diff --git a/LeanPool/IwaniecLinearSieve/Jacobsthal/Reduction.lean b/LeanPool/IwaniecLinearSieve/Jacobsthal/Reduction.lean
index db90ee5704..a24fd4b086 100644
--- a/LeanPool/IwaniecLinearSieve/Jacobsthal/Reduction.lean
+++ b/LeanPool/IwaniecLinearSieve/Jacobsthal/Reduction.lean
@@ -44,7 +44,7 @@ theorem exists_covering_length_le (hL : LinearSieveEstimate)
   refine ⟨K / (c * c'), max z₀ 2, fun z hz S hS hcard x m hm ↦ ?_⟩
   have hz0 : z₀ ≤ z := (le_max_left _ _).trans hz
   have hz2 : 2 ≤ z := (le_max_right _ _).trans hz
-  have hlog : 0 < log z := log_pos (by linarith)
+  have hlog : 0 < log z := log_pos (by linarith only [hz2])
   have hRz := R_pos z
   set M := rosserMain true (C₀ * z ^ 2) z
   obtain ⟨hmain, hcount⟩ := hL z hz0
@@ -56,7 +56,7 @@ theorem exists_covering_length_le (hL : LinearSieveEstimate)
     exact h q hq hqk
   rw [hzero, card_empty, Nat.cast_zero] at hsieve
   -- `M ≥ R(z) c / log z`
-  have hM : R z * (c / log z) ≤ M := by nlinarith
+  have hM : R z * (c / log z) ≤ M := by nlinarith only [hmain]
   have hM0 : 0 ≤ M := (mul_nonneg hRz.le (div_pos hc hlog).le).trans hM
   have hprod := R_le_prod_of_card_eq hS hcard
   have h1 : (m : ℝ) * M ≤ #(rosserSet true (C₀ * z ^ 2) z) := by
@@ -65,7 +65,7 @@ theorem exists_covering_length_le (hL : LinearSieveEstimate)
       refine mul_le_mul_of_nonneg_left ?_ m.cast_nonneg
       calc M = R z * (M / R z) := by field_simp
         _ ≤ _ := mul_le_mul_of_nonneg_right hprod (div_nonneg hM0 hRz.le)
-    linarith
+    linarith only [hsieve, this]
   have hRlog : c' ≤ R z * log z := by
     have := hR z hz2
     rwa [div_le_iff₀ hlog] at this
@@ -82,9 +82,9 @@ theorem exists_covering_length_le (hL : LinearSieveEstimate)
       exact (mul_le_mul_of_nonneg_left hM hm0).trans (h1.trans hcount)
     have e3 : K * z ^ 2 / log z ^ 2 * log z ^ 2 = K * z ^ 2 := by
       field_simp
-    linarith
+    linarith only [e1, e2, e3]
   rw [div_mul_eq_mul_div, le_div_iff₀ (mul_pos hc hc')]
-  linarith
+  linarith only [h2]
 
 
 /-- The primes below `p_N + 1`, where `p_N = Nat.nth Nat.Prime (N - 1)` is the `N`-th prime, are
diff --git a/LeanPool/IwaniecLinearSieve/Jacobsthal/ShiftedSieve.lean b/LeanPool/IwaniecLinearSieve/Jacobsthal/ShiftedSieve.lean
index 27ea5d85ce..ea87723f47 100644
--- a/LeanPool/IwaniecLinearSieve/Jacobsthal/ShiftedSieve.lean
+++ b/LeanPool/IwaniecLinearSieve/Jacobsthal/ShiftedSieve.lean
@@ -323,7 +323,7 @@ theorem abs_card_filter_dvd_sub_le (x : ℤ) (X : ℕ) {d : ℕ} (hd : 0 < d) :
     push_cast
     ring
   have hX : (0 : ℚ) ≤ X / d := by positivity
-  have hle : ⌈u⌉ ≤ ⌈v⌉ := Int.ceil_mono (by rw [hvu]; linarith)
+  have hle : ⌈u⌉ ≤ ⌈v⌉ := Int.ceil_mono (by rw [hvu]; linarith only [hX])
   rw [max_eq_left (sub_nonneg.2 hle)] at h
   have hq : |((⌈v⌉ - ⌈u⌉ : ℤ) : ℚ) - X / d| ≤ 1 := by
     have h1 := Int.le_ceil v
@@ -437,7 +437,7 @@ theorem shiftedSieve_of_bijOn (y : ℝ) {S : Finset ℕ} {e : ℕ → ℕ}
       ∑ A ∈ T.powerset, w A * #((range X).filter fun k : ℕ ↦ (n A : ℤ) ∣ x + k) := by
     rw [← sum_sub_distrib]
     exact sum_le_sum hc
-  linarith
+  linarith only [hb, hd, he', hsum]
 
 
 /-- Any `π(z)` primes can be matched with the primes below `z` so that each prime below `z` is
diff --git a/LeanPool/IwaniecLinearSieve/LinearSieve/Calculus.lean b/LeanPool/IwaniecLinearSieve/LinearSieve/Calculus.lean
index 67e8f3bb17..82a9547864 100644
--- a/LeanPool/IwaniecLinearSieve/LinearSieve/Calculus.lean
+++ b/LeanPool/IwaniecLinearSieve/LinearSieve/Calculus.lean
@@ -50,7 +50,7 @@ theorem mainMaj_antitone : ∀ lower, Antitone (mainMaj lower)
   | true => fSieve_antitone
   | false => fun u v h => by
     simp only [mainMaj_false]
-    exact add_le_add (FSieve_antitone h) (max_le_max (by linarith) le_rfl)
+    exact add_le_add (FSieve_antitone h) (max_le_max (by linarith only [h]) le_rfl)
 
 theorem mainMaj_le_MSieve : ∀ (lower : Bool) (s : ℝ), mainMaj lower s ≤ MSieve s
   | true, s => by
@@ -58,24 +58,24 @@ theorem mainMaj_le_MSieve : ∀ (lower : Bool) (s : ℝ), mainMaj lower s ≤ MS
     simp only [mainMaj_true, MSieve]; linarith
   | false, s => by
     have := fSieve_nonneg s
-    simp only [mainMaj_false, MSieve]; linarith
+    simp only [mainMaj_false, MSieve]; linarith only [this]
 
 /-- `g₂(s) = ∫_s^∞ (3 - (t-1))⁺/(t-1) dt` for `s ≥ 2`. -/
 theorem g_two_eq_integral {s : ℝ} (hs : 2 ≤ s) :
     IntegrableOn (fun t => max (3 - (t - 1)) 0 / (t - 1)) (Ioi s) ∧
       g 2 s = ∫ t in Ioi s, max (3 - (t - 1)) 0 / (t - 1) := by
   have hz : ∀ t : ℝ, 4 ≤ t → max (3 - (t - 1)) 0 / (t - 1) = 0 := fun t ht => by
-    rw [max_eq_right (by linarith), zero_div]
+    rw [max_eq_right (by linarith only [ht]), zero_div]
   rcases le_or_gt s 4 with hs4 | hs4
   · have heq : EqOn (fun t : ℝ => max (3 - (t - 1)) 0 / (t - 1)) (fun t => 3 / (t - 1) - 1)
         (Icc s 4) := fun t ht => by
-      have : 0 < t - 1 := by linarith [ht.1]
+      have : 0 < t - 1 := by linarith only [ht.1, hs, ht]
       simp only
-      rw [max_eq_left (by linarith [ht.2])]
+      rw [max_eq_left (by linarith only [ht.2, ht])]
       field_simp
     have hcont : ContinuousOn (fun t : ℝ => 3 / (t - 1) - 1) (Icc s 4) :=
       (continuousOn_const.div (continuousOn_id.sub continuousOn_const) fun t ht => by
-        simp only [Pi.sub_apply, id]; linarith [ht.1]).sub continuousOn_const
+        simp only [Pi.sub_apply, id]; linarith only [ht.1, hs, ht]).sub continuousOn_const
     obtain ⟨hI, hE⟩ := integral_Ioi_eq_of_eq_zero hs4
       (((hcont.congr heq).integrableOn_Icc).mono_set Ioc_subset_Icc_self) hz
     refine ⟨hI, ?_⟩
@@ -83,12 +83,12 @@ theorem g_two_eq_integral {s : ℝ} (hs : 2 ≤ s) :
     have hderiv : ∀ t ∈ uIcc s 4, HasDerivAt (fun t => 3 * log (t - 1) - t) (3 / (t - 1) - 1) t :=
       fun t ht => by
         rw [uIcc_of_le hs4] at ht
-        have h1 : t - 1 ≠ 0 := by linarith [ht.1]
+        have h1 : t - 1 ≠ 0 := by linarith only [ht.1, hs, ht]
         have := ((((hasDerivAt_id' t).sub_const 1).log h1).const_mul 3).sub (hasDerivAt_id' t)
         convert this using 1; field_simp
     rw [intervalIntegral.integral_eq_sub_of_hasDerivAt hderiv
       (hcont.mono (uIcc_of_le hs4).subset |>.intervalIntegrable), g_two_eq ⟨hs, hs4⟩,
-      log_div (by norm_num) (by linarith)]
+      log_div (by norm_num) (by linarith only [hs])]
     norm_num; ring
   · obtain ⟨hI, hE⟩ := integral_Ioi_eq_of_eq_zero le_rfl (by simp) fun t ht => hz t (by linarith)
     exact ⟨hI, by rw [hE, intervalIntegral.integral_same, g_two_of_four_le hs4.le]⟩
@@ -117,7 +117,7 @@ theorem mainMaj_false_eq_integral (s : ℝ) :
 
 /-- `mainMaj` in terms of `fr`: `M true = f` and, on `s ≥ 3`, `M false = F`. -/
 theorem mainMaj_false_of_three_le {s : ℝ} (hs : 3 ≤ s) : mainMaj false s = FSieve s := by
-  rw [mainMaj_false, max_eq_right (by linarith), add_zero]
+  rw [mainMaj_false, max_eq_right (by linarith only [hs]), add_zero]
 
 /-! ### `errMaj` -/
 
@@ -172,7 +172,7 @@ theorem errMaj_mem : ∀ (lower : Bool) (s : ℝ),
   | false, s => majF_mem s
 
 theorem errMaj_le_two (lower : Bool) (s : ℝ) : errMaj lower s ≤ 2 := by
-  linarith [(errMaj_mem lower s).2, bigM_le_three s]
+  linarith only [(errMaj_mem lower s).2, bigM_le_three s]
 
 theorem errMaj_false_of_le_three {s : ℝ} (hs : s ≤ 3) : errMaj false s = 1 :=
   majF_of_le_three hs
@@ -190,9 +190,9 @@ theorem tendsto_errMaj_atTop : ∀ lower, Tendsto (errMaj lower) atTop (𝓝 0)
 
 theorem errMaj_shift_pos (lower : Bool) {t : ℝ} (ht : 1 < t) :
     0 < errMaj lower (t - 1) * t / (t - 1) ^ 2 := by
-  have h1 : 0 < t - 1 := by linarith
+  have h1 : 0 < t - 1 := by linarith only [ht]
   have := errMaj_pos lower (t - 1)
-  have : 0 < t := by linarith
+  have : 0 < t := by linarith only [ht]
   positivity
 
 /-- (3.13), (3.14): for `s ≥ 2` (`lower = true`) or `s ≥ 3` (`lower = false`),
@@ -207,7 +207,7 @@ theorem errMaj_eq_integral (lower : Bool) {s : ℝ} (hs : errLower lower ≤ s)
       (errMaj (!lower) (t - 1) * t / (t - 1) ^ 2) t := fun t ht =>
     (hasDerivAt_errMaj lower (hs.trans_lt ht)).neg.congr_deriv (by ring)
   have hpos : ∀ t ∈ Ioi s, 0 ≤ errMaj (!lower) (t - 1) * t / (t - 1) ^ 2 := fun t ht =>
-    (errMaj_shift_pos _ (by linarith [ht.out])).le
+    (errMaj_shift_pos _ (by linarith only [ht.out, hs, h2, ht])).le
   have hlim : Tendsto (fun t => -errMaj lower t) atTop (𝓝 0) := by
     simpa using (tendsto_errMaj_atTop lower).neg
   refine ⟨integrableOn_Ioi_deriv_of_nonneg hcont hderiv hpos hlim, ?_⟩
diff --git a/LeanPool/IwaniecLinearSieve/LinearSieve/Corollaries.lean b/LeanPool/IwaniecLinearSieve/LinearSieve/Corollaries.lean
index 82f2cf608e..041a1d610b 100644
--- a/LeanPool/IwaniecLinearSieve/LinearSieve/Corollaries.lean
+++ b/LeanPool/IwaniecLinearSieve/LinearSieve/Corollaries.lean
@@ -45,11 +45,11 @@ theorem integral_comp_log_div {F : ℝ → ℝ} {y α β : ℝ} (hy : 1 < y) (h
       ∫ t in α..β, F t / t := by
   set L := log y
   have hL : 0 < L := log_pos hy
-  have hy0 : 0 < y := by linarith
+  have hy0 : 0 < y := by linarith only [hy]
   set f : ℝ → ℝ := fun t => exp (L * t⁻¹)
   set f' : ℝ → ℝ := fun t => exp (L * t⁻¹) * (L * -(t ^ 2)⁻¹)
   have hpos : ∀ x ∈ uIcc α β, 0 < x := fun x hx => by
-    rw [uIcc_of_le hαβ] at hx; linarith [hx.1]
+    rw [uIcc_of_le hαβ] at hx; linarith only [hx.1, hα, hx]
   have hderiv : ∀ x, 0 < x → HasDerivAt f (f' x) x := fun x hx =>
     ((hasDerivAt_inv hx.ne').const_mul L).exp
   have hfA : ∀ γ, f γ = y ^ (1 / γ) := fun γ => by
@@ -58,7 +58,7 @@ theorem integral_comp_log_div {F : ℝ → ℝ} {y α β : ℝ} (hy : 1 < y) (h
     (f' := f') (g := fun u => F (L / log u) / (u * log u))
     (continuousOn_of_forall_continuousAt fun x hx => (hderiv x (hpos x hx)).continuousAt)
     (fun x hx => hderiv x (by
-      rw [min_eq_left hαβ] at hx; linarith [hx.1]))
+      rw [min_eq_left hαβ] at hx; linarith only [hx.1, hα, hx]))
     (fun x hx => by
       simp only [f']
       rw [mul_neg]
@@ -84,7 +84,7 @@ theorem log_rpow_one_div {y : ℝ} (hy : 0 < y) (γ : ℝ) : log (y ^ (1 / γ))
 theorem div_log_mem_Icc {y α β u : ℝ} (hy : 1 < y) (hα : 0 < α) (hαβ : α ≤ β)
     (hu : u ∈ Icc (y ^ (1 / β)) (y ^ (1 / α))) : 0 < log u ∧ log y / log u ∈ Icc α β := by
   have hL : 0 < log y := log_pos hy
-  have hy0 : 0 < y := by linarith
+  have hy0 : 0 < y := by linarith only [hy]
   have hβ : 0 < β := hα.trans_le hαβ
   have hB0 : 0 < y ^ (1 / β) := rpow_pos_of_pos hy0 _
   have hu0 : 0 < u := hB0.trans_le hu.1
@@ -92,8 +92,8 @@ theorem div_log_mem_Icc {y α β u : ℝ} (hy : 1 < y) (hα : 0 < α) (hαβ : 
   have h2 : log u ≤ log y / α := log_rpow_one_div hy0 α ▸ log_le_log hu0 hu.2
   have hlu : 0 < log u := (div_pos hL hβ).trans_le h1
   refine ⟨hlu, ?_, ?_⟩
-  · rw [le_div_iff₀ hlu]; rw [le_div_iff₀ hα] at h2; linarith
-  · rw [div_le_iff₀ hlu]; rw [div_le_iff₀ hβ] at h1; linarith
+  · rw [le_div_iff₀ hlu]; rw [le_div_iff₀ hα] at h2; linarith only [h2]
+  · rw [div_le_iff₀ hlu]; rw [div_le_iff₀ hβ] at h1; linarith only [h1]
 
 /-- [I71, Lemma 13] in the variable `t = log y / log u`: for `F ≥ 0` antitone on `[α, β]`, and any
 set `S` of primes between those in `(y^{1/β}, y^{1/α})` and those in `[y^{1/β}, y^{1/α}]`,
@@ -106,7 +106,7 @@ theorem lemma13_param : ∃ C, 0 ≤ C ∧ ∀ (F : ℝ → ℝ) (y α β : ℝ)
   obtain ⟨C, hC0, hC⟩ := lemma13_mono_of_subset
   refine ⟨C, hC0, fun F y α β S hy hα hαβ hB hF hF0 hS1 hS2 => ?_⟩
   have hL : 0 < log y := log_pos hy
-  have hy0 : 0 < y := by linarith
+  have hy0 : 0 < y := by linarith only [hy]
   have hBA : y ^ (1 / β) ≤ y ^ (1 / α) :=
     rpow_le_rpow_of_exponent_le hy.le (one_div_le_one_div_of_le hα hαβ)
   have hmono : MonotoneOn (fun u => F (log y / log u)) (Icc (y ^ (1 / β)) (y ^ (1 / α))) := by
@@ -114,7 +114,7 @@ theorem lemma13_param : ∃ C, 0 ≤ C ∧ ∀ (F : ℝ → ℝ) (y α β : ℝ)
     obtain ⟨hlu, hmu⟩ := div_log_mem_Icc hy hα hαβ hu
     obtain ⟨hlv, hmv⟩ := div_log_mem_Icc hy hα hαβ hv
     exact hF hmv hmu (div_le_div_of_nonneg_left hL.le hlu
-      (log_le_log (by linarith [hu.1]) huv))
+      (log_le_log (by linarith only [hu.1, hB, hu]) huv))
   have h := hC (fun u => F (log y / log u)) (y ^ (1 / α)) (y ^ (1 / β)) S hB hBA hmono
     (fun u hu => hF0 _ (div_log_mem_Icc hy hα hαβ hu).2) hS1 hS2
   rwa [integral_comp_log_div hy hα hαβ, log_rpow_one_div hy0, div_div_cancel₀ hL.ne'] at h
@@ -130,15 +130,15 @@ theorem le_div_log_of_le_rpow {y α : ℝ} {p : ℕ} (hy : 1 < y) (hα : 0 < α)
     (hpA : (p : ℝ) ≤ y ^ (1 / α)) : α ≤ log y / log p := by
   have hlp : 0 < log (p : ℝ) := log_pos (by exact_mod_cast hp)
   have h := log_le_log (by positivity) hpA
-  rw [log_rpow_one_div (by linarith)] at h
-  rw [le_div_iff₀ hlp]; rw [le_div_iff₀ hα] at h; linarith
+  rw [log_rpow_one_div (by linarith only [hy])] at h
+  rw [le_div_iff₀ hlp]; rw [le_div_iff₀ hα] at h; linarith only [h]
 
 theorem antitoneOn_div_sub_one : AntitoneOn (fun t : ℝ => t / (t - 1)) (Ioi 1) := by
   intro u hu v hv huv
-  have hu1 : 0 < u - 1 := by linarith [hu.out]
-  have hv1 : 0 < v - 1 := by linarith [hv.out]
+  have hu1 : 0 < u - 1 := by linarith only [hu.out, hu]
+  have hv1 : 0 < v - 1 := by linarith only [hv.out, huv, hu1]
   simp only
-  rw [div_le_div_iff₀ hv1 hu1]; nlinarith
+  rw [div_le_div_iff₀ hv1 hu1]; nlinarith only [huv]
 
