hG, hG, hden]
 
 private theorem eventually_saddleSourceSecondBranch_sourceL1Tails :
     ∀ᶠ ε : ℝ in 𝓝[>] (0 : ℝ),
@@ -7354,7 +7441,7 @@ private theorem saddleDigamma_eq_complexDigamma_re
     have hre := congrArg Complex.re h
     have hn : 0 ≤ (n : ℝ) := Nat.cast_nonneg n
     simp only [Complex.ofReal_re, Complex.neg_re, Complex.natCast_re] at hre
-    linarith
+    linarith only [hx, hre]
   have hreal :
       HasDerivAt Real.Gamma
         (deriv Complex.Gamma (x : ℂ)).re x := by
@@ -7378,7 +7465,7 @@ private theorem complexGamma_differentiableOn_positiveHalfPlane :
   have hnreal : 0 ≤ (n : ℝ) := Nat.cast_nonneg n
   simp only [Complex.neg_re, Complex.natCast_re] at hre
   change 0 < z.re at hz
-  linarith
+  linarith only [hre, hz]
 
 private theorem complexDigamma_continuousOn_positiveHalfPlane :
     ContinuousOn Complex.digamma
@@ -7426,7 +7513,7 @@ private theorem tendsto_saddleDigamma_atTop :
     Tendsto saddleDigamma atTop atTop := by
   have h := Real.tendsto_log_atTop.atTop_add
     tendsto_saddleDigamma_sub_log
-  convert! h using 1
+  convert h using 1
   funext x
   ring
 
@@ -7557,7 +7644,7 @@ private theorem saddleSourceShellDerivative_hasDerivAt
             Real.cosh (u * a)) u := by
     have h := saddleSinhShellInterval_hasDerivAt
       w hw horder u
-    convert! h using 1
+    convert h using 1
     · funext v
       apply intervalIntegral.integral_congr
       intro a ha
@@ -7574,7 +7661,7 @@ private theorem saddleSourceShellDerivative_hasDerivAt
       congr 2
       ring
   have hremote : (ε⁻¹ ^ 3) ≤ (ε⁻¹ ^ 3) + 1 := by
-    linarith
+    linarith only []
   have hpositive :
       HasDerivAt
         (fun v : ℝ =>
@@ -7588,7 +7675,7 @@ private theorem saddleSourceShellDerivative_hasDerivAt
       (positiveShellDensity ε)
       (positiveShellDensity_continuous ε)
       hremote u
-    convert! h using 1
+    convert h using 1
     · funext v
       apply intervalIntegral.integral_congr
       intro a ha
@@ -7617,7 +7704,7 @@ private theorem saddleSourceShellDerivative_hasDerivAt
     ring_nf
   have hsum := hshort.add hpositive
   unfold saddleSourceShellDerivative
-  convert! hsum using 1
+  convert hsum using 1
   rw [hshortvariance, hpositivevariance]
   unfold upperNetShellVariance
   ring
@@ -7646,8 +7733,8 @@ private theorem eventually_saddleSourceShellDerivative_monotone_secondBranch :
       have hmem : u ∈ Ici (1 + ε / 2) :=
         interior_subset hu
       exact hmem
-    have hδ : ε / 2 ≤ u - 1 := by linarith
-    have hδnonneg : 0 ≤ u - 1 := by linarith
+    have hδ : ε / 2 ≤ u - 1 := by linear_combination hthreshold
+    have hδnonneg : 0 ≤ u - 1 := by linarith only [hε, hthreshold]
     have hvariance :=
       (upperPositiveShellVariance_bounds hε hδnonneg).1
     have hpositive : 0 ≤ upperPositiveShellVariance ε (u - 1) := by
@@ -7657,7 +7744,7 @@ private theorem eventually_saddleSourceShellDerivative_monotone_secondBranch :
             Real.exp ((u - 1) * (ε⁻¹ ^ 3)) by
           positivity [shellWeight_pos ε]).trans hvariance
     have hnetlower := (hnet (u - 1) hδ).1
-    linarith
+    linarith only [hpositive, hnetlower]
 
 private theorem saddleLogRadius_continuousOn_Ici
     {ε : ℝ} (hε : 0 < ε)
@@ -7677,7 +7764,7 @@ private theorem saddleLogRadius_continuousOn_Ici
     try dsimp [g]
     have hu' : u₀ ≤ u := hu
     have hupositive : 0 < 1 + u := by
-      linarith
+      linarith only [hu₀, hu']
     change 0 < ((d : ℝ) / 2) * (1 + u) / 2
     positivity
   have hdigamma :
@@ -7716,7 +7803,7 @@ private theorem tendsto_saddleGammaArgument_atTop
   have hlinear := tendsto_id.const_mul_atTop hslope
   have h := hlinear.atTop_add
     (tendsto_const_nhds (x := (d : ℝ) / 4))
-  convert! h using 1
+  convert h using 1
   funext u
   simp only [id_eq]
   ring
@@ -7757,7 +7844,7 @@ private theorem tendsto_saddleLogRadius_atTop_of_shell_monotone
       · exact hu
     rw [saddleLogRadius_eq_digamma_add_shellDerivative]
     try dsimp [C]
-    linarith
+    linear_combination hshell
   exact tendsto_atTop_mono' atTop hcomparison hbaseline
 
 private theorem eventually_tendsto_saddleLogRadius_atTop :
@@ -7833,7 +7920,7 @@ private theorem eventually_saddleSmallRadiusStarOrdinate_gt_neg_one :
   have hdreal : (3 : ℝ) ≤ (d : ℝ) := by
     exact_mod_cast hd
   have hdimension : 1 < (d : ℝ) / 2 := by
-    linarith
+    linarith only [hdreal]
   have hlog : 0 < Real.log ((d : ℝ) / 2) :=
     Real.log_pos hdimension
   have hdenominator : 0 < 4 * ((d : ℝ) / 2) := by
@@ -7843,7 +7930,7 @@ private theorem eventually_saddleSmallRadiusStarOrdinate_gt_neg_one :
         (4 * ((d : ℝ) / 2)) :=
     div_pos hlog hdenominator
   unfold saddleSmallRadiusStarOrdinate
-  linarith
+  linear_combination hratio
 
 private theorem eventually_saddleSmallRadiusStar_log_coverage :
     ∀ᶠ ε : ℝ in 𝓝[>] (0 : ℝ),
@@ -7879,7 +7966,7 @@ private theorem eventually_saddleSourceRadius_log_coverage :
     with ε hε hcoverage
   change 0 < ε at hε
   intro d hd r hr
-  have hu₀ : -1 < 1 + ε / 4 := by linarith
+  have hu₀ : -1 < 1 + ε / 4 := by linarith only [hε]
   apply hcoverage d hd (1 + ε / 4) hu₀ r
   exact hr
 
@@ -7924,7 +8011,7 @@ private theorem eventualLowerBound_of_uniform_and_constructive
     (hlower : UniformAdmissibleLowerBound)
     (hupper : ConstructivePrimalUpperBound) : EventualLowerBound := by
   intro c hc
-  have haux : Real.pi⁻¹ < Real.pi⁻¹ + 1 := by linarith
+  have haux : Real.pi⁻¹ < Real.pi⁻¹ + 1 := by linarith only []
   filter_upwards [hlower c hc, hupper (Real.pi⁻¹ + 1) haux]
     with d hcost ⟨f, _⟩
   unfold normalizedProgram
@@ -7940,14 +8027,14 @@ private theorem sharpQuotient_of_eventual_bounds
   refine tendsto_order.2 ⟨?_, ?_⟩
   · intro a ha
     have hmid : (a + Real.pi⁻¹) / 2 < Real.pi⁻¹ := by
-      linarith
+      linarith only [ha]
     filter_upwards [hlower _ hmid] with d hd
-    linarith
+    linarith only [ha, hd]
   · intro b hb
     have hmid : Real.pi⁻¹ < (Real.pi⁻¹ + b) / 2 := by
-      linarith
+      linarith only [hb]
     filter_upwards [hupper _ hmid] with d hd
-    linarith
+    linarith only [hb, hd]
 
 private theorem sharpQuotient_of_uniform_lower_and_constructive_upper
     (hlower : UniformAdmissibleLowerBound)
diff --git a/LeanPool/SpherePacking/MellinAnalysis.lean b/LeanPool/SpherePacking/MellinAnalysis.lean
index 694eb7090c..53bcfc0d9e 100644
--- a/LeanPool/SpherePacking/MellinAnalysis.lean
+++ b/LeanPool/SpherePacking/MellinAnalysis.lean
@@ -9,7 +9,6 @@ module
 import all LeanPool.SpherePacking.Foundations
 public import Mathlib.MeasureTheory.Function.L1Space.Integrable
 public import Mathlib.MeasureTheory.Measure.Haar.OfBasis
-import Mathlib.Algebra.Ring.IsFormallyReal
 import Mathlib.Analysis.Calculus.Taylor
 import Mathlib.Analysis.Real.Pi.Wallis
 import Mathlib.Analysis.SumIntegralComparisons
@@ -46,7 +45,7 @@ private theorem saddleCauchyPole_symmetric_intervalIntegral_tendsto_pos
   have hreal : Tendsto
       (fun T : ℝ => 2 * Real.arctan (T / a))
       Filter.atTop (𝓝 Real.pi) := by
-    convert! (tendsto_const_nhds.mul hatan) using 1
+    convert (tendsto_const_nhds.mul hatan) using 1
     all_goals ring_nf
   have hcomplex : Tendsto
       (fun T : ℝ =>
@@ -77,7 +76,7 @@ private theorem saddleCauchyPole_symmetric_intervalIntegral_tendsto_neg
   have hreal : Tendsto
       (fun T : ℝ => 2 * Real.arctan (T / a))
       Filter.atTop (𝓝 (-Real.pi)) := by
-    convert! (tendsto_const_nhds.mul hatan) using 1
+    convert (tendsto_const_nhds.mul hatan) using 1
     all_goals ring_nf
   have hcomplex : Tendsto
       (fun T : ℝ =>
@@ -102,7 +101,7 @@ private theorem saddleShiftedCauchyPole_symmetric_intervalIntegral_tendsto_pos
             ((2 * n : ℕ) : ℂ))⁻¹))
       Filter.atTop (𝓝 (Real.pi : ℂ)) := by
   have hshift : 0 < a + ((2 * n : ℕ) : ℝ) := by
-    linarith
+    linear_combination ha
   have hlimit :=
     saddleCauchyPole_symmetric_intervalIntegral_tendsto_pos
       hshift
@@ -123,7 +122,7 @@ private theorem saddleShiftedCauchyPole_symmetric_intervalIntegral_tendsto_neg
             ((2 * n : ℕ) : ℂ))⁻¹))
       Filter.atTop (𝓝 (-(Real.pi : ℂ))) := by
   have hshift : a + ((2 * n : ℕ) : ℝ) < 0 := by
-    linarith
+    linear_combination ha
   have hlimit :=
     saddleCauchyPole_symmetric_intervalIntegral_tendsto_neg
       hshift
@@ -361,7 +360,7 @@ private theorem saddleGaussianPoleShiftedSlope_symmetric_intervalIntegral
     have hre := congrArg Complex.re hzero
     norm_num [Complex.mul_re] at hre
     push_cast
-    linarith
+    linear_combination hre
   have hgaussian : IntervalIntegrable
       (fun t : ℝ =>
         saddleGaussianPoleRepresentative n
@@ -606,7 +605,7 @@ private theorem saddleGaussianPole_shiftedLine_ne_zero
   have hre := congrArg Complex.re hzero
   norm_num [Complex.mul_re] at hre
   push_cast
-  linarith
+  linear_combination hre
 
 private theorem saddleGaussianPoleWeightedCorrection_eq_sub
     {r : ℝ} (n : ℕ) {z : ℂ}
@@ -1454,7 +1453,7 @@ private theorem saddleTaylorContour_mem_halfPlane (N : ℕ) :
     -(2 * ((N : ℝ) + 1)) < saddleTaylorContour N := by
   unfold saddleTaylorContour
   push_cast
-  linarith
+  linarith only []
 
 private theorem saddleTaylorContour_ne_pole (N n : ℕ) :
     saddleTaylorContour N ≠ -((2 * n : ℕ) : ℝ) := by
@@ -1691,12 +1690,12 @@ private noncomputable def frullaniKernel (a b x : ℝ) : ℝ :=
 
 private theorem laplaceKernel_integrable {a : ℝ} (ha : 0 < a) :
     IntegrableOn (fun x : ℝ => Real.exp (-a * x)) (Ioi 0) := by
-  exact integrableOn_exp_mul_Ioi (by linarith : -a < 0) 0
+  exact integrableOn_exp_mul_Ioi (by linear_combination ha : -a < 0) 0
 
 private theorem integral_laplaceKernel {a : ℝ} (ha : 0 < a) :
     (∫ x : ℝ in Ioi 0, Real.exp (-a * x)) = a⁻¹ := by
   simpa only [neg_mul, mul_zero, Real.exp_zero, neg_div_neg_eq,
-    one_div] using! (integral_exp_mul_Ioi (by linarith : -a < 0) 0)
+    one_div] using! (integral_exp_mul_Ioi (by linear_combination ha : -a < 0) 0)
 
 private theorem intervalIntegral_laplaceKernel {x : ℝ} (hx : x ≠ 0)
     (a b : ℝ) :
@@ -1734,7 +1733,7 @@ private theorem laplaceParameter_integrable {a b : ℝ}
   · filter_upwards [ae_restrict_mem measurableSet_uIoc] with s hs
     have hspos : 0 < s := by
       rw [Set.uIoc_of_le hab] at hs
-      linarith [hs.1]
+      linarith only [hs.1, ha, hs]
     exact laplaceKernel_integrable hspos
   · have hnonzero :
         ∀ s ∈ Set.uIcc a b, s ≠ 0 := by
@@ -1751,7 +1750,7 @@ private theorem laplaceParameter_integrable {a b : ℝ}
     filter_upwards [ae_restrict_mem measurableSet_uIoc] with s hs
     have hspos : 0 < s := by
       rw [Set.uIoc_of_le hab] at hs
-      linarith [hs.1]
+      linarith only [hs.1, ha, hs]
     symm
     change (∫ y : ℝ in Ioi 0, ‖Real.exp (-s * y)‖) = s⁻¹
     simpa only [Real.norm_eq_abs, abs_of_pos (Real.exp_pos _)] using!
@@ -1821,8 +1820,8 @@ private theorem wallisPairKernel_integrable (n : ℕ) :
     IntegrableOn (wallisPairKernel n) (Ioi 0) := by
   unfold wallisPairKernel
   apply Integrable.sub
-  · exact frullaniKernel_integrable (by positivity) (by linarith)
-  · exact frullaniKernel_integrable (by positivity) (by linarith)
+  · exact frullaniKernel_integrable (by positivity) (by linarith only [])
+  · exact frullaniKernel_integrable (by positivity) (by linarith only [])
 
 private noncomputable def wallisPairFactor (n : ℕ) : ℝ :=
   ((2 * (n : ℝ) + 2) / (2 * (n : ℝ) + 1)) *
@@ -1833,10 +1832,10 @@ private theorem integral_wallisPairKernel (n : ℕ) :
       Real.log (wallisPairFactor n) := by
   unfold wallisPairKernel
   rw [integral_sub
-    (frullaniKernel_integrable (by positivity) (by linarith))
-    (frullaniKernel_integrable (by positivity) (by linarith)),
-    integral_frullaniKernel (by positivity) (by linarith),
-    integral_frullaniKernel (by positivity) (by linarith)]
+    (frullaniKernel_integrable (by positivity) (by linarith only []))
+    (frullaniKernel_integrable (by positivity) (by linarith only [])),
+    integral_frullaniKernel (by positivity) (by linarith only []),
+    integral_frullaniKernel (by positivity) (by linarith only [])]
   unfold wallisPairFactor
   rw [Real.log_mul (by positivity) (by positivity),
     Real.log_div (by positivity) (by positivity),
@@ -1934,7 +1933,7 @@ private theorem wallisLaplaceKernel_abs_le {x : ℝ} (hx : 0 < x) :
   unfold wallisLaplaceKernel
   have hq : 0 < Real.exp (-x) := Real.exp_pos _
   have hsub : 1 - Real.exp (-x) ≤ x := by
-    linarith [Real.add_one_le_exp (-x)]
+    linarith only [Real.add_one_le_exp (-x)]
   have hden : 0 < x * (1 + Real.exp (-x)) := by positivity
   apply (div_le_iff₀ hden).2
   have hmul : 0 ≤ x * Real.exp (-x) :=
@@ -1964,7 +1963,7 @@ private theorem wallisPartialKernel_abs_le (n : ℕ) {x : ℝ} (hx : 0 < x) :
   have hfactor : 0 ≤ 1 - Real.exp (-(2 * (n : ℝ)) * x) :=
     sub_nonneg.mpr hexp
   have hfactor_le : 1 - Real.exp (-(2 * (n : ℝ)) * x) ≤ 1 := by
-    linarith [Real.exp_pos (-(2 * (n : ℝ)) * x)]
+    linarith only [Real.exp_pos (-(2 * (n : ℝ)) * x)]
   rw [abs_of_nonneg
     (mul_nonneg (wallisLaplaceKernel_nonneg hx) hfactor)]
   exact mul_le_of_le_one_right (wallisLaplaceKernel_nonneg hx) hfactor_le
@@ -1978,7 +1977,7 @@ private theorem tendsto_wallisPartialKernel {x : ℝ} (hx : 0 < x) :
   have hexp :
       Tendsto (fun n : ℕ =>
         Real.exp (-(2 * (n : ℝ)) * x)) atTop (nhds 0) := by
-    convert! Real.tendsto_exp_neg_atTop_nhds_zero.comp hlinear using 1
+    convert Real.tendsto_exp_neg_atTop_nhds_zero.comp hlinear using 1
     funext n
     congr 1
     ring
@@ -2045,7 +2044,7 @@ private theorem tendsto_cubic_gaussian_atTop :
       Tendsto
         (fun x : ℝ => (x ^ 3 + 1) * Real.exp (-(1 / 8 : ℝ) * x))
         atTop (nhds 0) := by
-    convert! hpoly.add hone using 1
+    convert hpoly.add hone using 1
     · ext x
       ring
     · norm_num
@@ -2057,8 +2056,7 @@ private theorem tendsto_cubic_gaussian_atTop :
     have hxpoly : 0 ≤ x ^ 3 + 1 := by positivity
     apply mul_le_mul_of_nonneg_left _ hxpoly
     apply Real.exp_le_exp.mpr
-    linarith [mul_nonneg (by linarith : 0 ≤ x)
-      (by linarith : 0 ≤ x - 1)]
+    linarith only [mul_nonneg (by linarith : 0 ≤ x) (by linarith : 0 ≤ x - 1), hx]
 
 private noncomputable def shellRadiusMajorant (ε : ℝ) : ℝ :=
   ((ε⁻¹ ^ 3) + 1) * shellWeight ε *
@@ -2082,7 +2080,7 @@ private theorem tendsto_shellRadiusMajorant :
   apply tendsto_nhdsGT_zero_of_comp_inv_tendsto_atTop
   have hsmall :
       Tendsto (fun x : ℝ => x⁻¹ / 4) atTop (nhds 0) := by
-    convert! tendsto_inv_atTop_zero.div_const (4 : ℝ) using 1; norm_num
+    convert tendsto_inv_atTop_zero.div_const (4 : ℝ) using 1; norm_num
   have hexp :
       Tendsto (fun x : ℝ => Real.exp (x⁻¹ / 4)) atTop (nhds 1) := by
     simpa only [Real.exp_zero] using! hsmall.rexp
@@ -2132,7 +2130,7 @@ private theorem sinh_le_mul_cosh {a : ℝ} (ha : 0 ≤ a) :
     (show a ∈ Set.Ici 0 from ha) ha
   try dsimp [f] at h
   norm_num at h
-  linarith
+  exact h
 
 private noncomputable def shortShellRadiusIntegrand (ε a : ℝ) : ℝ :=
   shortShellDensity ε a * a * Real.sinh ((1 + ε / 4) * a)
@@ -2171,11 +2169,12 @@ private theorem shortMargin_abs_le_exp {ε a : ℝ}
       rw [abs_of_pos (by norm_num : (0 : ℝ) < 1),
         abs_of_nonneg hterm]
     _ ≤ 11 * (1 + a) := by
-      linarith [mul_le_mul_of_nonneg_right hε1
-        (show 0 ≤ 1 + a by linarith)]
+      linarith only [mul_le_mul_of_nonneg_right hε1 (show 0 ≤ 1 + a by linarith), hε1, ha]
     _ ≤ 11 * Real.exp a := by
-      gcongr
-      linarith [Real.add_one_le_exp a]
+      refine mul_le_mul_of_nonneg_left ?_
+          (le_of_lt
+            ((by norm_num)))
+      linarith only [Real.add_one_le_exp a]
 
 private theorem shortShellHyperbolicRatio_le {ε a : ℝ}
     (hε0 : 0 ≤ ε) (hε1 : ε ≤ 1) (ha : 0 ≤ a) :
@@ -2191,12 +2190,25 @@ private theorem shortShellHyperbolicRatio_le {ε a : ℝ}
           exact (div_le_div_iff_of_pos_right (Real.cosh_pos a)).2
             (sinh_le_mul_cosh harg)
     _ ≤ ((5 / 4 : ℝ) * a) * Real.exp ((ε / 4) * a) := by
-          gcongr
-          · linarith
+          refine mul_le_mul (mul_le_mul_of_nonneg_right ?_ ha) ?_
+              (le_of_lt (div_pos (Real.cosh_pos ((1 + ε / 4) * a)) (Real.cosh_pos a)))
+              (mul_nonneg
+                (le_of_lt
+                  (div_pos
+                    ((by norm_num))
+                    ((by norm_num))))
+                ha)
+          · linarith only [hε1]
           · exact cosh_ratio_upper ha hδ
     _ ≤ ((5 / 4 : ℝ) * a) * Real.exp (a / 4) := by
-          gcongr
-          linarith [mul_le_mul_of_nonneg_right hε1 ha]
+          refine mul_le_mul_of_nonneg_left (Real.exp_monotone ?_)
+              (mul_nonneg
+                (le_of_lt
+                  (div_pos
+                    ((by norm_num))
+                    ((by norm_num))))
+                ha)
+          linarith only [mul_le_mul_of_nonneg_right hε1 ha, hε1, ha]
 
 private theorem shortShellRadiusIntegrand_eq_ratio {ε a : ℝ} (ha : a ≠ 0) :
     shortShellRadiusIntegrand ε a =
@@ -2256,10 +2268,11 @@ private theorem shortShellRadiusIntegrand_measurable (ε : ℝ) :
     fun_prop
   have hd : Measurable (fun a : ℝ =>
       2 * a ^ 2 * Real.cosh a) := by
-    fun_prop
+    exact Measurable.fun_mul (Measurable.const_mul (Measurable.pow_const measurable_id' 2) 2)
+        (Measurable.cosh measurable_id')
   have hs : Measurable (fun a : ℝ =>
       Real.sinh ((1 + ε / 4) * a)) := by
-    fun_prop
+    exact Measurable.sinh (Measurable.const_mul measurable_id' (1 + ε / 4))
   exact ((hn.div hd).neg.mul measurable_id).mul hs
 
 private theorem tendsto_shortCutoff :
@@ -2577,6 +2590,7 @@ private theorem radialL1Mass_eq {d : ℕ} (hd : 0 < d)
       radialSurfaceArea d *
         ∫ r : ℝ in Ioi 0,
           r ^ (d - 1) * ‖radialProfile hd g r‖ := by
+  let : MeasureSpace (EuclideanSpace ℝ (Fin d)) := inferInstance
   let : Nonempty (Fin d) := Fin.pos_iff_nonempty.mp hd
   unfold radialL1Mass
   calc
@@ -2793,6 +2807,7 @@ private theorem integral_re_eq_zero_of_antiFourier {d : ℕ}
     (hanti : (𝓕 g : TestFunction d) = -g)
     (hzero : g (0 : Euclidean d) = 0) :
     (∫ x : Euclidean d, (g x).re) = 0 := by
+  let : MeasureSpace (EuclideanSpace ℝ (Fin d)) := inferInstance
   have hfourierzero :
       ((𝓕 g : TestFunction d) (0 : Euclidean d)) = 0 := by
     rw [hanti]
@@ -2996,7 +3011,7 @@ private theorem radialProfile_mellinConvergent {d : ℕ}
     (a := s.re + 1) (b := (-2 : ℝ))
     (radialProfile_locallyIntegrableOn hd f)
     (radialProfile_isBigO_rpow_atTop hd f (s.re + 1))
-    (by linarith)
+    (by linarith only [])
   · simpa only [neg_neg, Real.rpow_ofNat] using! radialProfile_isBigO_rpow_two_zero hd f hf hzero
   · exact hs
 
@@ -3009,7 +3024,7 @@ private theorem radialProfile_mellin_differentiableAt {d : ℕ}
     (a := s.re + 1) (b := (-2 : ℝ))
     (radialProfile_locallyIntegrableOn hd f)
     (radialProfile_isBigO_rpow_atTop hd f (s.re + 1))
-    (by linarith)
+    (by linarith only [])
   · simpa only [neg_neg, Real.rpow_ofNat] using! radialProfile_isBigO_rpow_two_zero hd f hf hzero
   · exact hs
 
@@ -3026,7 +3041,7 @@ private theorem radialMellinStrip_differentiableAt {d : ℕ}
   have hs :
       -2 < (((d : ℂ) / 2 - Complex.I * z).re) := by
     norm_num
-    linarith
+    linear_combination hz
   change
     DifferentiableAt ℂ
       (fun w : ℂ =>
@@ -3059,7 +3074,7 @@ private theorem radialMellinStrip_diffContOnCl {d : ℕ}
     closure_Ioo (ne_of_lt (neg_lt_self hhalf))] at hz
   apply
     (radialMellinStrip_differentiableAt
-      hd f hf hzero z (by linarith [hz.1])).differentiableWithinAt
+      hd f hf hzero z (by linarith only [hz.1, hz])).differentiableWithinAt
 
 private noncomputable def normalizedRadialMellinStrip {d : ℕ}
     (hd : 0 < d) (f : TestFunction d) (R : ℝ) (z : ℂ) : ℂ :=
@@ -3244,17 +3259,17 @@ private theorem radial_fourier_mellin_regularized_closed {d : ℕ}
       (radialProfile_mellin_differentiableAt hd
         (𝓕 f : TestFunction d)
         (gaussianMellin_fourier_radial hf) hhatZero w
-        (by linarith [hw.1])).continuousAt.continuousWithinAt
+        (by linarith only [hw.1, hw])).continuousAt.continuousWithinAt
   have hprimal : ContinuousOn
       (fun w : ℂ =>
         mellin (radialProfile hd f) ((d : ℂ) - w)) T := by
     intro w hw
     change 0 ≤ w.re ∧ w.re ≤ (d : ℝ) at hw
     have hinner : ContinuousAt (fun v : ℂ => (d : ℂ) - v) w := by
-      fun_prop
+      exact ContinuousAt.fun_sub continuousAt_const (continuousAt_id' w)
     have hre : -2 < (((d : ℂ) - w).re) := by
       norm_num
-      linarith [hw.2]
+      linarith only [hw.2, hw]
     exact
       ((radialProfile_mellin_differentiableAt hd f hf hzero
         ((d : ℂ) - w) hre).continuousAt.comp
@@ -3281,11 +3296,11 @@ private theorem radial_fourier_mellin_regularized_closed {d : ℕ}
     have hg₁ : Complex.Gamma (w / 2) ≠ 0 := by
       apply Complex.Gamma_ne_zero_of_re_pos
       norm_num
-      linarith [hw.1]
+      linarith only [hw.1, hw]
     have hg₂ : Complex.Gamma (((d : ℂ) - w) / 2) ≠ 0 := by
       apply Complex.Gamma_ne_zero_of_re_pos
       norm_num
-      linarith [hw.2]
+      linarith only [hw.2, hw]
     try dsimp [L, G]
     rw [radial_fourier_mellin_strip hd f hf w hw.1 hw.2]
     field_simp
@@ -3330,7 +3345,7 @@ private theorem radial_fourier_mellin_antifourier_boundary {d : ℕ}
     try dsimp [s] at him
     norm_num at him
     apply hy
-    linarith
+    exact him
   have hden : Complex.Gamma (((d : ℂ) - s) / 2) ≠ 0 := by
     apply Complex.Gamma_ne_zero_of_re_pos
     try dsimp [s]
@@ -3352,7 +3367,7 @@ private theorem radial_fourier_mellin_antifourier_boundary {d : ℕ}
           mellin (radialProfile hd f) ((d : ℂ) - s)) := by
     field_simp [hnum, hden] at heq ⊢
     linear_combination -heq
-  convert! hcross using 1 <;> dsimp [s] <;>
+  convert hcross using 1 <;> dsimp [s] <;>
     push_cast <;> ring_nf
 
 private theorem radial_fourier_mellin_antifourier_boundary_norm {d : ℕ}
@@ -3393,7 +3408,7 @@ private theorem radial_fourier_mellin_antifourier_boundary_norm {d : ℕ}
             (((d : ℝ) / 2 : ℝ) + Complex.I * (y : ℂ) / 2)‖ := by
       apply (eq_div_iff hden).2
       push_cast
-      convert! hnorm using 1; ring
+      convert hnorm using 1; ring
     _ = Real.pi ^ ((d : ℝ) / 2) *
         (‖Complex.Gamma (-(Complex.I * (y : ℂ)) / 2)‖ /
           ‖Complex.Gamma
@@ -3529,7 +3544,7 @@ private theorem normalizedRadialMellinStrip_bottom_norm_le_gamma {d : ℕ}
     have him := congrArg Complex.im hn
     norm_num at him
     apply hy
-    linarith
+    exact him
   have hdenGamma :
       Complex.Gamma
         (((d : ℝ) / 2 : ℝ) +
@@ -3640,7 +3655,7 @@ private theorem radialProfile_mellin_uniform_strip_bound {d : ℕ}
         ‖radialProfile hd f r‖) (Ioi (0 : ℝ)) := by
     have hre : -2 < ((d : ℂ).re) := by
       norm_num
-      linarith [show (0 : ℝ) ≤ (d : ℝ) from Nat.cast_nonneg d]
+      linarith only [show (0 : ℝ) ≤ (d : ℝ) from Nat.cast_nonneg d]
     have hconv := radialProfile_mellinConvergent
       hd f hf hzero (d : ℂ) hre
     simpa only [Complex.natCast_re] using!
@@ -3660,7 +3675,7 @@ private theorem radialProfile_mellin_uniform_strip_bound {d : ℕ}
   refine ⟨max 0 B, le_max_left _ _, ?_⟩
   intro s hs hsd
   have hconv : MellinConvergent (radialProfile hd f) s :=
-    radialProfile_mellinConvergent hd f hf hzero s (by linarith)
+    radialProfile_mellinConvergent hd f hf hzero s (by linear_combination hs)
   have hbound : ‖mellin (radialProfile hd f) s‖ ≤ B := by
     calc
       ‖mellin (radialProfile hd f) s‖ ≤
@@ -3681,7 +3696,7 @@ private theorem radialProfile_mellin_uniform_strip_bound {d : ℕ}
         · calc
             r ^ (s.re - 1) ≤ r ^ (-(1 : ℝ)) :=
               Real.rpow_le_rpow_of_exponent_ge hr hone
-                (by linarith)
+                (by linear_combination hs)
             _ ≤ r ^ (-(1 : ℝ)) + r ^ ((d : ℝ) - 1) := by
               exact le_add_of_nonneg_right
                 (Real.rpow_nonneg hr.le _)
@@ -3689,7 +3704,7 @@ private theorem radialProfile_mellin_uniform_strip_bound {d : ℕ}
           calc
             r ^ (s.re - 1) ≤ r ^ ((d : ℝ) - 1) :=
               Real.rpow_le_rpow_of_exponent_le hlarge
-                (by linarith)
+                (by linear_combination hsd)
             _ ≤ r ^ (-(1 : ℝ)) + r ^ ((d : ℝ) - 1) := by
               exact le_add_of_nonneg_left
                 (Real.rpow_nonneg hr.le _)
@@ -3714,11 +3729,11 @@ private theorem normalizedRadialMellinStrip_uniform_bound {d : ℕ}
   have hsnonneg :
       0 ≤ (((d : ℂ) / 2 - Complex.I * z).re) := by
     norm_num
-    linarith
+    linear_combination hzlower
   have hsupper :
       (((d : ℂ) / 2 - Complex.I * z).re) ≤ (d : ℝ) := by
     norm_num
-    linarith
+    linear_combination hzupper
   have hphase :
       ((((d : ℂ) / 2 + Complex.I * z) *
         (Real.log R : ℂ))).re ≤
@@ -3726,10 +3741,10 @@ private theorem normalizedRadialMellinStrip_uniform_bound {d : ℕ}
     norm_num
     have hcoefnonneg :
         0 ≤ (d : ℝ) / 2 - z.im := by
-      linarith
+      linear_combination hzupper
     have hcoefupper :
         (d : ℝ) / 2 - z.im ≤ (d : ℝ) := by
-      linarith
+      linear_combination hzlower
     calc
       ((d : ℝ) / 2 - z.im) * Real.log R ≤
           ((d : ℝ) / 2 - z.im) * |Real.log R| :=
@@ -3951,7 +3966,7 @@ private theorem normalizedRadialLogProfile_weighted_integrable {d : ℕ}
   let κ : ℝ := (d : ℝ) - a
   have hκ : -2 < κ := by
     try dsimp [κ]
-    linarith
+    linear_combination ha
   have hconv : MellinConvergent
       (radialProfile hd f) (κ : ℂ) := by
     apply radialProfile_mellinConvergent hd f hf hzero
@@ -4069,7 +4084,7 @@ private theorem integrable_fourier_of_integrable_two_derivatives
   have hquadratic (t : ℝ) :
       t ^ 2 * ‖(𝓕 g : ℝ → ℂ) t‖ ≤ D / p ^ 2 := by
     apply (le_div_iff₀ (sq_pos_of_pos hp)).2
-    linarith [hsecond t]
+    linarith only [hsecond t, hsecond]
   have hmajor : Integrable
       (fun t : ℝ => (A + D / p ^ 2) * (1 + t ^ 2)⁻¹) :=
     integrable_inv_one_add_sq.const_mul (A + D / p ^ 2)
@@ -4080,8 +4095,7 @@ private theorem integrable_fourier_of_integrable_two_derivatives
   change ‖(𝓕 g : ℝ → ℂ) t‖ ≤
     (A + D / p ^ 2) / (1 + t ^ 2)
   apply (le_div_iff₀ hden).2
-  linarith [hzero t, hquadratic t,
-    norm_nonneg ((𝓕 g : ℝ → ℂ) t)]
+  linarith only [hzero t, hquadratic t, norm_nonneg ((𝓕 g : ℝ → ℂ) t), hzero, hquadratic]
 