 /-- [I71, Corollary 1 to Lemma 13]: for `M ≥ 0` antitone on `[α - 1, β - 1]`, `2 ≤ α ≤ β`,
 `y^{1/β} ≥ 2`,
@@ -151,16 +151,16 @@ theorem cor1 : ∃ C, 0 ≤ C ∧ ∀ (M : ℝ → ℝ) (y α β : ℝ), 1 < y 
       (∫ t in α..β, M (t - 1) / (t - 1)) / log y| ≤
       C * M (α - 1) * pntE (y ^ (1 / β)) / log y := by
   obtain ⟨C, hC0, hC⟩ := lemma13_param
-  refine ⟨2 * C, by linarith, fun M y α β hy hα hαβ hB hM hM0 => ?_⟩
+  refine ⟨2 * C, by linarith only [hC0], fun M y α β hy hα hαβ hB hM hM0 => ?_⟩
   have hL : 0 < log y := log_pos hy
-  have hy0 : 0 < y := by linarith
+  have hy0 : 0 < y := by linarith only [hy]
   set F : ℝ → ℝ := fun t => M (t - 1) * (t / (t - 1)) / log y with hFdef
   have hMt : AntitoneOn (fun t => M (t - 1)) (Icc α β) := fun u hu v hv huv =>
     hM ⟨by linarith [hu.1], by linarith [hu.2]⟩ ⟨by linarith [hv.1], by linarith [hv.2]⟩
-      (by linarith)
+      (by linarith only [huv])
   have hF : AntitoneOn F (Icc α β) := by
     have := antitoneOn_mul_of_nonneg hMt (antitoneOn_div_sub_one.mono fun t ht =>
-      show (1 : ℝ) < t by linarith [ht.1])
+      show (1 : ℝ) < t by linarith only [ht.1, hα, ht])
       (fun t ht => hM0 _ ⟨by linarith [ht.1], by linarith [ht.2]⟩)
       fun t ht => div_nonneg (by linarith [ht.1]) (by linarith [ht.1])
     exact fun u hu v hv huv => div_le_div_of_nonneg_right (this hu hv huv) hL.le
@@ -168,7 +168,7 @@ theorem cor1 : ∃ C, 0 ≤ C ∧ ∀ (M : ℝ → ℝ) (y α β : ℝ), 1 < y 
     div_nonneg (mul_nonneg (hM0 _ ⟨by linarith [ht.1], by linarith [ht.2]⟩)
       (div_nonneg (by linarith [ht.1]) (by linarith [ht.1]))) hL.le
   have h := hC F y α β ((primesLT (y ^ (1 / α))).filter (fun p : ℕ => y ^ (1 / β) ≤ p)) hy
-    (by linarith) hαβ hB hF hF0
+    (by linarith only [hα]) hαβ hB hF hF0
     (fun p hp => by
       rw [mem_filter, mem_primesLT] at hp
       exact ⟨hp.1.1, hp.2, hp.1.2.le⟩)
@@ -181,7 +181,7 @@ theorem cor1 : ∃ C, 0 ≤ C ∧ ∀ (M : ℝ → ℝ) (y α β : ℝ), 1 < y 
     rw [mem_filter, mem_primesLT] at hp
     have hp1 := hp.1.1.one_lt
     have hlp : 0 < log (p : ℝ) := log_pos (by exact_mod_cast hp1)
-    have ht := le_div_log_of_le_rpow hy (by linarith) hp1 hp.1.2.le
+    have ht := le_div_log_of_le_rpow hy (by linarith only [hα]) hp1 hp.1.2.le
     rw [log_div_prime_eq hy0 hp1]
     simp only [F]
     have : (p : ℝ) ≠ 0 := by positivity
@@ -190,15 +190,15 @@ theorem cor1 : ∃ C, 0 ≤ C ∧ ∀ (M : ℝ → ℝ) (y α β : ℝ), 1 < y 
     rw [← intervalIntegral.integral_div]
     refine intervalIntegral.integral_congr fun t ht => ?_
     rw [uIcc_of_le hαβ] at ht
-    have : 0 < t := by linarith [ht.1]
-    have : t - 1 ≠ 0 := by linarith [ht.1]
+    have : 0 < t := by linarith only [ht.1, hα, ht]
+    have : t - 1 ≠ 0 := by linarith only [ht.1, hα, ht]
     simp only [F]
     field_simp
   have hFα : F α ≤ 2 * M (α - 1) / log y := by
-    have hMα := hM0 (α - 1) ⟨le_rfl, by linarith⟩
+    have hMα := hM0 (α - 1) ⟨le_rfl, by linarith only [hαβ]⟩
     have : α / (α - 1) ≤ 2 := by rw [div_le_iff₀ (by linarith)]; linarith
     simp only [F]
-    exact div_le_div_of_nonneg_right (by nlinarith) hL.le
+    exact div_le_div_of_nonneg_right (by nlinarith only [hMα, this]) hL.le
   rw [hsum, hint] at h
   refine h.trans ?_
   calc C * F α * pntE (y ^ (1 / β)) ≤ C * (2 * M (α - 1) / log y) * pntE (y ^ (1 / β)) := by
@@ -214,16 +214,16 @@ theorem cor1_le : ∃ C, 0 ≤ C ∧ ∀ (M : ℝ → ℝ) (y α β : ℝ), 1 <
       (∫ t in α..β, M (t - 1) / (t - 1)) / log y + C * M (α - 1) * pntE (y ^ (1 / β)) / log y := by
   obtain ⟨C, hC0, hC⟩ := cor1
   exact ⟨C, hC0, fun M y α β hy hα hαβ hB hM hM0 => by
-    linarith [(abs_le.1 (hC M y α β hy hα hαβ hB hM hM0)).2]⟩
+    linarith only [(abs_le.1 (hC M y α β hy hα hαβ hB hM hM0)).2, hC, hy, hα, hαβ, hB, hM, hM0]⟩
 
 /-! ### Corollary 3 -/
 
 /-- `G'(s-1) s²/(s-1)² ≤ 32 s² G(s)` for `s ≥ 2` (Lemma 8 and the Corollary to Lemma 6). -/
 theorem errMaj_shift_sq_le (lower lower' : Bool) {s : ℝ} (hs : 2 ≤ s) :
     errMaj lower' (s - 1) * (s ^ 2 / (s - 1) ^ 2) ≤ 32 * s ^ 2 * errMaj lower s := by
-  have hs1 : 0 < s - 1 := by linarith
+  have hs1 : 0 < s - 1 := by linarith only [hs]
   have hq : s ^ 2 / (s - 1) ^ 2 ≤ 4 := by
-    rw [div_le_iff₀ (pow_pos hs1 2)]; nlinarith
+    rw [div_le_iff₀ (pow_pos hs1 2)]; nlinarith only [hs]
   have hq0 : 0 ≤ s ^ 2 / (s - 1) ^ 2 := by positivity
   have hG' := errMaj_pos lower' (s - 1)
   have hG := (errMaj_mem lower s).1
@@ -245,7 +245,7 @@ theorem errMaj_shift_sq_le (lower lower' : Bool) {s : ℝ} (hs : 2 ≤ s) :
 theorem growth_le_delta {y t a : ℝ} (ht : 1 ≤ t) (hta : t ≤ a) :
     (1 + t ^ 2 * log t ^ 5 / log y ^ 2) ^ (5 * (t - 1)) ≤ delta a y := by
   have hlt := log_nonneg ht
-  have hla : log t ≤ log a := log_le_log (by linarith) hta
+  have hla : log t ≤ log a := log_le_log (by linarith only [ht]) hta
   have hx0 := lsx_nonneg (log y) ht
   have hxa : t ^ 2 * log t ^ 5 / log y ^ 2 ≤ a ^ 2 * log a ^ 5 / log y ^ 2 := by
     gcongr
@@ -265,17 +265,17 @@ theorem cor3_summand_le {G : ℝ → ℝ} {y : ℝ} {p : ℕ} (hy : 1 < y) (hp :
         (5 * (log y / log p - 1)) * G (log y / log p - 1) *
         ((log y / log p) ^ 2 / (log y / log p - 1) ^ 2) / log y ^ 2 / p := by
   have hlp : 0 < log (p : ℝ) := log_pos (by exact_mod_cast hp)
-  have hy0 : 0 < y := by linarith
+  have hy0 : 0 < y := by linarith only [hy]
   have hyp := log_div_prime_eq hy0 hp
   set t := log y / log p with htdef
   have hLt : log y = log p * t := by rw [htdef]; field_simp
-  have ht1 : 0 < t - 1 := by linarith
+  have ht1 : 0 < t - 1 := by linarith only [ht]
   have hp0 : (0 : ℝ) < p := by positivity
   have hb : (t - 1) ^ 2 * log (t - 1) ^ 5 / log (y / p) ^ 2 =
       t ^ 2 * log (t - 1) ^ 5 / log y ^ 2 := by
     rw [hyp, hLt]; field_simp
-  have hl1 : 0 ≤ log (t - 1) := log_nonneg (by linarith)
-  have hl2 : log (t - 1) ≤ log t := log_le_log ht1 (by linarith)
+  have hl1 : 0 ≤ log (t - 1) := log_nonneg (by linarith only [ht])
+  have hl2 : log (t - 1) ≤ log t := log_le_log ht1 (by linarith only [])
   have hbase : t ^ 2 * log (t - 1) ^ 5 / log y ^ 2 ≤ t ^ 2 * log t ^ 5 / log y ^ 2 := by
     gcongr
   have hb0 : 0 ≤ t ^ 2 * log (t - 1) ^ 5 / log y ^ 2 := by positivity
@@ -313,7 +313,7 @@ theorem cor3_large : ∃ C, 0 ≤ C ∧ ∀ (lower : Bool) (y s b : ℝ) (S : Fi
         (p * log (y / p) ^ 2) ≤
       delta s y * errMaj lower s / log y ^ 2 * (1 + C * b ^ 2 * pntE (y ^ (1 / b))) := by
   obtain ⟨C, hC0, hC⟩ := lemma13_param
-  refine ⟨32 * C, by linarith, fun lower y s b S hy hs hsb hB hb hS1 hS2 => ?_⟩
+  refine ⟨32 * C, by linarith only [hC0], fun lower y s b S hy hs hsb hB hb hS1 hS2 => ?_⟩
   set r : ℕ := if lower then 1 else 0
   have hG' := errMaj_not_eq_majG lower
   have hGs : errMaj lower s = majG (r + 1) s := by rw [errMaj_eq_majG_succ]
@@ -325,44 +325,44 @@ theorem cor3_large : ∃ C, 0 ≤ C ∧ ∀ (lower : Bool) (y s b : ℝ) (S : Fi
   have hΦ : AntitoneOn Φ (Icc s b) := fun u hu v hv huv =>
     div_le_div_of_nonneg_right (antitoneOn_cor3Weight r hs hb hu hv huv) hL2.le
   have hΦ0 : ∀ t ∈ Icc s b, 0 ≤ Φ t := fun t ht => by
-    have ht1 : (1 : ℝ) ≤ t := by linarith [ht.1]
+    have ht1 : (1 : ℝ) ≤ t := by linarith only [ht.1, hs4, ht]
     have := lsx_nonneg (log y) ht1
     have := majG_pos r (t - 1)
     exact div_nonneg (mul_nonneg (mul_nonneg (rpow_pos_of_pos (by linarith) _).le this.le)
       (by positivity)) hL2.le
-  have h13 := hC Φ y s b S hy (by linarith) hsb hB hΦ hΦ0 hS1 hS2
+  have h13 := hC Φ y s b S hy (by linarith only [hs4]) hsb hB hΦ hΦ0 hS1 hS2
   have hsum : ∑ p ∈ S, delta (log y / log p - 1) (y / p) * errMaj (!lower) (log y / log p - 1) /
       (p * log (y / p) ^ 2) ≤ ∑ p ∈ S, Φ (log y / log p) / p := by
     refine sum_le_sum fun p hp => ?_
     obtain ⟨hpp, hpB, hpA⟩ := hS1 p hp
-    have ht := (div_log_mem_Icc hy (by linarith) hsb ⟨hpB, hpA⟩).2
+    have ht := (div_log_mem_Icc hy (by linarith only [hs4]) hsb ⟨hpB, hpA⟩).2
     rw [hG']
-    exact cor3_summand_le hy hpp.one_lt (by linarith [ht.1]) (majG_pos _ _).le
+    exact cor3_summand_le hy hpp.one_lt (by linarith only [ht.1, hs4, ht]) (majG_pos _ _).le
   have hint : ∫ t in s..b, Φ t / t = (∫ t in s..b, (1 + t ^ 2 * log t ^ 5 / log y ^ 2) ^
       (5 * (t - 1)) * majG r (t - 1) * t / (t - 1) ^ 2) / log y ^ 2 := by
     rw [← intervalIntegral.integral_div]
     refine intervalIntegral.integral_congr fun t ht => ?_
     rw [uIcc_of_le hsb] at ht
-    have : t ≠ 0 := by linarith [ht.1]
-    have : t - 1 ≠ 0 := by linarith [ht.1]
+    have : t ≠ 0 := by linarith only [ht.1, hs4, ht]
+    have : t - 1 ≠ 0 := by linarith only [ht.1, hs4, ht]
     simp only [Φ]
     field_simp
   have h11 := lemma11 r hs hsb hb
   have hΦs : Φ s ≤ delta s y * (32 * s ^ 2 * majG (r + 1) s) / log y ^ 2 := by
-    have h1 := growth_le_delta (y := y) (by linarith : (1 : ℝ) ≤ s) le_rfl
-    have h2 := errMaj_shift_sq_le lower (!lower) (by linarith : (2 : ℝ) ≤ s)
+    have h1 := growth_le_delta (y := y) (by linarith only [hs4] : (1 : ℝ) ≤ s) le_rfl
+    have h2 := errMaj_shift_sq_le lower (!lower) (by linarith only [hs4] : (2 : ℝ) ≤ s)
     rw [hG', hGs] at h2
     have h3 : 0 ≤ majG r (s - 1) * (s ^ 2 / (s - 1) ^ 2) := by
       have := majG_pos r (s - 1); positivity
     change (1 + s ^ 2 * log s ^ 5 / log y ^ 2) ^ (5 * (s - 1)) * majG r (s - 1) *
       (s ^ 2 / (s - 1) ^ 2) / log y ^ 2 ≤ _
     rw [mul_assoc _ (majG r (s - 1))]
-    exact div_le_div_of_nonneg_right (mul_le_mul h1 h2 h3 (delta_pos (by linarith) y).le)
+    exact div_le_div_of_nonneg_right (mul_le_mul h1 h2 h3 (delta_pos (by linarith only [hs4]) y).le)
       hL2.le
   rw [abs_le] at h13
   rw [hint] at h13
   have hpE := pntE_pos (y ^ (1 / b))
-  have hδ := delta_pos (by linarith : (1 : ℝ) ≤ s) y
+  have hδ := delta_pos (by linarith only [hs4] : (1 : ℝ) ≤ s) y
   have hG := majG_pos (r + 1) s
   have hsb2 : s ^ 2 ≤ b ^ 2 := by gcongr
   rw [hGs]
@@ -383,7 +383,7 @@ theorem cor3_large : ∃ C, 0 ≤ C ∧ ∀ (lower : Bool) (y s b : ℝ) (S : Fi
       majG r (t - 1) * t / (t - 1) ^ 2) / log y ^ 2 ≤ delta s y * majG (r + 1) s / log y ^ 2 :=
     div_le_div_of_nonneg_right h11.le hL2.le
   calc _ ≤ ∑ p ∈ S, Φ (log y / log p) / p := hsum
-    _ ≤ _ := by nlinarith
+    _ ≤ _ := by nlinarith only [h13, e1, e2, e3]
 
 /-- Corollary 3 on `[s, a]` with `a ≤ e^{32}`: here `δ(t_p - 1, y/p) ≤ δ(e^{32}, y)` and Lemma 13
 is applied to `G'(t-1) t²/(t-1)²` directly. -/
@@ -396,28 +396,28 @@ theorem cor3_small : ∃ C, 0 ≤ C ∧ ∀ (lower : Bool) (y s a : ℝ) (S : Fi
       delta (exp 32) y / log y ^ 2 *
         (errMaj lower s - errMaj lower a + C * s ^ 2 * errMaj lower s * pntE (y ^ (1 / a))) := by
   obtain ⟨C, hC0, hC⟩ := lemma13_param
-  refine ⟨32 * C, by linarith, fun lower y s a S hy hs hsa ha hB hS1 hS2 => ?_⟩
+  refine ⟨32 * C, by linarith only [hC0], fun lower y s a S hy hs hsa ha hB hS1 hS2 => ?_⟩
   have hs2 : 2 ≤ s := (two_le_errLower lower).trans hs
   have hL : 0 < log y := log_pos hy
   have hL2 : 0 < log y ^ 2 := by positivity
   set F : ℝ → ℝ := fun t => errMaj (!lower) (t - 1) * (t ^ 2 / (t - 1) ^ 2) with hFdef
   have hF : AntitoneOn F (Icc s a) :=
-    antitoneOn_mul_of_nonneg (fun u _ v _ huv => errMaj_antitone _ (by linarith))
+    antitoneOn_mul_of_nonneg (fun u _ v _ huv => errMaj_antitone _ (by linarith only [huv]))
       (antitoneOn_sq_div_sq_sub_one.mono fun t ht => show (1 : ℝ) < t by linarith [ht.1])
       (fun t _ => (errMaj_pos _ _).le) fun t _ => by positivity
   have hF0 : ∀ t ∈ Icc s a, 0 ≤ F t := fun t _ => by
     have := errMaj_pos (!lower) (t - 1); positivity
-  have h13 := hC F y s a S hy (by linarith) hsa hB hF hF0 hS1 hS2
+  have h13 := hC F y s a S hy (by linarith only [hs2]) hsa hB hF hF0 hS1 hS2
   have hδ0 : 0 ≤ delta (exp 32) y :=
-    (delta_pos (by linarith [four_lt_of_exp_le (le_refl (exp 32))]) y).le
+    (delta_pos (by linarith only [four_lt_of_exp_le (le_refl (exp 32)), hsa, ha, hs2]) y).le
   have hsum : ∑ p ∈ S, delta (log y / log p - 1) (y / p) * errMaj (!lower) (log y / log p - 1) /
       (p * log (y / p) ^ 2) ≤ delta (exp 32) y / log y ^ 2 * ∑ p ∈ S, F (log y / log p) / p := by
     rw [mul_sum]
     refine sum_le_sum fun p hp => ?_
     obtain ⟨hpp, hpB, hpA⟩ := hS1 p hp
-    have ht := (div_log_mem_Icc hy (by linarith) hsa ⟨hpB, hpA⟩).2
+    have ht := (div_log_mem_Icc hy (by linarith only [hs2]) hsa ⟨hpB, hpA⟩).2
     refine (cor3_summand_le hy hpp.one_lt (by linarith [ht.1]) (errMaj_pos _ _).le).trans ?_
-    have hg := growth_le_delta (y := y) (by linarith [ht.1] : (1 : ℝ) ≤ log y / log p)
+    have hg := growth_le_delta (y := y) (by linarith only [ht.1, hs2, ht] : (1 : ℝ) ≤ log y / log p)
       (ht.2.trans ha)
     have hF1 : 0 ≤ F (log y / log p) := hF0 _ ht
     have hp0 : (0 : ℝ) < p := by exact_mod_cast hpp.pos
@@ -430,8 +430,8 @@ theorem cor3_small : ∃ C, 0 ≤ C ∧ ∀ (lower : Bool) (y s a : ℝ) (S : Fi
     rw [← integral_errMaj_shift lower hs hsa]
     refine intervalIntegral.integral_congr fun t ht => ?_
     rw [uIcc_of_le hsa] at ht
-    have : t ≠ 0 := by linarith [ht.1]
-    have : t - 1 ≠ 0 := by linarith [ht.1]
+    have : t ≠ 0 := by linarith only [ht.1, hs2, ht]
+    have : t - 1 ≠ 0 := by linarith only [ht.1, hs2, ht]
     simp only [F]
     field_simp
   have hFs : F s ≤ 32 * s ^ 2 * errMaj lower s := errMaj_shift_sq_le lower (!lower) hs2
@@ -441,7 +441,7 @@ theorem cor3_small : ∃ C, 0 ≤ C ∧ ∀ (lower : Bool) (y s a : ℝ) (S : Fi
       errMaj lower s - errMaj lower a + 32 * C * s ^ 2 * errMaj lower s * pntE (y ^ (1 / a)) := by
     have : C * F s * pntE (y ^ (1 / a)) ≤
         C * (32 * s ^ 2 * errMaj lower s) * pntE (y ^ (1 / a)) := by gcongr
-    linarith [h13.2]
+    linarith only [h13.2, h13, this]
   calc _ ≤ _ := hsum
     _ ≤ _ := mul_le_mul_of_nonneg_left hmain (div_nonneg hδ0 hL2.le)
 
@@ -460,7 +460,7 @@ theorem cor3_primesLT : ∃ C, 0 ≤ C ∧ ∀ (lower : Bool) (y s b : ℝ), 1 <
         (1 + C * b ^ 2 * pntE (y ^ (1 / b))) := by
   obtain ⟨C₁, hC₁, h₁⟩ := cor3_large
   obtain ⟨C₂, hC₂, h₂⟩ := cor3_small
-  refine ⟨C₁ + C₂, by linarith, fun lower y s b hy hs hb32 hB hb => ?_⟩
+  refine ⟨C₁ + C₂, by linarith only [hC₁, hC₂], fun lower y s b hy hs hb32 hB hb => ?_⟩
   set s₀ := exp 32 with hs₀
   have hs2 : 2 ≤ s := (two_le_errLower lower).trans hs
   have hs₀4 : 4 < s₀ := four_lt_of_exp_le le_rfl
@@ -470,17 +470,17 @@ theorem cor3_primesLT : ∃ C, 0 ≤ C ∧ ∀ (lower : Bool) (y s b : ℝ), 1 <
   set S := (primesLT (y ^ (1 / s))).filter (fun p : ℕ => y ^ (1 / b) ≤ p) with hS
   have hRHS : 0 ≤ delta (max s s₀) y * errMaj lower s / log y ^ 2 *
       (1 + (C₁ + C₂) * b ^ 2 * pntE (y ^ (1 / b))) := by
-    have := delta_pos (by linarith [le_max_left s s₀] : (1 : ℝ) ≤ max s s₀) y
+    have := delta_pos (by linarith only [le_max_left s s₀, hs2] : (1 : ℝ) ≤ max s s₀) y
     have : 0 ≤ (C₁ + C₂) * b ^ 2 * pntE (y ^ (1 / b)) :=
-      mul_nonneg (mul_nonneg (by linarith) (sq_nonneg b)) hpE.le
+      mul_nonneg (mul_nonneg (by linarith only [hC₁, hC₂]) (sq_nonneg b)) hpE.le
     positivity
   rcases lt_or_ge b s with hbs | hsb
   · -- no primes
     have hempty : S = ∅ := by
       refine Finset.eq_empty_of_forall_notMem fun p hp => ?_
       rw [hS, mem_filter, mem_primesLT] at hp
-      have := rpow_one_div_le_rpow_one_div hy.le (by linarith) hbs.le
-      linarith [hp.1.2, hp.2]
+      have := rpow_one_div_le_rpow_one_div hy.le (by linarith only [hb32, hs₀4]) hbs.le
+      linarith only [hp.1.2, hp.2, hp, this]
     rw [hempty, sum_empty]
     exact hRHS
   rcases le_total s₀ s with hs₀s | hss₀
@@ -489,35 +489,37 @@ theorem cor3_primesLT : ∃ C, 0 ≤ C ∧ ∀ (lower : Bool) (y s b : ℝ), 1 <
     refine (h₁ lower y s b S hy hs₀s hsb hB hb (fun p hp => ?_) fun p hp h1 h2 => ?_).trans ?_
     · rw [hS, mem_filter, mem_primesLT] at hp; exact ⟨hp.1.1, hp.2, hp.1.2.le⟩
     · rw [hS, mem_filter, mem_primesLT]; exact ⟨⟨hp, h2⟩, h1.le⟩
-    · have := delta_pos (by linarith : (1 : ℝ) ≤ s) y
+    · have := delta_pos (by linarith only [hs₀4, hs₀s] : (1 : ℝ) ≤ s) y
       gcongr
-      linarith
+      linarith only [hC₂]
   -- `s < s₀`: split at `y^{1/s₀}`
   rw [max_eq_right hss₀]
-  have hB₀ : y ^ (1 / b) ≤ y ^ (1 / s₀) := rpow_one_div_le_rpow_one_div hy.le (by linarith) hb32
-  have hB₀s : y ^ (1 / s₀) ≤ y ^ (1 / s) := rpow_one_div_le_rpow_one_div hy.le (by linarith) hss₀
+  have hB₀ : y ^ (1 / b) ≤ y ^ (1 / s₀) := rpow_one_div_le_rpow_one_div hy.le (by
+    linarith only [hs₀4]) hb32
+  have hB₀s : y ^ (1 / s₀) ≤ y ^ (1 / s) := rpow_one_div_le_rpow_one_div hy.le (by
+    linarith only [hs2]) hss₀
   rw [← sum_filter_add_sum_filter_not S (fun p : ℕ => y ^ (1 / s₀) ≤ p)]
   have e₁ := h₂ lower y s s₀ (S.filter fun p : ℕ => y ^ (1 / s₀) ≤ p) hy hs hss₀ le_rfl
-    (by linarith) (fun p hp => by
+    (by linarith only [hB, hB₀]) (fun p hp => by
       rw [mem_filter, hS, mem_filter, mem_primesLT] at hp
       exact ⟨hp.1.1.1, hp.2, hp.1.1.2.le⟩)
     (fun p hp h1 h2 => by
       rw [mem_filter, hS, mem_filter, mem_primesLT]
-      exact ⟨⟨⟨hp, h2⟩, by linarith⟩, h1.le⟩)
+      exact ⟨⟨⟨hp, h2⟩, by linarith only [hB₀, h1]⟩, h1.le⟩)
   have e₂ := h₁ lower y s₀ b (S.filter fun p : ℕ => ¬ y ^ (1 / s₀) ≤ p) hy le_rfl hb32 hB hb
     (fun p hp => by
       rw [mem_filter, hS, mem_filter, mem_primesLT] at hp
       exact ⟨hp.1.1.1, hp.1.2, (not_le.1 hp.2).le⟩)
     (fun p hp h1 h2 => by
       rw [mem_filter, hS, mem_filter, mem_primesLT]
-      exact ⟨⟨⟨hp, by linarith⟩, h1.le⟩, not_le.2 h2⟩)
+      exact ⟨⟨⟨hp, by linarith only [hB₀s, h2]⟩, h1.le⟩, not_le.2 h2⟩)
   refine (add_le_add e₁ e₂).trans ?_
   -- combine
-  have hδ := delta_pos (by linarith : (1 : ℝ) ≤ s₀) y
+  have hδ := delta_pos (by linarith only [hs₀4] : (1 : ℝ) ≤ s₀) y
   have hG₀ := errMaj_pos lower s₀
   have hGG : errMaj lower s₀ ≤ errMaj lower s := errMaj_antitone lower hss₀
   have hpE₀ : pntE (y ^ (1 / s₀)) ≤ pntE (y ^ (1 / b)) :=
-    pntE_le_pntE (by linarith) hB₀
+    pntE_le_pntE (by linarith only [hB]) hB₀
   have hsb2 : s ^ 2 * pntE (y ^ (1 / s₀)) ≤ b ^ 2 * pntE (y ^ (1 / b)) := by
     have : s ^ 2 ≤ b ^ 2 := by gcongr
     exact mul_le_mul this hpE₀ (pntE_pos _).le (sq_nonneg b)
@@ -531,7 +533,7 @@ theorem cor3_primesLT : ∃ C, 0 ≤ C ∧ ∀ (lower : Bool) (y s b : ℝ), 1 <
       C₂ * s ^ 2 * errMaj lower s * pntE (y ^ (1 / s₀)) +
       errMaj lower s₀ * (1 + C₁ * b ^ 2 * pntE (y ^ (1 / b))) ≤
       errMaj lower s * (1 + (C₁ + C₂) * b ^ 2 * pntE (y ^ (1 / b))) := by
-    nlinarith
+    nlinarith only [i1, i2]
   have hk : 0 ≤ delta s₀ y / log y ^ 2 := div_nonneg hδ.le hL2.le
   calc delta s₀ y / log y ^ 2 * (errMaj lower s - errMaj lower s₀ +
         C₂ * s ^ 2 * errMaj lower s * pntE (y ^ (1 / s₀))) +
@@ -548,7 +550,7 @@ theorem cor3_primesLT : ∃ C, 0 ≤ C ∧ ∀ (lower : Bool) (y s b : ℝ), 1 <
 theorem lt_rpow_one_div_max_three {y s x : ℝ} (hy : 1 < y) (hs : 0 < s) (hx : 0 ≤ x) :
     x < y ^ (1 / max s 3) ↔ x < y ^ (1 / s) ∧ x ^ 3 < y := by
   have h3 : x < y ^ (1 / (3 : ℝ)) ↔ x ^ 3 < y := by
-    rw [one_div, lt_rpow_inv_iff_of_pos hx (by linarith) (by norm_num)]
+    rw [one_div, lt_rpow_inv_iff_of_pos hx (by linarith only [hy]) (by norm_num)]
     norm_cast
   rcases le_total s 3 with hs3 | hs3
   · rw [max_eq_right hs3, h3]
@@ -586,14 +588,14 @@ theorem cor3 : ∃ C, 0 ≤ C ∧ ∀ (lower : Bool) (y s b : ℝ), 1 < y → sM
         (primesLT (y ^ (1 / max s 3))).filter (fun p : ℕ => y ^ (1 / b) ≤ p) := by
       ext p
       simp only [mem_filter, mem_rosserPrimes, mem_primesLT, Bool.false_eq_true, false_or]
-      rw [lt_rpow_one_div_max_three hy (by linarith) (Nat.cast_nonneg p)]
+      rw [lt_rpow_one_div_max_three hy (by linarith only [hs1]) (Nat.cast_nonneg p)]
       tauto
     have hG : errMaj false (max s 3) = errMaj false s := by
       rcases le_total s 3 with h | h
       · rw [max_eq_right h, errMaj_false_of_le_three le_rfl, errMaj_false_of_le_three h]
       · rw [max_eq_left h]
     have hmax : max (max s 3) (exp 32) = max s (exp 32) := by
-      have : (3 : ℝ) ≤ exp 32 := by linarith [four_lt_of_exp_le (le_refl (exp 32))]
+      have : (3 : ℝ) ≤ exp 32 := by linarith only [four_lt_of_exp_le (le_refl (exp 32))]
       rw [max_assoc, max_eq_right this]
     rw [hset, ← hG, ← hmax]
     exact hC false y (max s 3) b hy (le_max_right _ _) hb32 hB hb
@@ -604,7 +606,7 @@ theorem cor3 : ∃ C, 0 ≤ C ∧ ∀ (lower : Bool) (y s b : ℝ), 1 < y → sM
 theorem sq_mul_log_pow_four_le_of_le {b b' X : ℝ} (hb : 1 ≤ b) (hbb' : b ≤ b')
     (h : b' ^ 2 * log b' ^ 4 ≤ X) : b ^ 2 * log b ^ 4 ≤ X := by
   have := log_nonneg hb
-  have : log b ≤ log b' := log_le_log (by linarith) hbb'
+  have : log b ≤ log b' := log_le_log (by linarith only [hb]) hbb'
   have : b ^ 2 * log b ^ 4 ≤ b' ^ 2 * log b' ^ 4 := by gcongr
   linarith
 
diff --git a/LeanPool/IwaniecLinearSieve/LinearSieve/Crude.lean b/LeanPool/IwaniecLinearSieve/LinearSieve/Crude.lean
index b713b43aab..7759d722ab 100644
--- a/LeanPool/IwaniecLinearSieve/LinearSieve/Crude.lean
+++ b/LeanPool/IwaniecLinearSieve/LinearSieve/Crude.lean
@@ -53,7 +53,7 @@ theorem pow_succ_add_mul_le_add_pow {a b : ℝ} (ha : 0 ≤ a) (hb : 0 ≤ b) (n
         ≤ (a + b) * (a ^ (n + 1) + (n + 1) * a ^ n * b) := by
           push_cast
           rw [pow_succ a (n + 1), pow_succ a n]
-          nlinarith [mul_nonneg h1 hb]
+          nlinarith only [mul_nonneg h1 hb, h2]
       _ ≤ (a + b) * (a + b) ^ (n + 1) := by gcongr
       _ = (a + b) ^ (n + 1 + 1) := by ring
 
@@ -92,7 +92,7 @@ theorem sum_pow_sum_lt_mul_le (s : Finset ℕ) {w : ℕ → ℝ} (hw : ∀ p ∈
           exact ih hw'
       _ ≤ (w a + ∑ q ∈ s, w q) ^ (n + 1) / (n + 1) := by
           rw [add_comm (w a), le_div_iff₀ hn, add_mul, div_mul_cancel₀ _ hn.ne']
-          nlinarith
+          nlinarith only [this]
 
 /-- `∑_{p < z} SLT(p)^n / p ≤ SLT(z)^{n+1} / (n+1)`. -/
 theorem sum_SLT_pow_div_le (n : ℕ) (z : ℝ) :
@@ -240,7 +240,7 @@ theorem sum_pow_div_factorial_le {X u : ℝ} (hX : 0 ≤ X) (hu : 0 < u) (h : 2
     rw [hk, Nat.add_one_le_iff, Nat.floor_lt hu.le]
     exact hs l hl
   have he : 1 ≤ exp 1 := one_le_exp zero_le_one
-  have h2X : 2 * X ≤ k + 1 := by nlinarith
+  have h2X : 2 * X ≤ k + 1 := by nlinarith only [h, huk, hX, he]
   have hf : (0 : ℝ) < k.factorial := by exact_mod_cast k.factorial_pos
   -- each term is at most `X^k/k! · 2^{-(l-k)}`
   have hterm : ∀ j : ℕ, X ^ (k + j) / (k + j).factorial ≤
@@ -259,7 +259,7 @@ theorem sum_pow_div_factorial_le {X u : ℝ} (hX : 0 ≤ X) (hu : 0 < u) (h : 2
           refine mul_le_mul_of_nonneg_left (pow_le_pow_left₀ (by positivity) ?_ j)
             (by positivity)
           rw [div_le_iff₀ (by positivity)]
-          linarith
+          linarith only [h2X]
   set N := s.sup id + 1
   have hsub : s ⊆ Ico k N := fun l hl ↦
     mem_Ico.2 ⟨hks l hl, Nat.lt_succ_of_le (le_sup (f := id) hl)⟩
@@ -284,7 +284,7 @@ theorem sum_pow_div_factorial_le {X u : ℝ} (hX : 0 ≤ X) (hu : 0 < u) (h : 2
         refine mul_le_mul_of_nonneg_right ?_ (by norm_num)
         refine rpow_le_rpow_of_exponent_ge' (by positivity) ?_ hu.le huk.le
         rw [div_le_one hu]
-        nlinarith [exp_pos 1]
+        nlinarith only [exp_pos 1, hu, h]
     _ = 2 * (exp 1 * X / u) ^ u := mul_comm _ _
 
 /-- `(e X / u)^u = exp (-(u log u) + u log X + u)`. -/
@@ -307,22 +307,22 @@ theorem fail_le_tail {lower : Bool} {r : ℕ} {y z X u : ℝ} (hz : 1 < z) (hu :
     rw [← rpow_natCast] at hl
     have := (rpow_lt_rpow_left_iff hz).1 (hyz.trans_lt hl)
     push_cast at this
-    linarith
+    linarith only [this]
 