 private theorem schwartzRealLine_mellinConvergent_of_re_pos
     (g : 𝓢(ℝ, ℂ)) (s : ℂ) (hs : 0 < s.re) :
@@ -4109,7 +4123,7 @@ private theorem schwartzRealLine_mellinConvergent_of_re_pos
     simpa only [neg_zero, Real.rpow_zero, norm_one, mul_one] using! hbounded r
   exact mellinConvergent_of_isBigO_rpow
     (a := s.re + 1) (b := (0 : ℝ)) hlocal htop
-    (by linarith) hzero hs
+    (by linarith only []) hzero hs
 
 private noncomputable def schwartzExponentialTilt
     (g : 𝓢(ℝ, ℂ)) (κ R v : ℝ) : ℂ :=
@@ -4173,7 +4187,7 @@ private theorem schwartzExponentialTilt_differentiable
   unfold schwartzExponentialTilt
   have hexpreal :
       Differentiable ℝ (fun v : ℝ => Real.exp (κ * v)) := by
-    fun_prop
+    exact Differentiable.exp (Differentiable.const_mul differentiable_id κ)
   have hexp :
       Differentiable ℝ (fun v : ℝ =>
         (Real.exp (κ * v) : ℂ)) :=
@@ -4182,7 +4196,7 @@ private theorem schwartzExponentialTilt_differentiable
     (g.smooth 1).differentiable (by norm_num)
   have hradius :
       Differentiable ℝ (fun v : ℝ => R * Real.exp v) := by
-    fun_prop
+    exact Differentiable.const_mul (Differentiable.exp differentiable_id) R
   exact hexp.mul (hg.comp hradius)
 
 private theorem schwartzExponentialTilt_deriv
@@ -4240,7 +4254,7 @@ private theorem schwartzExponentialTilt_deriv_integrable
     (SchwartzMap.derivCLM ℂ ℂ) g
   have hzero := schwartzExponentialTilt_integrable g hκ hR
   have hone := schwartzExponentialTilt_integrable
-    g' (show 0 < κ + 1 by linarith) hR
+    g' (show 0 < κ + 1 by linear_combination hκ) hR
   have hsum :=
     (hzero.const_mul (κ : ℂ)).add
       (hone.const_mul (R : ℂ))
@@ -4301,7 +4315,7 @@ private theorem schwartzExponentialTilt_deriv_deriv_integrable
     schwartzExponentialTilt_deriv_integrable g hκ hR
   have hone :=
     schwartzExponentialTilt_deriv_integrable
-      g' (show 0 < κ + 1 by linarith) hR
+      g' (show 0 < κ + 1 by linear_combination hκ) hR
   have hsum :=
     (hzero.const_mul (κ : ℂ)).add
       (hone.const_mul (R : ℂ))
@@ -4358,7 +4372,7 @@ private theorem normalizedRadialLogProfile_weighted_fourier_integrable
     ((radialSurfaceArea d / radialL1Mass f * R ^ d : ℝ) : ℂ)
   have hκ : 0 < κ := by
     try dsimp [κ]
-    linarith
+    linear_combination ha
   have hweight :
       (fun v : ℝ =>
         (Real.exp (-a * v) : ℂ) *
@@ -4443,7 +4457,7 @@ private theorem normalizedRadialMellinStrip_shifted_fourier_inversion
     try dsimp [W]
     apply normalizedRadialLogProfile_weighted_integrable
       hd f hf hreal hzero hR
-    linarith
+    linear_combination ha
   have hFW : Integrable (𝓕 W : ℝ → ℂ) := by
     try dsimp [W]
     exact normalizedRadialLogProfile_weighted_fourier_integrable
@@ -4522,22 +4536,23 @@ private theorem stripAngle_mem_Ioo {σ : ℝ}
     0 < stripAngle σ ∧ stripAngle σ < Real.pi := by
   unfold stripAngle
   constructor
-  · exact div_pos (mul_pos Real.pi_pos (by linarith)) (by norm_num)
+  · exact div_pos (mul_pos Real.pi_pos (by linear_combination hbelow)) (by norm_num)
   · calc
       Real.pi * (1 + σ) / 2 < Real.pi * 2 / 2 := by
-        gcongr
-        linarith
+        refine div_lt_div_of_pos_right (mul_lt_mul_of_pos_left ?_ Real.pi_pos)
+            (zero_lt_two)
+        linear_combination habove
       _ = Real.pi := by ring
 
 private theorem stripBottomMass_pos {σ : ℝ} (hσ : σ < 1) :
     0 < stripBottomMass σ := by
   unfold stripBottomMass
-  linarith
+  linarith only [hσ]
 
 private theorem stripBottomMass_lt_one {σ : ℝ} (hσ : -1 < σ) :
     stripBottomMass σ < 1 := by
   unfold stripBottomMass
-  linarith
+  linarith only [hσ]
 
 private theorem stripPoissonKernel_pos {σ : ℝ}
     (hbelow : -1 < σ) (habove : σ < 1) (T : ℝ) :
@@ -4551,7 +4566,7 @@ private theorem stripPoissonKernel_pos {σ : ℝ}
     simpa only [gt_iff_lt, Real.cos_zero] using! h
   have hden : 0 < Real.cosh (Real.pi * T / 2) -
       Real.cos (stripAngle σ) := by
-    linarith [Real.one_le_cosh (Real.pi * T / 2)]
+    linarith only [Real.one_le_cosh (Real.pi * T / 2), hcos]
   exact div_pos hsin (mul_pos (by norm_num) hden)
 
 end
@@ -4609,22 +4624,25 @@ private theorem stripPoissonPrimitive_hasDerivAt {σ : ℝ}
   have hden : 0 <
       Real.exp (Real.pi * T / 2) ^ 2 + 1 -
         2 * Real.exp (Real.pi * T / 2) * Real.cos (stripAngle σ) := by
-    linarith [sq_nonneg
-      (Real.exp (Real.pi * T / 2) - Real.cos (stripAngle σ)),
-      sq_pos_of_pos hsin]
+    linarith only [
+      sq_nonneg (Real.exp (Real.pi * T / 2) - Real.cos (stripAngle σ)),
+      sq_pos_of_pos hsin,
+      hsin,
+      htrig
+    ]
   field_simp [hsin0, hpi, hexp.ne', hden.ne']
-  linarith
+  linarith only [htrig]
 
 private theorem stripPoissonPrimitive_zero {σ : ℝ}
     (hbelow : -1 < σ) (habove : σ < 1) :
     stripPoissonPrimitive σ 0 = stripAngle σ / (2 * Real.pi) := by
   obtain ⟨hangle, hangle'⟩ := stripAngle_mem_Ioo hbelow habove
   have hhalf : 0 < stripAngle σ / 2 := half_pos hangle
-  have hhalf' : stripAngle σ / 2 < Real.pi / 2 := by linarith
+  have hhalf' : stripAngle σ / 2 < Real.pi / 2 := by linarith only [hangle']
   have hcos : 0 < Real.cos (stripAngle σ / 2) :=
-    Real.cos_pos_of_mem_Ioo ⟨by linarith [Real.pi_pos], hhalf'⟩
+    Real.cos_pos_of_mem_Ioo ⟨by linarith only [Real.pi_pos, hangle, hangle'], hhalf'⟩
   have hsin : 0 < Real.sin (stripAngle σ / 2) :=
-    Real.sin_pos_of_pos_of_lt_pi hhalf (by linarith [Real.pi_pos])
+    Real.sin_pos_of_pos_of_lt_pi hhalf (by linarith only [Real.pi_pos, hangle, hangle'])
   have hratio :
       (1 - Real.cos (stripAngle σ)) / Real.sin (stripAngle σ) =
         Real.tan (stripAngle σ / 2) := by
@@ -4642,7 +4660,7 @@ private theorem stripPoissonPrimitive_zero {σ : ℝ}
     ring
   unfold stripPoissonPrimitive
   simp only [mul_zero, zero_div, Real.exp_zero]
-  rw [hratio, Real.arctan_tan (by linarith [Real.pi_pos]) hhalf']
+  rw [hratio, Real.arctan_tan (by linarith only [Real.pi_pos, hangle, hangle']) hhalf']
   ring
 
 private theorem stripPoissonPrimitive_tendsto_atTop {σ : ℝ}
@@ -4652,7 +4670,7 @@ private theorem stripPoissonPrimitive_tendsto_atTop {σ : ℝ}
   have hsin : 0 < Real.sin (stripAngle σ) :=
     Real.sin_pos_of_pos_of_lt_pi hangle hangle'
   have hscale : Tendsto (fun T : ℝ => Real.pi * T / 2) atTop atTop := by
-    convert! tendsto_id.atTop_mul_const (half_pos Real.pi_pos) using 1
+    convert tendsto_id.atTop_mul_const (half_pos Real.pi_pos) using 1
     ext T
     change Real.pi * T / 2 = T * (Real.pi / 2)
     ring
@@ -4678,7 +4696,7 @@ private theorem stripPoissonPrimitive_tendsto_atTop {σ : ℝ}
     (tendsto_nhds_of_tendsto_nhdsWithin Real.tendsto_arctan_atTop).comp
       hratio
   unfold stripPoissonPrimitive
-  convert! hatan.div_const Real.pi using 1
+  convert hatan.div_const Real.pi using 1
   field_simp [Real.pi_ne_zero]
 
 private theorem stripPoissonKernel_integrableOn_Ioi {σ : ℝ}
@@ -4754,7 +4772,7 @@ private theorem stripPoissonKernel_antitone_abs
         (Real.cosh (Real.pi * x / 2) -
           Real.cos (stripAngle σ)) := by
     have hxcosh := Real.one_le_cosh (Real.pi * x / 2)
-    linarith
+    linarith only [hcos, hxcosh]
   have hcosh :
       Real.cosh (Real.pi * x / 2) ≤
         Real.cosh (Real.pi * y / 2) := by
@@ -4766,7 +4784,7 @@ private theorem stripPoissonKernel_antitone_abs
           Real.cos (stripAngle σ)) ≤
         4 * (Real.cosh (Real.pi * y / 2) -
           Real.cos (stripAngle σ)) := by
-    linarith
+    linarith only [hcosh]
   unfold stripPoissonKernel
   exact div_le_div_of_nonneg_left hsin.le hxden hden
 
@@ -4809,7 +4827,7 @@ private theorem stripPoissonPrimitive_centered_antitoneOn
     apply stripPoissonKernel_antitone_abs hbelow habove
     apply (sq_le_sq₀ (abs_nonneg _) (abs_nonneg _)).mp
     rw [sq_abs, sq_abs]
-    linarith [mul_nonneg hxpos hr]
+    linarith only [mul_nonneg hxpos hr, hr, hxpos]
 
 private theorem intervalIntegral_stripPoissonKernel
     {σ : ℝ} (hbelow : -1 < σ) (habove : σ < 1)
@@ -4835,7 +4853,7 @@ private theorem stripPoissonPrimitive_centered_neg
   simp_rw [stripPoissonKernel_neg] at hneg
   rw [intervalIntegral_stripPoissonKernel hbelow habove,
     intervalIntegral_stripPoissonKernel hbelow habove] at hneg
-  convert! hneg.symm using 1
+  convert hneg.symm using 1
   all_goals ring_nf
 
 private theorem stripPoissonPrimitive_centered_le
@@ -4849,13 +4867,13 @@ private theorem stripPoissonPrimitive_centered_le
     stripPoissonPrimitive_centered_antitoneOn
       hbelow habove hr
   by_cases hs : 0 ≤ s
-  · convert! hanti (show (0 : ℝ) ∈ Ici 0 by simp only [mem_Ici, Std.le_refl])
+  · convert hanti (show (0 : ℝ) ∈ Ici 0 by simp only [mem_Ici, Std.le_refl])
       (show s ∈ Ici 0 from hs) hs using 1
     all_goals ring_nf
-  · have hsneg : 0 ≤ -s := by linarith
+  · have hsneg : 0 ≤ -s := by linarith only [hs]
     rw [← stripPoissonPrimitive_centered_neg
       hbelow habove r s]
-    convert! hanti (show (0 : ℝ) ∈ Ici 0 by simp only [mem_Ici, Std.le_refl])
+    convert hanti (show (0 : ℝ) ∈ Ici 0 by simp only [mem_Ici, Std.le_refl])
       (show -s ∈ Ici 0 from hsneg) hsneg using 1
     all_goals ring_nf
 
@@ -4866,8 +4884,8 @@ private theorem stripPoissonKernel_centered_interval_max
       ∫ x in Icc (-r) r, stripPoissonKernel σ x := by
   rw [integral_Icc_eq_integral_Ioc,
     integral_Icc_eq_integral_Ioc,
-    ← intervalIntegral.integral_of_le (by linarith : s - r ≤ s + r),
-    ← intervalIntegral.integral_of_le (by linarith : -r ≤ r),
+    ← intervalIntegral.integral_of_le (by linarith only [hr] : s - r ≤ s + r),
+    ← intervalIntegral.integral_of_le (by linarith only [hr] : -r ≤ r),
     intervalIntegral_stripPoissonKernel hbelow habove,
     intervalIntegral_stripPoissonKernel hbelow habove]
   exact stripPoissonPrimitive_centered_le hbelow habove hr s
@@ -4894,9 +4912,12 @@ private theorem stripComplexPoissonKernel_re
   have hden :
       0 < Real.exp (Real.pi * T / 2) ^ 2 + 1 -
         2 * Real.exp (Real.pi * T / 2) * Real.cos (stripAngle σ) := by
-    linarith [sq_nonneg
-      (Real.exp (Real.pi * T / 2) - Real.cos (stripAngle σ)),
-      sq_pos_of_pos hsin]
+    linarith only [
+      sq_nonneg (Real.exp (Real.pi * T / 2) - Real.cos (stripAngle σ)),
+      sq_pos_of_pos hsin,
+      hsin,
+      htrig
+    ]
   unfold stripComplexPoissonKernel stripPoissonKernel
   rw [Real.cosh_eq, Real.exp_neg]
   simp only [Complex.div_re, Complex.div_im, Complex.mul_re, Complex.I_re,
@@ -4933,7 +4954,7 @@ private theorem stripSchwarzExponential_hasDerivAt
       (Complex.I * (ℓ : ℂ))).const_mul (Real.pi : ℂ)).div_const
       (2 * (ℓ : ℂ))
   unfold stripSchwarzExponential
-  convert! haffine.cexp using 1
+  convert haffine.cexp using 1
   all_goals simp only [id_eq, mul_one]
 
 private theorem norm_stripSchwarzExponential (ℓ : ℝ) (z : ℂ) (y : ℝ) :
@@ -4977,10 +4998,10 @@ private theorem stripSchwarzAngle_mem_Ioo
       Real.pi * (z.im + ℓ) / (2 * ℓ) < Real.pi := by
   change -ℓ < z.im ∧ z.im < ℓ at hz
   constructor
-  · exact div_pos (mul_pos Real.pi_pos (by linarith))
+  · exact div_pos (mul_pos Real.pi_pos (by linarith only [hz]))
       (mul_pos (by norm_num) hℓ)
   · apply (div_lt_iff₀ (mul_pos (by norm_num) hℓ)).2
-    linarith [mul_pos Real.pi_pos (show 0 < ℓ - z.im by linarith)]
+    linarith only [mul_pos Real.pi_pos (show 0 < ℓ - z.im by linarith), hz]
 
 /-- The squared distance from `e * (cos θ + i sin θ)` to `1` dominates `sin θ ^ 2`. -/
 private theorem sin_sq_le_shifted_normSq {e s c : ℝ} (htrig : s ^ 2 + c ^ 2 = 1) :
@@ -5063,11 +5084,11 @@ private theorem stripHolomorphicPoissonKernel_denominator_ne_zero
         Complex.mul_re, zero_mul,
       sub_self, add_zero]
   have hpositive : 0 < Real.pi * (z.im + ℓ) / (2 * ℓ) := by
-    exact div_pos (mul_pos Real.pi_pos (by linarith))
+    exact div_pos (mul_pos Real.pi_pos (by linarith only [hz]))
       (mul_pos (by norm_num) hℓ)
   have hless : Real.pi * (z.im + ℓ) / (2 * ℓ) < Real.pi := by
     apply (div_lt_iff₀ (mul_pos (by norm_num) hℓ)).2
-    linarith [mul_pos Real.pi_pos (show 0 < ℓ - z.im by linarith)]
+    linarith only [mul_pos Real.pi_pos (show 0 < ℓ - z.im by linarith), hz]
   have hsin := Real.sin_pos_of_pos_of_lt_pi hpositive hless
   intro hzero
   have him := congrArg Complex.im hzero
@@ -5290,16 +5311,18 @@ private theorem stripRegularizedHolomorphicPoissonKernelDeriv_local_bound
     positivity
   have hA : Continuous A := by
     try dsimp [A]
-    fun_prop
+    exact Continuous.comp' Real.continuous_sin
+        (Continuous.comp' (Continuous.div_const continuous_id' (2 * ℓ))
+          (Continuous.const_mul (Continuous.add_const Complex.continuous_im ℓ) Real.pi))
   have hstrip :
       Complex.im ⁻¹' Ioo (-ℓ) ℓ ∈ 𝓝 z := by
     have him : Continuous (fun w : ℂ => w.im) := by
-      fun_prop
+      exact Complex.continuous_im
     exact (isOpen_Ioo.preimage him).mem_nhds hz
   have hsinset : A ⁻¹' Ioi (sin0 / 2) ∈ 𝓝 z := by
     apply (isOpen_Ioi.preimage hA).mem_nhds
     change sin0 / 2 < sin0
-    linarith
+    linarith only [hsin0]
   have hCpos : 0 ≤ Cpos := by
     try dsimp [Cpos]
     positivity
@@ -5319,9 +5342,9 @@ private theorem stripRegularizedHolomorphicPoissonKernelDeriv_local_bound
   have hreabs := Complex.abs_re_le_norm (w - z)
   simp only [Complex.sub_re] at hreabs
   have hreupper : w.re ≤ z.re + 1 := by
-    linarith [le_abs_self (w.re - z.re)]
+    linarith only [le_abs_self (w.re - z.re), hdist, hreabs]
   have hrelower : z.re - 1 ≤ w.re := by
-    linarith [neg_le_abs (w.re - z.re)]
+    linarith only [neg_le_abs (w.re - z.re), hdist, hreabs]
   have hsinw : sin0 / 2 <
       Real.sin (Real.pi * (w.im + ℓ) / (2 * ℓ)) := by
     exact hwsin
@@ -5345,7 +5368,7 @@ private theorem stripRegularizedHolomorphicPoissonKernelDeriv_local_bound
           try dsimp [a]
           ring
         _ ≤ a * (z.re + 1 - y) :=
-          mul_le_mul_of_nonneg_left (by linarith) ha.le
+          mul_le_mul_of_nonneg_left (by linear_combination hreupper) ha.le
     calc
       ‖stripRegularizedHolomorphicPoissonKernelDeriv ℓ w y‖ ≤
           Real.pi * Real.exp (Real.pi * (w.re - y) / (2 * ℓ)) /
@@ -5373,7 +5396,7 @@ private theorem stripRegularizedHolomorphicPoissonKernelDeriv_local_bound
           Cpos * Real.exp ((-a) * y) ≤
             (Cpos + Cneg) * Real.exp ((-a) * y)
         exact mul_le_mul_of_nonneg_right
-          (by linarith) (Real.exp_pos _).le
+          (by linear_combination hCneg) (Real.exp_pos _).le
   · have hnum :
         Real.pi * Real.exp (-(Real.pi * (w.re - y) / (2 * ℓ))) ≤
           Real.pi * Real.exp (-a * (z.re - 1 - y)) := by
@@ -5386,7 +5409,7 @@ private theorem stripRegularizedHolomorphicPoissonKernelDeriv_local_bound
           ring
         _ ≤ -(a * (z.re - 1 - y)) := by
           apply neg_le_neg
-          exact mul_le_mul_of_nonneg_left (by linarith) ha.le
+          exact mul_le_mul_of_nonneg_left (by linear_combination hrelower) ha.le
         _ = -a * (z.re - 1 - y) := by ring
     calc
       ‖stripRegularizedHolomorphicPoissonKernelDeriv ℓ w y‖ ≤
@@ -5420,7 +5443,7 @@ private theorem stripRegularizedHolomorphicPoissonKernelDeriv_local_bound
           ring
         rw [hexp]
         exact mul_le_mul_of_nonneg_right
-          (by linarith) (Real.exp_pos _).le
+          (by linear_combination hCpos) (Real.exp_pos _).le
 
 private theorem stripRegularizedHolomorphicPoissonKernel_of_nonneg
     {ℓ : ℝ} (hℓ : 0 < ℓ) {z : ℂ}
@@ -5629,13 +5652,13 @@ private theorem strip_abs_log_le_add_rpow {x : ℝ} (hx : 0 < x) :
   · rw [abs_of_nonneg (Real.log_nonneg hlarge)]
     have hlog := Real.log_le_sub_one_of_pos hx
     have hpower := Real.rpow_pos_of_pos hx (-(1 / 2 : ℝ))
-    linarith
+    linarith only [hlog, hpower]
   · have hsmall : x ≤ 1 := le_of_not_ge hlarge
     rw [abs_of_nonpos (Real.log_nonpos hx.le hsmall)]
     have hpower := Real.rpow_pos_of_pos hx (-(1 / 2 : ℝ))
     have hlog := Real.log_le_sub_one_of_pos hpower
     rw [Real.log_rpow hx] at hlog
-    linarith
+    linarith only [hx, hlarge, hlog]
 
 private theorem strip_exp_abs_log_integrableOn_Ioi {a : ℝ} (ha : 0 < a) :
     IntegrableOn
@@ -5667,7 +5690,7 @@ private theorem strip_exp_abs_log_integrableOn_Ioi {a : ℝ} (ha : 0 < a) :
   have hexpcontinuous :
       ContinuousOn (fun x : ℝ => Real.exp ((-a) * x))
         (Ioi (0 : ℝ)) := by
-    fun_prop
+    exact ContinuousOn.rexp (ContinuousOn.const_mul (continuousOn_id' (Ioi 0)) (-a))
   apply hmajorant.mono'
     ((hexpcontinuous.mul hlogcontinuous.abs).aestronglyMeasurable
       measurableSet_Ioi)
@@ -5762,9 +5785,9 @@ private theorem abs_sub_eq_two_profileNegativePart (φ : ℝ → ℝ) (v : ℝ)
     |φ v| - φ v = 2 * profileNegativePart φ v := by
   unfold profileNegativePart
   rcases le_total 0 (φ v) with h | h
-  · rw [abs_of_nonneg h, max_eq_right (by linarith)]
+  · rw [abs_of_nonneg h, max_eq_right (by linear_combination h)]
     ring
-  · rw [abs_of_nonpos h, max_eq_left (by linarith)]
+  · rw [abs_of_nonpos h, max_eq_left (by linear_combination h)]
     ring
 
 private theorem integral_profileNegativePart_eq_half {φ : ℝ → ℝ}
@@ -5786,7 +5809,7 @@ private theorem integral_profileNegativePart_eq_half {φ : ℝ → ℝ}
           (abs_sub_eq_two_profileNegativePart φ)
       _ = 2 * ∫ v : ℝ, profileNegativePart φ v := by
         rw [integral_const_mul]
-  linarith
+  linarith only [hsigned, htwice]
 
 private theorem profileNegativePart_setIntegral_Iic_eq_integral {φ : ℝ → ℝ}
     (hsign : ∀ v : ℝ, 0 ≤ v → 0 ≤ φ v) :
@@ -5796,7 +5819,7 @@ private theorem profileNegativePart_setIntegral_Iic_eq_integral {φ : ℝ → 
   intro v hv
   have hvpos : 0 < v := by simpa only [mem_Iic, not_le] using! hv
   unfold profileNegativePart
-  exact max_eq_right (by linarith [hsign v hvpos.le])
+  exact max_eq_right (by linarith only [hsign v hvpos.le, hsign, hvpos])
 
 private theorem normalizedProfile_negativeHalfline_mass_ge_half {φ : ℝ → ℝ}
     (hφ : Integrable φ)
@@ -5897,7 +5920,7 @@ private theorem no_normalizedProfile_of_fourierInversion_lt_half
     hφ hmean hmass hsign
   have hupper := negativeHalfline_le_of_fourierInversion
     hφ ha Z hinversion
-  linarith
+  linarith only [hsmall, hlower, hupper]
 
 private theorem no_antiFourierWitness_of_fourierInversion_lt_half
     {d : ℕ} (hd : 0 < d) {R : ℝ} (hR : 0 < R)
@@ -6010,7 +6033,7 @@ private theorem no_antiFourierWitness_of_interiorMellinL1_lt_half
     mul_pos (sub_pos.mpr hσabove) hℓ
   have haless :
       (1 - σ) * ((d : ℝ) / 2) < (d : ℝ) := by
-    linarith [mul_pos (by linarith : 0 < 1 + σ) hℓ]
+    linarith only [mul_pos (by linarith : 0 < 1 + σ) hℓ, hσbelow, hℓ]
   have hheight :
       (d : ℝ) / 2 - (1 - σ) * ((d : ℝ) / 2) =
         σ * ((d : ℝ) / 2) := by
@@ -6035,7 +6058,7 @@ private theorem lowerGammaBoundaryLog_continuousOn
     intro m hm
     have him := congrArg Complex.im hm
     norm_num at him
-    exact hS y hy (by linarith)
+    exact hS y hy (by exact him)
   have hdenPole (y : ℝ) :
       ∀ m : ℕ,
         (ℓ : ℂ) + Complex.I * (y : ℂ) / 2 ≠ -(m : ℂ) := by
@@ -6043,7 +6066,7 @@ private theorem lowerGammaBoundaryLog_continuousOn
     have hre := congrArg Complex.re hm
     norm_num at hre
     have hmnonneg : 0 ≤ (m : ℝ) := Nat.cast_nonneg m
-    linarith
+    linarith only [hℓ, hre]
   have hnum :
       ContinuousOn
         (fun y : ℝ => Complex.Gamma (-Complex.I * (y : ℂ) / 2)) S := by
@@ -6180,7 +6203,7 @@ private theorem integerGammaFactor_ne_zero
   intro hz
   have him := congrArg Complex.im hz
   norm_num at him
-  exact hy (by linarith)
+  exact hy (by exact him)
 
 private theorem gamma_imaginary_ne_zero {y : ℝ} (hy : y ≠ 0) :
     Complex.Gamma (Complex.I * (y : ℂ) / 2) ≠ 0 := by
@@ -6188,7 +6211,7 @@ private theorem gamma_imaginary_ne_zero {y : ℝ} (hy : y ≠ 0) :
   intro j hj
   have him := congrArg Complex.im hj
   norm_num at him
-  exact hy (by linarith)
+  exact hy (by exact him)
 
 private theorem norm_gamma_neg_imaginary (y : ℝ) :
     ‖Complex.Gamma (-Complex.I * (y : ℂ) / 2)‖ =
@@ -6242,7 +6265,7 @@ private theorem lowerGammaBoundaryLog_integer
 private theorem lower_sqrtFactor_ge_abs_half (c y : ℝ) :
     |y| / 2 ≤ Real.sqrt (c ^ 2 + (y / 2) ^ 2) := by
   apply (Real.le_sqrt (by positivity) (by positivity)).2
-  linarith [sq_nonneg c, sq_abs y]
+  linarith only [sq_nonneg c, sq_abs y]
 
 private theorem lowerGammaBoundaryLog_integer_log_tail
     (k : ℕ) {R y : ℝ} (hR : 0 < R) (hy : y ≠ 0) :
@@ -6282,7 +6305,7 @@ private theorem lowerGammaBoundaryLog_integer_log_tail
             (Real.sqrt ((j : ℝ) ^ 2 + (y / 2) ^ 2)) ≤
       (k : ℝ) * Real.log (Real.pi * R ^ 2) -
         (k : ℝ) * Real.log (|y| / 2) := by
-        linarith
+        linear_combination hsum
     _ = (k : ℝ) *
         (Real.log (Real.pi * R ^ 2) -
           Real.log (|y| / 2)) := by
@@ -6297,30 +6320,30 @@ private theorem lower_abs_log_sqrtFactor_le
       c + y / 2 + |Real.log (y / 2)| := by
   have ht : 0 < y / 2 := by positivity
   have hinside : 0 < c ^ 2 + (y / 2) ^ 2 := by
-    linarith [sq_nonneg c, sq_pos_of_pos ht]
+    linarith only [sq_nonneg c, sq_pos_of_pos ht, ht]
   have hsqrt : 0 < Real.sqrt (c ^ 2 + (y / 2) ^ 2) :=
     Real.sqrt_pos.2 hinside
   have hlower :
       y / 2 ≤ Real.sqrt (c ^ 2 + (y / 2) ^ 2) := by
     apply (Real.le_sqrt ht.le hinside.le).2
-    linarith [sq_nonneg c]
+    linarith only [sq_nonneg c]
   have hupper :
       Real.sqrt (c ^ 2 + (y / 2) ^ 2) ≤ c + y / 2 := by
     apply Real.sqrt_le_iff.mpr
     constructor
     · positivity
-    · linarith [mul_nonneg hc ht.le]
+    · linarith only [mul_nonneg hc ht.le, hc, ht]
   by_cases hlarge : 1 ≤ Real.sqrt (c ^ 2 + (y / 2) ^ 2)
   · rw [abs_of_nonneg (Real.log_nonneg hlarge)]
     have hlog := Real.log_le_sub_one_of_pos hsqrt
     have habs := abs_nonneg (Real.log (y / 2))
-    linarith
+    linear_combination hupper + hlog + habs
   · rw [abs_of_nonpos
       (Real.log_nonpos hsqrt.le (le_of_not_ge hlarge))]
     have hlog := Real.log_le_log ht hlower
     have habs := neg_le_abs (Real.log (y / 2))
     have hnonneg : 0 ≤ c + y / 2 := by positivity
-    linarith
+    linear_combination hsqrt + hupper + hlog + habs
 
 private theorem lower_exp_abs_log_div_two_integrableOn_Ioi
     {a : ℝ} (ha : 0 < a) :
@@ -6413,7 +6436,7 @@ private theorem lower_exp_log_sqrtFactor_integrableOn_Ioi
         apply (Real.sqrt_pos.2 ?_).ne'
         have ht : 0 < y / 2 := by
           exact half_pos (mem_Ioi.mp hy)
-        linarith [sq_nonneg c, sq_pos_of_pos ht]
+        linarith only [sq_nonneg c, sq_pos_of_pos ht, ht]
   apply hmajorant.mono'
     (hcontinuous.aestronglyMeasurable measurableSet_Ioi)
   filter_upwards [ae_restrict_mem measurableSet_Ioi] with y hy
@@ -6756,7 +6779,7 @@ private theorem norm_gamma_imaginary_sq {x : ℝ} (hx : x ≠ 0) :
       (mul_ne_zero Complex.I_ne_zero (Complex.ofReal_ne_zero.mpr hx))
   have hrec :
       Complex.Gamma (1 - z) = (-z) * Complex.Gamma (-z) := by
-    convert! Complex.Gamma_add_one (-z) hz using 1; ring_nf
+    convert Complex.Gamma_add_one (-z) hz using 1; ring_nf
   have hconjarg : -z = starRingEnd ℂ z := by
     try dsimp [z]
     simp only [map_mul, Complex.conj_I, Complex.conj_ofReal]
@@ -6823,7 +6846,7 @@ private theorem halfIntegerGammaFactor_ne_zero (j : ℕ) (y : ℝ) :
   have hre := congrArg Complex.re hz
   norm_num at hre
   have hj : 0 ≤ (j : ℝ) := Nat.cast_nonneg j
-  linarith
+  linarith only [hre]
 
 private theorem lowerGammaBoundaryLog_halfInteger_factorized
     (k : ℕ) (R : ℝ) {y : ℝ} (hy : y ≠ 0) :
@@ -6898,7 +6921,7 @@ private theorem lowerCoth_one_le {x : ℝ} (hx : 0 < x) :
   unfold lowerCoth
   apply (le_div_iff₀ hsinh).2
   rw [one_mul, Real.sinh_eq, Real.cosh_eq]
-  linarith [Real.exp_pos (-x)]
+  linarith only [Real.exp_pos (-x)]
 
 private theorem lowerCoth_log_nonneg {x : ℝ} (hx : 0 < x) :
     0 ≤ Real.log (lowerCoth x) :=
@@ -6913,11 +6936,11 @@ private theorem lowerCoth_hasDerivAt {x : ℝ} (hx : 0 < x) :
     (Real.hasDerivAt_cosh x).div
       (Real.hasDerivAt_sinh x) hsinh
   unfold lowerCoth
-  convert! hderiv using 1
+  convert hderiv using 1
   rw [div_eq_mul_inv]
   have hidentity := Real.cosh_sq_sub_sinh_sq x
   field_simp [hsinh]
-  linarith
+  linear_combination hidentity
 
 private theorem lowerCoth_antitoneOn :
     AntitoneOn lowerCoth (Ioi (0 : ℝ)) := by
@@ -6942,16 +6965,16 @@ private theorem lowerCoth_log_antitoneOn :
 private theorem lower_cosh_le_exp {x : ℝ} (hx : 0 ≤ x) :
     Real.cosh x ≤ Real.exp x := by
   have hnegative : Real.exp (-x) ≤ Real.exp x :=
-    Real.exp_le_exp.mpr (by linarith)
+    Real.exp_le_exp.mpr (by linarith only [hx])
   rw [Real.cosh_eq]
-  linarith
+  linarith only [hnegative]
 
 private theorem lower_sinh_le_exp (x : ℝ) :
     Real.sinh x ≤ Real.exp x := by
   have hpositive := Real.exp_pos (-x)
   have hpositive' := Real.exp_pos x
   rw [Real.sinh_eq]
-  linarith
+  linarith only [hpositive, hpositive']
 
 private theorem lower_abs_log_cosh_le {x : ℝ} (hx : 0 ≤ x) :
     |Real.log (Real.cosh x)| ≤ x := by
@@ -6971,12 +6994,12 @@ private theorem lower_abs_log_sinh_le {x : ℝ} (hx : 0 < x) :
       (lower_sinh_le_exp x)
     have habs := abs_nonneg (Real.log x)
     rw [Real.log_exp] at hlog
-    linarith
+    linarith only [hlog, habs]
   · rw [abs_of_nonpos
       (Real.log_nonpos hsinh.le (le_of_not_ge hlarge))]
     have hlog := Real.log_le_log hx hlower
     have habs := neg_le_abs (Real.log x)
-    linarith
+    linarith only [hx, hlog, habs]
 
 private theorem lower_abs_log_coth_div_le {x : ℝ} (hx : 0 < x) :
     |Real.log (lowerCoth (Real.pi * x) / x)| ≤
@@ -7013,10 +7036,10 @@ private theorem lower_abs_log_coth_div_le {x : ℝ} (hx : 0 < x) :
           (Real.log (Real.cosh (Real.pi * x)) -
             Real.log (Real.sinh (Real.pi * x)))
           (Real.log x)
-      linarith
+      linear_combination hfirst + hsecond
     _ ≤ 2 * (Real.pi * x) +
         |Real.log Real.pi| + 2 * |Real.log x| := by
-      linarith
+      linear_combination hlogpi + hcoshbound + hsinhbound
 
 private theorem lowerCoth_sub_one_eq
     {x : ℝ} (hx : 0 < x) :
@@ -7032,17 +7055,17 @@ private theorem lower_sinh_ge_exp_quarter
     {x : ℝ} (hx : 1 ≤ x) :
     Real.exp x / 4 ≤ Real.sinh x := by
   have hbig : 2 ≤ Real.exp x := by
-    linarith [Real.add_one_le_exp x]
+    linarith only [Real.add_one_le_exp x, hx]
   have hsmall : Real.exp (-x) ≤ 1 :=
-    Real.exp_le_one_iff.mpr (by linarith)
+    Real.exp_le_one_iff.mpr (by linear_combination hx)
   rw [Real.sinh_eq]
-  linarith
+  linarith only [hbig, hsmall]
 
 private theorem lowerCoth_log_le_four_exp_neg_two
     {x : ℝ} (hx : 1 ≤ x) :
     Real.log (lowerCoth x) ≤
       4 * Real.exp (-2 * x) := by
-  have hxpos : 0 < x := by linarith
+  have hxpos : 0 < x := by linear_combination hx
   have hsinh : 0 < Real.sinh x :=
     Real.sinh_pos_iff.mpr hxpos
   calc
@@ -7088,8 +7111,8 @@ private theorem lowerCoth_log_small_abs_bound
     (Real.log (lowerCoth (Real.pi * (|y| / 2)) / (|y| / 2)))
   have hlogu := le_abs_self (Real.log (|y| / 2))
   have hpibound : 2 * (Real.pi * (|y| / 2)) ≤ Real.pi := by
-    linarith [mul_nonneg Real.pi_pos.le (sub_nonneg.mpr hsmall)]
-  linarith
+    linarith only [mul_nonneg Real.pi_pos.le (sub_nonneg.mpr hsmall), hsmall]
+  linarith only [hloghalf, hbase, hlogdiv, hlogu, hpibound]
 
 private theorem lowerCoth_log_abs_integrable :
     Integrable (fun y : ℝ =>
@@ -7120,7 +7143,8 @@ private theorem lowerCoth_log_abs_integrable :
     (hnear.const_mul (Real.exp 1)).add hfar
   apply hmajor.mono'
   · have harg : Measurable (fun y : ℝ => Real.pi * |y| / 2) := by
-      fun_prop
+      exact Measurable.div_const
+          (Measurable.const_mul (Continuous.measurable (Continuous.abs continuous_id')) Real.pi) 2
     have hcoth : Measurable (fun y : ℝ =>
         lowerCoth (Real.pi * |y| / 2)) := by
       unfold lowerCoth
@@ -7152,7 +7176,7 @@ private theorem lowerCoth_log_abs_integrable :
         have hfactor :
             1 ≤ Real.exp 1 * Real.exp ((-1 : ℝ) * |y|) := by
           rw [← Real.exp_add]
-          exact (Real.one_le_exp_iff).2 (by linarith only [hsmall])
+          exact (Real.one_le_exp_iff).2 (by linear_combination hsmall)
         have hpolynonneg : 0 ≤ A + 3 * |Real.log (|y|)| := by
           positivity
         have hproduct :
@@ -7171,7 +7195,7 @@ private theorem lowerCoth_log_abs_integrable :
           ring
         try dsimp [A] at hsmallbound ⊢
         try dsimp [A] at hproduct hrewrite
-        linarith
+        linear_combination hfar_nonneg + hsmallbound + hproduct
       · have hylarge : 1 < |y| := lt_of_not_ge hsmall
         have harg : 1 ≤ Real.pi * |y| / 2 := by
           linarith [Real.pi_gt_three,
@@ -7184,7 +7208,7 @@ private theorem lowerCoth_log_abs_integrable :
           congr 1
           ring
         rw [hexp] at hbound
-        linarith
+        linear_combination hnear_nonneg + hbound
 
 private theorem lower_exp_log_coth_div_integrableOn_Ioi
     {a : ℝ} (ha : 0 < a) :
@@ -7254,7 +7278,7 @@ private theorem lower_exp_log_coth_div_integrableOn_Ioi
             Real.log (lowerCoth (Real.pi * y / 2) / (y / 2)))
         (Ioi (0 : ℝ)) := by
     apply ContinuousOn.mul
-    · fun_prop
+    · exact ContinuousOn.rexp (ContinuousOn.const_mul (continuousOn_id' (Ioi 0)) (-a))
     · exact hargument.log hargument_nonzero
   apply hmajorant.mono'
     (hcontinuous.aestronglyMeasurable measurableSet_Ioi)
@@ -7264,7 +7288,7 @@ private theorem lower_exp_log_coth_div_integrableOn_Ioi
       |Real.log (lowerCoth (Real.pi * y / 2) / (y / 2))| ≤
         Real.pi * y + |Real.log Real.pi| +
           2 * |Real.log (y / 2)| := by
-    convert! lower_abs_log_coth_div_le (half_pos hypos) using 1 <;>
+    convert lower_abs_log_coth_div_le (half_pos hypos) using 1 <;>
       ring_nf
   change
     ‖Real.exp ((-a) * y) *
@@ -7492,7 +7516,7 @@ private theorem lowerGammaBoundaryLog_halfInteger_log_tail
         (1 / 2 : ℝ) *
           (Real.log (lowerCoth (Real.pi * |y| / 2)) -
             Real.log (|y| / 2)) := by
-      linarith only [hsum]
+      linear_combination hsum
     _ = ((k : ℝ) + 1 / 2) *
           (Real.log (Real.pi * R ^ 2) -
             Real.log (|y| / 2)) +
@@ -7523,7 +7547,7 @@ private theorem lowerGammaBoundaryLog_dimension_log_tail
       ring
     rw [hq]
     have htail := lowerGammaBoundaryLog_integer_log_tail k hR hy
-    linarith
+    linarith only [hcoth, htail]
   · have hq : ((↑(2 * k + 1) : ℝ) / 2) =
         (k : ℝ) + 1 / 2 := by
       push_cast
@@ -7579,14 +7603,16 @@ private theorem lowerGammaBoundaryLog_dimension_scaled_log_tail_uniform
   have hcompare :
       Real.pi * |Y| / 2 ≤
         Real.pi * |((d : ℝ) / 2) * Y| / 2 := by
-    rw [abs_mul, abs_of_nonneg (by linarith : 0 ≤ (d : ℝ) / 2)]
-    linarith [mul_nonneg Real.pi_pos.le (abs_nonneg Y),
-      mul_nonneg (sub_nonneg.mpr hℓ)
-        (mul_nonneg Real.pi_pos.le (abs_nonneg Y))]
+    rw [abs_mul, abs_of_nonneg (by linear_combination hℓ : 0 ≤ (d : ℝ) / 2)]
+    linarith only [
+      mul_nonneg Real.pi_pos.le (abs_nonneg Y),
+      mul_nonneg (sub_nonneg.mpr hℓ) (mul_nonneg Real.pi_pos.le (abs_nonneg Y)),
+      hℓ
+    ]
   have hcoth := lowerCoth_log_antitoneOn ht ht' hcompare
   have htail := lowerGammaBoundaryLog_dimension_scaled_log_tail
     hdpos hc hY
-  linarith
+  linarith only [hcoth, htail]
 
 private theorem lower_positiveLogRatio_integrable
     {A : ℝ} (hA : 0 < A) :
@@ -7611,7 +7637,7 @@ private theorem lower_positiveLogRatio_integrable
     hnear.const_mul (Real.exp B)
   apply hmajor.mono'
   · have harg : Measurable (fun y : ℝ => A / |y|) := by
-      fun_prop
+      exact Measurable.const_div (Continuous.measurable (Continuous.abs continuous_id')) A
     exact (harg.log.max measurable_const).aestronglyMeasurable
   · filter_upwards [] with y
     rw [Real.norm_eq_abs, abs_of_nonneg (le_max_right _ _)]
@@ -7625,8 +7651,7 @@ private theorem lower_positiveLogRatio_integrable
             Real.log (A / |y|) ≤
               |Real.log A| + |Real.log (|y|)| := by
           rw [Real.log_div hA.ne' (abs_ne_zero.mpr hy)]
-          linarith [le_abs_self (Real.log A),
-            neg_le_abs (Real.log (|y|))]
+          linarith only [le_abs_self (Real.log A), neg_le_abs (Real.log (|y|))]
         have hpoly : 0 ≤
             |Real.log A| + |Real.log (|y|)| := by positivity
         have hmax :
@@ -7636,12 +7661,12 @@ private theorem lower_positiveLogRatio_integrable
         have hfactor :
             1 ≤ Real.exp B * Real.exp ((-1 : ℝ) * |y|) := by
           rw [← Real.exp_add]
-          exact (Real.one_le_exp_iff).2 (by linarith)
+          exact (Real.one_le_exp_iff).2 (by linarith only [hsmall])
         have hproduct :
             |Real.log A| + |Real.log (|y|)| ≤
               (Real.exp B * Real.exp ((-1 : ℝ) * |y|)) *
                 (|Real.log A| + |Real.log (|y|)|) := by
-          linarith [mul_nonneg (sub_nonneg.mpr hfactor) hpoly]
+          linarith only [mul_nonneg (sub_nonneg.mpr hfactor) hpoly, hpoly, hfactor]
         calc
           max (Real.log (A / |y|)) 0 ≤
               |Real.log A| + |Real.log (|y|)| := hmax
@@ -7690,7 +7715,7 @@ private theorem lowerGammaScaledPositivePart_le
     hd hc hY
   unfold lowerGammaScaledPositivePart
   apply max_le
-  · linarith
+  · linear_combination hlog + htail
   · positivity
 
 private theorem lowerGammaScaledPositivePart_integrable
@@ -7798,26 +7823,26 @@ private theorem lowerGammaBoundaryLog_dimension_scaled_nonpos_of_large
         rw [one_div, Real.log_inv]
   have hlogtwo : (1 / 2 : ℝ) ≤ Real.log (2 : ℝ) := by
     have h := Real.one_sub_inv_le_log_of_pos
-      (by norm_num : (0 : ℝ) < 2)
-    norm_num at h ⊢
+      (by norm_num1 : (0 : ℝ) < 2)
+    norm_num1 at h ⊢
     exact h
   have hpiabs : 3 ≤ Real.pi * |Y| := by
     linarith only [Real.pi_gt_three, mul_le_mul_of_nonneg_left hyone Real.pi_pos.le]
   have harg : 1 ≤ Real.pi * |Y| / 2 := by
     linarith only [hpiabs]
   have hexpthree : 4 ≤ Real.exp (3 : ℝ) := by
-    linarith [Real.add_one_le_exp (3 : ℝ)]
+    linarith only [Real.add_one_le_exp (3 : ℝ)]
   have hexpsmall :
       Real.exp ((-Real.pi) * |Y|) ≤ (1 / 4 : ℝ) := by
     calc
       Real.exp ((-Real.pi) * |Y|) ≤ Real.exp (-3 : ℝ) := by
         apply Real.exp_le_exp.mpr
-        linarith
+        linear_combination hpiabs
       _ = (Real.exp (3 : ℝ))⁻¹ := Real.exp_neg 3
       _ ≤ (1 / 4 : ℝ) := by
         simpa only [one_div] using!
           (one_div_le_one_div_of_le
-            (by norm_num : (0 : ℝ) < 4) hexpthree)
+            (by norm_num1 : (0 : ℝ) < 4) hexpthree)
   have hcoth := lowerCoth_log_le_four_exp_neg_two harg
   have hexp :
       Real.exp (-2 * (Real.pi * |Y| / 2)) =
@@ -7829,9 +7854,9 @@ private theorem lowerGammaBoundaryLog_dimension_scaled_nonpos_of_large
       (1 / 2 : ℝ) *
           Real.log (lowerCoth (Real.pi * |Y| / 2)) ≤
         (1 / 2 : ℝ) := by
-    linarith
+    linarith only [hexpsmall, hcoth]
   have hℓ : 1 ≤ (d : ℝ) / 2 := by
-    apply (le_div_iff₀ (by norm_num : (0 : ℝ) < 2)).2
+    apply (le_div_iff₀ (by norm_num1 : (0 : ℝ) < 2)).2
     exact_mod_cast hd
   have hmain :
       ((d : ℝ) / 2) *
@@ -7844,10 +7869,10 @@ private theorem lowerGammaBoundaryLog_dimension_scaled_nonpos_of_large
         mul_le_mul_of_nonneg_left hlogratio (by positivity)
       _ ≤ -(Real.log (2 : ℝ)) := by
         linarith only [mul_nonneg (sub_nonneg.mpr hℓ)
-          (show 0 ≤ Real.log (2 : ℝ) by linarith only [hlogtwo])]
+          (show 0 ≤ Real.log (2 : ℝ) by linear_combination hlogtwo)]
   have htail := lowerGammaBoundaryLog_dimension_scaled_log_tail_uniform
     hd hc hY
-  linarith
+  linarith only [hlogtwo, hexpsmall, hcoth, hmain, htail]
 
 private theorem lowerGammaScaledPositivePart_support
     {d : ℕ} (hd : 2 ≤ d) {c : ℝ} (hc : 0 < c) :
@@ -7895,7 +7920,7 @@ private theorem exists_lowerGammaScaledPositivePart_uniform_bound
       Real.sinh_zero,
         div_zero, Real.log_zero, Std.le_refl]
     · exact lowerCoth_log_nonneg (by positivity)
-  refine ⟨C, by linarith, ?_⟩
+  refine ⟨C, by linarith only [hB, hC], ?_⟩
   intro d hd
   constructor
   · intro Y hY
@@ -7914,7 +7939,7 @@ private theorem exists_lowerGammaScaledPositivePart_uniform_bound
         ((d : ℝ) / 2) * J + (1 / 2 : ℝ) * K ≤
           ((d : ℝ) / 2) *
             (J + (1 / 2 : ℝ) * K) := by
-      linarith [mul_nonneg (sub_nonneg.mpr hℓ) hK]
+      linarith only [mul_nonneg (sub_nonneg.mpr hℓ) hK, hK, hℓ]
     have hconstant : J + (1 / 2 : ℝ) * K ≤ C :=
       le_max_right B _
     calc
@@ -7982,7 +8007,7 @@ private theorem lowerGammaBoundaryLog_integer_antitoneOn
     apply Real.sqrt_le_sqrt
     exact add_le_add le_rfl
       (pow_le_pow_left₀ (half_pos hx).le (div_le_div_of_nonneg_right hxy zero_le_two) 2)
-  linarith
+  linear_combination hsum
 
 private theorem lowerGammaBoundaryLog_halfInteger_antitoneOn
     (k : ℕ) (R : ℝ) :
@@ -8015,7 +8040,8 @@ private theorem lowerGammaBoundaryLog_halfInteger_antitoneOn
   have hxarg : 0 < Real.pi * x / 2 := by positivity
   have hyarg : 0 < Real.pi * y / 2 := by positivity
   have harg : Real.pi * x / 2 ≤ Real.pi * y / 2 := by
-    gcongr
+    exact div_le_div_of_nonneg_right (mul_le_mul_of_nonneg_left hxy (le_of_lt Real.pi_pos))
+        zero_le_two
   have hcoth :
       lowerCoth (Real.pi * y / 2) ≤
         lowerCoth (Real.pi * x / 2) :=
@@ -8030,7 +8056,7 @@ private theorem lowerGammaBoundaryLog_halfInteger_antitoneOn
       _ ≤ lowerCoth (Real.pi * x / 2) / (x / 2) :=
         div_le_div_of_nonneg_left
           (lowerCoth_pos hxarg).le (half_pos hx)
-          (by linarith)
+          (by linarith only [hxy])
   have hcorr :
       Real.log (lowerCoth (Real.pi * y / 2) / (y / 2)) ≤
         Real.log (lowerCoth (Real.pi * x / 2) / (x / 2)) :=
@@ -8077,7 +8103,7 @@ private theorem even_antitone_superlevel_interval
       have hunonzero : f u ≠ 0 := by
         intro hzero
         rw [hzero] at hu
-        linarith [hu.2]
+        linarith only [hu.2, ht, hu]
       exact (hsupport hunonzero).2
     let r : ℝ := sSup S
     have hr : 0 ≤ r := by
@@ -8137,7 +8163,7 @@ private theorem lowerGammaBoundaryLog_halfInteger_exp_integrable
                   (((j : ℝ) + 1 / 2) ^ 2 + (y / 2) ^ 2))) := by
     exact integrable_finsetSum (Finset.range k)
       (fun j _ => lower_exp_log_sqrtFactor_integrable ha
-        (by have hj : 0 ≤ (j : ℝ) := Nat.cast_nonneg j; linarith))
+        (by have hj : 0 ≤ (j : ℝ) := Nat.cast_nonneg j; linarith only []))
   have hcorrection :
       Integrable
         (fun y : ℝ =>
@@ -8207,12 +8233,12 @@ private theorem lowerRiemannLog_monotoneOn {T : ℝ} (hT : T ≠ 0) :
     MonotoneOn (lowerRiemannLog T) (Ici (0 : ℝ)) := by
   intro x hx y hy hxy
   have hrad : 0 < x ^ 2 + T ^ 2 / 4 := by
-    linarith [sq_nonneg x, sq_pos_of_ne_zero hT]
+    linarith only [sq_nonneg x, sq_pos_of_ne_zero hT, hT]
   have hsquares : x ^ 2 ≤ y ^ 2 :=
     (sq_le_sq₀ hx hy).2 hxy
   unfold lowerRiemannLog
   exact Real.log_le_log (Real.sqrt_pos.2 hrad)
-    (Real.sqrt_le_sqrt (by linarith))
+    (Real.sqrt_le_sqrt (by linear_combination hsquares))
 
 private theorem monotone_leftRiemann_error
     (f : ℝ → ℝ) {k : ℕ} (hk : 0 < k)
@@ -8263,7 +8289,7 @@ private theorem monotone_leftRiemann_error
         (∑ j ∈ Finset.range k, f ((j : ℝ) / (k : ℝ))) =
           f 1 - f 0 := by
     rw [← Finset.sum_sub_distrib]
-    convert! Finset.sum_range_sub
+    convert Finset.sum_range_sub
       (fun j : ℕ => f ((j : ℝ) / (k : ℝ))) k using 1
     · apply Finset.sum_congr rfl
       intro j _
@@ -8271,9 +8297,9 @@ private theorem monotone_leftRiemann_error
     · simp only [ne_eq, hkne, not_false_eq_true, div_self, CharP.cast_eq_zero, zero_div]
   constructor
   · rw [← hintegral]
-    linarith
+    linear_combination hleft
   · rw [← hintegral]
-    linarith
+    linear_combination hright + hshift
 
 private theorem lower_integer_leftRiemann_error
     {T : ℝ} (hT : T ≠ 0) {k : ℕ} (hk : 0 < k) :
@@ -8315,8 +8341,8 @@ private theorem monotone_midpointIntegral_error
     have hjnonneg : 0 ≤ (j : ℝ) := Nat.cast_nonneg j
     have hjlast : (j : ℝ) + 1 ≤ (k : ℝ) := by
       exact_mod_cast (Nat.succ_le_of_lt hjk)
-    exact hf ⟨hjnonneg, by linarith⟩
-      ⟨by linarith, by linarith⟩ (by linarith)
+    exact hf ⟨hjnonneg, by linear_combination hjlast⟩
+      ⟨by linarith only [], by linear_combination hjlast⟩ (by linarith only [])
   have hmidright :
       (∑ j ∈ Finset.range k, f ((j : ℝ) + 1 / 2)) ≤
         ∑ j ∈ Finset.range k, f ((j : ℝ) + 1) := by
@@ -8326,14 +8352,14 @@ private theorem monotone_midpointIntegral_error
     have hjnonneg : 0 ≤ (j : ℝ) := Nat.cast_nonneg j
     have hjlast : (j : ℝ) + 1 ≤ (k : ℝ) := by
       exact_mod_cast (Nat.succ_le_of_lt hjk)
-    exact hf ⟨by linarith, by linarith⟩
-      ⟨by linarith, hjlast⟩ (by linarith)
+    exact hf ⟨by linarith only [], by linear_combination hjlast⟩
+      ⟨by linarith only [], hjlast⟩ (by linarith only [])
   have hshift :
       (∑ j ∈ Finset.range k, f ((j : ℝ) + 1)) -
         (∑ j ∈ Finset.range k, f (j : ℝ)) =
           f (k : ℝ) - f 0 := by
     rw [← Finset.sum_sub_distrib]
-    convert! Finset.sum_range_sub (fun j : ℕ => f (j : ℝ)) k using 1
+    convert Finset.sum_range_sub (fun j : ℕ => f (j : ℝ)) k using 1
     · apply Finset.sum_congr rfl
       intro j _
       simp only [Nat.cast_add, Nat.cast_one]
@@ -8382,7 +8408,7 @@ private theorem lowerRiemannLogPrimitive_hasDerivAt
     HasDerivAt (lowerRiemannLogPrimitive T)
       (lowerRiemannLog T x) x := by
   have hrad : 0 < x ^ 2 + T ^ 2 / 4 := by
-    linarith [sq_nonneg x, sq_pos_of_ne_zero hT]
+    linarith only [sq_nonneg x, sq_pos_of_ne_zero hT, hT]
   have ha : 0 < |T| / 2 := half_pos (abs_pos.mpr hT)
   have hquad :
       HasDerivAt (fun u : ℝ => u ^ 2 + T ^ 2 / 4) (2 * x) x := by
diff --git a/LeanPool/SpherePacking/PackingBound.lean b/LeanPool/SpherePacking/PackingBound.lean
index 00751d5db4..eac1c9536b 100644
--- a/LeanPool/SpherePacking/PackingBound.lean
+++ b/LeanPool/SpherePacking/PackingBound.lean
@@ -384,7 +384,7 @@ private theorem SpherePacking.volume_center_ball_union_eq_tsum
   intro ⟨x, hx⟩ ⟨y, hy⟩ h
   apply ball_disjoint_ball
   simp_rw [ne_eq, Subtype.mk.injEq] at h ⊢
-  linarith [S.distinct_centers_separation_bound x y hx.left hy.left h]
+  linarith only [S.distinct_centers_separation_bound x y hx.left hy.left h, hr', hx, hy, h]
 
 private theorem SpherePacking.center_count_in_ball_upper_bound (hd : 0 < d) (R : ℝ) :
     (S.centers ∩ ball 0 R).encard ≤
@@ -397,7 +397,7 @@ private theorem SpherePacking.center_count_in_ball_upper_bound (hd : 0 < d) (R :
     Measure.addHaar_ball_center, ENNReal.tsum_set_const] at h
   have : Nonempty (Fin d) := Fin.pos_iff_nonempty.mp hd
   rwa [← ENNReal.le_div_iff_mul_le] at h <;> left
-  · exact (euclidean_ball_volume_positive _ (by linarith [S.separation_pos])).ne.symm
+  · exact (euclidean_ball_volume_positive _ (by linarith only [S.separation_pos])).ne.symm
   · exact (euclidean_ball_volume_finite _).ne
 
 private theorem SpherePacking.center_count_in_ball_lower_bound (R : ℝ) :
@@ -424,7 +424,7 @@ private theorem SpherePacking.finite_centers_inside_ball (R : ℝ) :
       (ne_of_lt <|
         lt_of_le_of_lt (volume.mono Set.inter_subset_right)
           (EuclideanSpace.euclidean_ball_volume_finite _))
-      (euclidean_ball_volume_positive _ (by linarith [S.separation_pos])).ne.symm
+      (euclidean_ball_volume_positive _ (by linarith only [S.separation_pos])).ne.symm
 
 private theorem SpherePacking.local_density_lower_bound (hd : 0 < d) (R : ℝ) :
     S.densityInsideRadius R
@@ -435,7 +435,7 @@ private theorem SpherePacking.local_density_lower_bound (hd : 0 < d) (R : ℝ) :
   rw [densityInsideRadius, occupiedBallRegion]
   apply ENNReal.div_le_div_right
   exact (ENNReal.le_div_iff_mul_le
-    (Or.inl (euclidean_ball_volume_positive _ (by linarith [S.separation_pos])).ne.symm)
+    (Or.inl (euclidean_ball_volume_positive _ (by linarith only [S.separation_pos])).ne.symm)
     (Or.inl (euclidean_ball_volume_finite _).ne)).1 <|
       (by simpa only [Set.iUnion_coe_set,
         sub_add_cancel] using! (S.center_count_in_ball_upper_bound hd (R - S.separation / 2)))
@@ -449,7 +449,7 @@ private theorem SpherePacking.local_density_upper_bound (hd : 0 < d) (R : ℝ) :
   rw [densityInsideRadius, occupiedBallRegion]
   apply ENNReal.div_le_div_right
   exact (ENNReal.div_le_iff_le_mul
-    (Or.inl (euclidean_ball_volume_positive _ (by linarith [S.separation_pos])).ne.symm)
+    (Or.inl (euclidean_ball_volume_positive _ (by linarith only [S.separation_pos])).ne.symm)
     (Or.inl (euclidean_ball_volume_finite _).ne)).1 <|
       (by simpa only [Set.iUnion_coe_set, add_sub_cancel_right,
         ge_iff_le] using! (S.center_count_in_ball_lower_bound (R + S.separation / 2)))
@@ -697,8 +697,9 @@ private lemma finite_centers_in_bounded_region (hD_isBounded : IsBounded D) (hd
       (c := volume (ball (0 : EuclideanSpace ℝ (Fin d)) (S.separation / 2)))
       (hc := by
         simpa only  using!
-          euclidean_ball_volume_positive (0 : EuclideanSpace ℝ (Fin d)) (by linarith
-            [S.separation_pos]))
+          euclidean_ball_volume_positive (0 : EuclideanSpace ℝ (Fin d)) (by linarith only [
+            S.separation_pos
+          ]))
       (h_measurable := fun _ _ => measurableSet_ball)
       (h_bounded := bounded_union_of_center_balls S D hD_isBounded)
       (h_volume := fun _ _ => by simp only [Measure.addHaar_ball_center, Std.le_refl])
@@ -863,7 +864,7 @@ private theorem PeriodicSpherePacking.card_centers_in_fundamental_region
     haveI := @Fintype.ofFinite _ <| finite_centers_in_bounded_region S D hD_isBounded hd
     (S.centers ∩ D).toFinset.card = S.centerOrbitCardinality := by
   rw [centerOrbitCardinality]
-  convert! Finset.card_eq_of_equiv_fintype ?_
+  convert Finset.card_eq_of_equiv_fintype ?_
   simpa only [mem_toFinset,
     mem_inter_iff] using! (S.centerOrbitEquivFundamentalRegion D hD_unique_covers).symm
 