 /-- `fail_le_tail` with `z = y^{1/s}`: for `y > 1`, `s > 2`, `SLT (y^{1/s}) ≤ X` and
 `2 e X ≤ s - 2`, `fail lower r y y^{1/s} ≤ 2 (e X / (s - 2))^{s - 2}`. -/
 theorem fail_rpow_le_tail {lower : Bool} {r : ℕ} {y s X : ℝ} (hy : 1 < y) (hs : 2 < s)
     (hX : SLT (y ^ s⁻¹) ≤ X) (h : 2 * exp 1 * X ≤ s - 2) :
     fail lower r y (y ^ s⁻¹) ≤ 2 * (exp 1 * X / (s - 2)) ^ (s - 2) := by
-  have hs0 : 0 < s := by linarith
-  refine fail_le_tail (one_lt_rpow hy (inv_pos.2 hs0)) (by linarith) ?_ hX h
-  rw [sub_add_cancel, ← rpow_mul (by linarith), inv_mul_cancel₀ hs0.ne', rpow_one]
+  have hs0 : 0 < s := by linarith only [hs]
+  refine fail_le_tail (one_lt_rpow hy (inv_pos.2 hs0)) (by linarith only [hs]) ?_ hX h
+  rw [sub_add_cancel, ← rpow_mul (by linarith only [hy]), inv_mul_cancel₀ hs0.ne', rpow_one]
 
 /-- `SLT z ≤ log log z + C` for `z ≥ 2`. -/
 theorem SLT_le_loglog : ∃ C : ℝ, ∀ z ≥ 2, SLT z ≤ log (log z) + C := by
   obtain ⟨c₅, C, hC⟩ := S_asymp
   refine ⟨c₅ + |C|, fun z hz ↦ ?_⟩
-  have h1 := (S_sub_SLT (by linarith : (0 : ℝ) < z)).1
+  have h1 := (S_sub_SLT (by linarith only [hz] : (0 : ℝ) < z)).1
   have h2 := (abs_le.1 (hC z hz)).2
   have h3 : C * pntE z ≤ |C| := by
     calc
@@ -330,7 +330,7 @@ theorem SLT_le_loglog : ∃ C : ℝ, ∀ z ≥ 2, SLT z ≤ log (log z) + C := b
         mul_le_mul_of_nonneg_right (le_abs_self C) (pntE_nonneg z)
       _ ≤ |C| * 1 := mul_le_mul_of_nonneg_left (pntE_le_one z) (abs_nonneg C)
       _ = |C| := mul_one _
-  linarith
+  linarith only [h1, h2, h3]
 
 /-! ### Counts -/
 
diff --git a/LeanPool/IwaniecLinearSieve/LinearSieve/Depth.lean b/LeanPool/IwaniecLinearSieve/LinearSieve/Depth.lean
index 62fa246b7d..a72a626120 100644
--- a/LeanPool/IwaniecLinearSieve/LinearSieve/Depth.lean
+++ b/LeanPool/IwaniecLinearSieve/LinearSieve/Depth.lean
@@ -67,7 +67,7 @@ theorem LeProdPrimesLT.succ (h : LeProdPrimesLT r y z) : LeProdPrimesLT (r + 1)
   have h1 := h (T.erase a) ((erase_subset a T).trans hT) (by rw [card_erase_of_mem ha, hcard]; rfl)
   have h2 : (1 : ℝ) ≤ a := by exact_mod_cast (prime_of_mem_primesLT (hT ha)).one_lt.le
   have h3 := one_le_prod_primes ((erase_subset a T).trans hT)
-  nlinarith
+  nlinarith only [h1, h2, h3]
 
 theorem LeProdPrimesLT.mono {s : ℕ} (h : LeProdPrimesLT r y z) (hrs : r ≤ s) :
     LeProdPrimesLT s y z := by
@@ -210,7 +210,7 @@ theorem card_primeFactors_le_of_mem_rosserSet (hr : 1 ≤ r) (h : LeProdPrimesLT
     have h' := (Nat.cast_le (α := ℝ)).2 hTd
     push_cast at h'
     exact h'
-  linarith
+  linarith only [hdy, hyT, this]
 
 theorem card_filter_rosserSet_add_eq (hr : 1 ≤ r) (h : LeProdPrimesLT (r + 1) y z) (j : ℕ) :
     #((rosserSet lower y z).filter fun d ↦ #d.primeFactors ≤ r + j) =
@@ -232,13 +232,13 @@ theorem mul_log_sub_one_le_log_factorial (n : ℕ) :
   rw [div_le_iff₀ hf] at h
   have := log_le_log (by positivity) h
   rw [log_pow, log_mul (exp_pos _).ne' hf.ne', log_exp] at this
-  linarith
+  linarith only [this]
 
 /-- `log x ≤ 2 √x`. -/
 theorem log_le_two_mul_sqrt {x : ℝ} (hx : 0 ≤ x) : log x ≤ 2 * √x := by
   have := log_le_rpow_div hx (by norm_num : (0 : ℝ) < 1 / 2)
   rw [← sqrt_eq_rpow] at this
-  linarith
+  linarith only [this]
 
 /-- [I71, p. 23]: if `r + 2 > 2 log y / log log y` and `y` is large then `y ≤ (r + 1)!`, so every
 product of `r` distinct primes is at least `y`; moreover `r ≥ 2`. -/
@@ -251,21 +251,21 @@ theorem exists_le_factorial : ∃ y₀ : ℝ, ∀ y ≥ y₀, ∀ r : ℕ,
   have hL49 : exp 49 ≤ L := by rw [hL, le_log_iff_exp_le hy0]; exact hy
   have hL0 : 0 < L := (exp_pos _).trans_le hL49
   have hℓ49 : 49 ≤ ℓ := by rw [hℓ, le_log_iff_exp_le hL0]; exact hL49
-  have hℓ0 : 0 < ℓ := by linarith
+  have hℓ0 : 0 < ℓ := by linarith only [hℓ49]
   -- `ℓ ≤ L / 4`
   have hsqrtL : 64 ≤ L := by
     have := quadratic_le_exp_of_nonneg (by norm_num : (0 : ℝ) ≤ 49)
-    linarith
+    linarith only [hL49, this]
   have hℓL : 4 * ℓ ≤ L := by
     have h1 := log_le_two_mul_sqrt hL0.le
     have h2 : 8 ≤ √L := by
       rw [show (8 : ℝ) = √64 by rw [show (64 : ℝ) = 8 ^ 2 by norm_num, sqrt_sq (by norm_num)]]
       exact sqrt_le_sqrt hsqrtL
     have h3 : √L * √L = L := mul_self_sqrt hL0.le
-    nlinarith
-  have hratio : 4 ≤ L / ℓ := by rw [le_div_iff₀ hℓ0]; linarith
+    nlinarith only [hℓ49, h1, h3]
+  have hratio : 4 ≤ L / ℓ := by rw [le_div_iff₀ hℓ0]; linarith only [hℓL]
   have h2Lℓ : 2 * L / ℓ = 2 * (L / ℓ) := by ring
-  refine ⟨by exact_mod_cast (by linarith : (2 : ℝ) ≤ r), ?_⟩
+  refine ⟨by exact_mod_cast (by linarith only [hr, hratio, h2Lℓ] : (2 : ℝ) ≤ r), ?_⟩
   -- `log ℓ ≤ (ℓ - 3) / 3`
   have hlogℓ : 3 * log ℓ + 3 ≤ ℓ := by
     have h1 := log_le_two_mul_sqrt hℓ0.le
@@ -273,7 +273,7 @@ theorem exists_le_factorial : ∃ y₀ : ℝ, ∀ y ≥ y₀, ∀ r : ℕ,
       rw [show (7 : ℝ) = √49 by rw [show (49 : ℝ) = 7 ^ 2 by norm_num, sqrt_sq (by norm_num)]]
       exact sqrt_le_sqrt hℓ49
     have h3 : √ℓ * √ℓ = ℓ := mul_self_sqrt hℓ0.le
-    nlinarith
+    nlinarith only [hℓ49, h1, h3, h2]
   set m := 3 * L / (2 * ℓ) with hm
   have hm0 : 0 < m := by positivity
   set n : ℕ := r + 1 with hn
@@ -282,14 +282,14 @@ theorem exists_le_factorial : ∃ y₀ : ℝ, ∀ y ≥ y₀, ∀ r : ℕ,
     rw [hn_cast, hm]
     have : 3 * L / (2 * ℓ) = 3 / 2 * (L / ℓ) := by field_simp
     rw [this]
-    linarith
+    linarith only [hr, hratio, h2Lℓ]
   have hlogm : ℓ - log ℓ ≤ log m := by
     rw [hm, log_div (by positivity) (by positivity), log_mul (by norm_num) hL0.ne',
       log_mul (by norm_num) hℓ0.ne', ← hℓ]
     have : log 2 ≤ log 3 := log_le_log (by norm_num) (by norm_num)
-    linarith
+    linarith only [this]
   have hkey : L ≤ m * (log m - 1) := by
-    have h1 : 2 * ℓ / 3 ≤ log m - 1 := by linarith
+    have h1 : 2 * ℓ / 3 ≤ log m - 1 := by linarith only [hlogℓ, hlogm]
     calc L = m * (2 * ℓ / 3) := by rw [hm]; field_simp
       _ ≤ m * (log m - 1) := by gcongr
   have hmono : m * (log m - 1) ≤ n * (log n - 1) := by
@@ -297,10 +297,10 @@ theorem exists_le_factorial : ∃ y₀ : ℝ, ∀ y ≥ y₀, ∀ r : ℕ,
     have h2 : 0 ≤ log m - 1 := by
       by_contra h
       have : m * (log m - 1) < 0 := mul_neg_of_pos_of_neg hm0 (not_le.1 h)
-      linarith
-    nlinarith
+      linarith only [hℓ49, hlogℓ, hlogm, h]
+    nlinarith only [hmn, h1, hℓ49, hlogℓ, hlogm]
   have hfact := mul_log_sub_one_le_log_factorial n
-  have : L ≤ log n.factorial := by linarith
+  have : L ≤ log n.factorial := by linarith only [hkey, hmono, hfact]
   rw [hL, ← exp_le_exp, exp_log hy0, exp_log (by exact_mod_cast n.factorial_pos)] at this
   exact this
 
diff --git a/LeanPool/IwaniecLinearSieve/LinearSieve/Estimate.lean b/LeanPool/IwaniecLinearSieve/LinearSieve/Estimate.lean
index 41b51d7dd9..2dc4729b68 100644
--- a/LeanPool/IwaniecLinearSieve/LinearSieve/Estimate.lean
+++ b/LeanPool/IwaniecLinearSieve/LinearSieve/Estimate.lean
@@ -47,14 +47,14 @@ theorem rpow_one_div_log_div {y z : ℝ} (hy : 0 < y) (hz : 1 < z) (hyl : log y
     y ^ (1 / (log y / log z)) = z := by
   have hlz : log z ≠ 0 := (log_pos hz).ne'
   rw [rpow_def_of_pos hy, show log y * (1 / (log y / log z)) = log z by field_simp,
-    exp_log (by linarith)]
+    exp_log (by linarith only [hz])]
 
 /-- `log (1 + x) ≥ x / (1 + x)` for `x ≥ 0`. -/
 theorem div_one_add_le_log_one_add {x : ℝ} (hx : 0 ≤ x) : x / (1 + x) ≤ log (1 + x) := by
   have h := log_le_sub_one_of_pos (show 0 < (1 + x)⁻¹ by positivity)
   rw [log_inv] at h
   have : (1 + x)⁻¹ - 1 = -(x / (1 + x)) := by field_simp; ring
-  linarith
+  linarith only [h, this]
 
 /-- If `0 ≤ x ≤ 1/2` and `s ≥ 2 + x`, then `log(s - 1) ≥ 2x/3`.
 This supplies the logarithmic gain in the linear sieve estimate and Theorem 2. -/
diff --git a/LeanPool/IwaniecLinearSieve/LinearSieve/LemmaEleven.lean b/LeanPool/IwaniecLinearSieve/LinearSieve/LemmaEleven.lean
index 8704a11930..97bff3a754 100644
--- a/LeanPool/IwaniecLinearSieve/LinearSieve/LemmaEleven.lean
+++ b/LeanPool/IwaniecLinearSieve/LinearSieve/LemmaEleven.lean
@@ -61,8 +61,8 @@ theorem hasDerivAt_growth (L a : ℝ) {t : ℝ} (ht : 1 ≤ t) :
           ((2 * t * log t ^ 5 + 5 * t * log t ^ 4) / L ^ 2) /
             (1 + t ^ 2 * log t ^ 5 / L ^ 2))) t := by
   set x := t ^ 2 * log t ^ 5 / L ^ 2
-  have hx : 0 < 1 + x := by linarith [lsx_nonneg L ht]
-  have h := ((hasDerivAt_lsx L (by linarith)).const_add 1).rpow
+  have hx : 0 < 1 + x := by linarith only [lsx_nonneg L ht, ht]
+  have h := ((hasDerivAt_lsx L (by linarith only [ht])).const_add 1).rpow
     (((hasDerivAt_id' t).sub_const a).const_mul 5) hx
   convert h using 1
   rw [rpow_sub_one hx.ne']
@@ -132,11 +132,11 @@ theorem rate_bound {L a t : ℝ} (ha : 0 ≤ a) (ha1 : a ≤ 1) (ht1 : 1 ≤ t)
 theorem majG_succ_mul_log_lt (r : ℕ) {t : ℝ} (ht : 2 ≤ t) :
     majG (r + 1) t * log t < 4 * (majG r (t - 1) * t / (t - 1) ^ 2) := by
   have h := majG_succ_mul_log_div_lt r ht
-  have hK : 0 < majG r (t - 1) * t := mul_pos (majG_pos r _) (by linarith)
-  have h1 : 0 < (t - 1) ^ 2 := by nlinarith
+  have hK : 0 < majG r (t - 1) * t := mul_pos (majG_pos r _) (by linarith only [ht])
+  have h1 : 0 < (t - 1) ^ 2 := by nlinarith only [ht]
   rw [div_lt_iff₀ hK] at h
   rw [mul_div_assoc', lt_div_iff₀ h1]
-  linarith
+  linarith only [h]
 
 theorem five_add_neg_one_pow_div_le (r : ℕ) : (5 + (-1 : ℝ) ^ r) / 2 ≤ 3 := by
   rcases Nat.even_or_odd r with hr | hr
@@ -149,19 +149,19 @@ theorem five_add_neg_one_pow_div_le (r : ℕ) : (5 + (-1 : ℝ) ^ r) / 2 ≤ 3 :
 theorem range_facts {L t b : ℝ} (ht : exp 32 ≤ t) (htb : t ≤ b)
     (hb : b ^ 2 * log b ^ 4 ≤ L ^ 2 / 160) :
     1 ≤ t ∧ 32 ≤ log t ∧ t ^ 2 * log t ^ 4 / L ^ 2 ≤ 1 / 160 ∧ 0 < L ^ 2 := by
-  have ht1 : 1 ≤ t := le_trans (by linarith [add_one_le_exp (32 : ℝ)]) ht
-  have hlt : 32 ≤ log t := (le_log_iff_exp_le (by linarith)).2 ht
-  have hlb : log t ≤ log b := log_le_log (by linarith) htb
+  have ht1 : 1 ≤ t := le_trans (by linarith only [add_one_le_exp (32 : ℝ)]) ht
+  have hlt : 32 ≤ log t := (le_log_iff_exp_le (by linarith only [ht1])).2 ht
+  have hlb : log t ≤ log b := log_le_log (by linarith only [ht1]) htb
   have h4 : t ^ 2 * log t ^ 4 ≤ b ^ 2 * log b ^ 4 := by
-    have : 0 ≤ log t := by linarith
+    have : 0 ≤ log t := by linarith only [hlt]
     gcongr
   have hpos : 0 < t ^ 2 * log t ^ 4 := by
-    have : 0 < log t := by linarith
-    have : 0 < t := by linarith
+    have : 0 < log t := by linarith only [hlt]
+    have : 0 < t := by linarith only [ht1]
     positivity
-  have hL : 0 < L ^ 2 := by linarith
+  have hL : 0 < L ^ 2 := by linarith only [hb, h4, hpos]
   refine ⟨ht1, hlt, ?_, hL⟩
-  rw [div_le_iff₀ hL]; linarith
+  rw [div_le_iff₀ hL]; linarith only [hb, h4]
 
 /-- `(1 + x)^{5(t-1)} = (1 + x)^{5t} / (1 + x)^5`. -/
 theorem rpow_five_mul_sub_one {x : ℝ} (hx : 0 < x) (t : ℝ) :
@@ -177,8 +177,8 @@ theorem continuousOn_lemma11_integrand (L : ℝ) (r : ℕ) {s b : ℝ} (hs : 2 
     ContinuousOn (fun t => (1 + t ^ 2 * log t ^ 5 / L ^ 2) ^ (5 * (t - 1)) * majG r (t - 1) * t /
       (t - 1) ^ 2) (Icc s b) := by
   refine continuousOn_of_forall_continuousAt fun t ht => ?_
-  have ht1 : t - 1 ≠ 0 := by linarith [ht.1]
-  exact (((continuousAt_growth L 1 (by linarith [ht.1])).mul
+  have ht1 : t - 1 ≠ 0 := by linarith only [ht.1, hs, ht]
+  exact (((continuousAt_growth L 1 (by linarith only [ht.1, hs, ht])).mul
     ((continuous_majG r).continuousAt.comp (continuous_sub_right 1).continuousAt)).mul
     continuousAt_id).div ((continuous_sub_right 1).continuousAt.pow 2) (pow_ne_zero 2 ht1)
 
@@ -188,7 +188,7 @@ theorem delta_eq_growth (s y : ℝ) :
 
 theorem delta_pos {s : ℝ} (hs : 1 ≤ s) (y : ℝ) : 0 < delta s y := by
   have := lsx_nonneg (log y) hs
-  exact rpow_pos_of_pos (by linarith) _
+  exact rpow_pos_of_pos (by linarith only [this]) _
 
 /-- The algebraic decay estimate in Lemma 11: the bound on the growth rate `E`
 and `G ℓ ≤ 4K` imply `K / (1 + x)⁵ ≤ K - EG`. -/
@@ -219,7 +219,7 @@ theorem lemma11 (r : ℕ) {y s b : ℝ} (hs : exp 32 ≤ s) (hsb : s ≤ b)
     ∫ t in s..b, (1 + t ^ 2 * log t ^ 5 / log y ^ 2) ^ (5 * (t - 1)) * majG r (t - 1) * t /
       (t - 1) ^ 2 < delta s y * majG (r + 1) s := by
   set L := log y
-  have hs3 : 3 < s := by linarith [add_one_le_exp (32 : ℝ)]
+  have hs3 : 3 < s := by linarith only [add_one_le_exp (32 : ℝ), hs]
   -- `τ(t) = δ(t) G_{r+1}(t)` and its derivative
   set τ : ℝ → ℝ := fun t => delta t y * majG (r + 1) t
   have hτd : ∀ t, 3 < t → HasDerivAt τ
@@ -229,7 +229,7 @@ theorem lemma11 (r : ℕ) {y s b : ℝ} (hs : exp 32 ≤ s) (hsb : s ≤ b)
             (1 + t ^ 2 * log t ^ 5 / L ^ 2)) * majG (r + 1) t +
         (1 + t ^ 2 * log t ^ 5 / L ^ 2) ^ (5 * (t - 0)) *
           (-(majG r (t - 1) * t / (t - 1) ^ 2))) t := fun t ht => by
-    have h1 := hasDerivAt_growth L 0 (t := t) (by linarith)
+    have h1 := hasDerivAt_growth L 0 (t := t) (by linarith only [ht])
     have h2 := hasDerivAt_majG_succ r (t := t) (by linarith [five_add_neg_one_pow_div_le r])
     have := h1.mul h2
     simp only [τ, delta_eq_growth]
@@ -238,14 +238,14 @@ theorem lemma11 (r : ℕ) {y s b : ℝ} (hs : exp 32 ≤ s) (hsb : s ≤ b)
     (φ := fun t => (1 + t ^ 2 * log t ^ 5 / L ^ 2) ^ (5 * (t - 1)) * majG r (t - 1) * t /
       (t - 1) ^ 2) hsb
     (continuousOn_of_forall_continuousAt fun t ht => (hτd t (by linarith [ht.1])).continuousAt.neg)
-    (fun t ht => (hτd t (by linarith [ht.1])).neg.hasDerivWithinAt)
-    ((continuousOn_lemma11_integrand L r (by linarith)).integrableOn_Icc) ?_
-  · have hτb : 0 < τ b := mul_pos (delta_pos (by linarith) y) (majG_pos _ _)
+    (fun t ht => (hτd t (by linarith only [ht.1, hs3, ht])).neg.hasDerivWithinAt)
+    ((continuousOn_lemma11_integrand L r (by linarith only [hs3])).integrableOn_Icc) ?_
+  · have hτb : 0 < τ b := mul_pos (delta_pos (by linarith only [hsb, hs3]) y) (majG_pos _ _)
     simp only [τ] at key hτb ⊢
-    linarith
+    linarith only [key, hτb]
   -- the pointwise inequality `-τ' ≥ (1 + x)^{5(t-1)} G_r(t-1) t/(t-1)²`
   intro t ht
-  have ht3 : 3 < t := by linarith [ht.1]
+  have ht3 : 3 < t := by linarith only [ht.1, hs3, ht]
   obtain ⟨ht1, hlt, hw, hL⟩ := range_facts (L := L) (hs.trans ht.1.le) ht.2.le hb
   obtain ⟨hE0, -, hE2⟩ := rate_bound (L := L) (a := 0) le_rfl zero_le_one ht1 hlt hw
   set x := t ^ 2 * log t ^ 5 / L ^ 2
@@ -263,7 +263,7 @@ theorem lemma11 (r : ℕ) {y s b : ℝ} (hs : exp 32 ≤ s) (hsb : s ≤ b)
     (by linarith only [hlt] : 0 < log t) hG.le hE2
   change (1 + x) ^ (5 * (t - 1)) * majG r (t - 1) * t / (t - 1) ^ 2 ≤
     -((1 + x) ^ (5 * (t - 0)) * E * G + (1 + x) ^ (5 * (t - 0)) * -K)
-  rw [rpow_five_mul_sub_one (by linarith)]
+  rw [rpow_five_mul_sub_one (by linarith only [hx0])]
   simp only [sub_zero] at hP ⊢
   calc (1 + x) ^ (5 * t) / (1 + x) ^ 5 * majG r (t - 1) * t / (t - 1) ^ 2
       = (1 + x) ^ (5 * t) * (K / (1 + x) ^ 5) := by rw [hK]; ring
@@ -272,7 +272,7 @@ theorem lemma11 (r : ℕ) {y s b : ℝ} (hs : exp 32 ≤ s) (hsb : s ≤ b)
 
 /-! ### Lemma 12 and the monotonicity used in Corollary 3 -/
 theorem four_lt_of_exp_le {t : ℝ} (ht : exp 32 ≤ t) : 4 < t := by
-  linarith [add_one_le_exp (32 : ℝ)]
+  linarith only [add_one_le_exp (32 : ℝ), ht]
 
 /-- If the growth rate satisfies `4E ≤ ℓ` and the decay satisfies `Gℓ ≤ 4K`, then
 `EG ≤ K` for `G ≥ 0`. This is the scalar comparison used in Lemma 12. -/
@@ -320,26 +320,26 @@ theorem lemma12 (r : ℕ) {L s b : ℝ} (hs : exp 32 ≤ s) (hb : b ^ 2 * log b
     AntitoneOn (fun t => (1 + t ^ 2 * log t ^ 5 / L ^ 2) ^ (5 * (t - 1)) * majG (r + 1) t)
       (Icc s b) := by
   refine antitoneOn_growth_mul (k := fun t => majG r (t - 1) * t / (t - 1) ^ 2) (ℓ := log) hs hb
-    (fun t ht => ?_) (fun t _ => (majG_pos _ _).le) (fun t ht => ?_) fun t _ => by linarith
+    (fun t ht => ?_) (fun t _ => (majG_pos _ _).le) (fun t ht => ?_) fun t _ => by linarith only []
   · exact hasDerivAt_majG_succ r (by
-      linarith [five_add_neg_one_pow_div_le r, four_lt_of_exp_le (hs.trans ht.1)])
-  · exact (majG_succ_mul_log_lt r (by linarith [four_lt_of_exp_le (hs.trans ht.1)])).le
+      linarith only [five_add_neg_one_pow_div_le r, four_lt_of_exp_le (hs.trans ht.1), hs, ht])
+  · exact (majG_succ_mul_log_lt r (by linarith only [four_lt_of_exp_le (hs.trans ht.1), hs, ht])).le
 
 theorem log_sub_one_ge {t : ℝ} (ht : 2 ≤ t) : log t - 1 ≤ log (t - 1) := by
-  have h1 : 0 < t - 1 := by linarith
-  have h := log_le_sub_one_of_pos (div_pos (by linarith : (0 : ℝ) < t) h1)
-  rw [log_div (by linarith) h1.ne'] at h
+  have h1 : 0 < t - 1 := by linarith only [ht]
+  have h := log_le_sub_one_of_pos (div_pos (by linarith only [ht] : (0 : ℝ) < t) h1)
+  rw [log_div (by linarith only [ht]) h1.ne'] at h
   have : t / (t - 1) - 1 ≤ 1 := by
-    rw [div_sub_one h1.ne', div_le_one h1]; linarith
-  linarith
+    rw [div_sub_one h1.ne', div_le_one h1]; linarith only [ht]
+  linarith only [h, this]
 
 theorem antitoneOn_sq_div_sq_sub_one : AntitoneOn (fun t : ℝ => t ^ 2 / (t - 1) ^ 2) (Ioi 1) := by
   intro u hu v hv huv
-  have hu1 : 0 < u - 1 := by linarith [hu.out]
-  have hv1 : 0 < v - 1 := by linarith [hv.out]
+  have hu1 : 0 < u - 1 := by linarith only [hu.out, hu]
+  have hv1 : 0 < v - 1 := by linarith only [hv.out, huv, hu1]
   have h : v / (v - 1) ≤ u / (u - 1) := by
-    rw [div_le_div_iff₀ hv1 hu1]; nlinarith
-  have h0 : 0 ≤ v / (v - 1) := div_nonneg (by linarith) hv1.le
+    rw [div_le_div_iff₀ hv1 hu1]; nlinarith only [huv]
+  have h0 : 0 ≤ v / (v - 1) := div_nonneg (by linarith only [huv, hu1]) hv1.le
   simp only
   rw [← div_pow, ← div_pow]
   exact pow_le_pow_left₀ h0 h 2
@@ -361,9 +361,9 @@ theorem antitoneOn_cor3Weight (r : ℕ) {L s b : ℝ} (hs : exp 32 ≤ s)
     refine antitoneOn_growth_mul
       (k := fun t => majG (r + 1) (t - 1 - 1) * (t - 1) / (t - 1 - 1) ^ 2)
       (ℓ := fun t => log (t - 1)) hs hb (fun t ht => ?_) (fun t _ => (majG_pos _ _).le)
-      (fun t ht => ?_) fun t ht => log_sub_one_ge (by linarith [hfacts t ht])
+      (fun t ht => ?_) fun t ht => log_sub_one_ge (by linarith only [hfacts t ht, hfacts, ht])
     · have h := hasDerivAt_majG_succ (r + 1) (t := t - 1)
-        (by linarith [five_add_neg_one_pow_div_le (r + 1), hfacts t ht])
+        (by linarith only [five_add_neg_one_pow_div_le (r + 1), hfacts t ht, hfacts, ht])
       rw [majG_add_two] at h
       exact h.comp_sub_const t 1
     · have h := majG_succ_mul_log_lt (r + 1) (t := t - 1) (by linarith [hfacts t ht])
@@ -372,8 +372,8 @@ theorem antitoneOn_cor3Weight (r : ℕ) {L s b : ℝ} (hs : exp 32 ≤ s)
   refine antitoneOn_mul_of_nonneg hψ
     (antitoneOn_sq_div_sq_sub_one.mono fun t ht => show (1 : ℝ) < t by linarith [hfacts t ht])
     (fun t ht => ?_) fun t _ => by positivity
-  have := lsx_nonneg L (by linarith [hfacts t ht] : (1 : ℝ) ≤ t)
-  exact mul_nonneg (rpow_pos_of_pos (by linarith) _).le (majG_pos _ _).le
+  have := lsx_nonneg L (by linarith only [hfacts t ht, hfacts, ht] : (1 : ℝ) ≤ t)
+  exact mul_nonneg (rpow_pos_of_pos (by linarith only [this]) _).le (majG_pos _ _).le
 
 /-! ### The size of `ξ` -/
 
@@ -384,7 +384,7 @@ theorem xi_sq_mul_log_pow_four_div_le {y : ℝ} (hy : 1 < y) (hℓ : 1 ≤ log (
   set ℓ := log (log (3 * y)) with hℓdef
   set L := log y with hL
   have hL0 : 0 < L := log_pos hy
-  have hℓ0 : 0 < ℓ := by linarith
+  have hℓ0 : 0 < ℓ := by linarith only [hℓ]
   have hP : 1 ≤ ℓ ^ (11 / 5 : ℝ) := one_le_rpow hℓ (by norm_num)
   have hξL : xi y ≤ L := by
     rw [xi]; exact div_le_self hL0.le hP
@@ -418,13 +418,13 @@ theorem tendsto_xi : Tendsto xi atTop atTop := by
     filter_upwards [hv.eventually ho, hv.eventually (eventually_ge_atTop (exp 1)),
       hv.eventually (eventually_ge_atTop (2 * log 3)), eventually_gt_atTop 1] with y h1 h2 h3 hy
     simp only [one_mul] at h1 h2 h3
-    have hv0 : 0 < log (3 * y) := by linarith [exp_pos 1]
+    have hv0 : 0 < log (3 * y) := by linarith only [exp_pos 1, h2]
     have hℓ : 1 ≤ log (log (3 * y)) := (le_log_iff_exp_le hv0).2 h2
-    rw [norm_of_nonneg (rpow_nonneg (by linarith) _),
+    rw [norm_of_nonneg (rpow_nonneg (by linarith only [hℓ]) _),
       norm_of_nonneg (rpow_nonneg hv0.le _)] at h1
     have hL : log y = log (3 * y) - log 3 := by
-      rw [log_mul (by norm_num) (by linarith)]; ring
-    have hP : 0 < log (log (3 * y)) ^ (11 / 5 : ℝ) := rpow_pos_of_pos (by linarith) _
+      rw [log_mul (by norm_num) (by linarith only [hy])]; ring
+    have hP : 0 < log (log (3 * y)) ^ (11 / 5 : ℝ) := rpow_pos_of_pos (by linarith only [hℓ]) _
     have hsq : 0 < log (3 * y) ^ (1 / 2 : ℝ) := rpow_pos_of_pos hv0 _
     have hsq2 : log (3 * y) ^ (1 / 2 : ℝ) * log (3 * y) ^ (1 / 2 : ℝ) = log (3 * y) := by
       rw [← rpow_add hv0]; norm_num
@@ -432,7 +432,7 @@ theorem tendsto_xi : Tendsto xi atTop atTop := by
     calc log (3 * y) ^ (1 / 2 : ℝ) / 2 * log (log (3 * y)) ^ (11 / 5 : ℝ)
         ≤ log (3 * y) ^ (1 / 2 : ℝ) / 2 * log (3 * y) ^ (1 / 2 : ℝ) := by gcongr
       _ = log (3 * y) / 2 := by rw [div_mul_eq_mul_div, hsq2]
-      _ ≤ log (3 * y) - log 3 := by linarith
+      _ ≤ log (3 * y) - log 3 := by linarith only [h3]
   exact tendsto_atTop_mono' atTop hbound
     (((tendsto_rpow_atTop (by norm_num : (0 : ℝ) < 1 / 2)).comp hv).atTop_div_const (by norm_num))
 
@@ -448,16 +448,16 @@ theorem exists_xi_large : ∃ y₀ : ℝ, ∀ y ≥ y₀, 1 < y ∧ exp 32 ≤ x
       (eventually_ge_atTop 1)).and (eventually_gt_atTop 1))))
   refine ⟨y₀, fun y hy => ?_⟩
   obtain ⟨h1, h2, h3, h4⟩ := hy₀ y hy
-  have hξ1 : 1 ≤ xi y := le_trans (by linarith [add_one_le_exp (32 : ℝ)]) h2
+  have hξ1 : 1 ≤ xi y := le_trans (by linarith only [add_one_le_exp (32 : ℝ)]) h2
   have hL0 : 0 < log y := log_pos h4
   refine ⟨h4, h2, ?_, ?_⟩
   · have := (xi_sq_mul_log_pow_four_div_le h4 h3 hξ1).trans h1
     rwa [div_le_iff₀ (by positivity), div_mul_eq_mul_div, one_mul] at this
-  · have hℓ0 : 0 < log (log (3 * y)) := by linarith
+  · have hℓ0 : 0 < log (log (3 * y)) := by linarith only [h3]
     have hP : 0 < log (log (3 * y)) ^ (11 / 5 : ℝ) := rpow_pos_of_pos hℓ0 _
-    rw [rpow_def_of_pos (by linarith), xi, mul_one_div, div_div_cancel₀ hL0.ne']
+    rw [rpow_def_of_pos (by linarith only [h4]), xi, mul_one_div, div_div_cancel₀ hL0.ne']
     have : 1 ≤ log (log (3 * y)) ^ (11 / 5 : ℝ) := one_le_rpow h3 (by norm_num)
-    calc (2 : ℝ) ≤ exp 1 := by linarith [exp_one_gt_d9]
+    calc (2 : ℝ) ≤ exp 1 := by linarith only [exp_one_gt_d9]
       _ ≤ _ := exp_le_exp.2 this
 
 end IwaniecLinearSieve
diff --git a/LeanPool/IwaniecLinearSieve/LinearSieve/LemmaSeven.lean b/LeanPool/IwaniecLinearSieve/LinearSieve/LemmaSeven.lean
index f3b8055e13..7622879bd6 100644
--- a/LeanPool/IwaniecLinearSieve/LinearSieve/LemmaSeven.lean
+++ b/LeanPool/IwaniecLinearSieve/LinearSieve/LemmaSeven.lean
@@ -42,54 +42,54 @@ theorem FSieve_three_add_lt_four : FSieve 3 + 3 < 4 := by
   have h := fSieve_four_add
   have h4 := fSieve_pos 4
   have hl := one_lt_log_three
-  have hK : 0 < FSieve 3 + 3 := by linarith [FSieve_nonneg 3]
-  nlinarith
+  have hK : 0 < FSieve 3 + 3 := by linarith only [FSieve_nonneg 3]
+  nlinarith only [h, h4, hl, hK]
 
 theorem MSieve_eq_on_Icc {s : ℝ} (hs : s ∈ Icc (2 : ℝ) 3) :
     MSieve s = (FSieve 3 + 3) * (1 - log (s - 1)) := by
-  rw [MSieve_of_le_three hs.2, fSieve_eq_on_Icc ⟨hs.1, by linarith [hs.2]⟩]; ring
+  rw [MSieve_of_le_three hs.2, fSieve_eq_on_Icc ⟨hs.1, by linarith only [hs.2, hs]⟩]; ring
 
 theorem MSieve_lt_four_mul_bigM_of_le_three {s : ℝ} (hs : s ∈ Icc (2 : ℝ) 3) :
     MSieve s < 4 * bigM s := by
   rw [MSieve_eq_on_Icc hs, bigM_eq hs.1 hs.2]
-  have h1 : 0 < s - 1 := by linarith [hs.1]
-  have hl0 : 0 ≤ log (s - 1) := log_nonneg (by linarith [hs.1])
+  have h1 : 0 < s - 1 := by linarith only [hs.1, hs]
+  have hl0 : 0 ≤ log (s - 1) := log_nonneg (by linarith only [hs.1, hs])
   have hl1 : log (s - 1) < 1 := by
-    rw [log_lt_iff_lt_exp h1]; linarith [hs.2, exp_one_gt_d9]
+    rw [log_lt_iff_lt_exp h1]; linarith only [hs.2, exp_one_gt_d9, hs]
   have hK := FSieve_three_add_lt_four
   have hinv : 0 < 1 / (s - 1) := by positivity
-  nlinarith
+  nlinarith only [hinv, hl1, hK]
 
 /-- `(s - 1) M(s) = ∫_{s-1}^s M` for `s ≥ 3` (this is `lemma5Q s = 0`). -/
 theorem sub_one_mul_MSieve {s : ℝ} (hs : 3 ≤ s) :
     (s - 1) * MSieve s = ∫ x in (s - 1)..s, MSieve x := by
   have h := lemma5Q_const hs
   rw [lemma5Q_three, lemma5Q] at h
-  linarith
+  linarith only [h]
 