@@ -873,7 +874,7 @@ private theorem PeriodicSpherePacking.encard_centers_in_fundamental_region
     (hd : 0 < d) :
     (S.centers ∩ D).encard = S.centerOrbitCardinality := by
   rw [← S.card_centers_in_fundamental_region D hD_isBounded hD_unique_covers hd]
-  convert! Set.encard_eq_coe_toFinset_card _
+  convert Set.encard_eq_coe_toFinset_card _
 
 private theorem PeriodicSpherePacking.card_centers_in_translated_region (hd : 0 < d)
     {ι : Type*} [Finite ι] (b : Basis ι ℤ S.lattice) (v : EuclideanSpace ℝ (Fin d)) :
@@ -889,7 +890,7 @@ private theorem PeriodicSpherePacking.encard_centers_in_translated_region (hd :
     (S.centers ∩ (v +ᵥ fundamentalDomain (b.ofZLatticeBasis ℝ _))).encard =
       S.centerOrbitCardinality := by
   rw [← S.card_centers_in_translated_region hd b]
-  convert! Set.encard_eq_coe_toFinset_card _
+  convert Set.encard_eq_coe_toFinset_card _
 
 end centerOrbitCardinality
 
@@ -940,7 +941,7 @@ private theorem iUnion_lattice_inter_ball_sub_vadd_fundamentalDomain_subset_ball
     simpa only [mem_ball, dist_zero_right] using hx.2
   have hynorm : ‖y‖ ≤ L := hL y hy
   have hsum : ‖x + y‖ < R :=
-    lt_of_le_of_lt (norm_add_le x y) (by linarith)
+    lt_of_le_of_lt (norm_add_le x y) (by linarith only [hxnorm, hynorm])
   simpa only [vadd_eq_add, mem_ball, dist_zero_right, gt_iff_lt] using hsum
 
 private theorem fundamental_region_translates_disjoint
@@ -1300,7 +1301,7 @@ private theorem volume_ball_add_div_volume_ball_add_tendsto_one_of_nonneg
       simpa only [add_zero] using tendsto_const_nhds.add herror
     apply Tendsto.congr' (f₁ := fun R : ℝ => 1 + (C - C') / (R + C')) ?_ hsum
     filter_upwards [eventually_ge_atTop (1 : ℝ)] with R hR
-    have hden : R + C' ≠ 0 := ne_of_gt (by linarith)
+    have hden : R + C' ≠ 0 := ne_of_gt (by linarith only [hC', hR])
     field_simp; ring
   have hpow : Tendsto (fun R : ℝ => ((R + C) / (R + C')) ^ d) atTop (𝓝 1) := by
     simpa only [one_pow] using hratio.pow d
@@ -1329,8 +1330,8 @@ private theorem Filter.atTop_invariant_under_translation {β : Type*} {f : ℝ 
 private theorem volume_ball_add_div_volume_ball_add_tendsto_one {d : ℕ} {C C' : ℝ} (hd : 0 < d) :
     Tendsto (fun R ↦ volume (ball (0 : EuclideanSpace ℝ (Fin d)) (R + C))
       / volume (ball (0 : EuclideanSpace ℝ (Fin d)) (R + C'))) atTop (𝓝 1) := by
-  have hC₀ : 0 ≤ max (-C) (-C') + C := by linarith [le_max_left (-C) (-C')]
-  have hC'₀ : 0 ≤ max (-C) (-C') + C' := by linarith [le_max_right (-C) (-C')]
+  have hC₀ : 0 ≤ max (-C) (-C') + C := by linarith only [le_max_left (-C) (-C')]
+  have hC'₀ : 0 ≤ max (-C) (-C') + C' := by linarith only [le_max_right (-C) (-C')]
   refine (Filter.atTop_invariant_under_translation (f := fun R ↦
       volume (ball (0 : EuclideanSpace ℝ (Fin d)) (R + C)) /
         volume (ball (0 : EuclideanSpace ℝ (Fin d)) (R + C'))) (max (-C) (-C')) _).mpr ?_
@@ -1371,14 +1372,14 @@ private lemma PeriodicSpherePacking.local_packing_density_tends_to_formula
   · rw [show ∀ a : ENNReal, 𝓝 a = 𝓝 (a * 1) by intro; rw [mul_one]]
     apply ENNReal.Tendsto.const_mul
     · simp_rw [sub_sub, sub_eq_add_neg]
-      convert! volume_ball_add_div_volume_ball_add_tendsto_one hd (C := -(S.separation / 2 + L * 2))
+      convert volume_ball_add_div_volume_ball_add_tendsto_one hd (C := -(S.separation / 2 + L * 2))
       rw [add_zero]
     · left
       exact one_ne_zero
   · rw [show ∀ a : ENNReal, 𝓝 a = 𝓝 (a * 1) by intro; rw [mul_one]]
     apply ENNReal.Tendsto.const_mul
     · simp_rw [add_assoc]
-      convert! volume_ball_add_div_volume_ball_add_tendsto_one hd (C := S.separation / 2 + L * 2)
+      convert volume_ball_add_div_volume_ball_add_tendsto_one hd (C := S.separation / 2 + L * 2)
       rw [add_zero]
     · left
       exact one_ne_zero
@@ -1550,11 +1551,11 @@ private lemma metric_ball_subset_axis_cell {x : EuclideanSpace ℝ (Fin d)} {r L
   have hsub : |y i - x i| < r := coordinate_difference_small_inside_ball (d := d) hy i
   have hy0 : 0 ≤ y i := by
     have hx0 : 0 ≤ x i - r := sub_nonneg.mpr hxi.1
-    have : x i - r < y i := by linarith [(abs_lt.mp hsub).1]
+    have : x i - r < y i := by linarith only [(abs_lt.mp hsub).1, hsub]
     exact hx0.trans (le_of_lt this)
   have hyL : y i < L := by
-    have : y i < x i + r := by linarith [(abs_lt.mp hsub).2]
-    exact lt_of_lt_of_le this (by linarith [hxi.2])
+    have : y i < x i + r := by linarith only [(abs_lt.mp hsub).2, hsub]
+    exact lt_of_lt_of_le this (by linarith only [hxi.2, hxi])
   exact ⟨hy0, hyL⟩
 
 private lemma center_distance_bound_of_disjoint_regions {x y : EuclideanSpace ℝ (Fin d)} {r : ℝ}
@@ -1564,7 +1565,7 @@ private lemma center_distance_bound_of_disjoint_regions {x y : EuclideanSpace 
   by_contra hlt
   have hlt' : dist x y < 2 * r := lt_of_not_ge hlt
   let m : EuclideanSpace ℝ (Fin d) := midpoint ℝ x y
-  have hhalf : (1 / 2 : ℝ) * dist x y < r := by linarith
+  have hhalf : (1 / 2 : ℝ) * dist x y < r := by linarith only [hlt]
   have hmx : m ∈ ball x r := by
     simpa only [mem_ball, dist_comm, dist_left_midpoint,
       Real.norm_ofNat] using! (by simpa only [dist_midpoint_left, Real.norm_ofNat, one_div,
@@ -2208,7 +2209,7 @@ private lemma unit_inset_cell_subset_shifted_shell (L : ℝ) :
     WithLp.ofLp_neg, Pi.add_apply, Pi.neg_apply, neg_neg]
   exact fun i => by
     let hxi := hx' i
-    refine ⟨by linarith [hxi.1], by linarith [hxi.2]⟩
+    refine ⟨by linarith only [hxi.1, hxi], by linarith only [hxi.2, hxi]⟩
 
 private lemma axis_shell_volume_difference (L : ℝ) :
     volume (((uniformShellShift d (- (1 / 2 : ℝ))) +ᵥ insetAxisAlignedCell (d := d) (L + 1) 0) \
@@ -2400,9 +2401,9 @@ private lemma axis_shell_relative_cell_volume_tends_zero :
         (axis_shell_volume_ratio_tends_zero (d := d))
   refine hlimit.congr' ?_
   filter_upwards [eventually_gt_atTop (2 : ℝ)] with L hL
-  have hL0 : 0 < L := by linarith
-  have hLplus : 0 ≤ L + 1 := by linarith
-  have hLminus : 0 ≤ L - 2 := by linarith
+  have hL0 : 0 < L := by linear_combination hL
+  have hLplus : 0 ≤ L + 1 := by linear_combination hL
+  have hLminus : 0 ≤ L - 2 := by linear_combination hL
   rw [axis_shell_volume_power_formula, PeriodicConstant.axis_cell_volume_formula,
     ← ENNReal.ofReal_pow hLplus d, ← ENNReal.ofReal_pow hLminus d,
     ← ENNReal.ofReal_pow hL0.le d,
@@ -3279,7 +3280,7 @@ private lemma summable_restricted_lattice_translate_norms (K : TopologicalSpace.
         linarith only [hxnorm, hnorm_lt]
       have : (1 / 2 : ℝ) * ‖(ℓ : (EuclideanSpace ℝ (Fin d)))‖ ≤ ‖(ℓ : (EuclideanSpace ℝ (Fin
         d)))‖ - ‖(x : (EuclideanSpace ℝ (Fin d)))‖ := by
-        linarith [le_of_lt hxlt]
+        linarith only [le_of_lt hxlt, hnorm_lt, hxnorm]
       have : (1 / 2 : ℝ) * ‖(ℓ : (EuclideanSpace ℝ (Fin d)))‖ ≤ ‖(ℓ : (EuclideanSpace ℝ (Fin
         d))) + x‖ := le_trans this hsub
       simpa only [one_div, ge_iff_le, add_comm] using! this
@@ -4212,7 +4213,7 @@ private theorem integer_lattice_poisson_identity (f : SchwartzMap (EuclideanSpac
         𝓕 (fun x : (EuclideanSpace ℝ (Fin d)) => g x) w =
           cC * 𝓕 (fun x : (EuclideanSpace ℝ (Fin d)) => f x) ((dualCoordinateTransport (d := d)
             L) w) := by
-      simpa [g, A, dualCoordinateTransport, detA, cC, Complex.real_smul] using!
+      simpa only [g, A, dualCoordinateTransport, detA, cC, Complex.real_smul] using!
         (SpherePacking.ForMathlib.Fourier.fourier_precompose_linear_equivalence
           (A := A) (f := fun x : (EuclideanSpace ℝ (Fin d)) => f x) w)
     have hexp (w : (EuclideanSpace ℝ (Fin d))) :
@@ -4336,7 +4337,7 @@ private theorem Continuous.nonnegative_integral_vanishes_iff_function_vanishes {
       hopen.measure_pos volume ⟨x, hx⟩
     have hpositive : 0 < ∫ v : E, f v :=
       (integral_pos_iff_support_of_nonneg hnn hf₂).2 hmeasure
-    linarith
+    linarith only [hzero, hpositive]
   · intro hzero
     simp only [hzero, Pi.zero_apply, integral_zero]
 
@@ -4496,7 +4497,7 @@ private lemma summable_norm_on_translated_integral_lattice (f : 𝓢(EuclideanSp
           ‖a + (ℓ : EuclideanSpace ℝ (Fin d))‖ := by
       simpa only [tsub_le_iff_right, add_comm, norm_neg, sub_neg_eq_add] using!
         (norm_sub_norm_le (ℓ : EuclideanSpace ℝ (Fin d)) (-a))
-    linarith
+    linarith only [hlarge, htriangle]
   have htranslatePositive :
       0 < ‖a + (ℓ : EuclideanSpace ℝ (Fin d))‖ :=
     (mul_pos (by norm_num : (0 : ℝ) < 1 / 2) hpositive).trans_le htranslate
@@ -5383,7 +5384,7 @@ private theorem packing_bound_geometric_estimate (hd : 0 < d) :
     (f := f) hCohnElkies₁ hP hD_isBounded hd hD_unique_covers
   rw [SpherePacking.CohnElkies.center_double_sum_eq_region_lattice_sum
     (f := f) (P := P) (D := D) hD_isBounded hD_unique_covers hd] at hbound
-  linarith [hgeom]
+  linarith only [hgeom, hD_isBounded, hd, hbound]
 
 include d f hP hne_zero hReal hRealFourier hCohnElkies₁ hCohnElkies₂ in
 omit hne_zero hReal hRealFourier hCohnElkies₁ hP [Nonempty ↑P.centers] in
@@ -5471,7 +5472,7 @@ private theorem packing_bound_spectral_estimate (hd : 0 < d) :
       P hd hD_isBounded]
   have hsum : (𝓕 f 0).re * N ^ 2 ≤ ∑' m, F m := by
     rw [hFsummable.tsum_eq_add_tsum_ite 0, horigin]
-    linarith
+    linarith only [htail]
   have hcovol : 0 ≤ ZLattice.covolume P.lattice volume := by
     rw [SchwartzMap.lattice_covolume_eq_coordinate_determinant]
     exact abs_nonneg _
diff --git a/LeanPool/SpherePacking/RadialConstruction.lean b/LeanPool/SpherePacking/RadialConstruction.lean
index 498ba8cf6c..f073b18982 100644
--- a/LeanPool/SpherePacking/RadialConstruction.lean
+++ b/LeanPool/SpherePacking/RadialConstruction.lean
@@ -129,14 +129,14 @@ private theorem lowerGammaBoundaryLog_pole_decomposition
     have him := congrArg Complex.im h
     try dsimp [s] at him
     norm_num at him
-    exact hy (by linarith)
+    exact hy (by exact him)
   have hgammas : Complex.Gamma s ≠ 0 := by
     apply Complex.Gamma_ne_zero
     intro m hm
     have him := congrArg Complex.im hm
     try dsimp [s] at him
     norm_num at him
-    exact hy (by linarith)
+    exact hy (by exact him)
   have hnorm :
       ‖Complex.Gamma (s + 1)‖ =
         ‖s‖ * ‖Complex.Gamma s‖ := by
@@ -188,20 +188,22 @@ private theorem lowerGammaBoundaryLog_tendsto_atTop_zero
     have hre := congrArg Complex.re hm
     norm_num at hre
     have hmnonneg : 0 ≤ (m : ℝ) := Nat.cast_nonneg m
-    linarith
+    linarith only [hre]
   have hdenPole :
       ∀ m : ℕ, (ℓ : ℂ) ≠ -(m : ℂ) := by
     intro m hm
     have hre := congrArg Complex.re hm
     norm_num at hre
     have hmnonneg : 0 ≤ (m : ℝ) := Nat.cast_nonneg m
-    linarith
+    linarith only [hℓ, hre]
   have hnumGamma :
       ContinuousAt (fun y : ℝ =>
         Complex.Gamma (1 - Complex.I * (y : ℂ) / 2)) 0 := by
     apply (Complex.continuousAt_Gamma (1 : ℂ)
       hnumPole).comp_of_eq
-    · fun_prop
+    · exact ContinuousAt.fun_sub continuousAt_const
+        (ContinuousAt.comp' (Continuous.continuousAt (Continuous.div_const continuous_id' 2))
+          (ContinuousAt.const_mul (Continuous.continuousAt Complex.continuous_ofReal) Complex.I))
     · norm_num
   have hdenGamma :
       ContinuousAt (fun y : ℝ =>
@@ -209,7 +211,10 @@ private theorem lowerGammaBoundaryLog_tendsto_atTop_zero
           ((ℓ : ℂ) + Complex.I * (y : ℂ) / 2)) 0 := by
     apply (Complex.continuousAt_Gamma (ℓ : ℂ)
       hdenPole).comp_of_eq
-    · fun_prop
+    · exact ContinuousAt.const_add
+        (ContinuousAt.comp' (Continuous.continuousAt (Continuous.div_const continuous_id' 2))
+          (ContinuousAt.const_mul (Continuous.continuousAt Complex.continuous_ofReal) Complex.I))
+        ↑ℓ
     · norm_num
   have hnumLog :
       ContinuousAt (fun y : ℝ =>
@@ -246,7 +251,7 @@ private theorem lowerGammaBoundaryLog_tendsto_atTop_zero
         (𝓝 (ℓ * Real.log (Real.pi * R ^ 2) +
           Real.log ‖Complex.Gamma (1 : ℂ)‖ -
           Real.log ‖Complex.Gamma (ℓ : ℂ)‖)) := by
-    convert! hregular.tendsto.mono_left
+    convert hregular.tendsto.mono_left
       (nhdsWithin_le_nhds (s := {(0 : ℝ)}ᶜ)) using 1;
         norm_num
   have hnegative :
@@ -331,7 +336,7 @@ private theorem lowerGammaBoundaryCapped_exp_integrable_of_exp_integrable
     hgammaabs.add (hbase.const_mul |D|)
   have hweight : Continuous
       (fun y : ℝ => Real.exp ((-a) * |y|)) := by
-    fun_prop
+    exact Continuous.rexp (Continuous.const_mul (Continuous.abs continuous_id') (-a))
   apply hmajor.mono'
     ((hweight.mul
       (lowerGammaBoundaryCapped_continuous
@@ -565,7 +570,7 @@ private theorem stripRegularizedOuter_differentiableAt_of_exp_integrable
   have hstrip :
       Complex.im ⁻¹' Ioo (-ℓ) ℓ ∈ 𝓝 z := by
     have him : Continuous (fun w : ℂ => w.im) := by
-      fun_prop
+      exact Complex.continuous_im
     exact (isOpen_Ioo.preimage him).mem_nhds hz
   have hneighborhood :
       S ∩ (Complex.im ⁻¹' Ioo (-ℓ) ℓ) ∈ 𝓝 z :=
@@ -782,8 +787,8 @@ private theorem lowerStripCappedGammaOuter_re_dimension
       Complex.I_re, Complex.ofReal_re, zero_mul,
       Complex.I_im, one_mul, zero_add]
     constructor
-    · linarith [mul_pos (show 0 < 1 + σ by linarith) hℓ]
-    · linarith [mul_pos (show 0 < 1 - σ by linarith) hℓ]
+    · linarith only [mul_pos (show 0 < 1 + σ by linarith) hℓ, hσbelow, hℓ]
+    · linarith only [mul_pos (show 0 < 1 - σ by linarith) hℓ, hσabove, hℓ]
   unfold lowerStripCappedGammaOuter
   exact stripRegularizedOuter_re hℓ hσbelow hσabove s
     (lowerGammaBoundaryCapped ((d : ℝ) / 2) R D)
@@ -801,13 +806,14 @@ private theorem stripPoissonKernel_tendsto_zero_bottom_of_ne
     Real.one_lt_cosh.mpr hu
   have hangle : Continuous (fun σ : ℝ => stripAngle σ) := by
     unfold stripAngle
-    fun_prop
+    exact Continuous.comp' (Continuous.div_const continuous_id' 2)
+        (Continuous.const_mul (Continuous.const_add continuous_id' 1) Real.pi)
   have hden :
       4 * (Real.cosh (Real.pi * T / 2) -
         Real.cos (stripAngle (-1))) ≠ 0 := by
     simp only [stripAngle]
     norm_num
-    linarith
+    linarith only [hcosh]
   have hcontinuous :
       ContinuousAt (fun σ : ℝ => stripPoissonKernel σ T)
         (-1 : ℝ) := by
@@ -816,7 +822,7 @@ private theorem stripPoissonKernel_tendsto_zero_bottom_of_ne
       (continuousAt_const.mul
         (continuousAt_const.sub
           (Real.continuous_cos.comp hangle).continuousAt)) hden)
-  convert! hcontinuous.tendsto using 1
+  convert hcontinuous.tendsto using 1
   all_goals simp only [stripPoissonKernel, stripAngle, add_neg_cancel, mul_zero, zero_div,
     Real.sin_zero, Real.cos_zero]
 
@@ -839,19 +845,20 @@ private theorem stripPoissonKernel_le_center_of_lower_of_abs_ge
   have hc : 0 < c := by
     try dsimp [c]
     have hrecip : C⁻¹ < 1 := (inv_lt_one₀ hCpos).mpr hC
-    linarith
+    linear_combination hrecip
   have hA : 0 < A := Real.cosh_pos _
   have hCA : C ≤ A := by
     apply Real.cosh_le_cosh.mpr
     rw [abs_div, abs_div, abs_mul, abs_mul,
       abs_of_pos Real.pi_pos, abs_of_pos hδ]
     norm_num
-    gcongr
+    exact div_le_div_of_nonneg_right (mul_le_mul_of_nonneg_left hT (le_of_lt Real.pi_pos))
+        zero_le_two
   have hratio : 1 ≤ A / C := by
     apply (le_div_iff₀ hCpos).2
     simpa only [one_mul] using! hCA
   have hangle := stripAngle_mem_Ioo hbelow
-    (show σ < 1 by linarith)
+    (show σ < 1 by linear_combination hnonpos)
   have hcoslt : Real.cos (stripAngle σ) < 1 := by
     have h := Real.cos_lt_cos_of_nonneg_of_le_pi
       (x := 0) (y := stripAngle σ)
@@ -861,12 +868,12 @@ private theorem stripPoissonKernel_le_center_of_lower_of_abs_ge
     Real.sin_pos_of_pos_of_lt_pi hangle.1 hangle.2
   have hden : 0 < A - Real.cos (stripAngle σ) := by
     try dsimp [A]
-    linarith [Real.one_le_cosh (Real.pi * T / 2)]
+    linarith only [Real.one_le_cosh (Real.pi * T / 2), hC, hCA, hcoslt]
   have hcompare : c * A ≤ A - Real.cos (stripAngle σ) := by
     have hcos := Real.cos_le_one (stripAngle σ)
     try dsimp [c]
     rw [sub_mul, one_mul, inv_mul_eq_div]
-    linarith
+    linear_combination hratio + hcoslt
   have hcA : 0 < 4 * (c * A) := by positivity
   calc
     stripPoissonKernel σ T =
@@ -895,15 +902,14 @@ private theorem stripPoissonKernel_le_center_of_lower
   let q : ℝ := Real.cos (stripAngle σ)
   let c : ℝ := 1 - q
   have hangle := stripAngle_mem_Ioo hbelow
-    (show σ < 1 by linarith)
+    (show σ < 1 by linear_combination hnonpos)
   have hhalf : stripAngle σ ≤ Real.pi / 2 := by
     unfold stripAngle
-    linarith [mul_nonpos_of_nonneg_of_nonpos
-      Real.pi_pos.le hnonpos]
+    linarith only [mul_nonpos_of_nonneg_of_nonpos Real.pi_pos.le hnonpos, hnonpos]
   have hq : 0 ≤ q := by
     try dsimp [q]
     apply Real.cos_nonneg_of_mem_Icc
-    exact ⟨by linarith [Real.pi_pos], hhalf⟩
+    exact ⟨by linarith only [Real.pi_pos, hangle], hhalf⟩
   have hqlt : q < 1 := by
     try dsimp [q]
     have h := Real.cos_lt_cos_of_nonneg_of_le_pi
@@ -912,12 +918,12 @@ private theorem stripPoissonKernel_le_center_of_lower
     simpa only [gt_iff_lt, Real.cos_zero] using! h
   have hc : 0 < c := by
     try dsimp [c]
-    linarith
+    linear_combination hqlt
   have hA : 0 < A := Real.cosh_pos _
   have hAone : 1 ≤ A := Real.one_le_cosh _
   have hcompare : c * A ≤ A - q := by
     try dsimp [c]
-    linarith [mul_nonneg hq (sub_nonneg.mpr hAone)]
+    linarith only [mul_nonneg hq (sub_nonneg.mpr hAone), hq, hAone]
   have hsin : 0 < Real.sin (stripAngle σ) :=
     Real.sin_pos_of_pos_of_lt_pi hangle.1 hangle.2
   have hcA : 0 < 4 * (c * A) := by positivity
@@ -951,7 +957,7 @@ private theorem stripPoissonKernel_lower_product_integrable
       stripPoissonKernel σ T * g T) := by
   let C : ℝ := 1 / (1 - Real.cos (stripAngle σ))
   have hangle := stripAngle_mem_Ioo hbelow
-    (show σ < 1 by linarith)
+    (show σ < 1 by linear_combination hnonpos)
   have hqlt : Real.cos (stripAngle σ) < 1 := by
     have h := Real.cos_lt_cos_of_nonneg_of_le_pi
       (x := 0) (y := stripAngle σ)
@@ -959,7 +965,7 @@ private theorem stripPoissonKernel_lower_product_integrable
     simpa only [gt_iff_lt, Real.cos_zero] using! h
   have hC : 0 < C := by
     try dsimp [C]
-    exact one_div_pos.mpr (by linarith)
+    exact one_div_pos.mpr (by linear_combination hqlt)
   have hmajor : Integrable
       (fun T : ℝ => C *
         ‖stripPoissonKernel 0 T * g T‖) :=
@@ -974,7 +980,7 @@ private theorem stripPoissonKernel_lower_product_integrable
   apply hmajor.mono' hmeas.aestronglyMeasurable
   filter_upwards [] with T
   have hσpositive := stripPoissonKernel_pos
-    hbelow (show σ < 1 by linarith) T
+    hbelow (show σ < 1 by linear_combination hnonpos) T
   have hzero := stripPoissonKernel_pos
     (by norm_num : (-1 : ℝ) < 0)
     (by norm_num : (0 : ℝ) < 1) T
@@ -1008,14 +1014,14 @@ private theorem lowerGammaBoundaryCapped_central_poisson_shift_integrable
       Complex.add_im, Complex.ofReal_im, Complex.mul_im,
       Complex.I_re, Complex.I_im, Complex.ofReal_re,
       zero_mul, one_mul, zero_add]
-    constructor <;> linarith
+    constructor <;> linarith only [hℓ]
   have houter := lowerStripCappedGammaOuter_integrable_dimension
     hd (R := R) (D := D) hz
   have hreal := houter.re
   have htranslated := hreal.comp_sub_left s
   have hscaled := htranslated.comp_mul_left' hℓ.ne'
   have hproduct := hscaled.const_mul ℓ
-  convert! hproduct using 1
+  convert hproduct using 1
   ext T
   change
     stripPoissonKernel 0 T *
@@ -1192,8 +1198,8 @@ private theorem horizontalStrip_norm_extension_majorization
   obtain ⟨m, r, rfl, rfl⟩ :
       ∃ m r : ℝ, a = m - r ∧ b = m + r :=
     ⟨(a + b) / 2, (b - a) / 2, by ring, by ring⟩
-  have hr : 0 < r := by linarith
-  have hwidth : m - r < m + r := by linarith
+  have hr : 0 < r := by linarith only [hza, hzb]
+  have hwidth : m - r < m + r := by linarith only [hza, hzb]
   rw [add_sub_sub_cancel, ← two_mul,
     div_mul_eq_div_div] at hgrowth
   have hπr : 0 < Real.pi / 2 / r :=
@@ -1251,7 +1257,7 @@ private theorem horizontalStrip_norm_extension_majorization
       rw [Complex.im_ofReal_mul, Complex.sub_im,
         Complex.mul_I_im, Complex.ofReal_re,
         abs_mul, abs_of_pos hq]
-      gcongr
+      exact mul_le_mul_of_nonneg_left hw (le_of_lt hq)
     simpa only [aff, Complex.re_ofReal_mul,
       abs_mul, abs_of_pos hq, Complex.sub_re,
       Complex.mul_I_re, Complex.ofReal_im,
@@ -1379,21 +1385,21 @@ private theorem horizontalStrip_norm_extension_majorization
 private theorem harmonic_abs_log_half_le_half
     {x : ℝ} (hx : 2 ≤ x) :
     |Real.log (x / 2)| ≤ x / 2 := by
-  have hhalf : 1 ≤ x / 2 := by linarith
+  have hhalf : 1 ≤ x / 2 := by linarith only [hx]
   rw [abs_of_nonneg (Real.log_nonneg hhalf)]
   have hlog :=
     Real.log_le_sub_one_of_pos
-      (show 0 < x / 2 by linarith)
-  linarith
+      (show 0 < x / 2 by linarith only [hx])
+  linear_combination hlog
 
 private theorem harmonic_abs_log_sqrtFactor_le_linear
     {c x : ℝ} (hc : 0 ≤ c) (hx : 2 ≤ x) :
     |Real.log
       (Real.sqrt (c ^ 2 + (x / 2) ^ 2))| ≤ c + x := by
   have hfactor := lower_abs_log_sqrtFactor_le
-    hc (show 0 < x by linarith)
+    hc (show 0 < x by linear_combination hx)
   have hlog := harmonic_abs_log_half_le_half hx
-  linarith
+  linear_combination hfactor + hlog
 
 private theorem harmonic_abs_log_coth_div_le_linear
     {x : ℝ} (hx : 2 ≤ x) :
@@ -1401,9 +1407,9 @@ private theorem harmonic_abs_log_coth_div_le_linear
       (lowerCoth (Real.pi * (x / 2)) / (x / 2))| ≤
       Real.pi * x + |Real.log Real.pi| + x := by
   have hcorr := lower_abs_log_coth_div_le
-    (show 0 < x / 2 by linarith)
+    (show 0 < x / 2 by linarith only [hx])
   have hlog := harmonic_abs_log_half_le_half hx
-  linarith
+  linarith only [hcorr, hlog]
 
 private theorem harmonic_integerGammaBoundary_abs_le_linear
     (k : ℕ) (R : ℝ) :
@@ -1425,7 +1431,7 @@ private theorem harmonic_integerGammaBoundary_abs_le_linear
     positivity
   refine ⟨A, hA, ?_⟩
   intro x hx
-  have hxzero : x ≠ 0 := by linarith
+  have hxzero : x ≠ 0 := by linarith only [hx]
   have hsum :
       |∑ j ∈ Finset.range k,
         Real.log
@@ -1455,11 +1461,20 @@ private theorem harmonic_integerGammaBoundary_abs_le_linear
       Real.log (Real.sqrt
         ((j : ℝ) ^ 2 + (x / 2) ^ 2)))
   have hk : 0 ≤ (k : ℝ) := Nat.cast_nonneg k
-  have hxpos : 0 ≤ x := by linarith
+  have hxpos : 0 ≤ x := by linear_combination hx
   try dsimp [A, L]
   try dsimp [L] at hL
-  linarith [mul_nonneg hL hxpos,
-    mul_nonneg hS hxpos, mul_nonneg hk hxpos]
+  linarith only [
+    mul_nonneg hL hxpos,
+    mul_nonneg hS hxpos,
+    mul_nonneg hk hxpos,
+    hS,
+    hL,
+    hx,
+    hsum,
+    habs,
+    hxpos
+  ]
 
 private theorem harmonic_halfIntegerGammaBoundary_abs_le_linear
     (k : ℕ) (R : ℝ) :
@@ -1485,7 +1500,7 @@ private theorem harmonic_halfIntegerGammaBoundary_abs_le_linear
       Real.pi_pos.le) hQ) zero_le_two
   refine ⟨A, hA, ?_⟩
   intro x hx
-  have hxpos : 0 < x := by linarith
+  have hxpos : 0 < x := by linarith only [hx]
   have hsum :
       |∑ j ∈ Finset.range k,
         Real.log
@@ -1646,7 +1661,7 @@ private theorem lowerGammaBoundaryCapped_dimension_abs_le_linear
   refine ⟨A, hA, ?_⟩
   intro y
   have hfactor : 1 ≤ 1 + |y| := by
-    linarith [abs_nonneg y]
+    linarith only [abs_nonneg y]
   by_cases hy : |y| < 2
   · have hymem : y ∈ Icc (-2 : ℝ) 2 := by
       have hbounds := abs_lt.mp hy
@@ -1658,7 +1673,7 @@ private theorem lowerGammaBoundaryCapped_dimension_abs_le_linear
           ((d : ℝ) / 2) R D y| ≤ K := hcompact
       _ ≤ A := hKA
       _ ≤ A * (1 + |y|) := by
-        linarith [mul_nonneg hA (abs_nonneg y)]
+        linarith only [mul_nonneg hA (abs_nonneg y), hA]
   · have hylarge : 2 ≤ |y| := le_of_not_gt hy
     have hyzero : y ≠ 0 := by
       intro heq
@@ -1680,14 +1695,14 @@ private theorem lowerGammaBoundaryCapped_dimension_abs_le_linear
       calc
         |D| ≤ A := hDA
         _ ≤ A * (1 + |y|) := by
-          linarith [mul_nonneg hA (abs_nonneg y)]
+          linarith only [mul_nonneg hA (abs_nonneg y), hA]
 
 private theorem stripPoissonKernel_le_exponentialMajorant_of_nonneg
     {σ : ℝ} (hσ : 0 ≤ σ) (hσone : σ < 1)
     (T : ℝ) :
     stripPoissonKernel σ T ≤
       stripPoissonExponentialMajorant T := by
-  have hbelow : -1 < σ := by linarith
+  have hbelow : -1 < σ := by linear_combination hσ
   have hmass := stripBottomMass_pos hσone
   have hmassone :=
     (stripBottomMass_lt_one hbelow).le
@@ -1719,10 +1734,9 @@ private theorem harmonic_stripPoissonExponentialMajorant_abs_integrable :
     integrable_abs_pow_mul_exp_neg_mul_abs 1
       (half_pos Real.pi_pos)
   have hconstant := hbase.const_mul (Real.pi / 2)
-  convert! hconstant using 1
+  convert hconstant using 1
   ext T
   unfold stripPoissonExponentialMajorant
-  norm_num
   ring
 
 private theorem harmonic_stripPoissonKernel_zero_abs_integrable :
@@ -1800,7 +1814,7 @@ private theorem exists_stripPoissonKernel_uniform_abs_moment :
     try dsimp [C]
     have hpositive := Real.cosh_pos (Real.pi / 2)
     have hinv := (inv_lt_one₀ hpositive).mpr hcosh
-    exact one_div_pos.mpr (by linarith)
+    exact one_div_pos.mpr (by linear_combination hinv)
   have hJ : 0 ≤ J := by
     try dsimp [J]
     apply integral_nonneg
@@ -1863,9 +1877,7 @@ private theorem exists_stripPoissonKernel_uniform_abs_moment :
             congr 2
             ring_nf
           rw [hCeq] at hcompare
-          linarith [mul_nonneg
-            (sub_nonneg.mpr hcompare)
-            (abs_nonneg T)]
+          linarith only [mul_nonneg (sub_nonneg.mpr hcompare) (abs_nonneg T), hcompare]
         _ ≤ ∫ T : ℝ,
             C * (stripPoissonKernel 0 T * |T|) := by
           apply setIntegral_le_integral hscaled
@@ -1898,8 +1910,7 @@ private theorem exists_stripPoissonKernel_uniform_abs_moment :
           have hkpos :=
             stripPoissonKernel_pos
               hbelow habove T
-          linarith [mul_nonneg hkpos.le
-            (sub_nonneg.mpr hTabs)]
+          linarith only [mul_nonneg hkpos.le (sub_nonneg.mpr hTabs), hTabs, hkpos]
         _ ≤ ∫ T : ℝ,
             stripPoissonKernel σ T := by
           apply setIntegral_le_integral hk
@@ -1911,7 +1922,7 @@ private theorem exists_stripPoissonKernel_uniform_abs_moment :
         _ ≤ 1 := (stripBottomMass_lt_one hbelow).le
     have hsplit := integral_add_compl hS hmoment
     try dsimp [M]
-    linarith
+    linarith only [hE, hfar, hnear, hsplit]
   · have hσnonneg : 0 ≤ σ := le_of_not_ge hσ
     have hmajor :=
       harmonic_stripPoissonExponentialMajorant_abs_integrable
@@ -1926,7 +1937,7 @@ private theorem exists_stripPoissonKernel_uniform_abs_moment :
           hσnonneg habove T)
         (abs_nonneg T)
     try dsimp [M]
-    linarith [mul_nonneg hC.le hJ]
+    linarith only [mul_nonneg hC.le hJ, hC, hJ, habove, hσ, hineq]
 
 private theorem lowerGammaBoundaryCapped_poisson_abs_le_linear
     {d : ℕ} (hd : 0 < d) (R D : ℝ) :
@@ -1997,9 +2008,8 @@ private theorem lowerGammaBoundaryCapped_poisson_abs_le_linear
             A * (1 + |s - ℓ * T|) := hb
         _ ≤ A * (1 + |s| + ℓ * |T|) := by
           apply mul_le_mul_of_nonneg_left _ hA
-          linarith
-    linarith [mul_nonneg hkpos.le
-      (sub_nonneg.mpr hbig)]
+          linarith only [htriangle]
+    linarith only [mul_nonneg hkpos.le (sub_nonneg.mpr hbig), hkpos, hbig]
   have hmass :=
     (stripBottomMass_lt_one hbelow).le
   have hmasspos :=
@@ -2034,12 +2044,10 @@ private theorem lowerGammaBoundaryCapped_poisson_abs_le_linear
         hmass (by positivity : 0 ≤ A * (1 + |s|))
       have hsecond := mul_le_mul_of_nonneg_left
         hmomentle (by positivity : 0 ≤ A * ℓ)
-      linarith
+      linarith only [hfirst, hsecond]
     _ ≤ B * (1 + |s|) := by
       try dsimp [B]
-      linarith [mul_nonneg
-        (show 0 ≤ A * ℓ * M by positivity)
-        (abs_nonneg s)]
+      linarith only [mul_nonneg (show 0 ≤ A * ℓ * M by positivity) (abs_nonneg s), hd, hA, hM]
 