 /-- `∫_{s-1}^s 𝔐 ≤ (s-1)² 𝔐(s)/s` for `s ≥ 3`, from (3.12). -/
 theorem integral_bigM_le {s : ℝ} (hs : 3 ≤ s) :
     ∫ x in (s - 1)..s, bigM x ≤ (s - 1) ^ 2 * bigM s / s := by
-  have hs0 : 0 < s := by linarith
+  have hs0 : 0 < s := by linarith only [hs]
   have hc : 0 < 1 - 1 / (2 * (s - 1) ^ 2) := by
     have : 1 / (2 * (s - 1) ^ 2) < 1 := by
       rw [div_lt_one (by nlinarith)]; nlinarith
-    linarith
+    linarith only [this]
   have hle : ∫ x in (s - 1)..s, (1 - 1 / (2 * (s - 1) ^ 2)) * bigM x ≤
       ∫ x in (s - 1)..s, (1 - 1 / (2 * x ^ 2)) * bigM x := by
-    refine intervalIntegral.integral_mono_on (by linarith)
+    refine intervalIntegral.integral_mono_on (by linarith only [])
       (continuous_bigM.intervalIntegrable _ _ |>.const_mul _)
-      ((continuousOn_weight_mul continuous_bigM (by linarith)).intervalIntegrable_of_Icc
-        (by linarith)) fun x hx => ?_
-    have hx1 : 0 < s - 1 := by linarith
+      ((continuousOn_weight_mul continuous_bigM (by linarith only [hs])).intervalIntegrable_of_Icc
+        (by linarith only [])) fun x hx => ?_
+    have hx1 : 0 < s - 1 := by linarith only [hs]
     have : 1 / (2 * x ^ 2) ≤ 1 / (2 * (s - 1) ^ 2) := by
       apply one_div_le_one_div_of_le (by positivity)
-      have := hx.1; nlinarith
-    exact mul_le_mul_of_nonneg_right (by linarith) (bigM_pos x).le
+      have := hx.1; nlinarith only [this, hs]
+    exact mul_le_mul_of_nonneg_right (by linarith only [this]) (bigM_pos x).le
   rw [intervalIntegral.integral_const_mul, ← bigM_integral_identity hs] at hle
   have hkey : (1 - 1 / (2 * (s - 1) ^ 2)) * ((s - 1) ^ 2 * bigM s / s) =
       ((s - 1) ^ 2 - 1 / 2) * bigM s / s := by
-    have h0 : s - 1 ≠ 0 := by linarith
+    have h0 : s - 1 ≠ 0 := by linarith only [hs]
     have : (1 - 1 / (2 * (s - 1) ^ 2)) * (s - 1) ^ 2 = (s - 1) ^ 2 - 1 / 2 := by
       field_simp
     calc _ = ((1 - 1 / (2 * (s - 1) ^ 2)) * (s - 1) ^ 2) * bigM s / s := by ring
@@ -106,7 +106,7 @@ theorem MSieve_lt_four_mul_bigM {s : ℝ} (hs : 2 ≤ s) : MSieve s < 4 * bigM s
     (fun x hx => (sub_pos.2 (MSieve_lt_four_mul_bigM_of_le_three hx)).le)
     (sub_pos.2 (MSieve_lt_four_mul_bigM_of_le_three ⟨by norm_num, le_rfl⟩)) ?_ s h3
   intro s hs3 hnn _
-  have hs0 : 0 < s := by linarith
+  have hs0 : 0 < s := by linarith only [hs3]
   have hint : ∫ x in (s - 1)..s, MSieve x ≤ ∫ x in (s - 1)..s, 4 * bigM x :=
     intervalIntegral.integral_mono_on (by linarith) (continuous_MSieve.intervalIntegrable _ _)
       ((continuous_bigM.intervalIntegrable _ _).const_mul _) fun x hx => by
@@ -114,15 +114,15 @@ theorem MSieve_lt_four_mul_bigM {s : ℝ} (hs : 2 ≤ s) : MSieve s < 4 * bigM s
   rw [intervalIntegral.integral_const_mul, ← sub_one_mul_MSieve hs3.le] at hint
   have hB := integral_bigM_le hs3.le
   have hMs := bigM_pos s
-  have h1 : (s - 1) * MSieve s ≤ 4 * ((s - 1) ^ 2 * bigM s / s) := by nlinarith
+  have h1 : (s - 1) * MSieve s ≤ 4 * ((s - 1) ^ 2 * bigM s / s) := by nlinarith only [hint, hB]
   have h2 : 4 * ((s - 1) ^ 2 * bigM s / s) < (s - 1) * (4 * bigM s) := by
     rw [div_eq_mul_inv]
-    have : (s - 1) * s⁻¹ < 1 := by rw [← div_eq_mul_inv, div_lt_one hs0]; linarith
-    have hs1 : 0 < s - 1 := by linarith
-    nlinarith [mul_pos hs1 hMs]
+    have : (s - 1) * s⁻¹ < 1 := by rw [← div_eq_mul_inv, div_lt_one hs0]; linarith only []
+    have hs1 : 0 < s - 1 := by linarith only [hs3]
+    nlinarith only [mul_pos hs1 hMs, this, hs1, hMs]
   have := lt_of_le_of_lt h1 h2
-  have hs1 : 0 < s - 1 := by linarith
-  nlinarith
+  have hs1 : 0 < s - 1 := by linarith only [hs3]
+  nlinarith only [hint, hB, h2, hs3]
 
 /-- [I71, Lemma 7]: `f_r(s) < M(s) ≤ 4 𝔐(s)` for `s ≥ 2`. -/
 theorem lemma7 (r : ℕ) {s : ℝ} (hs : 2 ≤ s) : fr r s < MSieve s ∧ MSieve s ≤ 4 * bigM s :=
@@ -135,16 +135,16 @@ theorem mainMaj_lt_four_mul_bigM (lower : Bool) {s : ℝ} (hs : 2 ≤ s) :
 /-- `M lower (s) ≤ 12 G lower' (s)` for `s ≥ 2`. -/
 theorem mainMaj_le_errMaj (lower lower' : Bool) {s : ℝ} (hs : 2 ≤ s) :
     mainMaj lower s ≤ 12 * errMaj lower' s := by
-  linarith [mainMaj_lt_four_mul_bigM lower hs, (errMaj_mem lower' s).1]
+  linarith only [mainMaj_lt_four_mul_bigM lower hs, (errMaj_mem lower' s).1, hs]
 
 /-- `M(s - 1) < 16 s² 𝔐(s)` for `s ≥ 3` (Lemmas 7 and 8). -/
 theorem MSieve_sub_one_lt {s : ℝ} (hs : 3 ≤ s) : MSieve (s - 1) < 16 * s ^ 2 * bigM s := by
-  have h1 := MSieve_lt_four_mul_bigM (s := s - 1) (by linarith)
+  have h1 := MSieve_lt_four_mul_bigM (s := s - 1) (by linarith only [hs])
   have h2 := bigM_sub_one_lt hs
-  linarith
+  linarith only [h1, h2]
 
 theorem bigM_three_gt : 3 / 2 < bigM 3 := by
-  rw [bigM_three]; linarith [log_two_lt_d9]
+  rw [bigM_three]; linarith only [log_two_lt_d9]
 
 /-- The comparison of Corollary 1's error term with the error majorant:
 `M lower (s - 1) ≤ 48 s² G lower' (s)` for `s ≥ 1` (any flags). -/
@@ -154,15 +154,15 @@ theorem mainMaj_sub_one_le (lower lower' : Bool) {s : ℝ} (hs : 1 ≤ s) :
   have hM := mainMaj_le_MSieve lower (s - 1)
   rcases le_total 3 s with h3 | h3
   · have := MSieve_sub_one_lt h3
-    nlinarith
-  · have h0 : MSieve (s - 1) ≤ MSieve 0 := MSieve_antitone (by linarith)
+    nlinarith only [hM, this, hG]
+  · have h0 : MSieve (s - 1) ≤ MSieve 0 := MSieve_antitone (by linarith only [hs])
     rw [MSieve_of_le_three (s := 0) (by norm_num), fSieve_of_le_two (by norm_num),
       fSieve_two] at h0
     have hK := FSieve_three_add_lt_four
     have hB : bigM 3 ≤ bigM s := bigM_antitone h3
     have := bigM_three_gt
-    have hs2 : 1 ≤ s ^ 2 := by nlinarith
-    have : 24 ≤ 48 * s ^ 2 * errMaj lower' s := by nlinarith
+    have hs2 : 1 ≤ s ^ 2 := by nlinarith only [hs]
+    have : 24 ≤ 48 * s ^ 2 * errMaj lower' s := by nlinarith only [hs2, hG, hB, this]
     linarith
 
 end IwaniecLinearSieve
diff --git a/LeanPool/IwaniecLinearSieve/LinearSieve/TheoremFive.lean b/LeanPool/IwaniecLinearSieve/LinearSieve/TheoremFive.lean
index ad809a1aaa..c5366b02ce 100644
--- a/LeanPool/IwaniecLinearSieve/LinearSieve/TheoremFive.lean
+++ b/LeanPool/IwaniecLinearSieve/LinearSieve/TheoremFive.lean
@@ -93,7 +93,7 @@ theorem inner_le {c₇ : ℝ} {r : ℕ} (ih : Bound c₇ r) {lower : Bool} {y s
         errMaj (!lower) (log y / log p - 1) / (p * log (y / p) ^ 2)) := by
   obtain ⟨hp1, hpy, hsp⟩ := rosserPrimes_facts hy hs hp
   have hp0 : (0 : ℝ) < p := by exact_mod_cast (zero_lt_one.trans hp1)
-  have hyp : 1 < y / p := by rw [lt_div_iff₀ hp0]; linarith
+  have hyp : 1 < y / p := by rw [lt_div_iff₀ hp0]; linarith only [hpy]
   have h := ih (!lower) (y / p) (log y / log p - 1) hyp hsp (sub_one_le_xi_div hy hp1 hpy ht)
   rw [rpow_inv_sub_one_eq hp1 hpy] at h
   refine h.trans (le_of_eq ?_)
@@ -126,16 +126,16 @@ theorem sum_inner_le {c₇ : ℝ} (hc₇ : 0 ≤ c₇) {r : ℕ} (ih : Bound c
       have hlp : 0 < log (p : ℝ) := log_pos hp1'
       have ht : log y / log p ≤ xi y := by
         have hlog := log_le_log (by positivity) hwp
-        rw [hw, log_rpow_one_div (by linarith)] at hlog
-        rw [div_le_iff₀ (by linarith)] at hlog
+        rw [hw, log_rpow_one_div (by linarith only [hy])] at hlog
+        rw [div_le_iff₀ (by linarith only [hξ])] at hlog
         rw [div_le_iff₀ hlp]
         nlinarith only [hlog, hlp]
       exact inner_le ih hy hs hpP ht
     _ ≤ ∑ p ∈ P.filter (fun p : ℕ => y ^ (1 / xi y) ≤ p), c₇ * φ * y * term p := by
       refine sum_le_sum_of_subset_of_nonneg (fun p hp => ?_) fun p hp _ => ?_
       · obtain ⟨hpP, hwp⟩ := mem_filter.1 hp
-        exact mem_filter.2 ⟨hpP, (rpow_one_div_le_rpow_one_div hy.le (by linarith)
-          (by linarith)).trans hwp⟩
+        exact mem_filter.2 ⟨hpP, (rpow_one_div_le_rpow_one_div hy.le (by linarith only [hξ])
+          (by linarith only [])).trans hwp⟩
       · obtain ⟨-, -, hsp⟩ := rosserPrimes_facts hy hs (mem_filter.1 hp).1
         have := delta_pos (one_le_of_sMin_le hsp) (y / p)
         have := errMaj_pos (!lower) (log y / log p - 1)
@@ -158,7 +158,7 @@ theorem gap_le {r : ℕ} {L ℓ : ℝ} (hL : 0 < L) (hℓ : 0 < ℓ) (h : (r : 
   rw [e, le_div_iff₀ (by positivity)]
   rw [le_div_iff₀ hℓ] at h
   have h2 : ((r + 3) * ℓ) ^ 2 ≤ (2 * L) ^ 2 := by gcongr
-  have : (r + 2) * (r + 3) * ℓ ^ 2 ≤ 4 * L ^ 2 := by nlinarith [sq_nonneg ℓ]
+  have : (r + 2) * (r + 3) * ℓ ^ 2 ≤ 4 * L ^ 2 := by nlinarith only [sq_nonneg ℓ, h2]
   rw [show 2 * (ℓ ^ 2 / (8 * L ^ 2)) * ((r + 2) * (r + 3)) =
     (r + 2) * (r + 3) * ℓ ^ 2 / (4 * L ^ 2) by field_simp; ring]
   rw [div_le_one (by positivity)]
@@ -170,10 +170,10 @@ theorem close_step {c₇ φ φ' Q X ε : ℝ} (hc₇ : 1 ≤ c₇) (hQ : 0 ≤ Q
     Q * ε + c₇ * φ * Q * (1 + X) ≤ c₇ * φ' * Q := by
   have hε : 0 ≤ ε := hX0.trans hX
   have h1 : φ * X ≤ ε := (mul_le_of_le_one_left hX0 hφ1).trans hX
-  have h2 : ε ≤ φ' - φ - φ * X := by linarith
-  have h3 : c₇ * ε ≤ c₇ * (φ' - φ - φ * X) := mul_le_mul_of_nonneg_left h2 (by linarith)
+  have h2 : ε ≤ φ' - φ - φ * X := by linarith only [hgap, h1]
+  have h3 : c₇ * ε ≤ c₇ * (φ' - φ - φ * X) := mul_le_mul_of_nonneg_left h2 (by linarith only [hc₇])
   have h4 : ε ≤ c₇ * ε := le_mul_of_one_le_left hε hc₇
-  nlinarith [mul_le_mul_of_nonneg_left (h4.trans h3) hQ]
+  nlinarith only [mul_le_mul_of_nonneg_left (h4.trans h3) hQ, h4, h3, hQ]
 
 /-- The main case of the inductive step ([I71, p. 27]): `y` large and
 `r + 3 ≤ 2 log y / log log y`. The hypotheses are the large-`y` facts: the crude count
@@ -209,7 +209,7 @@ theorem step_main {c₇ C : ℝ} (hc₇ : 1 ≤ c₇) {r : ℕ} (ih : Bound c₇
   have hGs := errMaj_pos lower s
   have hQ0 : 0 ≤ Q := by positivity
   have hφ0 : 0 ≤ φ := by positivity
-  have hφ1 : φ ≤ 1 := by rw [hφ, div_le_one (by positivity)]; linarith
+  have hφ1 : φ ≤ 1 := by rw [hφ, div_le_one (by positivity)]; linarith only []
   have hE0 : 0 ≤ E := by have := pntE_pos (y ^ (1 / xi y)); positivity
   have hs₀ : (1 : ℝ) ≤ exp 32 := one_le_exp (by norm_num)
   have hδ₀ := one_le_delta hs₀ y
@@ -283,7 +283,7 @@ theorem small_le {c₈ c₇ : ℝ}
   have hGm0 : 0 < Gm := lt_min (errMaj_pos _ _) (errMaj_pos _ _)
   have hs1 := one_le_of_sMin_le hs
   have hL0 : 0 < log y := log_pos hy
-  have hLc : log y ≤ log c₈ := log_le_log (by linarith) hyc.le
+  have hLc : log y ≤ log c₈ := log_le_log (by linarith only [hy]) hyc.le
   have hG : Gm ≤ errMaj lower s := by
     have h1 : errMaj lower Ξ ≤ errMaj lower s :=
       errMaj_antitone lower (hsξ.trans (xi_le_of_lt hy hyc))
@@ -292,7 +292,7 @@ theorem small_le {c₈ c₇ : ℝ}
     · exact (min_le_left _ _).trans h1
   have hδ := one_le_delta hs1 y
   have hφ : (1 : ℝ) / 2 ≤ ((r : ℝ) + 1) / (r + 2) := by
-    rw [div_le_div_iff₀ (by norm_num) (by positivity)]; linarith [r.cast_nonneg (α := ℝ)]
+    rw [div_le_div_iff₀ (by norm_num) (by positivity)]; linarith only [r.cast_nonneg (α := ℝ)]
   have hc₇' : 2 * log c₈ ^ 2 ≤ c₇ * Gm := by rwa [div_le_iff₀ hGm0] at hc₇
   have hcount : (#{d ∈ rosserSet lower y (y ^ (1 / s)) | #d.primeFactors ≤ r} : ℝ) ≤ y :=
     (Nat.cast_le.2 (card_filter_le _ _)).trans (card_rosserSet_le hy hs1)
@@ -300,15 +300,15 @@ theorem small_le {c₈ c₇ : ℝ}
   rw [le_div_iff₀ (by positivity)]
   have hc₇0 : 0 ≤ c₇ := by
     have := mul_nonneg (by norm_num : (0 : ℝ) ≤ 2) (sq_nonneg (log c₈))
-    nlinarith
+    nlinarith only [hc₇', hGm0]
   have key : log y ^ 2 ≤ c₇ * (((r : ℝ) + 1) / (r + 2)) * delta s y * errMaj lower s := by
     have h1 : log y ^ 2 ≤ log c₈ ^ 2 := by gcongr
     have h2 : c₇ * Gm / 2 ≤ c₇ * (((r : ℝ) + 1) / (r + 2)) * delta s y * errMaj lower s := by
       have : c₇ * Gm / 2 = c₇ * (1 / 2) * 1 * Gm := by ring
       rw [this]
       gcongr
-    linarith
-  nlinarith
+    linarith only [hc₇', h1, h2]
+  nlinarith only [key, hy]
 