 private theorem lowerStripCappedGammaOuter_abs_re_le_linear
     {d : ℕ} (hd : 0 < d) (R D : ℝ) :
@@ -2124,7 +2132,7 @@ private theorem antiFourierWitness_cappedWeightedMellinStrip_growth
     try dsimp [c]
     apply (div_lt_div_iff₀
       (by positivity : 0 < 4 * ℓ)
-      (by linarith : 0 < ℓ - (-ℓ))).2
+      (by linarith only [hℓ] : 0 < ℓ - (-ℓ))).2
     exact mul_lt_mul_of_pos_left (by linarith only [hℓ]) Real.pi_pos
   let B : ℝ := G * (1 + 1 / c)
   refine ⟨c, hclt, B, ?_⟩
@@ -2195,8 +2203,7 @@ private theorem antiFourierWitness_cappedWeightedMellinStrip_growth
     _ ≤ (K + 1) *
         Real.exp
           (B * Real.exp (c * |z.re|)) := by
-      linarith [Real.exp_pos
-        (B * Real.exp (c * |z.re|))]
+      linarith only [Real.exp_pos (B * Real.exp (c * |z.re|))]
 
 private theorem harmonic_bottom_normalized_height_tendsto
     {ℓ : ℝ} (hℓ : 0 < ℓ) (s : ℝ) :
@@ -2207,8 +2214,8 @@ private theorem harmonic_bottom_normalized_height_tendsto
       (𝓝 (-1 : ℝ)) := by
   have hcontinuous : Continuous
       (fun z : ℂ => z.im / ℓ) := by
-    fun_prop
-  convert! hcontinuous.continuousAt.tendsto.mono_left
+    exact Continuous.comp' (Continuous.div_const continuous_id' ℓ) continuous_im
+  convert hcontinuous.continuousAt.tendsto.mono_left
     nhdsWithin_le_nhds using 1;
       simp only [sub_im, ofReal_im, mul_im, I_re, mul_zero, I_im, ofReal_re, one_mul, zero_add,
         zero_sub, ne_eq,
@@ -2220,7 +2227,7 @@ private theorem harmonic_bottom_real_tendsto
       (𝓝[Complex.im ⁻¹' Ioo (-ℓ) ℓ]
         ((s : ℂ) - Complex.I * (ℓ : ℂ)))
       (𝓝 s) := by
-  convert! Complex.continuous_re.continuousAt.tendsto.mono_left
+  convert Complex.continuous_re.continuousAt.tendsto.mono_left
     nhdsWithin_le_nhds using 1;
       simp only [sub_re, ofReal_re, mul_re, I_re, zero_mul, I_im, ofReal_im, mul_zero, sub_self,
         sub_zero]
@@ -2265,7 +2272,7 @@ private theorem harmonic_bottom_far_joint_tendsto_zero
     try dsimp [C]
     have hpositive := Real.cosh_pos (Real.pi * δ / 2)
     have hinv := (inv_lt_one₀ hpositive).mpr hcosh
-    exact one_div_pos.mpr (by linarith)
+    exact one_div_pos.mpr (by linear_combination hinv)
   have hσ :
       Tendsto (fun z : ℂ => z.im / ℓ)
         (𝓝[U] z₀) (𝓝 (-1 : ℝ)) := by
@@ -2304,7 +2311,7 @@ private theorem harmonic_bottom_far_joint_tendsto_zero
       (z.re - s) s
     have heq : z.re - s + s = z.re := by ring
     rw [heq] at htriangle
-    linarith
+    linear_combination hsmall + htriangle
   have hkzero := stripPoissonKernel_integrable
     (by norm_num : (-1 : ℝ) < 0)
     (by norm_num : (0 : ℝ) < 1)
@@ -2345,7 +2352,7 @@ private theorem harmonic_bottom_far_joint_tendsto_zero
           hzbelow hzupper hδ
           (show δ ≤ |T| from hT)
       have hkpos := stripPoissonKernel_pos
-        hzbelow (by linarith) T
+        hzbelow (by linear_combination hzupper) T
       have hzero := stripPoissonKernel_pos
         (by norm_num : (-1 : ℝ) < 0)
         (by norm_num : (0 : ℝ) < 1) T
@@ -2362,7 +2369,7 @@ private theorem harmonic_bottom_far_joint_tendsto_zero
             hbound _
           _ ≤ A * (2 + |s| + ℓ * |T|) := by
             apply mul_le_mul_of_nonneg_left _ hA
-            linarith
+            linear_combination hzreal + htri
       rw [norm_mul, Real.norm_eq_abs,
         abs_of_pos hkpos, Real.norm_eq_abs]
       change
@@ -2388,8 +2395,13 @@ private theorem harmonic_bottom_far_joint_tendsto_zero
         (by norm_num : (0 : ℝ) < 1) T
       exact mul_nonneg hC.le
         (add_nonneg
-          (mul_nonneg (by positivity) hzero.le)
-          (mul_nonneg (by positivity)
+          (mul_nonneg (by
+            exact mul_nonneg hA
+                (le_of_lt
+                  (add_pos_of_pos_of_nonneg
+                    (zero_lt_two)
+                    (abs_nonneg s)))) hzero.le)
+          (mul_nonneg (by exact mul_nonneg hA (le_of_lt hℓ))
             (mul_nonneg hzero.le (abs_nonneg T))))
   have hpoint :
       ∀ᵐ T : ℝ,
@@ -2404,7 +2416,7 @@ private theorem harmonic_bottom_far_joint_tendsto_zero
         subst T
         have hbad : δ ≤ (0 : ℝ) := by
           simpa [S] using! hT
-        linarith
+        linarith only [hδ, hbad]
       simp_rw [Set.indicator_of_mem hT]
       have hkernel :=
         (stripPoissonKernel_tendsto_zero_bottom_of_ne
@@ -2417,7 +2429,7 @@ private theorem harmonic_bottom_far_joint_tendsto_zero
             (fun z : ℂ => b (z.re - ℓ * T))
             (𝓝[U] z₀)
             (𝓝 (b (s - ℓ * T))) := by
-        convert! hcont.continuousAt.tendsto.mono_left
+        convert hcont.continuousAt.tendsto.mono_left
           nhdsWithin_le_nhds using 1;
             simp only [sub_re, ofReal_re, mul_re, I_re, zero_mul, I_im, ofReal_im, mul_zero,
               sub_self, sub_zero, z₀]
@@ -2510,7 +2522,7 @@ private theorem harmonic_bottom_joint_tendsto_zero_of_zero
   filter_upwards [hlower, hupper,
     hfarevent, hrealclose]
     with z hzbelow hzupper hzfar hzreal
-  have hzabove : z.im / ℓ < 1 := by linarith
+  have hzabove : z.im / ℓ < 1 := by linear_combination hzupper
   have hg : Continuous
       (fun T : ℝ => b (z.re - ℓ * T)) :=
     hb.comp (by fun_prop)
@@ -2573,7 +2585,7 @@ private theorem harmonic_bottom_joint_tendsto_zero_of_zero
               (z.re - ℓ * T) - s =
                 (z.re - s) - ℓ * T := by ring
           rw [hring]
-          linarith
+          linear_combination hzreal + hscaled + htriangle
         have hbdist :
             dist (z.re - ℓ * T) s < η := by
           rw [Real.dist_eq]
@@ -2586,8 +2598,7 @@ private theorem harmonic_bottom_joint_tendsto_zero_of_zero
           hzbelow hzabove T
         rw [norm_mul, Real.norm_eq_abs,
           abs_of_pos hkpos, Real.norm_eq_abs]
-        linarith [mul_nonneg hkpos.le
-          (sub_nonneg.mpr hbabs.le)]
+        linarith only [mul_nonneg hkpos.le (sub_nonneg.mpr hbabs.le), hbabs, hkpos]
       _ ≤ ∫ T : ℝ,
           (ε / 2) *
             stripPoissonKernel (z.im / ℓ) T :=
@@ -2601,8 +2612,7 @@ private theorem harmonic_bottom_joint_tendsto_zero_of_zero
       _ ≤ ε / 2 := by
         have hmass :=
           (stripBottomMass_lt_one hzbelow).le
-        linarith [mul_nonneg hhalf.le
-          (sub_nonneg.mpr hmass)]
+        linarith only [mul_nonneg hhalf.le (sub_nonneg.mpr hmass), hhalf, hmass]
   have hsplit := integral_add_compl hS hproduct
   rw [dist_zero_right]
   calc
@@ -2623,7 +2633,7 @@ private theorem harmonic_bottom_joint_tendsto_zero_of_zero
           stripPoissonKernel (z.im / ℓ) T *
             b (z.re - ℓ * T)‖ :=
       norm_add_le _ _
-    _ < ε := by linarith
+    _ < ε := by linear_combination hzfar + hnear
 
 private theorem lowerGammaBoundaryCapped_bottom_poisson_joint_tendsto
     {d : ℕ} (hd : 0 < d) (R D s : ℝ) :
@@ -2649,7 +2659,7 @@ private theorem lowerGammaBoundaryCapped_bottom_poisson_joint_tendsto
     lowerGammaBoundaryCapped_continuous hℓ R D
   have hb₀ : Continuous b₀ := by
     try dsimp [b₀]
-    fun_prop
+    exact Continuous.fun_sub hb continuous_const
   obtain ⟨A, hA, hbound⟩ :=
     lowerGammaBoundaryCapped_dimension_abs_le_linear hd R D
   let A₀ : ℝ := A + |b s|
@@ -2665,7 +2675,7 @@ private theorem lowerGammaBoundaryCapped_bottom_poisson_joint_tendsto
     have hy : 0 ≤ |y| := abs_nonneg y
     have hbs : 0 ≤ |b s| := abs_nonneg _
     try dsimp [b₀, A₀]
-    linarith [mul_nonneg hbs hy]
+    linarith only [mul_nonneg hbs hy, htriangle, hbmain, hy, hbs]
   have hcentral : ∀ t : ℝ,
       Integrable (fun T : ℝ =>
         stripPoissonKernel 0 T * b (t - ℓ * T)) := by
@@ -2692,7 +2702,8 @@ private theorem lowerGammaBoundaryCapped_bottom_poisson_joint_tendsto
     hℓ s
   have hmasscontinuous : Continuous stripBottomMass := by
     unfold stripBottomMass
-    fun_prop
+    exact Continuous.comp' (Continuous.div_const continuous_id' 2)
+        (Continuous.fun_sub continuous_const continuous_id')
   have hmass : Tendsto
       (fun z : ℂ => stripBottomMass (z.im / ℓ))
       (𝓝[U] z₀) (𝓝 (1 : ℝ)) := by
@@ -2720,7 +2731,7 @@ private theorem lowerGammaBoundaryCapped_bottom_poisson_joint_tendsto
     have hzlower : -1 < z.im / ℓ := by
       apply (lt_div_iff₀ hℓ).2
       simpa only [neg_mul, one_mul] using! hz.1
-    have hzabove : z.im / ℓ < 1 := by linarith
+    have hzabove : z.im / ℓ < 1 := by linear_combination hzupper
     have hg₀ : Continuous
         (fun T : ℝ => b₀ (z.re - ℓ * T)) := by
       exact hb₀.comp (by fun_prop)
@@ -2769,17 +2780,24 @@ private theorem stripPoissonKernel_tendsto_zero_top
         Real.cos (stripAngle (1 : ℝ))) ≠ 0 := by
     rw [hangle, Real.cos_pi]
     have hcosh := Real.one_le_cosh (Real.pi * T / 2)
-    linarith
+    linarith only [hcosh]
   have hnum : ContinuousAt
       (fun σ : ℝ => Real.sin (stripAngle σ)) 1 := by
     unfold stripAngle
-    fun_prop
+    exact ContinuousAt.comp' (Continuous.continuousAt Real.continuous_sin)
+        (ContinuousAt.comp' (Continuous.continuousAt (Continuous.div_const continuous_id' 2))
+          (ContinuousAt.const_mul (ContinuousAt.const_add (continuousAt_id' 1) 1) π))
   have hdencont : ContinuousAt
       (fun σ : ℝ =>
         4 * (Real.cosh (Real.pi * T / 2) -
           Real.cos (stripAngle σ))) 1 := by
     unfold stripAngle
-    fun_prop
+    exact ContinuousAt.const_mul
+        (ContinuousAt.fun_sub continuousAt_const
+          (ContinuousAt.comp' (Continuous.continuousAt Real.continuous_cos)
+            (ContinuousAt.comp' (Continuous.continuousAt (Continuous.div_const continuous_id' 2))
+              (ContinuousAt.const_mul (ContinuousAt.const_add (continuousAt_id' 1) 1) π))))
+        4
   have h := (hnum.div hdencont hden).tendsto
   simpa only [stripPoissonKernel, Pi.div_apply, hangle, Real.sin_pi, Real.cos_pi, sub_neg_eq_add,
     zero_div] using! h
@@ -2793,8 +2811,8 @@ private theorem harmonic_top_normalized_height_tendsto
       (𝓝 (1 : ℝ)) := by
   have hcontinuous : Continuous
       (fun z : ℂ => z.im / ℓ) := by
-    fun_prop
-  convert! hcontinuous.continuousAt.tendsto.mono_left
+    exact Continuous.comp' (Continuous.div_const continuous_id' ℓ) continuous_im
+  convert hcontinuous.continuousAt.tendsto.mono_left
     nhdsWithin_le_nhds using 1;
       simp only [add_im, ofReal_im, mul_im, I_re, mul_zero, I_im, ofReal_re, one_mul, zero_add,
         ne_eq, hℓ.ne',
@@ -2824,7 +2842,7 @@ private theorem harmonic_upper_joint_tendsto_zero
     harmonic_top_normalized_height_tendsto hℓ s
   have hreal : Tendsto Complex.re
       (𝓝[U] z₀) (𝓝 s) := by
-    convert! Complex.continuous_re.continuousAt.tendsto.mono_left
+    convert Complex.continuous_re.continuousAt.tendsto.mono_left
       nhdsWithin_le_nhds using 1;
       simp only [add_re, ofReal_re, mul_re, I_re, zero_mul, I_im, ofReal_im, mul_zero, sub_self,
         add_zero, z₀]
@@ -2850,7 +2868,7 @@ private theorem harmonic_upper_joint_tendsto_zero
     have htri := abs_add_le (z.re - s) s
     have heq : z.re - s + s = z.re := by ring
     rw [heq] at htri
-    linarith
+    linear_combination hsmall + htri
   have hmajor : Integrable
       (fun T : ℝ =>
         (A * (2 + |s|)) *
@@ -2886,7 +2904,7 @@ private theorem harmonic_upper_joint_tendsto_zero
     filter_upwards [hnonneg, habove, hrealbound]
       with z hznonneg hzabove hzreal
     filter_upwards [] with T
-    have hzbelow : -1 < z.im / ℓ := by linarith
+    have hzbelow : -1 < z.im / ℓ := by linear_combination hznonneg
     have hkpos := stripPoissonKernel_pos hzbelow hzabove T
     have hkbound :=
       stripPoissonKernel_le_exponentialMajorant_of_nonneg
@@ -2906,7 +2924,7 @@ private theorem harmonic_upper_joint_tendsto_zero
           A * (1 + |z.re - ℓ * T|) := hbound _
         _ ≤ A * (2 + |s| + ℓ * |T|) := by
           apply mul_le_mul_of_nonneg_left _ hA
-          linarith
+          linear_combination hzreal + htri
     rw [norm_mul, Real.norm_eq_abs,
       abs_of_pos hkpos, Real.norm_eq_abs]
     calc
@@ -2936,7 +2954,7 @@ private theorem harmonic_upper_joint_tendsto_zero
     have hdatum : Tendsto
         (fun z : ℂ => b (z.re - ℓ * T))
         (𝓝[U] z₀) (𝓝 (b (s - ℓ * T))) := by
-      convert! hcont.continuousAt.tendsto.mono_left
+      convert hcont.continuousAt.tendsto.mono_left
         nhdsWithin_le_nhds using 1;
           simp only [add_re, ofReal_re, mul_re, I_re, zero_mul, I_im, ofReal_im, mul_zero,
             sub_self, add_zero, z₀]
@@ -2967,7 +2985,7 @@ private theorem exists_antiFourierWitness_eventually_capped_bottom_majorant
   have hD₀ : Real.exp D₀ = C + 1 := by
     try dsimp [D₀]
     apply Real.exp_log
-    linarith
+    linear_combination hC
   refine ⟨D₀, ?_⟩
   intro D hD y
   have hbounded :
@@ -2995,7 +3013,7 @@ private theorem exists_antiFourierWitness_eventually_capped_bottom_majorant
         ((y : ℂ) -
           Complex.I * (((d : ℝ) / 2 : ℝ) : ℂ))‖ ≤ C :=
         hbounded
-      _ ≤ C + 1 := by linarith
+      _ ≤ C + 1 := by linarith only []
       _ = Real.exp D₀ := hD₀.symm
       _ ≤ Real.exp D := Real.exp_le_exp.mpr hD
   by_cases hy : y = 0
@@ -3285,12 +3303,12 @@ private theorem lowerStripCappedGammaHarmonic_continuousOn
   have hℓ : 0 < (d : ℝ) / 2 := by positivity
   unfold lowerStripCappedGammaHarmonic
   apply horizontalStripRealTraceExtension_continuousOn
-    (show -((d : ℝ) / 2) < (d : ℝ) / 2 by linarith)
+    (show -((d : ℝ) / 2) < (d : ℝ) / 2 by linarith only [hℓ])
   · exact Complex.continuous_re.comp_continuousOn
       (lowerStripCappedGammaOuter_differentiableOn_dimension
         hd R D).continuousOn
   · exact lowerGammaBoundaryCapped_continuous hℓ R D
-  · fun_prop
+  · exact continuous_const
   · intro s
     simpa only [ofReal_neg, ofReal_div, ofReal_natCast, ofReal_ofNat, mul_neg,
       sub_eq_add_neg] using!
@@ -3343,7 +3361,7 @@ private theorem antiFourierWitness_capped_poisson_majorization_of_real_extension
   let f : ℂ → ℂ := fun z => Complex.exp (-(W z)) * Z z
   let N : ℂ → ℝ := fun z => Real.exp (-(E z)) * ‖Z z‖
   have hℓ : 0 < ℓ := half_pos (Nat.cast_pos.mpr hd)
-  have hwidth : -ℓ < ℓ := by linarith
+  have hwidth : -ℓ < ℓ := by linarith only [hℓ]
   have houter : DifferentiableOn ℂ W U := by
     exact lowerStripCappedGammaOuter_differentiableOn_dimension
       hd R D
@@ -3430,13 +3448,13 @@ private theorem antiFourierWitness_capped_poisson_majorization_of_real_extension
     simp only [Complex.ofReal_im,
       Complex.mul_im, Complex.I_re, Complex.ofReal_re,
       zero_mul, Complex.I_im, one_mul, zero_add]
-    linarith [mul_pos (show 0 < 1 + σ by linarith) hℓ]
+    linarith only [mul_pos (show 0 < 1 + σ by linarith) hℓ, hbelow, hℓ]
   have hzabove : z.im ≤ ℓ := by
     try dsimp [z]
     simp only [Complex.ofReal_im,
       Complex.mul_im, Complex.I_re, Complex.ofReal_re,
       zero_mul, Complex.I_im, one_mul, zero_add]
-    linarith [mul_pos (show 0 < 1 - σ by linarith) hℓ]
+    linarith only [mul_pos (show 0 < 1 - σ by linarith) hℓ, habove, hℓ]
   have hmax : N z ≤ (1 : ℝ) :=
     horizontalStrip_norm_extension_majorization
       hwidth (by norm_num) f N hf hN
@@ -3451,8 +3469,8 @@ private theorem antiFourierWitness_capped_poisson_majorization_of_real_extension
       Complex.ofReal_re, zero_mul, Complex.I_im,
       one_mul, zero_add]
     constructor
-    · linarith [mul_pos (show 0 < 1 + σ by linarith) hℓ]
-    · linarith [mul_pos (show 0 < 1 - σ by linarith) hℓ]
+    · linarith only [mul_pos (show 0 < 1 + σ by linarith) hℓ, hbelow, hℓ]
+    · linarith only [mul_pos (show 0 < 1 - σ by linarith) hℓ, habove, hℓ]
   have hreal := hEinterior z hzinterior
   have hpoisson := lowerStripCappedGammaOuter_re_dimension
     (R := R) (D := D) hd hbelow habove s
@@ -3470,7 +3488,7 @@ private theorem antiFourierWitness_capped_poisson_majorization_of_real_extension
     mul_le_mul_of_nonneg_left hweighted
       (Real.exp_pos (E z)).le
   have hfinal : ‖Z z‖ ≤ Real.exp (E z) := by
-    convert! hscale using 1
+    convert hscale using 1
     · rw [← mul_assoc, ← Real.exp_add]
       simp only [add_neg_cancel, Real.exp_zero, one_mul]
     · simp only [mul_one]
@@ -3514,7 +3532,7 @@ private theorem exists_antiFourierWitness_capped_poisson_majorization
     have hℓ : 0 < (d : ℝ) / 2 :=
       half_pos (Nat.cast_pos.mpr hd)
     have hne : (d : ℝ) / 2 ≠ -((d : ℝ) / 2) := by
-      linarith
+      linarith only [hℓ]
     simp only [lowerStripCappedGammaHarmonic, horizontalStripRealTraceExtension, hz, hne,
       ↓reduceIte]
   · exact hbottom D hD
@@ -3542,9 +3560,9 @@ private theorem stripPoissonKernel_shifted_centered_interval_max
           stripPoissonKernel σ x := by
     rw [integral_Icc_eq_integral_Ioc,
       integral_Icc_eq_integral_Ioc,
-      ← intervalIntegral.integral_of_le (by linarith : -r ≤ r),
+      ← intervalIntegral.integral_of_le (by linarith only [hr] : -r ≤ r),
       ← intervalIntegral.integral_of_le
-        (by linarith : s - r ≤ s + r),
+        (by linarith only [hr] : s - r ≤ s + r),
       intervalIntegral.integral_comp_sub_left]
     congr 1; ring
   have hright :
@@ -3703,7 +3721,7 @@ private theorem stripPoissonWeightedMeasure_integrable
   have hproduct :=
     stripPoissonKernel_weighted_product_integrable
       hbelow habove hf s
-  convert! hproduct using 1
+  convert hproduct using 1
   ext x
   simp only [NNReal.smul_def, Real.coe_toNNReal _ (stripPoissonKernel_pos hbelow habove (s - x)).le,
     smul_eq_mul]
@@ -3850,13 +3868,13 @@ private theorem lowerGammaBoundaryLog_dimension_scaled_le_neg_of_large
   have harg : 1 ≤ Real.pi * |Y| / 2 := by
     linarith only [hpiabs]
   have hexpthree : 4 ≤ Real.exp (3 : ℝ) := by
-    linarith [Real.add_one_le_exp (3 : ℝ)]
+    linarith only [Real.add_one_le_exp (3 : ℝ)]
   have hexpsmall :
       Real.exp ((-Real.pi) * |Y|) ≤ (1 / 4 : ℝ) := by
     calc
       Real.exp ((-Real.pi) * |Y|) ≤ Real.exp (-3 : ℝ) := by
         apply Real.exp_le_exp.mpr
-        linarith
+        linear_combination hpiabs
       _ = (Real.exp (3 : ℝ))⁻¹ := Real.exp_neg 3
       _ ≤ (1 / 4 : ℝ) := by
         simpa only [one_div] using!
@@ -3873,12 +3891,12 @@ private theorem lowerGammaBoundaryLog_dimension_scaled_le_neg_of_large
       (1 / 2 : ℝ) *
           Real.log (lowerCoth (Real.pi * |Y| / 2)) ≤
         (1 / 2 : ℝ) := by
-    linarith
+    linarith only [hexpsmall, hcoth]
   have hℓ : 1 ≤ (d : ℝ) / 2 := by
     apply (le_div_iff₀ (by norm_num : (0 : ℝ) < 2)).2
     exact_mod_cast hd
   have hlognonneg : 0 ≤ Real.log (2 : ℝ) + n := by
-    linarith
+    linear_combination hn + hlogtwo
   have hmain :
       ((d : ℝ) / 2) *
         Real.log (4 * Real.pi * c ^ 2 / |Y|) ≤
@@ -3889,11 +3907,10 @@ private theorem lowerGammaBoundaryLog_dimension_scaled_le_neg_of_large
         ((d : ℝ) / 2) * (-(Real.log (2 : ℝ)) - n) :=
         mul_le_mul_of_nonneg_left hlogratio (by positivity)
       _ ≤ -(Real.log (2 : ℝ)) - n := by
-        linarith [mul_nonneg
-          (sub_nonneg.mpr hℓ) hlognonneg]
+        linarith only [mul_nonneg (sub_nonneg.mpr hℓ) hlognonneg, hℓ, hlognonneg]
   have htail := lowerGammaBoundaryLog_dimension_scaled_log_tail_uniform
     hd hc hY
-  linarith
+  linarith only [hlogtwo, hexpsmall, hcoth, hmain, htail]
 
 private noncomputable def lowerGammaScaledCappedClipped
     (d : ℕ) (c D n Y : ℝ) : ℝ :=
@@ -3942,7 +3959,7 @@ private theorem lowerGammaScaledCappedClipped_antitoneOn
         mul_nonneg hℓ hy)
       (mul_le_mul_of_nonneg_left hxy hℓ)
   unfold lowerGammaScaledCappedClipped
-  exact max_le_max (by linarith) (le_refl (0 : ℝ))
+  exact max_le_max (by linear_combination hgamma) (le_refl (0 : ℝ))
 
 private theorem lowerGammaScaledCappedClipped_support
     {d : ℕ} (hd : 2 ≤ d) {c D n : ℝ}
@@ -3976,7 +3993,7 @@ private theorem lowerGammaScaledCappedClipped_support
     have hmin := min_le_left
       (lowerGammaBoundaryLog ((d : ℝ) / 2)
         (c * Real.sqrt d) (((d : ℝ) / 2) * Y)) D
-    linarith
+    linear_combination hnonpos + hmin
   exact ⟨(neg_lt_of_abs_lt hsmall).le,
     (lt_of_abs_lt hsmall).le⟩
 
@@ -4029,14 +4046,14 @@ private theorem lowerGammaScaledCapped_poisson_product_integrable
       Complex.I_re, Complex.ofReal_re, zero_mul,
       Complex.I_im, one_mul, zero_add]
     constructor
-    · linarith [mul_pos (show 0 < 1 + σ by linarith) hℓ]
-    · linarith [mul_pos (show 0 < 1 - σ by linarith) hℓ]
+    · linarith only [mul_pos (show 0 < 1 + σ by linarith) hℓ, hbelow, hℓ]
+    · linarith only [mul_pos (show 0 < 1 - σ by linarith) hℓ, habove, hℓ]
   have houter := lowerStripCappedGammaOuter_integrable_dimension
     hd (R := R) (D := D) hz
   have hreal := houter.re
   have hscaled := hreal.comp_mul_left' hℓ.ne'
   have hproduct := hscaled.const_mul ((d : ℝ) / 2)
-  convert! hproduct using 1
+  convert hproduct using 1
   ext Y
   change
     stripPoissonKernel σ (s - Y) *
@@ -4079,14 +4096,14 @@ private theorem lowerGammaScaled_poisson_product_integrable
       Complex.I_re, Complex.ofReal_re, zero_mul,
       Complex.I_im, one_mul, zero_add]
     constructor
-    · linarith [mul_pos (show 0 < 1 + σ by linarith) hℓ]
-    · linarith [mul_pos (show 0 < 1 - σ by linarith) hℓ]
+    · linarith only [mul_pos (show 0 < 1 + σ by linarith) hℓ, hbelow, hℓ]
+    · linarith only [mul_pos (show 0 < 1 - σ by linarith) hℓ, habove, hℓ]
   have houter := lowerStripGammaOuter_integrable_dimension
     hd (R := R) hz
   have hreal := houter.re
   have hscaled := hreal.comp_mul_left' hℓ.ne'
   have hproduct := hscaled.const_mul ((d : ℝ) / 2)
-  convert! hproduct using 1
+  convert hproduct using 1
   ext Y
   change
     stripPoissonKernel σ (s - Y) *
@@ -4141,7 +4158,7 @@ private theorem lowerGammaScaledCappedLowerClip_poisson_integrable
   have hk := (stripPoissonKernel_integrable hbelow habove).comp_sub_left s
   have hconstant := hk.const_mul (-n)
   have hmax := hbase.sup hconstant
-  convert! hmax using 1
+  convert hmax using 1
   ext Y
   change
     stripPoissonKernel σ (s - Y) *
@@ -4217,7 +4234,7 @@ private theorem lowerGammaScaledCappedLowerClip_poisson_convolution_max
     hdpos hbelow habove s,
     lowerGammaScaledCappedClipped_integral_eq
       hdpos hbelow habove 0] at hplus
-  linarith
+  linear_combination hplus
 
 private theorem lowerGammaScaledCappedLowerClip_poisson_tendsto
     {d : ℕ} (hd : 0 < d) {c D σ : ℝ}
@@ -4257,7 +4274,7 @@ private theorem lowerGammaScaledCappedLowerClip_poisson_tendsto
       · rw [max_eq_right hle,
           abs_of_nonpos (neg_nonpos.mpr hn),
           abs_of_nonpos (le_trans hle (neg_nonpos.mpr hn))]
-        linarith
+        linear_combination hle
       · rw [max_eq_left hle]
     change
       ‖K Y * max (b Y) (-(n : ℝ))‖ ≤ |K Y * b Y|
@@ -4467,8 +4484,7 @@ private theorem lowerGammaBoundaryLog_integer_scaled
     rw [lowerRiemannLog_scaled_factor hkreal]
     have hrad :
         0 < ((j : ℝ) / (k : ℝ)) ^ 2 + T ^ 2 / 4 := by
-      linarith [sq_nonneg ((j : ℝ) / (k : ℝ)),
-        sq_pos_of_ne_zero hT]
+      linarith only [sq_nonneg ((j : ℝ) / (k : ℝ)), sq_pos_of_ne_zero hT, hT]
     rw [Real.log_mul hkreal.ne'
       (Real.sqrt_pos.mpr hrad).ne']
     rfl
@@ -4513,8 +4529,7 @@ private theorem lowerGammaBoundaryLog_halfInteger_scaled
     rw [lowerRiemannLog_scaled_factor hℓ]
     have hrad :
         0 < (((j : ℝ) + 1 / 2) / ℓ) ^ 2 + T ^ 2 / 4 := by
-      linarith [sq_nonneg (((j : ℝ) + 1 / 2) / ℓ),
-        sq_pos_of_ne_zero hT]
+      linarith only [sq_nonneg (((j : ℝ) + 1 / 2) / ℓ), sq_pos_of_ne_zero hT, hT]
     rw [Real.log_mul hℓ.ne'
       (Real.sqrt_pos.mpr hrad).ne']
     rfl
@@ -4550,11 +4565,11 @@ private theorem lowerRiemannLog_continuous
     {T : ℝ} (hT : T ≠ 0) :
     Continuous (lowerRiemannLog T) := by
   have hrad (x : ℝ) : 0 < x ^ 2 + T ^ 2 / 4 := by
-    linarith [sq_nonneg x, sq_pos_of_ne_zero hT]
+    linarith only [sq_nonneg x, sq_pos_of_ne_zero hT, hT]
   have hsqrt :
       Continuous (fun x : ℝ =>
         Real.sqrt (x ^ 2 + T ^ 2 / 4)) := by
-    fun_prop
+    exact Continuous.sqrt (Continuous.add_const (Continuous.fun_pow continuous_id' 2) (T ^ 2 / 4))
   unfold lowerRiemannLog
   exact hsqrt.log (fun x =>
     (Real.sqrt_pos.mpr (hrad x)).ne')
@@ -4601,7 +4616,7 @@ private theorem lowerRiemannLog_halfInteger_tail_integral_le
   have hratio_le : (k : ℝ) / ℓ ≤ 1 := by
     apply (div_le_one hℓ).2
     rw [hℓeq]
-    linarith
+    linarith only []
   have hcont := lowerRiemannLog_continuous hT
   have hint : IntervalIntegrable
       (lowerRiemannLog T) volume ((k : ℝ) / ℓ) 1 :=
@@ -4647,12 +4662,12 @@ private theorem lowerGammaBoundaryLog_halfInteger_riemann_le
       ℓ * (Real.log (Real.pi * R ^ 2 / ℓ) +
         1 + lowerEndpointPhase T) +
         lowerRiemannErrorMajorant T := by
-  have hℓ : 0 < ℓ := by linarith
+  have hℓ : 0 < ℓ := by linarith only [hℓone]
   have hratio_nonneg : 0 ≤ (k : ℝ) / ℓ := by positivity
   have hratio_le : (k : ℝ) / ℓ ≤ 1 := by
     apply (div_le_one hℓ).2
     rw [hℓeq]
-    linarith
+    linarith only []
   let q : ℝ → ℝ := lowerRiemannLog T
   have hcont := lowerRiemannLog_continuous hT
   have hfirst : IntervalIntegrable q volume
@@ -4757,7 +4772,7 @@ private theorem lowerGammaBoundaryLog_dimension_riemann_le
     apply lowerGammaBoundaryLog_halfInteger_riemann_le
       k rfl
     · have hkre : 1 ≤ (k : ℝ) := by exact_mod_cast hk
-      linarith
+      linear_combination hkre
     · exact hR
     · exact hT
 