 /-! ### Theorem 5 -/
 theorem exists_bound : ∃ c₇ : ℝ, 1 ≤ c₇ ∧ ∀ r, Bound c₇ r := by
@@ -336,28 +336,28 @@ theorem exists_bound : ∃ c₇ : ℝ, 1 ≤ c₇ ∧ ∀ r, Bound c₇ r := by
     obtain ⟨hy3, hsmall, -, -, -, -⟩ := hlarge y hyc
     have hL1 : 1 ≤ log y := by
       have := log_le_log (by norm_num) hy3
-      linarith [one_lt_log_three]
+      linarith only [one_lt_log_three, this]
     have h := hsmall lower s hs hsξ
     rw [card_filter_rosserSet_zero]
     have hN : (0 : ℝ) ≤ #(rosserSet lower y (y ^ (1 / (xi y - 1)))) := Nat.cast_nonneg _
     have hQ : 0 ≤ delta s y * errMaj lower s * y := by
       have := delta_pos (one_le_of_sMin_le hs) y
       have := errMaj_pos lower s
-      have : 0 < y := by linarith
+      have : 0 < y := by linarith only [hy3]
       positivity
     push_cast
     have : delta s y * errMaj lower s * y / (8 * log y ^ 4) ≤
         c₇ * ((0 + 1) / (0 + 2)) * delta s y * errMaj lower s * y / log y ^ 2 := by
       rw [div_le_div_iff₀ (by positivity) (by positivity)]
       have h4 : log y ^ 2 ≤ 4 * log y ^ 4 := by
-        have h1 : 1 ≤ log y ^ 2 := by nlinarith
-        nlinarith [mul_le_mul_of_nonneg_left h1 (sq_nonneg (log y))]
+        have h1 : 1 ≤ log y ^ 2 := by nlinarith only [hL1]
+        nlinarith only [mul_le_mul_of_nonneg_left h1 (sq_nonneg (log y)), h1]
       have h5 : delta s y * errMaj lower s * y * log y ^ 2 ≤
           delta s y * errMaj lower s * y * (4 * log y ^ 4) :=
         mul_le_mul_of_nonneg_left h4 hQ
-      nlinarith [mul_le_mul_of_nonneg_right hc₇1 (mul_nonneg hQ (pow_pos (by linarith :
+      nlinarith [mul_le_mul_of_nonneg_right hc₇1 (mul_nonneg hQ (pow_pos (by linarith only [hL1] :
         (0 : ℝ) < log y) 4).le)]
-    linarith
+    linarith only [h, this]
   | succ r ih =>
     intro lower y s hy hs hsξ
     rcases lt_or_ge y c₈ with hyc | hyc
@@ -372,11 +372,11 @@ theorem exists_bound : ∃ c₇ : ℝ, 1 ≤ c₇ ∧ ∀ r, Bound c₇ r := by
       have hQ : 0 ≤ delta s y * errMaj lower s * y / log y ^ 2 := by
         have := delta_pos (one_le_of_sMin_le hs) y
         have := errMaj_pos lower s
-        have : 0 < y := by linarith
+        have : 0 < y := by linarith only [hy]
         positivity
       have hφ : ((r : ℝ) + 1) / (r + 2) ≤ (((r + 1 : ℕ) : ℝ) + 1) / (((r + 1 : ℕ) : ℝ) + 2) := by
         push_cast
-        rw [div_le_div_iff₀ (by positivity) (by positivity)]; nlinarith
+        rw [div_le_div_iff₀ (by positivity) (by positivity)]; nlinarith only []
       calc c₇ * ((r + 1) / (r + 2)) * delta s y * errMaj lower s * y / log y ^ 2
           = c₇ * ((r + 1) / (r + 2)) * (delta s y * errMaj lower s * y / log y ^ 2) := by ring
         _ ≤ c₇ * ((((r + 1 : ℕ) : ℝ) + 1) / (((r + 1 : ℕ) : ℝ) + 2)) *
@@ -386,7 +386,7 @@ theorem exists_bound : ∃ c₇ : ℝ, 1 ≤ c₇ ∧ ∀ r, Bound c₇ r := by
       obtain ⟨-, hξ32, -, -⟩ := hxi
       obtain ⟨hsl, hℓ⟩ := hslack
       have hmain : (r : ℝ) + 3 ≤ 2 * log y / log (log y) := by
-        push_cast at hdeep; linarith
+        push_cast at hdeep; linarith only [hdeep]
       exact step_main hc₇1 ih hy hs hξ32 (hsmall lower s hs hsξ)
         (hcor lower s hs) hC0 hsl hℓ hmain
 
@@ -405,27 +405,27 @@ theorem theorem5 : ∃ c₇ : ℝ, 0 ≤ c₇ ∧ ∀ (r : ℕ) (lower : Bool) (
     (#{d ∈ rosserSet lower y (y ^ (1 / s)) | #d.primeFactors ≤ r} : ℝ) ≤
       c₇ * ((r + 1) / (r + 2)) * delta s y * errMaj lower s * y / Real.log y ^ 2 := by
   obtain ⟨c₇, hc₇, h⟩ := exists_bound
-  exact ⟨c₇, by linarith, fun r => h r⟩
+  exact ⟨c₇, by linarith only [hc₇], fun r => h r⟩
 
 /-- `δ(s, y) ≤ (1 + 9 log⁵ 3)^{15}` for `1 ≤ s ≤ 3` and `log y ≥ 1`. -/
 theorem delta_le_of_le_three {s y : ℝ} (hs1 : 1 ≤ s) (hs3 : s ≤ 3) (hy : 1 ≤ Real.log y) :
     delta s y ≤ (1 + 9 * Real.log 3 ^ 5) ^ (15 : ℝ) := by
   have hl0 : 0 ≤ Real.log s := Real.log_nonneg hs1
-  have hl3 : Real.log s ≤ Real.log 3 := Real.log_le_log (by linarith) hs3
+  have hl3 : Real.log s ≤ Real.log 3 := Real.log_le_log (by linarith only [hs1]) hs3
   have hx : s ^ 2 * Real.log s ^ 5 / Real.log y ^ 2 ≤ 9 * Real.log 3 ^ 5 := by
     rw [div_le_iff₀ (by positivity)]
-    have h1 : s ^ 2 ≤ 9 := by nlinarith
+    have h1 : s ^ 2 ≤ 9 := by nlinarith only [hs3, hs1]
     have h2 : Real.log s ^ 5 ≤ Real.log 3 ^ 5 := by gcongr
-    have h3 : 1 ≤ Real.log y ^ 2 := by nlinarith
+    have h3 : 1 ≤ Real.log y ^ 2 := by nlinarith only [hy]
     have h4 : s ^ 2 * Real.log s ^ 5 ≤ 9 * Real.log 3 ^ 5 :=
       mul_le_mul h1 h2 (by positivity) (by norm_num)
     have h5 : 0 ≤ Real.log 3 ^ 5 := by positivity
-    nlinarith
+    nlinarith only [h4, h3, h5]
   have hx0 : 0 ≤ s ^ 2 * Real.log s ^ 5 / Real.log y ^ 2 := by positivity
   rw [delta]
   calc (1 + s ^ 2 * Real.log s ^ 5 / Real.log y ^ 2) ^ (5 * s)
       ≤ (1 + 9 * Real.log 3 ^ 5) ^ (5 * s) := Real.rpow_le_rpow (by linarith) (by linarith)
-        (by linarith)
+        (by linarith only [hs1])
     _ ≤ (1 + 9 * Real.log 3 ^ 5) ^ (15 : ℝ) :=
         Real.rpow_le_rpow_of_exponent_le (by linarith) (by linarith)
 
@@ -441,8 +441,8 @@ theorem theorem5_card_rosserSet_le : ∃ K y₀ : ℝ, ∀ y ≥ y₀, ∀ s ∈
   have hy3 : 3 ≤ y := le_of_max_le_right hy
   have hL1 : 1 ≤ Real.log y := by
     have := Real.log_le_log (by norm_num) hy3
-    linarith [one_lt_log_three]
-  have hsξ : s ≤ xi y := hs.2.trans (by linarith [Real.add_one_le_exp (32 : ℝ)])
+    linarith only [one_lt_log_three, this]
+  have hsξ : s ≤ xi y := hs.2.trans (by linarith only [Real.add_one_le_exp (32 : ℝ), hξ])
   set z := y ^ (1 / s)
   have hall : (rosserSet true y z).filter (fun d => #d.primeFactors ≤ #(primesLT z)) =
       rosserSet true y z :=
@@ -450,12 +450,12 @@ theorem theorem5_card_rosserSet_le : ∃ K y₀ : ℝ, ∀ y ≥ y₀, ∀ s ∈
   have h := h5 #(primesLT z) true y s hy1 hs.1 hsξ
   rw [hall] at h
   refine h.trans ?_
-  have hδ := delta_le_of_le_three (by linarith [hs.1]) hs.2 hL1 (y := y)
-  have hδ0 := delta_pos (by linarith [hs.1] : (1 : ℝ) ≤ s) y
+  have hδ := delta_le_of_le_three (by linarith only [hs.1, hs]) hs.2 hL1 (y := y)
+  have hδ0 := delta_pos (by linarith only [hs.1, hs] : (1 : ℝ) ≤ s) y
   have hG := errMaj_le_two true s
   have hG0 := errMaj_pos true s
   have hφ : ((#(primesLT z) : ℕ) + 1 : ℝ) / ((#(primesLT z) : ℕ) + 2) ≤ 1 := by
-    rw [div_le_one (by positivity)]; linarith
+    rw [div_le_one (by positivity)]; linarith only []
   have hφ0 : (0 : ℝ) ≤ ((#(primesLT z) : ℕ) + 1 : ℝ) / ((#(primesLT z) : ℕ) + 2) := by positivity
   have hyL : 0 ≤ y / Real.log y ^ 2 := by positivity
   calc c₇ * ((#(primesLT z) + 1) / (#(primesLT z) + 2)) * delta s y * errMaj true s * y /
diff --git a/LeanPool/IwaniecLinearSieve/LinearSieve/TheoremFiveAux.lean b/LeanPool/IwaniecLinearSieve/LinearSieve/TheoremFiveAux.lean
index 014377dc04..72dcfc9eed 100644
--- a/LeanPool/IwaniecLinearSieve/LinearSieve/TheoremFiveAux.lean
+++ b/LeanPool/IwaniecLinearSieve/LinearSieve/TheoremFiveAux.lean
@@ -46,25 +46,25 @@ theorem eventually_add_mul_log_le (α β : ℝ) : ∀ᶠ x in atTop, α + β * l
   filter_upwards [isLittleO_log_id_atTop.bound hε, eventually_ge_atTop (2 * α),
     eventually_ge_atTop 1] with x hx hxα hx1
   have hl : 0 ≤ log x := log_nonneg hx1
-  rw [norm_of_nonneg hl, id, norm_of_nonneg (by linarith)] at hx
+  rw [norm_of_nonneg hl, id, norm_of_nonneg (by linarith only [hx1])] at hx
   have h1 : β * log x ≤ |β| * log x := mul_le_mul_of_nonneg_right (le_abs_self β) hl
   have h2 : |β| * log x ≤ x / 2 := by
     have hq : |β| / (|β| + 1) ≤ 1 := by
-      rw [div_le_one (by positivity)]; linarith
+      rw [div_le_one (by positivity)]; linarith only []
     calc |β| * log x ≤ |β| * (1 / (2 * (|β| + 1)) * x) := by gcongr
       _ = |β| / (|β| + 1) * (x / 2) := by field_simp
       _ ≤ 1 * (x / 2) := by gcongr
       _ = x / 2 := one_mul _
-  linarith
+  linarith only [hxα, h1, h2]
 
 theorem one_lt_log_three : 1 < log 3 := by
   rw [lt_log_iff_exp_lt (by norm_num)]
-  linarith [exp_one_lt_d9]
+  linarith only [exp_one_lt_d9]
 
 theorem lam_pos {y : ℝ} (hy : 1 < y) : 0 < lam y := by
-  have h3 : log 3 + log y = log (3 * y) := (log_mul (by norm_num) (by linarith)).symm
+  have h3 : log 3 + log y = log (3 * y) := (log_mul (by norm_num) (by linarith only [hy])).symm
   have := log_pos hy
-  exact log_pos (by linarith [one_lt_log_three])
+  exact log_pos (by linarith only [one_lt_log_three, h3, this])
 
 /-- `log ξ = log L - (11/5) log λ`. -/
 theorem log_xi_eq {y : ℝ} (hy : 1 < y) : log (xi y) = log (log y) - 11 / 5 * log (lam y) := by
@@ -87,40 +87,40 @@ theorem eventually_scalar (c : ℝ) (hc : 100 ≤ c) : ∀ᶠ y in atTop,
       (eventually_ge_atTop c),
     tendsto_lam.eventually (eventually_add_mul_log_le (c + 10) 8)] with y hy3 h1 h2 h3 h4
   simp only [Function.comp] at h2 h3
-  have hy : 1 < y := by linarith
+  have hy : 1 < y := by linarith only [hy3]
   have hL : 1 < log y := by
-    have := log_le_log (by norm_num) hy3; linarith [one_lt_log_three]
-  have hL0 : 0 < log y := by linarith
+    have := log_le_log (by norm_num) hy3; linarith only [one_lt_log_three, this]
+  have hL0 : 0 < log y := by linarith only [hL]
   have hlam := lam_pos hy
-  have h3y : log (3 * y) = log 3 + log y := log_mul (by norm_num) (by linarith)
-  have ha : 0 ≤ log (lam y) := by linarith
+  have h3y : log (3 * y) = log 3 + log y := log_mul (by norm_num) (by linarith only [hy3])
+  have ha : 0 ≤ log (lam y) := by linarith only [hc, h2]
   -- `log L ≤ λ ≤ log L + 1`
   have hℓ1 : log (log y) ≤ lam y := by
-    unfold lam; exact log_le_log hL0 (by rw [h3y]; linarith [one_lt_log_three])
+    unfold lam; exact log_le_log hL0 (by rw [h3y]; linarith only [one_lt_log_three])
   have hℓ2 : lam y - 1 ≤ log (log y) := by
     have hle : log (3 * y) ≤ exp 1 * log y := by
       have : log 3 ≤ log y := log_le_log (by norm_num) hy3
-      have : 2 ≤ exp 1 := by linarith [add_one_le_exp (1 : ℝ)]
+      have : 2 ≤ exp 1 := by linarith only [add_one_le_exp (1 : ℝ)]
       rw [h3y]; nlinarith
-    have := log_le_log (by rw [h3y]; linarith [one_lt_log_three]) hle
+    have := log_le_log (by rw [h3y]; linarith only [one_lt_log_three, hL]) hle
     rw [log_mul (exp_pos 1).ne' hL0.ne', log_exp] at this
-    unfold lam; linarith
+    unfold lam; linarith only [this]
   have hlogξ := log_xi_eq hy
   have hξ := xi_pos hy
-  have hl2 : log 2 ≤ 1 := by linarith [log_le_sub_one_of_pos (by norm_num : (0 : ℝ) < 2)]
-  have hl16 : log 16 ≤ 15 := by linarith [log_le_sub_one_of_pos (by norm_num : (0 : ℝ) < 16)]
-  have hl24 : log 24 ≤ 23 := by linarith [log_le_sub_one_of_pos (by norm_num : (0 : ℝ) < 24)]
+  have hl2 : log 2 ≤ 1 := by linarith only [log_le_sub_one_of_pos (by norm_num : (0 : ℝ) < 2)]
+  have hl16 : log 16 ≤ 15 := by linarith only [log_le_sub_one_of_pos (by norm_num : (0 : ℝ) < 16)]
+  have hl24 : log 24 ≤ 23 := by linarith only [log_le_sub_one_of_pos (by norm_num : (0 : ℝ) < 24)]
   refine ⟨hy3, h2, h3, h1, hℓ1, hℓ2, ?_, ?_, ?_, ?_, ?_⟩
   · rw [← log_le_log_iff (by positivity) hξ, log_mul (by norm_num) hlam.ne']
-    linarith
+    linarith only [hc, h2, h4, hℓ2, hlogξ, hl24]
   · have h := (log_le_log_iff (by positivity) hL0).1 (by
       rw [log_mul (by norm_num) (by positivity), log_pow]; push_cast
-      linarith : log (16 * lam y ^ 2) ≤ log (log y))
+      linarith only [hc, h2, h4, hℓ2, hl16] : log (16 * lam y ^ 2) ≤ log (log y))
     exact h
   · rw [log_div hξ.ne' (by norm_num)]
-    linarith
-  · linarith
-  · linarith
+    linarith only [hc, h2, h4, hℓ2, hlogξ, hl2]
+  · linarith only [hc, h2, h4, hℓ2, hlogξ]
+  · linarith only [hc, h2, hℓ1, hlogξ]
 
 /-! ### The crude part ([I71, p. 27]) -/
 
@@ -132,47 +132,52 @@ theorem crude_exponent_le {L ℓ lam ξ a : ℝ} (hL : 0 < L) (hℓ : ℓ = log
     (h16 : 16 * lam ^ 2 ≤ L) (hlogξ : log ξ ≤ lam) :
     8 * L ^ 4 * (1 + exp (L + 2 * ξ - L / lam) + 2 * exp (L - ξ * log ξ + ξ * a + 5 * ξ)) ≤
       exp (L - ξ * log ξ + 3 / 2 * ξ * a) := by
-  have hlam0 : 0 < lam := by linarith
-  have hξ0 : 0 < ξ := by linarith
+  have hlam0 : 0 < lam := by linarith only [hlam]
+  have hξ0 : 0 < ξ := by linarith only [hlam, h24]
   have h8 : 8 * L ^ 4 = exp (log 8 + 4 * ℓ) := by
     rw [exp_add, exp_log (by norm_num), hℓ,
       show (4 : ℝ) * log L = log (L ^ 4) by rw [log_pow]; norm_num, exp_log (by positivity)]
-  have hl3 : log 3 ≤ 2 := by linarith [log_le_sub_one_of_pos (by norm_num : (0 : ℝ) < 3)]
-  have hl8 : log 8 ≤ 7 := by linarith [log_le_sub_one_of_pos (by norm_num : (0 : ℝ) < 8)]
-  have hl2 : log 2 ≤ 1 := by linarith [log_le_sub_one_of_pos (by norm_num : (0 : ℝ) < 2)]
+  have hl3 : log 3 ≤ 2 := by linarith only [log_le_sub_one_of_pos (by norm_num : (0 : ℝ) < 3)]
+  have hl8 : log 8 ≤ 7 := by linarith only [log_le_sub_one_of_pos (by norm_num : (0 : ℝ) < 8)]
+  have hl2 : log 2 ≤ 1 := by linarith only [log_le_sub_one_of_pos (by norm_num : (0 : ℝ) < 2)]
   set T := L - ξ * log ξ + 3 / 2 * ξ * a with hT
   have h3 : exp T = 3 * exp (T - log 3) := by
     rw [exp_sub, exp_log (by norm_num)]; field_simp
   -- `ξ log ξ + 2 ξ ≤ L / (2λ)` and `8 + 4λ ≤ L / (2λ)`
   have hLl : ξ * log ξ + 2 * ξ ≤ L / (2 * lam) := by
     rw [le_div_iff₀ (by positivity)]
-    have : ξ * log ξ ≤ ξ * lam := mul_le_mul_of_nonneg_left hlogξ hξ0.le
-    nlinarith
+    calc
+      (ξ * log ξ + 2 * ξ) * (2 * lam) = 2 * ξ * lam * (log ξ + 2) := by ring
+      _ ≤ 2 * ξ * lam * (2 * lam) :=
+        mul_le_mul_of_nonneg_left (by linarith only [hlogξ, hlam]) (by positivity)
+      _ = 4 * (ξ * lam ^ 2) := by ring
+      _ ≤ L := hxilam
   have hLm : 8 + 4 * lam ≤ L / (2 * lam) := by
-    rw [le_div_iff₀ (by positivity)]; nlinarith
-  have hLlam : L / lam ≤ L := div_le_self hL.le (by linarith)
+    rw [le_div_iff₀ (by positivity)]
+    nlinarith only [h16, hlam]
+  have hLlam : L / lam ≤ L := div_le_self hL.le (by linarith only [hlam])
   have hξa : 0 ≤ ξ * a := by positivity
   have e1 : 8 * L ^ 4 ≤ exp (T - log 3) := by
     rw [h8, exp_le_exp, hT]
     have : L / lam = 2 * (L / (2 * lam)) := by field_simp
-    nlinarith
+    nlinarith only [this, hLl, hLm, hLlam, hl3, hl8, hℓlam, hξa, h24, hlam]
   have e2 : 8 * L ^ 4 * exp (L + 2 * ξ - L / lam) ≤ exp (T - log 3) := by
     rw [h8, ← exp_add, exp_le_exp, hT]
     have : L / lam = 2 * (L / (2 * lam)) := by field_simp
-    nlinarith
+    nlinarith only [this, hLl, hLm, hl3, hl8, hℓlam, ha, hξ0, h24, hlam]
   have e3 : 8 * L ^ 4 * (2 * exp (L - ξ * log ξ + ξ * a + 5 * ξ)) ≤ exp (T - log 3) := by
     rw [h8, mul_left_comm, ← exp_add, ← exp_log (by norm_num : (0 : ℝ) < 2), ← exp_add,
       exp_le_exp, hT]
-    have : 6 * ξ ≤ 1 / 2 * ξ * a := by nlinarith
-    nlinarith
+    have : 6 * ξ ≤ 1 / 2 * ξ * a := by nlinarith only [ha, hξ0]
+    nlinarith only [this, hl2, hl3, hl8, hℓlam, h24, hlam]
   rw [h3]
-  nlinarith
+  nlinarith only [e1, e2, e3]
 