@@ -4810,7 +4825,7 @@ private theorem stripPoissonKernel_le_mass_mul_exponential
     (T : ℝ) :
     stripPoissonKernel σ T ≤
       stripBottomMass σ * stripPoissonExponentialMajorant T := by
-  have hbelow : -1 < σ := by linarith
+  have hbelow : -1 < σ := by linear_combination hzero
   have hmass := stripBottomMass_pos habove
   have hnormalize := stripNormalizedPoissonKernel_eq_extension
     hbelow habove T
@@ -4824,7 +4839,7 @@ private theorem stripPoissonKernel_le_mass_mul_exponential
     rw [hnormalize]
     exact hbound.2
   have h := (div_le_iff₀ hmass).mp hquotient
-  linarith
+  linear_combination h
 
 private theorem stripPoissonExponentialMajorant_abs_moment_integrable :
     Integrable (fun T : ℝ =>
@@ -4832,7 +4847,7 @@ private theorem stripPoissonExponentialMajorant_abs_moment_integrable :
   have hmoment := integrable_abs_pow_mul_exp_neg_mul_abs
     1 (half_pos Real.pi_pos)
   have hscaled := hmoment.const_mul (Real.pi / 2)
-  convert! hscaled using 1
+  convert hscaled using 1
   ext T
   simp only [stripPoissonExponentialMajorant, neg_mul, pow_one]
   ring
@@ -4840,12 +4855,12 @@ private theorem stripPoissonExponentialMajorant_abs_moment_integrable :
 private theorem stripPoissonKernel_abs_moment_integrable
     {σ : ℝ} (hzero : 0 ≤ σ) (habove : σ < 1) :
     Integrable (fun T : ℝ => stripPoissonKernel σ T * |T|) := by
-  have hbelow : -1 < σ := by linarith
+  have hbelow : -1 < σ := by linear_combination hzero
   have hmajor :=
     stripPoissonExponentialMajorant_abs_moment_integrable.const_mul
       (stripBottomMass σ)
   have habsmeas : Measurable (fun T : ℝ => |T|) := by
-    fun_prop
+    exact Continuous.measurable (Continuous.abs continuous_id')
   apply hmajor.mono'
     ((stripPoissonKernel_integrable hbelow habove).aestronglyMeasurable.mul
       habsmeas.aestronglyMeasurable)
@@ -4906,30 +4921,30 @@ private theorem lowerRiemannLog_one_nonneg_le (T : ℝ) :
     0 ≤ lowerRiemannLog T 1 ∧
       lowerRiemannLog T 1 ≤ |T| / 2 := by
   have hrad : 0 < (1 : ℝ) + T ^ 2 / 4 := by
-    linarith [sq_nonneg T]
+    linarith only [sq_nonneg T]
   have hsqrtone :
       1 ≤ Real.sqrt ((1 : ℝ) + T ^ 2 / 4) := by
     apply (Real.le_sqrt (by norm_num) hrad.le).2
-    linarith [sq_nonneg T]
+    linarith only [sq_nonneg T]
   have hsqrtupper :
       Real.sqrt ((1 : ℝ) + T ^ 2 / 4) ≤
         1 + |T| / 2 := by
     apply Real.sqrt_le_iff.mpr
     constructor
     · positivity
-    · linarith [abs_nonneg T, sq_abs T]
+    · linarith only [abs_nonneg T, sq_abs T]
   unfold lowerRiemannLog
   simp only [one_pow]
   constructor
   · exact Real.log_nonneg hsqrtone
   · have hlog := Real.log_le_sub_one_of_pos
       (Real.sqrt_pos.mpr hrad)
-    linarith
+    linear_combination hsqrtupper + hlog
 
 private theorem lowerRiemannLog_one_continuous :
     Continuous (fun T : ℝ => lowerRiemannLog T 1) := by
   have hrad (T : ℝ) : 0 < (1 : ℝ) + T ^ 2 / 4 := by
-    linarith [sq_nonneg T]
+    linarith only [sq_nonneg T]
   have hsqrt :
       Continuous (fun T : ℝ =>
         Real.sqrt ((1 : ℝ) + T ^ 2 / 4)) := by
@@ -4942,7 +4957,7 @@ private theorem stripPoissonKernel_mul_abs_lowerRiemannLog_one_integrable
     {σ : ℝ} (hzero : 0 ≤ σ) (habove : σ < 1) :
     Integrable (fun T : ℝ =>
       stripPoissonKernel σ T * |lowerRiemannLog T 1|) := by
-  have hbelow : -1 < σ := by linarith
+  have hbelow : -1 < σ := by linear_combination hzero
   have hmoment := stripPoissonKernel_abs_moment_integrable
     hzero habove
   have hmajor := hmoment.const_mul (1 / 2 : ℝ)
@@ -4958,9 +4973,12 @@ private theorem stripPoissonKernel_mul_abs_lowerRiemannLog_one_integrable
   rw [Real.norm_eq_abs, abs_mul,
     abs_of_pos (stripPoissonKernel_pos hbelow habove T),
     abs_abs, abs_of_nonneg hq.1]
-  linarith [mul_nonneg
-    (stripPoissonKernel_pos hbelow habove T).le
-      (sub_nonneg.mpr hq.2)]
+  linarith only [
+    mul_nonneg (stripPoissonKernel_pos hbelow habove T).le (sub_nonneg.mpr hq.2),
+    habove,
+    hbelow,
+    hq
+  ]
 
 private theorem stripPoissonKernel_mul_abs_lowerRiemannLog_zero_integrable
     {σ : ℝ} (hbelow : -1 < σ) (habove : σ < 1) :
@@ -4990,7 +5008,7 @@ private theorem lowerRiemannErrorMajorant_poisson_integrable
     Integrable (fun T : ℝ =>
       stripPoissonKernel σ T *
         lowerRiemannErrorMajorant T) := by
-  have hbelow : -1 < σ := by linarith
+  have hbelow : -1 < σ := by linear_combination hzero
   have hqzero :=
     (stripPoissonKernel_mul_abs_lowerRiemannLog_zero_integrable
       hbelow habove).const_mul (3 : ℝ)
@@ -5001,7 +5019,7 @@ private theorem lowerRiemannErrorMajorant_poisson_integrable
     (stripPoissonKernel_mul_coth_log_integrable
       hbelow habove).const_mul (1 / 2 : ℝ)
   have hsum := hqzero.add (hone.add hcoth)
-  convert! hsum using 1
+  convert hsum using 1
   ext T
   change
     stripPoissonKernel σ T * lowerRiemannErrorMajorant T =
@@ -5017,7 +5035,7 @@ private theorem stripPoissonKernel_mul_lowerEndpointPhase_integrable
     {σ : ℝ} (hzero : 0 ≤ σ) (habove : σ < 1) :
     Integrable (fun T : ℝ =>
       stripPoissonKernel σ T * lowerEndpointPhase T) := by
-  have hbelow : -1 < σ := by linarith
+  have hbelow : -1 < σ := by linear_combination hzero
   have hmajor :=
     stripPoissonExponentialMajorant_mul_lowerEndpointPhase_integrable.const_mul
       (stripBottomMass σ)
@@ -5071,7 +5089,7 @@ private theorem lowerStripPoissonMajorant_dimension_central_bound
         (Real.log (2 * Real.pi * Real.exp 1 * c ^ 2) +
           lowerPoissonEndpointExpectation σ) +
         lowerRiemannPoissonError σ := by
-  have hbelow : -1 < σ := by linarith
+  have hbelow : -1 < σ := by linear_combination hzero
   have hdpos : 0 < d := lt_of_lt_of_le (by norm_num) hd
   have hℓ : 0 < (d : ℝ) / 2 :=
     half_pos (Nat.cast_pos.mpr hdpos)
@@ -5100,7 +5118,7 @@ private theorem lowerStripPoissonMajorant_dimension_central_bound
   have hsum := hconstant.add (hphaseterm.add hE)
   have hright : Integrable (fun T : ℝ =>
       K T * (ℓ * (A + q T) + E T)) := by
-    convert! hsum using 1
+    convert hsum using 1
     ext T
     change
       K T * (ℓ * (A + q T) + E T) =
@@ -5194,19 +5212,19 @@ private theorem exists_lowerStripPoissonMajorant_uniform_negative
   let γ : ℝ := -(stripBottomMass σ * A) / 2
   have hγ : 0 < γ := by
     try dsimp [γ]
-    linarith [mul_neg_of_pos_of_neg hmass hA]
+    linarith only [mul_neg_of_pos_of_neg hmass hA, hmass, hA]
   have hscale : Tendsto
       (fun d : ℕ => (d : ℝ) / 2) atTop atTop := by
     have hcast := tendsto_natCast_atTop_atTop (R := ℝ)
     have hmul := hcast.atTop_mul_const
       (by norm_num : (0 : ℝ) < 1 / 2)
-    convert! hmul using 1
+    convert hmul using 1
     ext d
     ring
   have hγscale : Tendsto
       (fun d : ℕ => γ * ((d : ℝ) / 2)) atTop atTop := by
     have hmul := hscale.atTop_mul_const hγ
-    convert! hmul using 1
+    convert hmul using 1
     ext d
     ring
   have herror : ∀ᶠ d : ℕ in atTop,
@@ -5219,7 +5237,7 @@ private theorem exists_lowerStripPoissonMajorant_uniform_negative
     with d hd hderr
   intro s
   have hcenter := lowerStripPoissonMajorant_dimension_centered_max
-    hd hc (by linarith) hσless s
+    hd hc (by linarith only [hσpos, hσless]) hσless s
   have hbound :=
     lowerStripPoissonMajorant_dimension_central_bound
       hd hc hσpos.le hσless
@@ -5232,7 +5250,7 @@ private theorem exists_lowerStripPoissonMajorant_uniform_negative
       lowerRiemannPoissonError σ := hbound
     _ ≤ -γ * ((d : ℝ) / 2) := by
       try dsimp [γ] at hderr ⊢
-      linarith
+      linear_combination hderr
 
 private theorem lowerCoth_log_half_le_of_one_le_abs
     {Y : ℝ} (hY : 1 ≤ |Y|) :
@@ -5240,20 +5258,21 @@ private theorem lowerCoth_log_half_le_of_one_le_abs
       Real.log (lowerCoth (Real.pi * |Y| / 2)) ≤
         (1 / 2 : ℝ) := by
   have hpiabs : 3 ≤ Real.pi * |Y| := by
-    linarith [Real.pi_gt_three,
-      mul_nonneg
-        (by linarith [Real.pi_gt_three] : 0 ≤ Real.pi - 3)
-        (sub_nonneg.mpr hY)]
+    linarith only [
+      Real.pi_gt_three,
+      mul_nonneg (by linarith [Real.pi_gt_three] : 0 ≤ Real.pi - 3) (sub_nonneg.mpr hY),
+      hY
+    ]
   have harg : 1 ≤ Real.pi * |Y| / 2 := by
-    linarith
+    linarith only [hpiabs]
   have hexpthree : 4 ≤ Real.exp (3 : ℝ) := by
-    linarith [Real.add_one_le_exp (3 : ℝ)]
+    linarith only [Real.add_one_le_exp (3 : ℝ)]
   have hexpsmall :
       Real.exp ((-Real.pi) * |Y|) ≤ (1 / 4 : ℝ) := by
     calc
       Real.exp ((-Real.pi) * |Y|) ≤ Real.exp (-3 : ℝ) := by
         apply Real.exp_le_exp.mpr
-        linarith
+        linarith only [hpiabs]
       _ = (Real.exp (3 : ℝ))⁻¹ := Real.exp_neg 3
       _ ≤ (1 / 4 : ℝ) := by
         simpa only [one_div] using!
@@ -5266,7 +5285,7 @@ private theorem lowerCoth_log_half_le_of_one_le_abs
     congr 1
     ring
   rw [hexp] at hcoth
-  linarith
+  linarith only [hexpsmall, hcoth]
 
 private theorem lowerGammaBoundaryLog_dimension_scaled_log_tail_simple
     {d : ℕ} (hd : 2 ≤ d) {c Y : ℝ}
@@ -5296,7 +5315,7 @@ private theorem lowerGammaBoundaryLog_dimension_scaled_log_tail_simple
         (show 4 * Real.pi * c ^ 2 / |Y| ≠ 0 by positivity)
         (Real.exp_ne_zero _), Real.log_exp]
   rw [hlog]
-  linarith
+  linear_combination htail + hcorr + hℓ
 
 private noncomputable def stripPoissonCoreMass (σ : ℝ) : ℝ :=
   ∫ T in Icc (-1 : ℝ) 1, stripPoissonKernel σ T
@@ -5330,7 +5349,7 @@ private theorem stripPoissonCoreMass_pos
     norm_num
   rw [hvalue] at hcompare
   unfold stripPoissonCoreMass
-  linarith
+  linarith only [hkone, hcompare]
 
 private theorem lowerGammaScaledPositivePart_poisson_exponential_tail
     {d : ℕ} (hd : 2 ≤ d) {c σ C S : ℝ}
@@ -5349,7 +5368,7 @@ private theorem lowerGammaScaledPositivePart_poisson_exponential_tail
       (stripBottomMass σ * (Real.pi / 2) *
         Real.exp (-(Real.pi / 2) * (S - C))) *
           (C * ((d : ℝ) / 2)) := by
-  have hbelow : -1 < σ := by linarith
+  have hbelow : -1 < σ := by linear_combination hσ
   let E : ℝ :=
     stripBottomMass σ * (Real.pi / 2) *
       Real.exp (-(Real.pi / 2) * (S - C))
@@ -5380,8 +5399,8 @@ private theorem lowerGammaScaledPositivePart_poisson_exponential_tail
       · simp only [hzero, mul_zero, Std.le_refl]
       · have hY := hsupport hzero
         have hdist : S - C ≤ |S - Y| := by
-          rw [abs_of_nonneg (by linarith [hY.2] : 0 ≤ S - Y)]
-          linarith [hY.2]
+          rw [abs_of_nonneg (by linarith only [hY.2, hS, hY] : 0 ≤ S - Y)]
+          linarith only [hY.2, hY]
         have hexp :
             Real.exp (-(Real.pi / 2) * |S - Y|) ≤
               Real.exp (-(Real.pi / 2) * (S - C)) := by
@@ -5432,10 +5451,10 @@ private theorem lowerStripPoissonMajorant_core_tail_split
         ∫ Y : ℝ,
           stripPoissonKernel σ (S - Y) *
             lowerGammaScaledPositivePart d c Y := by
-  have hbelow : -1 < σ := by linarith
+  have hbelow : -1 < σ := by linear_combination hσ
   have hdpos : 0 < d := lt_of_lt_of_le (by norm_num) hd
   have hℓ : 0 < (d : ℝ) / 2 := by positivity
-  have hSpos : 0 < S := by linarith
+  have hSpos : 0 < S := by linear_combination hS
   let ℓ : ℝ := (d : ℝ) / 2
   let P : ℝ := 4 * Real.pi * Real.exp 1 * c ^ 2
   let A : ℝ := 8 * Real.pi * Real.exp 1 * c ^ 2
@@ -5454,7 +5473,7 @@ private theorem lowerStripPoissonMajorant_core_tail_split
     have hbase := lowerGammaScaled_poisson_product_integrable
       hdpos (R := c * Real.sqrt d) hbelow hσone S
     have hcomp := hbase.comp_sub_left S
-    convert! hcomp using 1
+    convert hcomp using 1
     ext T
     try dsimp [b, ℓ]
     congr 1; ring_nf
@@ -5464,7 +5483,7 @@ private theorem lowerStripPoissonMajorant_core_tail_split
       hbelow hσone
       (lowerGammaScaledPositivePart_integrable hd hc) S
     have hcomp := hbase.comp_sub_left S
-    convert! hcomp using 1
+    convert hcomp using 1
     ext T
     try dsimp [p]
     congr 1; ring_nf
@@ -5475,7 +5494,7 @@ private theorem lowerStripPoissonMajorant_core_tail_split
     have hbase :=
       ((stripPoissonKernel_integrable hbelow hσone).const_mul L).indicator
         (s := Icc (-1 : ℝ) 1) measurableSet_Icc
-    convert! hbase using 1
+    convert hbase using 1
     ext T
     by_cases hT : T ∈ Icc (-1 : ℝ) 1
     · simp only [hT, indicator_of_mem]
@@ -5483,15 +5502,14 @@ private theorem lowerStripPoissonMajorant_core_tail_split
     · simp only [hT, not_false_eq_true, indicator_of_notMem, mul_zero]
   have hnear : ∀ T ∈ Icc (-1 : ℝ) 1, b (S - T) ≤ L := by
     intro T hT
-    have hdiff : 0 < S - T := by linarith [hT.2]
+    have hdiff : 0 < S - T := by linarith only [hT.2, hS, hT]
     have hlarge : 1 ≤ |S - T| := by
       rw [abs_of_pos hdiff]
-      linarith [hT.2]
+      linarith only [hT.2, hS, hT]
     have hratio : P / |S - T| ≤ A / S := by
       apply (div_le_div_iff₀ (abs_pos.mpr hdiff.ne') hSpos).2
       rw [abs_of_pos hdiff, hA]
-      linarith [mul_nonneg hP.le
-        (show 0 ≤ S - 2 * T by linarith [hT.2])]
+      linarith only [mul_nonneg hP.le (show 0 ≤ S - 2 * T by linarith [hT.2]), hS, hP, hT]
     have hlog : Real.log (P / |S - T|) ≤
         Real.log (A / S) := by
       apply Real.log_le_log (by positivity)
@@ -5519,8 +5537,13 @@ private theorem lowerStripPoissonMajorant_core_tail_split
     by_cases hT : T ∈ Icc (-1 : ℝ) 1
     · simp only [Set.indicator_of_mem hT]
       have h := hnear T hT
-      linarith [mul_nonneg hkernel hpnonneg,
-        mul_nonneg hkernel (sub_nonneg.mpr h)]
+      linarith only [
+        mul_nonneg hkernel hpnonneg,
+        mul_nonneg hkernel (sub_nonneg.mpr h),
+        hkernel,
+        hpnonneg,
+        h
+      ]
     · simp only [Set.indicator_of_notMem hT, mul_zero,
         zero_add]
       exact mul_le_mul_of_nonneg_left hb_le_p hkernel
@@ -5643,7 +5666,7 @@ private theorem lowerStripPoissonMajorant_dimension_neg
           intro hzero
           apply hT
           apply (eq_div_iff hℓ.ne').2
-          linarith
+          linear_combination hzero
         try dsimp [f]
         rw [stripPoissonKernel_neg]
         have harg :
@@ -5670,7 +5693,7 @@ private theorem exists_lowerStripPoissonMajorant_positive_logarithmic_tail
           lowerStripPoissonMajorant ((d : ℝ) / 2)
             (c * Real.sqrt d) σ (((d : ℝ) / 2) * S) ≤
               -κ * ((d : ℝ) / 2) * Real.log (S / A) := by
-  have hbelow : -1 < σ := by linarith
+  have hbelow : -1 < σ := by linear_combination hσ
   obtain ⟨C, hC, huniform⟩ :=
     exists_lowerGammaScaledPositivePart_uniform_bound hc
   let A : ℝ := 8 * Real.pi * Real.exp 1 * c ^ 2
@@ -5707,7 +5730,7 @@ private theorem exists_lowerStripPoissonMajorant_positive_logarithmic_tail
         atTop (𝓝 0) := by
     have hmul :=
       hexponential.const_mul (β * Real.exp (a * C))
-    convert! hmul using 1
+    convert hmul using 1
     · ext S
       calc
         β * Real.exp (-a * (S - C)) =
@@ -5733,7 +5756,7 @@ private theorem exists_lowerStripPoissonMajorant_positive_logarithmic_tail
   let B : ℝ := max 1 B₀
   have hB : 0 < B := by
     try dsimp [B]
-    linarith [le_max_left (1 : ℝ) B₀]
+    linarith only [le_max_left (1 : ℝ) B₀]
   refine ⟨A, B, κ, hA, hB, hκ, ?_⟩
   intro d hd S hSB
   have hBzero : B₀ ≤ S :=
@@ -5747,7 +5770,7 @@ private theorem exists_lowerStripPoissonMajorant_positive_logarithmic_tail
   have hSratio : 2 * A ≤ S :=
     le_trans (le_trans (le_max_right C (2 * A))
       (le_max_right 2 _)) hlargeS
-  have hSpos : 0 < S := by linarith
+  have hSpos : 0 < S := by linear_combination hStwo
   obtain ⟨hsupport, hpositive⟩ := huniform d hd
   have htail := lowerStripPoissonMajorant_core_tail_split
     hd hc hσ hσone hStwo
@@ -5774,7 +5797,7 @@ private theorem exists_lowerStripPoissonMajorant_positive_logarithmic_tail
     have h := Real.one_sub_inv_le_log_of_pos
       (by norm_num : (0 : ℝ) < 2)
     norm_num at h ⊢
-    linarith
+    exact h
   have hratio : (2 : ℝ) ≤ S / A :=
     (le_div_iff₀ hA).2 hSratio
   have hlogratio : (1 / 2 : ℝ) ≤ Real.log (S / A) :=
@@ -5796,7 +5819,7 @@ private theorem exists_lowerStripPoissonMajorant_positive_logarithmic_tail
     _ ≤ (((d : ℝ) / 2) * Real.log (A / S)) * m +
         (β * Real.exp (-a * (S - C))) *
           ((d : ℝ) / 2) := by
-      linarith [hpositive_bound]
+      linear_combination hpositive_bound
     _ ≤ -κ * ((d : ℝ) / 2) * Real.log (S / A) := by
       rw [hflip]
       try dsimp [κ]
@@ -5854,7 +5877,7 @@ private theorem inverseQuadraticAbs_integrable :
   have hbase := integrable_one_add_norm
     (E := ℝ) (μ := volume) (r := (2 : ℝ))
       (by norm_num)
-  convert! hbase using 1
+  convert hbase using 1
   ext S
   rw [Real.norm_eq_abs,
     Real.rpow_neg (by positivity)]
@@ -5891,7 +5914,7 @@ private theorem exists_lowerStripPoissonMajorant_integrable_majorant
     exact le_max_left B (max A 1)
   have hC : 0 < C := by
     try dsimp [C]
-    have hsq : 0 < (1 + T) ^ 2 := sq_pos_of_pos (by linarith)
+    have hsq : 0 < (1 + T) ^ 2 := sq_pos_of_pos (by linear_combination hσpos + hσone + hT)
     exact lt_of_lt_of_le hsq (le_max_left _ _)
   have hγ : 0 < γ := by
     try dsimp [γ]
@@ -5901,7 +5924,7 @@ private theorem exists_lowerStripPoissonMajorant_integrable_majorant
     have hcast := tendsto_natCast_atTop_atTop (R := ℝ)
     have hmul := hcast.atTop_mul_const
       (by norm_num : (0 : ℝ) < 1 / 2)
-    convert! hmul using 1
+    convert hmul using 1
     ext d
     ring
   have hdimension : ∀ᶠ d : ℕ in atTop,
@@ -5922,7 +5945,7 @@ private theorem exists_lowerStripPoissonMajorant_integrable_majorant
       Real.log_nonneg hratio
     have hκscale : 4 ≤ κ * ((d : ℝ) / 2) := by
       have h := (div_le_iff₀ hκ).1 hdim
-      linarith only [h]
+      linear_combination h
     have hnegative := hcen (((d : ℝ) / 2) * S)
     have hfrequency := htail d hd S hBS
     have haverage :
@@ -5995,7 +6018,7 @@ private theorem exists_lowerStripPoissonMajorant_integrable_majorant
     have hden : 0 < (1 + |S|) ^ 2 :=
       sq_pos_of_pos (by positivity)
     have hnearquad : (1 + |S|) ^ 2 ≤ (1 + T) ^ 2 :=
-      pow_le_pow_left₀ (by positivity) (by linarith) 2
+      pow_le_pow_left₀ (by positivity) (by linarith only [hfar]) 2
     have hdenmajor : (1 + |S|) ^ 2 ≤ C :=
       hnearquad.trans (le_max_left _ _)
     have hexpcentral :
@@ -6006,7 +6029,7 @@ private theorem exists_lowerStripPoissonMajorant_integrable_majorant
       apply Real.exp_le_exp.mpr
       have h := hcen (((d : ℝ) / 2) * S)
       try dsimp [γ]
-      linarith [mul_nonneg hγ₀.le hℓ.le]
+      linarith only [mul_nonneg hγ₀.le hℓ.le, hγ₀, hℓ, h]
     calc
       Real.exp
           (lowerStripPoissonMajorant ((d : ℝ) / 2)
@@ -6058,19 +6081,19 @@ private theorem antiFourierWitness_interiorMellinL1_le_of_integrable_majorant
       ((s : ℂ) + Complex.I * (((σ * ℓ : ℝ) : ℂ)))
   have ha : (1 - σ) * ℓ < (d : ℝ) := by
     have hplus : 0 < (1 + σ) * ℓ :=
-      mul_pos (by linarith) hℓ
+      mul_pos (by linarith only [hσbelow]) hℓ
     have hinner : 0 < (1 - σ) * ℓ :=
       mul_pos (sub_pos.mpr hσabove) hℓ
     apply (mul_lt_mul_iff_right₀ hinner).mp
     try dsimp [ℓ] at hplus hinner ⊢
-    linarith [mul_pos hplus hinner]
+    linarith only [mul_pos hplus hinner, hplus, hinner]
   have hheight : ℓ - (1 - σ) * ℓ = σ * ℓ := by
     ring
   have hZ : Integrable Z := by
     have h :=
       antiFourierWitness_normalizedMellinStrip_shifted_integrable
         hd hR w ha
-    convert! h using 1
+    convert h using 1
     ext s
     try dsimp [Z, ℓ] at *
     congr 2
@@ -6080,12 +6103,12 @@ private theorem antiFourierWitness_interiorMellinL1_le_of_integrable_majorant
   have hprofile : Integrable
       (fun S : ℝ => E / (1 + |S|) ^ 2) := by
     have h := inverseQuadraticAbs_integrable.const_mul E
-    convert! h using 1
+    convert h using 1
     ext S
     ring
   have hscaled : Integrable (fun S : ℝ => ‖Z (ℓ * S)‖) := by
     have h := hZ.norm.comp_mul_left' hℓ.ne'
-    convert! h using 1
+    convert h using 1
   have hbound :
       (∫ S : ℝ, ‖Z (ℓ * S)‖) ≤
         E * lowerInverseQuadraticMass := by
@@ -6155,7 +6178,7 @@ private theorem lowerStripCappedPoisson_tendsto
   have h := lowerGammaScaledCapped_poisson_tendsto
     (c := c) hd hσbelow hσabove
       (s / ((d : ℝ) / 2))
-  convert! h using 1
+  convert h using 1
   ext n
   let f : ℝ → ℝ := fun Y =>
     stripPoissonKernel σ (s / ((d : ℝ) / 2) - Y) *
@@ -6212,20 +6235,20 @@ private theorem uniformAntiFourierSignRadius_of_poisson_majorization
   let J : ℝ := lowerInverseQuadraticMass
   let Q : ℝ := C * J
   let K : ℝ := (2 * Real.pi)⁻¹ * Q / (1 - σ)
-  have hσbelow : -1 < σ := by linarith
+  have hσbelow : -1 < σ := by linarith only [hσpos, hσone]
   have hsigmapos : 0 < 1 - σ := sub_pos.mpr hσone
   have hscale : Tendsto
       (fun d : ℕ => (d : ℝ) / 2) atTop atTop := by
     have hcast := tendsto_natCast_atTop_atTop (R := ℝ)
     have hmul := hcast.atTop_mul_const
       (by norm_num : (0 : ℝ) < 1 / 2)
-    convert! hmul using 1
+    convert hmul using 1
     ext d
     ring
   have hγscale : Tendsto
       (fun d : ℕ => γ * ((d : ℝ) / 2)) atTop atTop := by
     have h := hscale.atTop_mul_const hγ
-    convert! h using 1
+    convert h using 1
     ext d
     ring
   have hnegative : Tendsto
@@ -6239,7 +6262,7 @@ private theorem uniformAntiFourierSignRadius_of_poisson_majorization
       (fun d : ℕ => K *
         Real.exp (-γ * ((d : ℝ) / 2))) atTop (𝓝 0) := by
     have h := hexp.const_mul K
-    convert! h using 1
+    convert h using 1
     · ext d
       congr 1
       ring_nf
@@ -6489,7 +6512,7 @@ private theorem unitBallVolume_odd (k : ℕ) :
         ((2 * k + 1)‼ : ℝ) * Real.sqrt Real.pi /
           (2 : ℝ) ^ (k + 1) := by
     rw [hhalf]
-    convert! Real.Gamma_nat_add_one_add_half k using 1; ring_nf
+    convert Real.Gamma_nat_add_one_add_half k using 1; ring_nf
   have hpi :
       Real.pi ^ (((2 * k + 1 : ℕ) : ℝ) / 2) =
         Real.pi ^ k * Real.sqrt Real.pi := by
@@ -6529,7 +6552,7 @@ private theorem unitBallVolume_odd_factorial (k : ℕ) :
     omega
   rw [hpower]
   field_simp
-  linarith [hidentity]
+  linarith only [hidentity]
 
 private theorem tendsto_factorialStirlingSequence :
     Tendsto Stirling.stirlingSeq atTop
@@ -6593,7 +6616,7 @@ private theorem tendsto_log_factorial_div_nat_sub_log_nat :
             (1 / 2 : ℝ) *
               (Real.log ((2 : ℝ) * (k : ℝ)) / (k : ℝ)) - 1)
         atTop (nhds (-1)) := by
-    convert! hlimit using 1; norm_num
+    convert hlimit using 1; norm_num
   refine htarget.congr' ?_
   filter_upwards [eventually_gt_atTop (0 : ℕ)] with k hk
   have hkreal : (k : ℝ) ≠ 0 := by
@@ -6605,7 +6628,7 @@ private theorem tendsto_log_factorial_div_nat_sub_log_nat :
       Real.log ((k : ℝ) * 2) = Real.log (2 * (k : ℝ)) := by
     rw [mul_comm]
   field_simp
-  linarith [hformula, hcomm]
+  linarith only [hformula, hcomm]
 
 private theorem tendsto_oddDimension_atTop :
     Tendsto (fun k : ℕ => 2 * k + 1) atTop atTop := by
@@ -6624,7 +6647,7 @@ private theorem tendsto_log_nat_div_oddDimension :
           (Real.log (k : ℝ) / (k : ℝ)) *
             ((k : ℝ) / (2 * (k : ℝ) + 1)))
         atTop (nhds 0) := by
-    convert! hproduct using 1; norm_num
+    convert hproduct using 1; norm_num
   refine hlimit.congr' ?_
   filter_upwards [eventually_gt_atTop (0 : ℕ)] with k hk
   have hkreal : (k : ℝ) ≠ 0 := by
@@ -6702,7 +6725,7 @@ private theorem tendsto_normalizedVolumeLog_even :
               (Real.log (k.factorial : ℝ) / (k : ℝ) -
                 Real.log (k : ℝ)))
         atTop (nhds ((Real.log (2 * Real.pi) + 1) / 2)) := by
-    convert! hcore using 1; norm_num; ring
+    convert hcore using 1; norm_num; ring
   refine hlimit.congr' ?_
   filter_upwards [eventually_gt_atTop (0 : ℕ)] with k hk
   have hkreal : (k : ℝ) ≠ 0 := by
@@ -6735,7 +6758,7 @@ private theorem tendsto_odd_halfDimension_log_correction :
           (-1 / 2 : ℝ) *
             (Real.log (k : ℝ) / (2 * (k : ℝ) + 1)))
         atTop (nhds 0) := by
-    convert! hscaled using 1; norm_num
+    convert hscaled using 1; norm_num
   refine hlimit.congr' (Filter.Eventually.of_forall ?_)
   intro k
   have hodd : 2 * (k : ℝ) + 1 ≠ 0 := by positivity
@@ -7136,7 +7159,7 @@ private theorem radialAutocorrelation_outside_eq_zero (d : ℕ)
   have hball := support_radialAutocorrelation_subset d hsupport
   have hnorm : ‖x‖ < (1 : ℝ) := by
     simpa only [Metric.mem_ball, dist_zero_right] using! hball
-  linarith
+  linarith only [hx, hnorm]
 
 private theorem radialAutocorrelation_real (d : ℕ) :
     IsRealValued (radialAutocorrelation d) := by
@@ -7215,7 +7238,7 @@ private theorem criticalPackingBase_lt_one : criticalPackingBase < 1 := by
   unfold criticalPackingBase
   have hratio : Real.exp 1 / (2 * Real.pi) < 1 := by
     apply (div_lt_one (by positivity)).2
-    linarith [Real.exp_one_lt_three, Real.pi_gt_three]
+    linarith only [Real.exp_one_lt_three, Real.pi_gt_three]
   exact (Real.sqrt_lt' (by norm_num : (0 : ℝ) < 1)).2
     (by simpa only [one_pow] using! hratio)
 
@@ -7224,7 +7247,7 @@ private theorem criticalBinaryExponent_pos : 0 < criticalBinaryExponent := by
     exact (Real.logb_neg (by norm_num) criticalPackingBase_pos
       criticalPackingBase_lt_one)
   rw [logb_criticalPackingBase] at hlog
-  linarith
+  linear_combination hlog
 
 end
 
@@ -7523,7 +7546,7 @@ private theorem saddleSmallRadiusStarOrdinate_sourceScale
   change Real.log ℓ / 4 ≤ ℓ * (1 + u)
   rw [← hstar]
   apply mul_le_mul_of_nonneg_left _ hℓ.le
-  linarith
+  linear_combination hu
 
 private theorem saddleSource_positiveOrdinate_sourceScale
     {ℓ u : ℝ} (hℓ : 0 < ℓ) (hu : 1 ≤ u) :
@@ -7531,7 +7554,7 @@ private theorem saddleSource_positiveOrdinate_sourceScale
   have hlog := Real.log_le_sub_one_of_pos hℓ
   have hproduct :=
     mul_nonneg hℓ.le (sub_nonneg.mpr hu)
-  linarith
+  linarith only [hℓ, hlog, hproduct]
 
 private theorem eventually_plusSaddleProfile_re_pos_at_firstBranchSaddles :
     ∀ᶠ ε : ℝ in 𝓝[>] (0 : ℝ),
@@ -7594,8 +7617,8 @@ private theorem eventually_minusSaddleProfile_re_neg_at_firstBranchSaddles :
     eventually_gt_atTop (0 : ℕ)] with d hdimen hd
   intro u hulower hupper
   have hℓ : 0 < (d : ℝ) / 2 := by positivity
-  have hu : -1 < u := by linarith
-  have huone : 1 ≤ u := by linarith
+  have hu : -1 < u := by linarith only [hε, hulower]
+  have huone : 1 ≤ u := by linarith only [hε, hulower]
   have hscale := saddleSource_positiveOrdinate_sourceScale hℓ huone
   have herr := (hdimen u hu hupper hscale).2 hulower
   have hV := hvariance ((d : ℝ) / 2) hℓ u hu hupper
@@ -7634,11 +7657,11 @@ private theorem eventually_plusSaddleProfile_re_pos_at_secondBranchSaddles :
   let δ : ℝ := u - 1
   have hδ : ε / 2 ≤ δ := by
     try dsimp [δ]
-    linarith
+    linear_combination hu
   have hidentity : 1 + δ = u := by
     try dsimp [δ]
     ring
-  have hulower : -1 < u := by linarith
+  have hulower : -1 < u := by linarith only [hε, hu]
   have hℓ : 0 < (d : ℝ) / 2 := by positivity
   have hV : 0 <
       saddleSourceGaussianVariance ε ((d : ℝ) / 2) u := by
@@ -7681,12 +7704,12 @@ private theorem eventually_minusSaddleProfile_re_neg_at_secondBranchSaddles :
   let δ : ℝ := u - 1
   have hδ : ε / 2 ≤ δ := by
     try dsimp [δ]
-    linarith
+    linear_combination hu
   have hidentity : 1 + δ = u := by
     try dsimp [δ]
     ring
-  have hulower : -1 < u := by linarith
-  have huminus : 1 + ε / 4 ≤ u := by linarith
+  have hulower : -1 < u := by linarith only [hε, hu]
+  have huminus : 1 + ε / 4 ≤ u := by linarith only [hε, hu]
   have hℓ : 0 < (d : ℝ) / 2 := by positivity
   have hV : 0 <
       saddleSourceGaussianVariance ε ((d : ℝ) / 2) u := by
@@ -7878,7 +7901,7 @@ private theorem manuscriptPackingDeficit_le_criticalPackingBase (d : ℕ) :
   refine max_le criticalPackingBase_pos.le ?_
   have hroot : 0 ≤ (linearProgram d) ^ ((d : ℝ)⁻¹) :=
     Real.rpow_nonneg (linearProgram_nonneg d) _
-  linarith
+  linear_combination hroot
 
 private theorem tendsto_manuscriptPackingDeficit
     (hpacking : SharpPackingRootAsymptotic) :
@@ -7904,7 +7927,7 @@ private theorem manuscriptPackingRoot_sub_deficit_le (d : ℕ) :
       criticalPackingBase - (linearProgram d) ^ ((d : ℝ)⁻¹) ≤
         manuscriptPackingDeficit d := by
     exact le_max_right _ _
-  linarith
+  linear_combination hdeficit
 
 private theorem manuscriptPackingRoot_sub_deficit_pow_le
     {d : ℕ} (hd : 0 < d) :
diff --git a/LeanPool/SpherePacking/SaddleAnalysis.lean b/LeanPool/SpherePacking/SaddleAnalysis.lean
index 7cee39c57b..7f72ad5daa 100644
--- a/LeanPool/SpherePacking/SaddleAnalysis.lean
+++ b/LeanPool/SpherePacking/SaddleAnalysis.lean
@@ -213,7 +213,7 @@ private theorem norm_saddleShellExponential_eq_exp_neg_damping
     hε horder ℓ T u
   rw [← Real.exp_add]
   congr 1
-  linarith
+  linarith only [hphase]
 
 private noncomputable def saddleSourceShellDerivative (ε u : ℝ) : ℝ :=
   (∫ a in (ε ^ 3)..(10 * Real.log (1 / ε)),
@@ -410,7 +410,7 @@ private theorem exists_saddleSourceShellDerivative_endpoint_bound
       C * (u - -1) := hbound
     _ ≤ max C 0 * (u + 1) := by
       have hnonneg : 0 ≤ u + 1 := by
-        linarith [hu.1]
+        linarith only [hu.1, hu]
       calc
         C * (u - -1) = C * (u + 1) := by ring
         _ ≤ max C 0 * (u + 1) :=
@@ -420,7 +420,7 @@ private theorem exists_saddleSourceShellDerivative_endpoint_bound
 private theorem saddle_log_sq_le_four_mul
     {x : ℝ} (hx : 1 ≤ x) :
     (Real.log x) ^ 2 ≤ 4 * x := by
-  have hxpos : 0 < x := by linarith
+  have hxpos : 0 < x := by linear_combination hx
   have hspos : 0 < Real.sqrt x :=
     Real.sqrt_pos.2 hxpos
   have hsquare := Real.sq_sqrt hxpos.le
@@ -433,14 +433,14 @@ private theorem saddle_log_sq_le_four_mul
     Real.log_nonneg hx
   have hupper : Real.log x ≤ 2 * Real.sqrt x := by
     rw [hlogsplit]
-    linarith
+    linarith only [hslog]
   have hfactor := mul_nonneg
     (sub_nonneg.mpr hupper)
     (add_nonneg
       (mul_nonneg (by norm_num : (0 : ℝ) ≤ 2)
         (Real.sqrt_nonneg x))
       hlognonnegative)
-  linarith
+  linarith only [hsquare, hfactor]
 
 private theorem exists_saddleSmallRadiusStar_coordinate_bound
     {ε : ℝ} (hε : 0 < ε)
@@ -469,28 +469,28 @@ private theorem exists_saddleSmallRadiusStar_coordinate_bound
     positivity
   have hlogpositive : 0 < Real.log ℓ := by
     try dsimp [ℓ]
-    linarith
+    linear_combination hloglarge
   have hℓone : 1 < ℓ :=
     (Real.log_pos_iff hℓnonnegative).mp hlogpositive
-  have hℓ : 0 < ℓ := by linarith
+  have hℓ : 0 < ℓ := by linear_combination hℓone
   have hdreal : 0 < (d : ℝ) := by
     try dsimp [ℓ] at hℓ
-    linarith
+    linarith only [hℓ]
   have hd : 0 < d := by
     exact_mod_cast hdreal
   have hm : 1 < m := by
     try dsimp [m, ℓ]
-    linarith
-  have hmpositive : 0 < m := by linarith
+    linarith only [hloglarge]
+  have hmpositive : 0 < m := by linear_combination hm
   have hqnonnegative : 0 ≤ q := by
     try dsimp [q]
     positivity
   have hlogupper : Real.log ℓ ≤ ℓ := by
-    linarith [Real.log_le_sub_one_of_pos hℓ]
+    linarith only [Real.log_le_sub_one_of_pos hℓ, hℓ]
   have hqbound : q ≤ 1 / 4 := by
     try dsimp [q]
     apply (div_le_iff₀ (show 0 < 4 * ℓ by positivity)).mpr
-    linarith
+    linear_combination hlogupper
   have hstar :
       saddleSmallRadiusStarOrdinate d = -1 + q := by
     rfl
@@ -525,7 +525,10 @@ private theorem exists_saddleSmallRadiusStar_coordinate_bound
     try dsimp [z]
     calc
       2 * K * q ≤ 2 * K * (1 / 4 : ℝ) := by
-        gcongr
+        exact mul_le_mul_of_nonneg_left hqbound
+            (mul_nonneg
+              zero_le_two
+              hK)
       _ = K / 2 := by ring
   have hlogquad := saddle_log_sq_le_four_mul hℓone.le
   have hmz : m * z ≤ K / 4 := by
@@ -538,8 +541,7 @@ private theorem exists_saddleSmallRadiusStar_coordinate_bound
     rw [hid]
     apply (div_le_iff₀
       (show 0 < 16 * ℓ by positivity)).mpr
-    linarith [mul_nonneg hK
-      (sub_nonneg.mpr hlogquad)]
+    linarith only [mul_nonneg hK (sub_nonneg.mpr hlogquad), hK, hlogquad]
   have hexpdifference :
       Real.exp z - 1 ≤ z * Real.exp z := by
     have hsource :=
@@ -562,7 +564,7 @@ private theorem exists_saddleSmallRadiusStar_coordinate_bound
           (K / 4) * Real.exp (K / 2) := by
       exact mul_le_mul hmz hexpbound
         (Real.exp_pos z).le (by positivity)
-    linarith
+    linear_combination hdifference + hscaled
   calc
     saddleSmallRadiusVariable ε
         (saddleSmallRadiusStar ε d) =
@@ -578,7 +580,7 @@ private theorem exists_saddleSmallRadiusStar_coordinate_bound
       apply Real.exp_le_exp.mpr
       have hdigamma := (saddleDigamma_bounds hm).2
       try dsimp [z]
-      linarith
+      linarith only [hshell, hdigamma]
     _ = m * Real.exp z := by
       rw [Real.exp_add, Real.exp_log hmpositive]
     _ ≤ m + K / 4 * Real.exp (K / 2) := hproduct
@@ -610,23 +612,27 @@ private theorem exists_eventually_y_star_le_log_eighth_add
   intro r hr hrstar
   have hℓ : 0 < (d : ℝ) / 2 := by
     have he := Real.exp_pos (8 : ℝ)
-    linarith
+    linarith only [hd, he]
   have hlog : 8 < Real.log ((d : ℝ) / 2) := by
     apply (Real.lt_log_iff_exp_lt hℓ).mpr
-    linarith
+    linarith only [hd]
   have hstarpositive : 0 < saddleSmallRadiusStar ε d :=
     saddleSmallRadiusStar_pos ε d
   have hsquare :
       r ^ 2 ≤ (saddleSmallRadiusStar ε d) ^ 2 := by
-    linarith [mul_nonneg
-      (sub_nonneg.mpr hrstar)
-      (add_nonneg hstarpositive.le hr)]
+    linarith only [
+      mul_nonneg (sub_nonneg.mpr hrstar) (add_nonneg hstarpositive.le hr),
+      hr,
+      hrstar,
+      hstarpositive
+    ]
   calc
     saddleSmallRadiusVariable ε r ≤
         saddleSmallRadiusVariable ε
           (saddleSmallRadiusStar ε d) := by
       unfold saddleSmallRadiusVariable
-      gcongr
+      exact mul_le_mul_of_nonneg_left hsquare
+          (le_of_lt (mul_pos Real.pi_pos (Real.exp_pos (2 * saddleShellDerivativeOne ε))))
     _ ≤ Real.log ((d : ℝ) / 2) / 8 + C :=
       hstar d hlog
 
@@ -664,7 +670,7 @@ private theorem tendsto_logLinear_div_atTop :
       (tendsto_inv_atTop_zero :
         Tendsto (fun ℓ : ℝ => ℓ⁻¹)
           atTop (𝓝 0))
-  convert! (hlog.const_mul 20).add hinv using 1
+  convert (hlog.const_mul 20).add hinv using 1
   · funext ℓ
     ring
   · norm_num
@@ -692,7 +698,7 @@ private theorem tendsto_logLinear_sq_div_atTop :
       (tendsto_inv_atTop_zero :
         Tendsto (fun ℓ : ℝ => ℓ⁻¹)
           atTop (𝓝 0))
-  convert! ((hlog2.const_mul 400).add
+  convert ((hlog2.const_mul 400).add
     (hlog1.const_mul 40)).add hinv using 1
   · funext ℓ
     ring
@@ -714,7 +720,7 @@ private theorem tendsto_saddleSmallResidueTruncation_div :
       with ℓ hℓ
     exact div_le_div_of_nonneg_right
       (saddleSmallResidueTruncation_upper hℓ)
-      (by linarith)
+      (by linear_combination hℓ)
   · exact tendsto_logLinear_div_atTop
 
 private theorem tendsto_saddleSmallResidueTruncation_sq_div :
@@ -732,11 +738,11 @@ private theorem tendsto_saddleSmallResidueTruncation_sq_div :
     positivity
   · filter_upwards [eventually_ge_atTop (1 : ℝ)]
       with ℓ hℓ
-    apply div_le_div_of_nonneg_right _ (by linarith)
+    apply div_le_div_of_nonneg_right _ (by linear_combination hℓ)
     exact (sq_le_sq₀
       (by exact_mod_cast (Nat.zero_le
         (saddleSmallResidueTruncation ℓ)))
-      (by linarith [Real.log_nonneg hℓ])).mpr
+      (by linarith only [Real.log_nonneg hℓ, hℓ])).mpr
       (saddleSmallResidueTruncation_upper hℓ)
   · exact tendsto_logLinear_sq_div_atTop
 
@@ -750,7 +756,7 @@ private theorem eventually_saddleSmallResidueTruncation_double_le :
     eventually_gt_atTop (0 : ℝ)]
     with ℓ hratio hℓ
   have h := (div_lt_iff₀ hℓ).mp hratio
-  linarith
+  linarith only [h]
 
 private theorem eventually_saddleSmallResidueTruncation_succ_double_le :
     ∀ᶠ ℓ : ℝ in atTop,
@@ -761,10 +767,10 @@ private theorem eventually_saddleSmallResidueTruncation_succ_double_le :
   filter_upwards [hsmall,
     eventually_ge_atTop (4 : ℝ)]
     with ℓ hratio hℓ
-  have hℓpos : 0 < ℓ := by linarith
+  have hℓpos : 0 < ℓ := by linear_combination hℓ
   have h := (div_lt_iff₀ hℓpos).mp hratio
   push_cast
-  linarith
+  linarith only [hℓ, h]
 
 private theorem eventually_saddleSmallResidueTruncation_dominates_window
     {C : ℝ} (hC : 0 ≤ C) :
@@ -780,7 +786,7 @@ private theorem eventually_saddleSmallResidueTruncation_dominates_window
   have hlogC : C ≤ Real.log ℓ := by
     simpa only [max_eq_left hC] using! hlog
   have hN := saddleSmallResidueTruncation_lower ℓ
-  linarith [hlogC]
+  linarith only [hlogC, hyupper, hN]
 
 private theorem saddleExpSeries_term_le_exp_mul_half_pow
     {y : ℝ} (hy : 0 ≤ y) (m : ℕ) :
@@ -810,7 +816,7 @@ private theorem saddleSmallResidue_half_log_le :
     Real.log (1 / 2 : ℝ) ≤ -(1 / 2 : ℝ) := by
   have h := Real.log_le_sub_one_of_pos
     (by norm_num : (0 : ℝ) < 1 / 2)
-  linarith
+  linear_combination h
 
 private theorem saddleSmallResidueTruncation_half_pow_le
     (ℓ : ℝ) :
@@ -822,7 +828,7 @@ private theorem saddleSmallResidueTruncation_half_pow_le
       20 * Real.log ℓ ≤ (m : ℝ) := by
     try dsimp [m]
     push_cast
-    linarith [saddleSmallResidueTruncation_lower ℓ]
+    linarith only [saddleSmallResidueTruncation_lower ℓ]
   have hhalf := saddleSmallResidue_half_log_le
   have hproduct :=
     mul_le_mul_of_nonneg_left hhalf
@@ -830,7 +836,7 @@ private theorem saddleSmallResidueTruncation_half_pow_le
   have hexponent :
       (m : ℝ) * Real.log (1 / 2 : ℝ) ≤
         -10 * Real.log ℓ := by
-    linarith
+    linarith only [hmlower, hproduct]
   change (1 / 2 : ℝ) ^ m ≤ _
   calc
     (1 / 2 : ℝ) ^ m =
@@ -870,7 +876,7 @@ private theorem saddleSmallResidue_tail_le_majorant
           (3 * (Real.log ℓ / 8 + C)) *
         Real.exp (-10 * Real.log ℓ) := by
       apply mul_le_mul
-      · exact Real.exp_le_exp.mpr (by linarith)
+      · exact Real.exp_le_exp.mpr (by linarith only [hyupper])
       · exact hgeo
       · positivity
       · positivity
@@ -894,7 +900,7 @@ private theorem tendsto_saddleSmallResidueTailMajorant
   have hsmall :=
     (Real.tendsto_exp_atBot.comp hneg).const_mul
       (Real.exp (3 * C))
-  convert! hsmall using 1
+  convert hsmall using 1
   · funext ℓ
     unfold saddleSmallResidueTailMajorant
     rw [show
@@ -992,7 +998,7 @@ private theorem tendsto_saddleLogWindowPolynomial_exp_neg
         (fun t : ℝ =>
           t ^ 2 * Real.exp (-(3 / 4 : ℝ) * t))
         atTop (𝓝 0) := by
-    convert! h2base.const_mul ((4 / 3 : ℝ) ^ 2)
+    convert h2base.const_mul ((4 / 3 : ℝ) ^ 2)
       using 1
     · funext t
       try dsimp
@@ -1010,7 +1016,7 @@ private theorem tendsto_saddleLogWindowPolynomial_exp_neg
         (fun t : ℝ =>
           t * Real.exp (-(3 / 4 : ℝ) * t))
         atTop (𝓝 0) := by
-    convert! h1base.const_mul (4 / 3 : ℝ)
+    convert h1base.const_mul (4 / 3 : ℝ)
       using 1
     · funext t
       try dsimp
@@ -1033,7 +1039,7 @@ private theorem tendsto_saddleLogWindowPolynomial_exp_neg
     ((h2.const_mul (1 / 64 : ℝ)).add
       (h1.const_mul (C / 4 + 1 / 4))).add
         (h0.const_mul (C ^ 2 + 2 * C))
-  convert! hpoly using 1
+  convert hpoly using 1
   · funext t
     ring
   · norm_num
@@ -1047,7 +1053,7 @@ private theorem tendsto_saddleSmallResidueCoefficientMajorant
         (fun ℓ : ℝ =>
           K * (saddleSmallResidueTruncation ℓ : ℝ) ^ 2 / ℓ)
         atTop (𝓝 0) := by
-    convert! tendsto_saddleSmallResidueTruncation_sq_div.const_mul K
+    convert tendsto_saddleSmallResidueTruncation_sq_div.const_mul K
       using 1
     · funext ℓ
       ring
@@ -1066,7 +1072,7 @@ private theorem tendsto_saddleSmallResidueCoefficientMajorant
     (Real.exp (2 * C))
   have htotal :=
     (hfactor.const_mul K).mul hwindowScaled
-  convert! htotal using 1
+  convert htotal using 1
   · funext ℓ
     unfold saddleSmallResidueCoefficientMajorant
     rw [show
@@ -1172,7 +1178,7 @@ theorem tendsto_saddleResidue_dimension_half :
   have hcast := tendsto_natCast_atTop_atTop (R := ℝ)
   have hmul := hcast.atTop_mul_const
     (by norm_num : (0 : ℝ) < 1 / 2)
-  convert! hmul using 1
+  convert hmul using 1
   funext d
   ring
 
@@ -1225,7 +1231,7 @@ private theorem gamma_half_factorial_lower (N : ℕ) :
         Real.Gamma (((N + 1 : ℕ) : ℝ) + 3 / 2) =
           ((N : ℝ) + 3 / 2) *
             Real.Gamma ((N : ℝ) + 3 / 2) := by
-      convert! Real.Gamma_add_one hq.ne' using 1
+      convert Real.Gamma_add_one hq.ne' using 1
       all_goals
         push_cast
         ring_nf
@@ -1286,7 +1292,7 @@ private theorem saddleNegative_factorialTail_le_majorant
     _ ≤ Real.exp (3 * (Real.log ℓ / 8 + C)) *
         (2 * Real.exp (-10 * Real.log ℓ)) := by
       apply mul_le_mul
-      · exact Real.exp_le_exp.mpr (by linarith)
+      · exact Real.exp_le_exp.mpr (by linarith only [hyupper])
       · exact hgeo
       · positivity
       · positivity
@@ -1314,7 +1320,7 @@ private theorem saddleNegative_sqrt_le_one_add
     Real.sqrt y ≤ 1 + y := by
   have hs := Real.sqrt_nonneg y
   have hsq := Real.sq_sqrt hy
-  linarith [sq_nonneg (Real.sqrt y - 1)]
+  linarith only [sq_nonneg (Real.sqrt y - 1), hy, hsq]
 
 private noncomputable def saddleNegativeRelativeGammaTailMajorant
     (C K Kε ℓ : ℝ) : ℝ :=
@@ -1373,7 +1379,7 @@ private theorem saddleNegative_relativeGammaTail_le_majorant
   have hsqrtY : Real.sqrt y ≤ 1 + Y := by
     calc
       Real.sqrt y ≤ 1 + y := hsqrt
-      _ ≤ 1 + Y := by dsimp [Y]; linarith
+      _ ≤ 1 + Y := by dsimp [Y]; linear_combination hyupper
   have htail :=
     saddleNegative_factorialTail_le_majorant hy hyupper
   have hbase : 0 ≤ y ^ N / (N.factorial : ℝ) := by
@@ -1399,7 +1405,10 @@ private theorem saddleNegative_relativeGammaTail_le_majorant
         (Real.exp y *
           ((y ^ N / (N.factorial : ℝ)) /
             Real.Gamma (3 / 2 : ℝ))) * E := by
-      gcongr
+      exact mul_le_mul_of_nonneg_right
+          (mul_le_mul_of_nonneg_left (mul_le_mul_of_nonneg_left hfrac (le_of_lt (Real.exp_pos y)))
+            (mul_nonneg hKε (Real.sqrt_nonneg y)))
+          (le_of_lt (Real.exp_pos (K * (2 * ↑N + 1) ^ 2 / ℓ)))
     _ = (Kε / Real.Gamma (3 / 2 : ℝ)) *
         Real.sqrt y *
           (Real.exp y * (y ^ N / (N.factorial : ℝ))) * E := by
@@ -1407,7 +1416,11 @@ private theorem saddleNegative_relativeGammaTail_le_majorant
     _ ≤ (Kε / Real.Gamma (3 / 2 : ℝ)) *
         (1 + Y) *
           (2 * saddleSmallResidueTailMajorant C ℓ) * E := by
-      gcongr
+      apply mul_le_mul_of_nonneg_right _ hE
+      exact mul_le_mul
+        (mul_le_mul_of_nonneg_left hsqrtY (div_nonneg hKε hΓ.le))
+        htail (mul_nonneg (Real.exp_pos y).le hbase)
+        (mul_nonneg (div_nonneg hKε hΓ.le) (add_nonneg zero_le_one hY))
     _ = saddleNegativeRelativeGammaTailMajorant C K Kε ℓ := by
       unfold saddleNegativeRelativeGammaTailMajorant
       try dsimp [N, Y, E]
@@ -1428,7 +1441,7 @@ private theorem tendsto_saddleNegativeTruncation_odd_sq_div :
     ((tendsto_saddleSmallResidueTruncation_sq_div.const_mul 4).add
       (tendsto_saddleSmallResidueTruncation_div.const_mul 4)).add
         hinv
-  convert! h using 1
+  convert h using 1
   · funext ℓ
     ring
   · norm_num
@@ -1454,7 +1467,7 @@ private theorem tendsto_saddleNegativeLogWindowTailMajorant
         (fun t : ℝ =>
           t * Real.exp (-(77 / 8 : ℝ) * t))
         atTop (𝓝 0) := by
-    convert! h1base.const_mul (8 / 77 : ℝ) using 1
+    convert h1base.const_mul (8 / 77 : ℝ) using 1
     · funext t
       try dsimp
       ring_nf
@@ -1472,7 +1485,7 @@ private theorem tendsto_saddleNegativeLogWindowTailMajorant
       (h0.const_mul (1 + C))
   have hlog := hpoly.comp Real.tendsto_log_atTop
   have hscaled := hlog.const_mul (Real.exp (3 * C))
-  convert! hscaled using 1
+  convert hscaled using 1
   · funext ℓ
     unfold saddleSmallResidueTailMajorant
     rw [show
@@ -1494,7 +1507,7 @@ private theorem tendsto_saddleNegativeRelativeGammaTailMajorant
   have htotal :=
     (hsmall.const_mul
       (2 * Kε / Real.Gamma (3 / 2 : ℝ))).mul herror
-  convert! htotal using 1
+  convert htotal using 1
   · funext ℓ
     unfold saddleNegativeRelativeGammaTailMajorant
     ring_nf
@@ -1662,7 +1675,7 @@ private theorem tendsto_integral_upperGammaTruncatedDampingIntegrand
       apply Real.exp_lt_one_iff.mpr
       have : 0 < 2 * a / ℓ :=
         div_pos (mul_pos (by norm_num) ha) hℓ
-      linarith
+      linear_combination this
     have hbase : 0 ≤ upperCosLaplaceKernel η T a := by
       unfold upperCosLaplaceKernel
       exact div_nonneg
@@ -1700,7 +1713,7 @@ private theorem tendsto_integral_upperGammaTruncatedDampingIntegrand
       apply Real.exp_lt_one_iff.mpr
       have : 0 < 2 * a / ℓ :=
         div_pos (mul_pos (by norm_num) ha) hℓ
-      linarith
+      linear_combination this
     have hgeo :=
       (hasSum_geometric_of_lt_one hq0 hq1).tendsto_sum_nat
     have hshift := hgeo.comp (tendsto_add_atTop_nat 1)
@@ -1810,7 +1823,7 @@ private theorem upperGammaEuler_real_factor_norm
     {m : ℝ} (hm : 0 < m) (k : ℕ) :
     ‖(m : ℂ) + (k : ℂ)‖ = m + (k : ℝ) := by
   have hp : 0 ≤ m + (k : ℝ) := by positivity
-  convert! Complex.norm_of_nonneg hp using 1;
+  convert Complex.norm_of_nonneg hp using 1;
     push_cast; ring
 
 private theorem upperGammaEuler_complex_factor_pos
@@ -2119,18 +2132,18 @@ private theorem plusSaddleProfile_re_pos_of_relative_residue_bounds
       (1 / 2 : ℝ) < Real.exp y * S := by
     have hscaled := mul_le_mul_of_nonneg_left
       hSabs hexp.le
-    linarith
+    linarith only [hfinite, hone, hscaled]
   have hQabs := Complex.abs_re_le_norm Q
   have hQneg : -‖Q‖ ≤ Q.re := by
-    linarith [neg_abs_le Q.re]
+    linarith only [neg_abs_le Q.re, hQabs]
   have hQlower :
       -(1 / 2 : ℝ) < Real.exp y * Q.re := by
     have hscaled := mul_le_mul_of_nonneg_left
       hQneg hexp.le
-    linarith
+    linear_combination hremainder + hscaled
   have hsum : 0 < S + Q.re := by
     have hscaled : 0 < Real.exp y * (S + Q.re) := by
-      linarith
+      linear_combination hSlower + hQlower
     exact (mul_pos_iff_of_pos_left hexp).mp hscaled
   exact (div_pos_iff_of_pos_right hO).mp
     (hnormal.symm ▸ hsum)
@@ -2156,7 +2169,7 @@ private theorem upperPositiveHalfGamma_scaled_sq_le
           ‖Complex.Gamma
             (((1 / 2 : ℝ) : ℂ) + Complex.I * (x : ℂ))‖ ^ 2 =
             Real.pi / Real.cosh (Real.pi * x) := by
-        convert! norm_gamma_half_add_imaginary_sq x using 1; norm_num
+        convert norm_gamma_half_add_imaginary_sq x using 1; norm_num
       rw [hhalf, Real.Gamma_one_half_eq,
         Real.sq_sqrt Real.pi_pos.le]
       field_simp [(Real.cosh_pos (Real.pi * x)).ne']; norm_num
@@ -2168,7 +2181,7 @@ private theorem upperPositiveHalfGamma_scaled_sq_le
       have hreal :
           Real.Gamma (((n + 1 : ℕ) : ℝ) + 1 / 2) =
             q * Real.Gamma q := by
-        convert! Real.Gamma_add_one hq.ne' using 1
+        convert Real.Gamma_add_one hq.ne' using 1
         · simp only [Nat.cast_add, Nat.cast_one, one_div, q]
           ring_nf
       let z : ℂ := (q : ℂ) + Complex.I * (x : ℂ)
@@ -2182,7 +2195,7 @@ private theorem upperPositiveHalfGamma_scaled_sq_le
               (((((n + 1 : ℕ) : ℝ) + 1 / 2 : ℝ) : ℂ) +
                 Complex.I * (x : ℂ)) =
             z * Complex.Gamma z := by
-        convert! Complex.Gamma_add_one z hz using 1
+        convert Complex.Gamma_add_one z hz using 1
         · simp only [Nat.cast_add, Nat.cast_one, one_div, Complex.ofReal_add,
           Complex.ofReal_natCast,
             Complex.ofReal_one, Complex.ofReal_inv, Complex.ofReal_ofNat, z, q]
@@ -2225,9 +2238,9 @@ private theorem upperNegativeContour_shortMeasure_pointwise
       (1 - 4 * ε) * upperGammaMeasureDensity ℓ η a := by
   have hfactor : 0 ≤ 1 - 4 * ε := by
     apply (mul_nonneg_iff_of_pos_right hη).mp
-    exact mul_nonneg (by linarith [hεsmall]) hη.le
+    exact mul_nonneg (by linarith only [hεsmall]) hη.le
   have hmargintop : (1 - 10 * ε * (1 + a)) ≤ 1 - 10 * ε := by
-    linarith [mul_nonneg hε.le ha.le]
+    linarith only [mul_nonneg hε.le ha.le, hε, ha]
   have hbase :
       (ℓ / 2) * Real.exp (-η * a) / a ^ 2 ≤
         upperGammaMeasureDensity ℓ η a := by
@@ -2235,21 +2248,20 @@ private theorem upperNegativeContour_shortMeasure_pointwise
       (upperGammaVarianceDensity_pointwise_bounds
         (η := η) hℓ ha).1
     apply (div_le_iff₀ (sq_pos_of_pos ha)).2
-    linarith
+    linear_combination hvariance
   have hbasepos :
       0 ≤ (ℓ / 2) * Real.exp (-η * a) / a ^ 2 := by
     positivity
   have hratio :
       Real.cosh (κ * a) / Real.cosh a ≤
         Real.exp ((κ - 1) * a) := by
-    convert! cosh_ratio_upper ha.le
+    convert cosh_ratio_upper ha.le
       (sub_nonneg.mpr hκ) using 1; ring_nf
   have hexp :
       Real.exp ((η - 2) * a) *
         Real.exp ((κ - 1) * a) ≤ 1 := by
     rw [← Real.exp_add, Real.exp_le_one_iff]
-    linarith [mul_nonneg
-      (show 0 ≤ 3 - (κ + η) by linarith) ha.le]
+    linarith only [mul_nonneg (show 0 ≤ 3 - (κ + η) by linarith) ha.le, hκη, ha]
   have hcoefficient :
       (1 - 10 * ε * (1 + a)) * Real.exp ((η - 2) * a) *
           (Real.cosh (κ * a) / Real.cosh a) ≤
@@ -2266,7 +2278,7 @@ private theorem upperNegativeContour_shortMeasure_pointwise
       _ ≤ (1 - 10 * ε * (1 + a)) := by
           simpa only [mul_one] using! mul_le_mul_of_nonneg_left hexp hmargin
       _ ≤ 1 - 10 * ε := hmargintop
-      _ ≤ 1 - 4 * ε := by linarith
+      _ ≤ 1 - 4 * ε := by linarith only [hε]
   have hidentity :
       ℓ * (-shortShellDensity ε a) * Real.cosh (κ * a) =
         ((1 - 10 * ε * (1 + a)) * Real.exp ((η - 2) * a) *
@@ -2319,7 +2331,7 @@ private theorem upperNegativeContour_shortDamping_le_gamma
   have ha₀ : 0 < a₀ := by
     try dsimp [a₀]
     positivity
-  have hfactor : 0 ≤ 1 - 4 * ε := by linarith
+  have hfactor : 0 ≤ 1 - 4 * ε := by linarith only [hεsmall]
   have hsubset : Ioc a₀ A ⊆ Ioi (0 : ℝ) := by
     intro a ha
     exact ha₀.trans ha.1
@@ -2335,7 +2347,7 @@ private theorem upperNegativeContour_shortDamping_le_gamma
   have hs := shortShellDensity_intervalIntegrable hε horder
   have hcosh : Continuous
       (fun a : ℝ => Real.cosh (κ * a)) := by
-    fun_prop
+    exact Continuous.comp' Real.continuous_cosh (Continuous.const_mul continuous_id' κ)
   have hosc : Continuous
       (fun a : ℝ => 1 - Real.cos (a * T)) := by
     fun_prop
@@ -2454,7 +2466,7 @@ private theorem one_le_saddleNegativeContourOrdinate
   unfold saddleNegativeContourOrdinate
   have hN : 0 ≤ (N : ℝ) := Nat.cast_nonneg N
   have hq : 0 ≤ (2 * (N : ℝ) + 1) / ℓ := by positivity
-  linarith
+  linear_combination hq
 
 private theorem saddleNegativeContourOrdinate_add_rate_le_three
     {ℓ : ℝ} (hℓ : 0 < ℓ) (N : ℕ)
@@ -2465,7 +2477,7 @@ private theorem saddleNegativeContourOrdinate_add_rate_le_three
   have hratio : (4 * (N : ℝ) + 4) / ℓ ≤ 2 := by
     apply (div_le_iff₀ hℓ).2
     norm_num [Nat.cast_add, Nat.cast_one] at hN
-    linarith
+    linarith only [hN]
   calc
     1 + (2 * (N : ℝ) + 1) / ℓ +
         (2 * (N : ℝ) + 3) / ℓ =
@@ -2534,7 +2546,7 @@ private theorem upperNegativeContour_reflectedGamma_damping_exp_le_cosh
   have hinverse :
       Real.exp (2 * D) * Real.exp (-D) ^ 2 = 1 := by
     rw [pow_two, ← Real.exp_add, ← Real.exp_add]
-    convert! Real.exp_zero using 1; ring_nf
+    convert Real.exp_zero using 1; ring_nf
   change Real.exp (2 * D) ≤ Real.cosh (Real.pi * (s / 2))
   calc
     Real.exp (2 * D) = Real.exp (2 * D) * 1 := by ring
@@ -2605,7 +2617,7 @@ private theorem upperNegativeHalfGamma_reflection_norm
           ring
         _ = Real.pi / Real.cosh (Real.pi * (s / 2)) := by
           try dsimp [z]
-          convert! norm_gamma_half_add_imaginary_sq (s / 2)
+          convert norm_gamma_half_add_imaginary_sq (s / 2)
             using 1
   | succ N ih =>
       let z : ℂ :=
@@ -2622,7 +2634,7 @@ private theorem upperNegativeHalfGamma_reflection_norm
             zero_div, mul_zero, sub_self,
           add_zero, Complex.zero_re, z] at h
         have hN : 0 ≤ (N : ℝ) := Nat.cast_nonneg N
-        linarith
+        linarith only [h]
       have harg :
           upperNegativeHalfGammaArgument (N + 1) s = -z := by
         unfold upperNegativeHalfGammaArgument
@@ -2714,14 +2726,14 @@ private theorem upperNegativeHalfGamma_norm_eq_reflected_damping
   rw [Real.exp_neg] at href
   field_simp [hΓ.ne', (Real.exp_pos D).ne',
     (Real.cosh_pos (Real.pi * (s / 2))).ne'] at href ⊢
-  simpa [D, neg_div, mul_comm, mul_left_comm, mul_assoc] using! href
+  simpa only [D, neg_div, mul_comm, mul_left_comm, mul_assoc] using! href
 
 private theorem upper_log_cosh_ge_abs_sub_log_two (x : ℝ) :
     |x| - Real.log 2 ≤ Real.log (Real.cosh x) := by
   have hhalf : Real.exp |x| / 2 ≤ Real.cosh x := by
     rw [← Real.cosh_abs, Real.cosh_eq]
     have hp := (Real.exp_pos (-|x|)).le
-    linarith
+    linarith only [hp]
   apply Real.exp_le_exp.mp
   rw [Real.exp_log (Real.cosh_pos x), Real.exp_sub,
     Real.exp_log (by norm_num : (0 : ℝ) < 2)]
@@ -2766,12 +2778,11 @@ private theorem upperNegativeContour_gamma_mul_exp_short_le
     exact hreflect
   have hlog := upper_log_cosh_ge_abs_sub_log_two
     (Real.pi * (s / 2))
-  have hfactor : 0 ≤ 2 - 4 * ε := by linarith
+  have hfactor : 0 ≤ 2 - 4 * ε := by linarith only [hε, hεsmall]
   have hphase :
       (2 - 4 * ε) * D - Real.log C ≤
         -(2 * ε) * Real.log C := by
-    linarith [mul_nonneg hfactor
-      (show 0 ≤ Real.log C - 2 * D by linarith)]
+    linarith only [mul_nonneg hfactor (show 0 ≤ Real.log C - 2 * D by linarith), hDlog, hfactor]
   have hlogphase :
       -(2 * ε) * Real.log C ≤
         2 * ε * Real.log 2 - ε * Real.pi * |s| := by
@@ -2831,11 +2842,25 @@ private theorem upperNegativeContour_gamma_mul_exp_short_le
             (Real.exp ((2 - 4 * ε) * D) / C) := by ring
     _ ≤ (Real.pi / Real.Gamma ((N : ℝ) + 3 / 2)) *
         Real.exp (-(2 * ε) * Real.log C) := by
-      gcongr
+      exact mul_le_mul_of_nonneg_left (Real.exp_monotone hphase)
+          (le_of_lt
+            (div_pos Real.pi_pos
+              (Real.Gamma_pos_of_pos
+                (Right.add_pos_of_nonneg_of_pos (Nat.cast_nonneg' N)
+                  (div_pos
+                    ((by norm_num))
+                    (zero_lt_two))))))
     _ ≤ (Real.pi / Real.Gamma ((N : ℝ) + 3 / 2)) *
         Real.exp
           (2 * ε * Real.log 2 - ε * Real.pi * |s|) := by
-      gcongr
+      exact mul_le_mul_of_nonneg_left (Real.exp_monotone hlogphase)
+          (le_of_lt
+            (div_pos Real.pi_pos
+              (Real.Gamma_pos_of_pos
+                (Right.add_pos_of_nonneg_of_pos (Nat.cast_nonneg' N)
+                  (div_pos
+                    ((by norm_num))
+                    (zero_lt_two))))))
     _ = (Real.pi / Real.Gamma ((N : ℝ) + 3 / 2)) *
         Real.exp (2 * ε * Real.log 2) *
           Real.exp (-ε * Real.pi * |s|) := by
@@ -2893,8 +2918,8 @@ private theorem saddleNegativeContourOrdinate_le_two
   have hratio : (2 * (N : ℝ) + 1) / ℓ ≤ 1 := by
     apply (div_le_iff₀ hℓ).2
     norm_num [Nat.cast_add, Nat.cast_one] at hN
-    linarith
-  linarith
+    linear_combination hN
+  linear_combination hratio
 
 private theorem upperNegativeContour_gamma_mul_shellExponential_le
     {ε ℓ : ℝ}
@@ -2967,10 +2992,10 @@ private theorem upperNegativeContour_gamma_mul_shellExponential_le
         Real.exp (ℓ * realHyperbolicShellPhase ε κ) *
           Real.exp (-(P - S)) := by
     rw [realHyperbolicShellPhase_neg] at hshell
-    convert! hshell using 1
+    convert hshell using 1
   have hexp : Real.exp (-(P - S)) ≤ Real.exp S := by
     apply Real.exp_le_exp.mpr
-    linarith
+    linear_combination hP
   rw [saddleTaylorContour_gammaArgument,
     saddleTaylorContour_shellArgument hℓ N s,
     norm_mul, hshell']
@@ -3029,7 +3054,7 @@ private theorem norm_plusPolynomial_negativeContour_le
   have hℓone : 1 ≤ ℓ := by
     norm_num [Nat.cast_add, Nat.cast_one] at hN
     have hcast : 0 ≤ (N : ℝ) := Nat.cast_nonneg N
-    linarith
+    linarith only [hN]
   have hdivide : |s| / ℓ ≤ |s| :=
     (div_le_self (abs_nonneg s) hℓone)
   have hnorm :
@@ -3046,13 +3071,13 @@ private theorem norm_plusPolynomial_negativeContour_le
         simp only [Complex.ofReal_div, Complex.ofReal_neg, Complex.norm_div, norm_neg,
           Complex.norm_real,
           Real.norm_eq_abs, abs_of_pos hℓ, mul_neg, Complex.norm_mul, Complex.norm_I,
-            abs_of_nonneg (show 0 ≤ κ by linarith),
+            abs_of_nonneg (show 0 ≤ κ by linarith only [hκ]),
           one_mul]
   have hbase :
       1 + ‖((-s / ℓ : ℝ) : ℂ) +
         Complex.I * (((-κ : ℝ) : ℂ))‖ ≤
         3 * (1 + |s|) := by
-    linarith [abs_nonneg s]
+    linarith only [abs_nonneg s, hκtop, hdivide, hnorm]
   rw [saddleTaylorContour_shellArgument hℓ N s]
   calc
     ‖plusPolynomial ε
@@ -3717,7 +3742,7 @@ private theorem eventually_plusSaddleTaylorRemainder_relative_lt_half_on_star
         (Kε * Real.sqrt y * y ^ N /
           Real.Gamma ((N : ℝ) + 3 / 2) *
             Real.exp (saddleNegativeContourPhaseError ε ℓ N)) := by
-      gcongr
+      exact mul_le_mul_of_nonneg_left hrelative (le_of_lt (Real.exp_pos y))
     _ ≤ Real.exp y *
         (Kε * Real.sqrt y * y ^ N /
           Real.Gamma ((N : ℝ) + 3 / 2) *
@@ -3775,7 +3800,7 @@ private theorem eventually_plusSaddleProfile_re_pos_on_star :
     hε (le_of_lt hεsmall) horder
   intro a ha
   have h := hmargin a ha
-  linarith
+  linear_combination h
 
 end
 
@@ -3832,7 +3857,7 @@ private theorem saddleRealCpow_hasDerivAt
       intro heq
       have hre := congrArg Complex.re heq
       norm_num at hre
-      linarith
+      linarith only [hz, hre]
     simpa only [Complex.ofReal_zero, Complex.zero_cpow hsub, mul_zero] using!
       saddleRealCpow_hasDerivAt_zero hz
   · exact hasDerivAt_ofReal_cpow_const hx hz0
@@ -3857,12 +3882,12 @@ private theorem saddlePositiveCpow_hasDerivAt_zero
     norm_num at hz
   have hsub : 0 < (z - 1).re := by
     change 0 < z.re - 1
-    linarith
+    linarith only [hz]
   have hsub0 : z - 1 ≠ 0 := by
     intro heq
     have hre := congrArg Complex.re heq
     norm_num at hre
-    linarith
+    linarith only [hz, hre]
   rw [hasDerivAt_iff_tendsto_slope_zero]
   have htend :
       Tendsto (saddlePositiveCpow (z - 1))
@@ -3901,7 +3926,7 @@ private theorem saddlePositiveCpow_hasDerivAt
     intro heq
     have hre := congrArg Complex.re heq
     norm_num at hre
-    linarith
+    linarith only [hz, hre]
   rcases lt_trichotomy x 0 with hneg | hzero | hpos
   · have hevent :
         saddlePositiveCpow z =ᶠ[𝓝 x]
@@ -4043,7 +4068,7 @@ private theorem saddlePositiveContourPower_frequency_continuous
   have hpositive :
       0 < (saddleContourExponent a t - (j : ℂ)).re := by
     rw [saddleContourExponent_sub_nat_re]
-    linarith
+    linear_combination ha
   simpa only [Complex.sub_re, saddleContourExponent_re, Complex.natCast_re, Complex.zero_re,
     ne_eq] using! hpositive.ne'
 
@@ -4065,10 +4090,10 @@ private theorem saddlePositiveContourMoment_hasDerivAt
     exact saddlePolynomialWeightedData_integrable hD
       (saddleContourFallingPolynomial a k)
   have hjpos : (j : ℝ) < -a / 2 := by
-    linarith
+    linear_combination ha
   have hsuccpos : ((j + 1 : ℕ) : ℝ) < -a / 2 := by
     push_cast
-    linarith
+    exact ha
   have hkernel (k : ℕ) (hk : (k : ℝ) < -a / 2)
       (v : ℝ) :
       AEStronglyMeasurable
@@ -4094,10 +4119,10 @@ private theorem saddlePositiveContourMoment_hasDerivAt
       ‖saddlePositiveCpow
             (saddleContourExponent a t - (j : ℂ)) v‖ *
           ‖W j t‖ ≤ 1 * ‖W j t‖ := by
-        gcongr
+        refine mul_le_mul_of_nonneg_right ?_ (norm_nonneg (W j t))
         apply saddlePositiveCpow_norm_le_one
         · rw [saddleContourExponent_sub_nat_re]
-          linarith
+          linear_combination ha
         · exact hv
       _ = ‖W j t‖ := one_mul _
   have hdiff (t v : ℝ)
@@ -4113,7 +4138,7 @@ private theorem saddlePositiveContourMoment_hasDerivAt
     have hreal :
         1 < (saddleContourExponent a t - (j : ℂ)).re := by
       rw [saddleContourExponent_sub_nat_re]
-      linarith
+      linear_combination ha
     have hderiv :=
       (saddlePositiveCpow_hasDerivAt hreal v).mul_const
         (W j t)
@@ -4129,7 +4154,7 @@ private theorem saddlePositiveContourMoment_hasDerivAt
       rw [saddleContourFallingPolynomial_eval_succ]
       ring
     rw [harg, hfall]
-    convert! hderiv using 1
+    convert hderiv using 1
     all_goals ring
   have hresult :=
     _root_.hasDerivAt_integral_of_dominated_loc_of_deriv_le
@@ -4157,7 +4182,7 @@ private theorem saddlePositiveContourMoment_hasDerivAt
                   ((j + 1 : ℕ) : ℂ)) v‖ *
               ‖W (j + 1) t‖ ≤
             1 * ‖W (j + 1) t‖ := by
-              gcongr
+              refine mul_le_mul_of_nonneg_right ?_ (norm_nonneg (W (j + 1) t))
               apply saddlePositiveCpow_norm_le_one
               · rw [saddleContourExponent_sub_nat_re]
                 exact sub_pos.mpr hsuccpos
@@ -4205,11 +4230,11 @@ private theorem saddlePositiveContourMoment_contDiffOn
       have hj : (j : ℝ) + 1 < -a / 2 := by
         push_cast at ha
         have hn : (0 : ℝ) ≤ (n : ℝ) := Nat.cast_nonneg n
-        linarith
+        linarith only [ha]
       have hnext :
           (n : ℝ) + ((j + 1 : ℕ) : ℝ) + 1 < -a / 2 := by
         push_cast at ha ⊢
-        linarith
+        linear_combination ha
       rw [show (↑(n + 1) : WithTop ℕ∞) =
           (↑n : WithTop ℕ∞) + 1 by simp only [Nat.cast_add, Nat.cast_one],
         contDiffOn_succ_iff_deriv_of_isOpen isOpen_Ioo]
@@ -4259,7 +4284,7 @@ private theorem saddleMellinInversePower_eq_squaredPositiveCpow
       have hpositive :
           0 < (saddleContourExponent a t - (j : ℂ)).re := by
         rw [saddleContourExponent_sub_nat_re]
-        linarith
+        linear_combination ha
       simpa only [Complex.sub_re, saddleContourExponent_re, Complex.natCast_re, Complex.zero_re,
         ne_eq] using! hpositive.ne'
     simp only [saddlePositiveCpow, max_self, Complex.ofReal_zero, Complex.zero_cpow hexp, zero_mul]
@@ -4398,7 +4423,7 @@ private theorem saddleTaylorContour_smoothShift (n : ℕ) :
       -(saddleTaylorContour (n + 2)) / 2 := by
   simp only [saddleTaylorContour, neg_neg]
   push_cast
-  linarith
+  linarith only []
 
 private theorem SaddleSign.saddleFunction_contDiff_nat (s : SaddleSign)
     {ε : ℝ} (hε : 0 < ε)
@@ -4717,7 +4742,7 @@ private theorem saddlePositiveContourMoment_hasDerivAt_of_positiveContour
       (saddleContourExponent a t - (k : ℂ)).re ≤ 0 := by
     rw [saddleContourExponent_sub_nat_re]
     have hk : (0 : ℝ) ≤ k := Nat.cast_nonneg k
-    linarith
+    linarith only [ha]
   have hpoint (v : ℝ)
       (hv : v ∈ Set.Ioi (1 : ℝ)) :
       Integrable
@@ -4733,7 +4758,7 @@ private theorem saddlePositiveContourMoment_hasDerivAt_of_positiveContour
       ‖saddlePositiveCpow
             (saddleContourExponent a t - (j : ℂ)) v‖ *
           ‖W j t‖ ≤ 1 * ‖W j t‖ := by
-        gcongr
+        refine mul_le_mul_of_nonneg_right ?_ (norm_nonneg (W j t))
         exact saddlePositiveCpow_norm_le_one_of_nonpos
           (hpower j t) hv
       _ = ‖W j t‖ := one_mul _
@@ -4753,7 +4778,7 @@ private theorem saddlePositiveContourMoment_hasDerivAt_of_positiveContour
       rw [saddleContourExponent_sub_nat_re]
       have hk : (0 : ℝ) ≤ j := Nat.cast_nonneg j
       have hneg : -a / 2 - (j : ℝ) < 0 := by
-        linarith
+        linarith only [ha]
       simpa only [Complex.zero_re, ne_eq] using! hneg.ne
     have hderiv :=
       (saddlePositiveCpow_hasDerivAt_of_pos
@@ -4771,7 +4796,7 @@ private theorem saddlePositiveContourMoment_hasDerivAt_of_positiveContour
       rw [saddleContourFallingPolynomial_eval_succ]
       ring
     rw [harg, hfall]
-    convert! hderiv using 1
+    convert hderiv using 1
     all_goals ring
   have hmeas :
       ∀ᶠ v in 𝓝 u,
@@ -4807,7 +4832,7 @@ private theorem saddlePositiveContourMoment_hasDerivAt_of_positiveContour
                   ((j + 1 : ℕ) : ℂ)) v‖ *
               ‖W (j + 1) t‖ ≤
             1 * ‖W (j + 1) t‖ := by
-              gcongr
+              refine mul_le_mul_of_nonneg_right ?_ (norm_nonneg (W (j + 1) t))
               exact saddlePositiveCpow_norm_le_one_of_nonpos
                 (hpower (j + 1) t) hv
           _ = ‖W (j + 1) t‖ := one_mul _))
@@ -5017,13 +5042,13 @@ private theorem SaddleSign.outerSquaredProfile_contDiff (s : SaddleSign)
       change v < 2 at hv
       have hvzero :
           Real.smoothTransition (v - 2) = 0 :=
-        Real.smoothTransition.zero_of_nonpos (by linarith)
+        Real.smoothTransition.zero_of_nonpos (by linear_combination hv)
       simp only [SaddleSign.outerSquaredProfile, saddleOuterCutoff, hvzero, Complex.ofReal_zero,
         zero_mul]
     exact contDiffAt_const.congr_of_eventuallyEq hevent
   · have hone : u ∈ Set.Ioi (1 : ℝ) := by
       change 1 < u
-      linarith
+      linarith only [hu]
     have hcontour :
         ContDiffAt ℝ ∞
           (s.positiveSquaredContour ε ℓ 2) u :=
@@ -5036,7 +5061,7 @@ private theorem SaddleSign.outerSquaredProfile_eq_zero (s : SaddleSign)
     (ε ℓ : ℝ) {u : ℝ} (hu : u < 2) :
     s.outerSquaredProfile ε ℓ u = 0 := by
   have hcut : Real.smoothTransition (u - 2) = 0 :=
-    Real.smoothTransition.zero_of_nonpos (by linarith)
+    Real.smoothTransition.zero_of_nonpos (by linear_combination hu)
   simp only [SaddleSign.outerSquaredProfile, saddleOuterCutoff, hcut, Complex.ofReal_zero, zero_mul]
 
 private theorem SaddleSign.outerSquaredProfile_eq_positiveContour (s : SaddleSign)
@@ -5047,12 +5072,12 @@ private theorem SaddleSign.outerSquaredProfile_eq_positiveContour (s : SaddleSig
     s.outerSquaredProfile ε ℓ u =
       s.positiveSquaredContour ε ℓ a u := by
   have hcut : Real.smoothTransition (u - 2) = 1 :=
-    Real.smoothTransition.one_of_one_le (by linarith)
+    Real.smoothTransition.one_of_one_le (by linear_combination hu)
   unfold SaddleSign.outerSquaredProfile saddleOuterCutoff
   rw [hcut]
   norm_num
   exact s.positiveSquaredContour_eq_of_pos
-    hε hℓ horder (by norm_num) ha (by linarith)
+    hε hℓ horder (by norm_num) ha (by linear_combination hu)
 
 private theorem saddleOuterSquaredProfile_schwartz_decay
     {G : ℝ → ℂ}
@@ -5113,12 +5138,12 @@ private theorem saddleOuterSquaredProfile_schwartz_decay
         ((le_max_left B (‖c‖ * L)).trans
           (le_max_right 0 _))
     · have hu4 : (4 : ℝ) < u := lt_of_not_ge hupper
-      have hu3 : (3 : ℝ) < u := by linarith
-      have hu0 : (0 : ℝ) < u := by linarith
-      have hu1 : (1 : ℝ) ≤ u := by linarith
+      have hu3 : (3 : ℝ) < u := by linarith only [hupper]
+      have hu0 : (0 : ℝ) < u := by linarith only [hupper]
+      have hu1 : (1 : ℝ) ≤ u := by linarith only [hupper]
       have huoi : u ∈ Set.Ioi (1 : ℝ) := by
         change 1 < u
-        linarith
+        linarith only [hupper]
       have hevent :
           G =ᶠ[𝓝 u]
             (fun v : ℝ =>
@@ -5143,7 +5168,7 @@ private theorem saddleOuterSquaredProfile_schwartz_decay
         try dsimp [a]
         push_cast
         have hn : (0 : ℝ) ≤ (n : ℝ) := Nat.cast_nonneg n
-        linarith
+        linarith only []
       have hpower :
           u ^ (-a / 2 - (n : ℝ)) ≤
             u ^ (-(k : ℝ)) :=
@@ -5165,7 +5190,13 @@ private theorem saddleOuterSquaredProfile_schwartz_decay
           _ ≤ u ^ k *
               (‖c‖ *
                 (u ^ (-a / 2 - (n : ℝ)) * L)) := by
-                gcongr
+                exact mul_le_mul_of_nonneg_left (mul_le_mul_of_nonneg_left hmoment (norm_nonneg c))
+                    (le_of_lt
+                      (pow_pos
+                        (lt_trans
+                          ((by norm_num))
+                          hu4)
+                        k))
           _ ≤ u ^ k *
               (‖c‖ * (u ^ (-(k : ℝ)) * L)) := by
                 gcongr
@@ -5256,9 +5287,9 @@ private theorem SaddleSign.outerDifference_hasCompactSupport (s : SaddleSign)
     by_contra hnot
     apply houtside
     exact mem_closedBall_zero_iff.mpr (le_of_not_gt hnot)
-  have hr : 0 < ‖x‖ := by linarith
+  have hr : 0 < ‖x‖ := by linear_combination hr2
   have hsquare : (3 : ℝ) < ‖x‖ ^ 2 := by
-    linarith [sq_nonneg (‖x‖ - 2)]
+    linarith only [sq_nonneg (‖x‖ - 2), hr2]
   change
     s.profile ε ℓ ‖x‖ -
       s.outerSchwartz hε hℓ horder d x ≠ 0 at hx
@@ -5345,7 +5376,7 @@ private noncomputable def saddleSourceContourDamping
 private theorem saddleSourceContourEnvelopeScale_pos
     {ε ℓ u : ℝ} (hℓ : 0 < ℓ) (hu : -1 < u) :
     0 < saddleSourceContourEnvelopeScale ε ℓ u := by
-  have hη : 0 < 1 + u := by linarith
+  have hη : 0 < 1 + u := by linear_combination hu
   unfold saddleSourceContourEnvelopeScale
   exact mul_pos
     (mul_pos (Real.exp_pos _)
@@ -5379,7 +5410,7 @@ private theorem saddleSourceContour_gamma_norm
         Real.exp (-upperGammaDamping ℓ (1 + u) T) := by
   rw [saddleSourceMellinContour_gammaArgument]
   exact upperGammaShifted_modulus_eq_exp_neg_damping
-    hℓ (by linarith) T
+    hℓ (by linear_combination hu) T
 
 private theorem saddleSourceContour_shellExponential_norm
     {ε ℓ u : ℝ}
@@ -5575,8 +5606,8 @@ private theorem SaddleSign.profile_eq_sourceContourIntegral (s : SaddleSign)
             s.mellinData ε ℓ
               (saddleSourceMellinContour ℓ u T)) := by
   have ha : 0 < ℓ * (1 + u) := by
-    have hη : 0 < 1 + u := by linarith
-    positivity
+    have hη : 0 < 1 + u := by linear_combination hu
+    exact mul_pos hℓ hη
   rw [s.profile_eq_positive_contour
     (a := ℓ * (1 + u)) hε hℓ horder hr ha]
   rw [saddleSourceMellinContour_integral_change
@@ -5820,7 +5851,7 @@ private theorem eventually_saddleSourceGaussianVariance_secondBranch_pos :
   filter_upwards [eventually_upperSaddleVariance_pos]
     with ε hpositive
   intro ℓ hℓ δ hδ
-  convert! hpositive ℓ hℓ δ hδ using 1
+  convert hpositive ℓ hℓ δ hδ using 1
   all_goals simp only [saddleSourceGaussianVariance, add_sub_cancel_left]
 
 private theorem plusSaddleProfile_exp_re_pos_of_gaussian_error
@@ -5851,7 +5882,7 @@ private theorem plusSaddleProfile_exp_re_pos_of_gaussian_error
       have := (neg_le_of_abs_le hreal)
       exact this
     rw [Complex.sub_re] at hlower
-    linarith
+    linarith only [herror, hlower]
   rw [plusSaddleProfile_exp_eq_centeredIntegral
     hε hℓ hu horder v]
   change 0 <
@@ -5889,7 +5920,7 @@ private theorem minusSaddleProfile_exp_re_neg_of_gaussian_error
     have hupper : (J - G).re ≤ ‖J - G‖ :=
       (le_abs_self _).trans hreal
     rw [Complex.sub_re] at hupper
-    linarith
+    linarith only [herror, hupper]
   rw [minusSaddleProfile_exp_eq_centeredIntegral
     hε hℓ hu horder v]
   change
@@ -5905,7 +5936,7 @@ private theorem saddleSourcePositiveShellVariance_nonneg
     0 ≤ upperPositiveShellVariance ε δ := by
   unfold upperPositiveShellVariance
   apply intervalIntegral.integral_nonneg
-    (show (ε⁻¹ ^ 3) ≤ (ε⁻¹ ^ 3) + 1 by linarith)
+    (show (ε⁻¹ ^ 3) ≤ (ε⁻¹ ^ 3) + 1 by linarith only [])
   intro a ha
   unfold positiveShellDensity
   exact mul_nonneg
@@ -5933,12 +5964,12 @@ private theorem upperFirstBranch_shortVariance_le_gamma
     a ^ 2 * upperGammaMeasureDensity ℓ η a
   have hη : 0 < η := by
     try dsimp [η]
-    linarith
+    linarith only [hulower]
   have ha₀ : 0 < a₀ := by
     try dsimp [a₀]
     positivity
   have hfactor : 0 ≤ 1 - 4 * ε := by
-    linarith
+    linarith only [hεsmall]
   have hsubset : Ioc a₀ A ⊆ Ioi (0 : ℝ) := by
     intro a ha
     exact ha₀.trans ha.1
@@ -5953,9 +5984,9 @@ private theorem upperFirstBranch_shortVariance_le_gamma
   have hs := shortShellDensity_intervalIntegrable hε horder
   have hcosh : Continuous
       (fun a : ℝ => Real.cosh (u * a)) := by
-    fun_prop
+    exact Continuous.comp' Real.continuous_cosh (Continuous.const_mul continuous_id' u)
   have hsquare : Continuous (fun a : ℝ => a ^ 2) := by
-    fun_prop
+    exact Continuous.fun_pow continuous_id' 2
   have hshortInterval : IntervalIntegrable
       (fun a : ℝ =>
         ℓ * (-shortShellDensity ε a) *
@@ -5986,7 +6017,7 @@ private theorem upperFirstBranch_shortVariance_le_gamma
         (hmargin a ⟨ha.1.le, ha.2⟩)
     have hmul :=
       mul_le_mul_of_nonneg_right hcomparison (sq_nonneg a)
-    simpa [γ, η, mul_assoc, mul_left_comm, mul_comm] using! hmul
+    simpa only [γ, η, mul_assoc, mul_left_comm, mul_comm] using! hmul
   have hmono := setIntegral_mono_on
     hshortOn hscaledOn measurableSet_Ioc hpoint
   have hnonnegative :
@@ -6063,7 +6094,7 @@ private theorem upperFirstBranch_saddleSourceGaussianVariance_lower_bound
     upperSaddleVariance upperNetShellVariance
   have hη : 2 + (u - 1) = 1 + u := by ring
   rw [hη]
-  linarith
+  linarith only [hshort, hpositive]
 
 private theorem eventually_saddleSourceGaussianVariance_firstBranch_pos :
     ∀ᶠ ε : ℝ in 𝓝[>] (0 : ℝ),
@@ -6086,7 +6117,7 @@ private theorem eventually_saddleSourceGaussianVariance_firstBranch_pos :
     with ε hε hεsmall horder hmargin
   change 0 < ε at hε
   intro ℓ hℓ u hulower huupper
-  have hη : 0 < 1 + u := by linarith
+  have hη : 0 < 1 + u := by linear_combination hulower
   have hgamma :=
     (upperGammaVariance_bounds hℓ hη).1
   have hgammaPos : 0 < upperGammaVariance ℓ (1 + u) :=
@@ -6132,8 +6163,8 @@ private theorem SaddleSign.centeredIntegrand_integrable (s : SaddleSign)
       saddleSourceContourEnvelopeScale ε ℓ u : ℝ) : ℂ)
   have ha : 0 < a := by
     try dsimp [a]
-    have : 0 < 1 + u := by linarith
-    positivity
+    have : 0 < 1 + u := by linear_combination hu
+    exact mul_pos hℓ this
   have hline :=
     s.mellinData_shiftedLine_weighted_integrable
       (a := a) (r := Real.exp v)
@@ -6442,7 +6473,7 @@ private theorem upperImaginaryExp_quadratic_remainder_norm_le
           rw [hconj, Complex.norm_conj]
       _ ≤ (-x) ^ 3 / 6 :=
         upperImaginaryExp_quadratic_remainder_norm_le_of_nonneg
-          (by linarith)
+          (by linarith only [hx])
       _ = |x| ^ 3 / 6 := by
         rw [abs_of_neg hxnegative]
 
@@ -6658,7 +6689,7 @@ private theorem saddleSourcePositiveShellQuadraticRemainder_norm_le
   have hbound :=
     saddleSourceWeightedCosineQuadraticRemainder_norm_le
       (positiveShellDensity ε)
-      (show (ε⁻¹ ^ 3) ≤ (ε⁻¹ ^ 3) + 1 by linarith)
+      (show (ε⁻¹ ^ 3) ≤ (ε⁻¹ ^ 3) + 1 by linarith only [])
       hB
       (positiveShellDensity_continuous ε).continuousOn
       (fun a ha => by
@@ -6666,7 +6697,7 @@ private theorem saddleSourcePositiveShellQuadraticRemainder_norm_le
         exact div_nonneg (shellWeight_pos ε).le
           (Real.cosh_pos a).le)
       u T
-  convert! hbound using 1
+  convert hbound using 1
   unfold upperPositiveShellThirdMoment
   congr 1
   apply intervalIntegral.integral_congr
@@ -6730,7 +6761,7 @@ private theorem saddleSourceShortShellQuadraticRemainder_norm_le
       ring
     rw [heq, norm_neg]
   rw [hnorm]
-  convert! hbound using 1
+  convert hbound using 1
   unfold upperShortShellThirdMoment
   congr 1
   apply intervalIntegral.integral_congr
@@ -6775,7 +6806,10 @@ private theorem saddleSourceWeightedCosineQuadraticRemainder_integral_eq
       Complex.cos
         ((a : ℂ) *
           ((T : ℂ) + Complex.I * (u : ℂ))) - 1) := by
-    fun_prop
+    exact Continuous.fun_sub
+        (Continuous.comp' Complex.continuous_cos
+          (Continuous.comp' (continuous_mul_const (↑T + Complex.I * ↑u)) Complex.continuous_ofReal))
+        continuous_const
   have hF : IntervalIntegrable F volume b c :=
     (hwc.mul hkernel.continuousOn).intervalIntegrable_of_Icc
       hbc
@@ -6919,7 +6953,7 @@ private theorem saddleSourceShellQuadraticRemainder_eq
     saddleSourceWeightedCosineQuadraticRemainder_integral_eq
       (positiveShellDensity ε)
       (show (ε⁻¹ ^ 3) ≤ (ε⁻¹ ^ 3) + 1 by
-        linarith)
+        linarith only [])
       (positiveShellDensity_continuous ε).continuousOn u T
   have hvariance :
       (∫ a in (ε ^ 3)..(10 * Real.log (1 / ε)),