 /-! ### The slack ([I71, (4.2), (4.6)]) -/
 
 /-- `(1 + x)^p ≤ e^{p x}` for `x ≥ 0`, `p ≥ 0`. -/
 theorem one_add_rpow_le_exp {x p : ℝ} (hx : 0 ≤ x) (hp : 0 ≤ p) : (1 + x) ^ p ≤ exp (p * x) := by
-  rw [rpow_def_of_pos (by linarith), exp_le_exp, mul_comm]
+  rw [rpow_def_of_pos (by linarith only [hx]), exp_le_exp, mul_comm]
   gcongr
   linarith [log_le_sub_one_of_pos (by linarith : (0 : ℝ) < 1 + x)]
 
diff --git a/LeanPool/IwaniecLinearSieve/LinearSieve/TheoremFiveCount.lean b/LeanPool/IwaniecLinearSieve/LinearSieve/TheoremFiveCount.lean
index 1ad0535ed5..1e465fab6a 100644
--- a/LeanPool/IwaniecLinearSieve/LinearSieve/TheoremFiveCount.lean
+++ b/LeanPool/IwaniecLinearSieve/LinearSieve/TheoremFiveCount.lean
@@ -14,7 +14,6 @@ import LeanPool.IwaniecLinearSieve.LinearSieve.Crude
 import LeanPool.IwaniecLinearSieve.LinearSieve.Depth
 import LeanPool.IwaniecLinearSieve.LinearSieve.LemmaEleven
 import LeanPool.IwaniecLinearSieve.SieveMajorants.Lemmas
-import Mathlib.Algebra.Order.Star.Real
 import Mathlib.Analysis.Complex.ExponentialBounds
 import Mathlib.Data.Finset.Slice
 import Mathlib.Tactic.Polynomial.Basic
@@ -72,10 +71,10 @@ theorem card_rosserSet_le (hy : 1 < y) (hs : 1 ≤ s) :
     exact mem_Ico.2 ⟨pos_of_mem_rosserSet hd, Nat.lt_ceil.2 this⟩
   have h := card_le_card hsub
   rw [Nat.card_Ico] at h
-  have hc := Nat.ceil_lt_add_one (by linarith : (0 : ℝ) ≤ y)
+  have hc := Nat.ceil_lt_add_one (by linarith only [hy] : (0 : ℝ) ≤ y)
   have : ((⌈y⌉₊ - 1 : ℕ) : ℝ) ≤ y := by
     rw [Nat.cast_sub (Nat.one_le_iff_ne_zero.2 (by positivity))]
-    push_cast; linarith
+    push_cast; linarith only [hc]
   exact (Nat.cast_le.2 h).trans this
 
 /-- Lemma 17 split at `w`: the primes `p < w` contribute (with the `1`) at most
@@ -105,7 +104,7 @@ theorem card_filter_succ_le (n : ℕ) (lower : Bool) (y z w : ℝ) :
       (rosserPrimes lower y z).filter (fun p : ℕ ↦ w ≤ p) :=
     filter_congr fun p _ ↦ not_lt
   rw [h2]
-  linarith
+  linarith only [h1]
 
 theorem card_primesLT_le {w : ℝ} (hw : 0 ≤ w) : (#(primesLT w) : ℝ) ≤ w + 1 := by
   have h : #(primesLT w) ≤ ⌈w⌉₊ := by
@@ -137,7 +136,7 @@ theorem card_filter_le_le (lower : Bool) (y : ℝ) {w : ℝ} (hw : 1 ≤ w) (K :
         calc (#(primesLT w) : ℝ) ^ l / l.factorial ≤ (#(primesLT w) : ℝ) ^ l :=
               div_le_self (by positivity) hf
           _ ≤ (2 * w) ^ l := by gcongr
-          _ ≤ (2 * w) ^ K := pow_le_pow_right₀ (by linarith) hlK
+          _ ≤ (2 * w) ^ K := pow_le_pow_right₀ (by linarith only [hw]) hlK
     _ = (K + 1) * (2 * w) ^ K := by simp
 
 /-- The cutoff `u = ξ(1 - 2/λ)` leaves a saving of `1/λ` in the exponent of `w`. -/
@@ -213,8 +212,7 @@ theorem card_rosserSet_rpow_le (hy : 1 < y) (hw : 2 ≤ y ^ (1 / (xi y - 1)))
   · -- Few prime factors: bound the three factors `K + 1`, `2^u`, and `w^u`.
     refine (card_filter_le_le lower y (by linarith only [hw]) K).trans ?_
     have h2w : 1 ≤ 2 * w := by linarith only [hw]
-    have hcount_factor : (K : ℝ) + 1 ≤ exp ξ := by
-      linarith only [hKu, huξ, add_one_le_exp ξ]
+    have hcount_factor : (K : ℝ) + 1 ≤ exp ξ := by linarith only [hKu, huξ, add_one_le_exp ξ]
     have htwo_power : (2 : ℝ) ^ u ≤ exp ξ := by
       rw [rpow_def_of_pos (by norm_num), exp_le_exp]
       have hlogtwo : log 2 ≤ 1 := by linarith only [log_le_sub_one_of_pos two_pos]
@@ -267,7 +265,7 @@ theorem card_rosserSet_rpow_le (hy : 1 < y) (hw : 2 ≤ y ^ (1 / (xi y - 1)))
 
 /-! ### The comparison (4.9), (4.10) -/
 theorem one_le_of_sMin_le (hs : sMin lower ≤ s) : 1 ≤ s := by
-  cases lower <;> simp [sMin] at hs <;> linarith
+  cases lower <;> simp [sMin] at hs <;> linarith only [hs]
 
 theorem one_le_delta (hs : 1 ≤ s) (y : ℝ) : 1 ≤ delta s y :=
   one_le_rpow (by linarith [lsx_nonneg (log y) hs]) (by linarith)
@@ -396,8 +394,8 @@ theorem exists_card_small : ∃ y₀ : ℝ, ∀ y ≥ y₀, ∀ (lower : Bool) (
       exp (-(s * log s) - s * log (log s) - cG * s) ≤ majG r s := by
     intro r s hs
     refine le_trans (exp_le_exp.2 ?_) (hG₀ r s hs)
-    have : cG₀ * s ≤ cG * s := mul_le_mul_of_nonneg_right (le_max_left _ _) (by linarith)
-    linarith
+    have : cG₀ * s ≤ cG * s := mul_le_mul_of_nonneg_right (le_max_left _ _) (by linarith only [hs])
+    linarith only [this]
   obtain ⟨C₅, hC₅⟩ := SLT_le_loglog
   obtain ⟨y₁, hy₁⟩ := exists_xi_large
   set c := max 100 (max (2 * (cG + 5 * log 128)) (max cG (max C₅ 12))) with hc
@@ -413,23 +411,27 @@ theorem exists_card_small : ∃ y₀ : ℝ, ∀ y ≥ y₀, ∀ (lower : Bool) (
     ((eventually_scalar c hc1).and (eventually_ge_atTop y₁))
   refine ⟨y₀, fun y hy lower s hs hsξ ↦ ?_⟩
   obtain ⟨⟨hy3, ha, hμ, hlam, hℓ1, -, h24, h16, h8, h9, h10⟩, hyy₁⟩ := hy₀ y hy
-  obtain ⟨hy1, -, -, hw2⟩ := hy₁ y hyy₁
+  obtain ⟨hy1, hξlarge, -, hw2⟩ := hy₁ y hyy₁
   have hL0 : 0 < log y := log_pos hy1
   have hm0 := lam_pos hy1
   have hξ := xi_pos hy1
+  have hξ32 : 32 + 1 ≤ xi y := (add_one_le_exp (32 : ℝ)).trans hξlarge
+  have hC₅lam : C₅ ≤ lam y := hc7.trans (hc6.trans (hc4.trans (hc2.trans hlam)))
   -- `w = y^{1/(ξ-1)}`
-  have hξ1 : 0 < xi y - 1 := by linarith
+  have hξ1 : 0 < xi y - 1 := by linarith only [hξ32]
   have hw : 2 ≤ y ^ (1 / (xi y - 1)) :=
-    hw2.trans (rpow_one_div_le_rpow_one_div hy1.le hξ1 (by linarith))
+    hw2.trans (rpow_one_div_le_rpow_one_div hy1.le hξ1 (by linarith only []))
   have hwy : y ^ (1 / (xi y - 1)) ≤ y := by
     conv_rhs => rw [← rpow_one y]
-    exact rpow_le_rpow_of_exponent_le hy1.le (by rw [div_le_one hξ1]; linarith)
+    exact rpow_le_rpow_of_exponent_le hy1.le (by
+      rw [div_le_one hξ1]
+      linarith only [hξ32])
   have hSLT : SLT (y ^ (1 / (xi y - 1))) ≤ 2 * lam y := by
     have h1 := hC₅ _ hw
     have h2 : log (log (y ^ (1 / (xi y - 1)))) ≤ log (log y) :=
       log_le_log (log_pos (by linarith)) (log_le_log (by linarith) hwy)
-    linarith
-  have hcard := card_rosserSet_rpow_le (lower := lower) hy1 hw hSLT (by linarith) h24 h10
+    linarith only [h1, h2, hℓ1, hC₅lam]
+  have hcard := card_rosserSet_rpow_le (lower := lower) hy1 hw hSLT (hc1.trans hlam) h24 h10
   -- `4 ξ λ² ≤ L`
   have hxl : 4 * (xi y * lam y ^ 2) ≤ log y := by
     have hsplit : lam y ^ (11 / 5 : ℝ) = lam y ^ 2 * lam y ^ (1 / 5 : ℝ) := by
diff --git a/LeanPool/IwaniecLinearSieve/LinearSieve/TheoremFour.lean b/LeanPool/IwaniecLinearSieve/LinearSieve/TheoremFour.lean
index 873edd18f8..1cf42f4d99 100644
--- a/LeanPool/IwaniecLinearSieve/LinearSieve/TheoremFour.lean
+++ b/LeanPool/IwaniecLinearSieve/LinearSieve/TheoremFour.lean
@@ -122,19 +122,19 @@ theorem cor1_part : ∃ C, 0 ≤ C ∧ ∀ (lower : Bool) (y s : ℝ), 1 < y →
         (primesLT (y ^ (1 / max s 3))).filter (fun p : ℕ => y ^ (1 / xi y) ≤ p) := by
       ext p
       simp only [mem_filter, mem_rosserPrimes, mem_primesLT, Bool.false_eq_true, false_or]
-      rw [lt_rpow_one_div_max_three hy (by linarith) (Nat.cast_nonneg p)]
+      rw [lt_rpow_one_div_max_three hy (by linarith only [hs1]) (Nat.cast_nonneg p)]
       tauto
     rw [hset]
     have hα : max s 3 ≤ xi y := max_le hsξ hξ3
-    have h := hC fSieve y (max s 3) (xi y) hy (by linarith [le_max_right s 3]) hα hw2
+    have h := hC fSieve y (max s 3) (xi y) hy (by linarith only [le_max_right s 3]) hα hw2
       (fSieve_antitone.antitoneOn _) (fun t _ => (fSieve_pos t).le)
     refine h.trans (add_le_add ?_ ?_)
     · have hint := intervalIntegral_le_integral_Ioi hα
         (integrableOn_fSieve_shift (le_max_right s 3))
-        (fun t ht => div_nonneg (fSieve_pos _).le (by linarith [ht.out, le_max_right s 3]))
+        (fun t ht => div_nonneg (fSieve_pos _).le (by linarith only [ht.out, le_max_right s 3, ht]))
       have heq := mainMaj_false_eq_integral s
-      exact div_le_div_of_nonneg_right (by linarith) hL.le
-    · have h1 := mainMaj_sub_one_le true false (by linarith [le_max_right s 3] : 1 ≤ max s 3)
+      exact div_le_div_of_nonneg_right (by linarith only [hint, heq]) hL.le
+    · have h1 := mainMaj_sub_one_le true false (by linarith only [le_max_right s 3] : 1 ≤ max s 3)
       rw [mainMaj_true] at h1
       have hG : errMaj false (max s 3) = errMaj false s := by
         rcases le_total s 3 with h | h
@@ -143,10 +143,10 @@ theorem cor1_part : ∃ C, 0 ≤ C ∧ ∀ (lower : Bool) (y s : ℝ), 1 < y →
       rw [hG] at h1
       have hsq : max s 3 ^ 2 ≤ 9 * s ^ 2 := by
         rcases le_total s 3 with h | h
-        · rw [max_eq_right h]; nlinarith
-        · rw [max_eq_left h]; nlinarith
+        · rw [max_eq_right h]; nlinarith only [hs1]
+        · rw [max_eq_left h]; nlinarith only []
       have hGs := errMaj_pos false s
-      have : fSieve (max s 3 - 1) ≤ 432 * s ^ 2 * errMaj false s := by nlinarith
+      have : fSieve (max s 3 - 1) ≤ 432 * s ^ 2 * errMaj false s := by nlinarith only [h1, hsq, hGs]
       apply div_le_div_of_nonneg_right _ hL.le
       calc C * fSieve (max s 3 - 1) * pntE (y ^ (1 / xi y))
           ≤ C * (432 * s ^ 2 * errMaj false s) * pntE (y ^ (1 / xi y)) := by gcongr
@@ -158,7 +158,7 @@ theorem cor1_part : ∃ C, 0 ≤ C ∧ ∀ (lower : Bool) (y s : ℝ), 1 < y →
       ((mainMaj_antitone false).antitoneOn _) (fun t _ => mainMaj_nonneg false t)
     refine h.trans (add_le_add ?_ ?_)
     · have hint := intervalIntegral_le_integral_Ioi hsξ (integrableOn_mainMaj_false_shift hs2)
-        (fun t ht => div_nonneg (mainMaj_nonneg _ _) (by linarith [ht.out]))
+        (fun t ht => div_nonneg (mainMaj_nonneg _ _) (by linarith only [ht.out, hs1, ht]))
       rw [mainMaj_true, fSieve_eq_integral_mainMaj hs2]
       exact div_le_div_of_nonneg_right hint hL.le
     · have h1 := mainMaj_sub_one_le false true hs1
@@ -166,7 +166,7 @@ theorem cor1_part : ∃ C, 0 ≤ C ∧ ∀ (lower : Bool) (y s : ℝ), 1 < y →
       apply div_le_div_of_nonneg_right _ hL.le
       calc C * mainMaj false (s - 1) * pntE (y ^ (1 / xi y))
           ≤ C * (432 * s ^ 2 * errMaj true s) * pntE (y ^ (1 / xi y)) := by
-            gcongr; nlinarith
+            gcongr; nlinarith only [h1, hGs]
         _ = 432 * C * s ^ 2 * errMaj true s * pntE (y ^ (1 / xi y)) := by ring
 
 /-- The source term in the form needed for the induction. -/
@@ -193,15 +193,15 @@ theorem src_le_of_le_xi {cR CR : ℝ} (hR : ∀ z ≥ 2, |R z * log z - cR| ≤
         rw [mem_filter, mem_primesLT] at hp
         have hlt : (p : ℝ) < y ^ (1 / (3 : ℝ)) := hp.1.2.trans_le
           (rpow_one_div_le_rpow_one_div hy.le (by norm_num) h3)
-        exact absurd ((not_cube_lt_iff (by linarith) p.cast_nonneg).1 hp.2) (not_le.2 hlt)
-      rw [this, max_eq_right (by linarith)]
+        exact absurd ((not_cube_lt_iff (by linarith only [hy]) p.cast_nonneg).1 hp.2) (not_le.2 hlt)
+      rw [this, max_eq_right (by linarith only [h3])]
       simpa using hE
-    · refine (src_le hR hy hs1 hw2 (rpow_one_div_le_rpow_one_div hy.le (by linarith) hsξ)
+    · refine (src_le hR hy hs1 hw2 (rpow_one_div_le_rpow_one_div hy.le (by linarith only [hs1]) hsξ)
         (rpow_one_div_le_rpow_one_div hy.le (by norm_num) hξ3)).trans ?_
       simp only [Bool.false_eq_true, ite_false]
       rw [errMaj_false_of_le_three h3]
       have : 6 * CR * pntE (y ^ (1 / xi y)) ≤ 6 * CR * s ^ 2 * 1 * pntE (y ^ (1 / xi y)) := by
-        have : 1 ≤ s ^ 2 := by nlinarith
+        have : 1 ≤ s ^ 2 := by nlinarith only [hs1]
         have := mul_nonneg hCR hpE.le
         nlinarith
       gcongr
@@ -242,18 +242,18 @@ theorem fail_le_exp_SLT (lower : Bool) (r : ℕ) (y z : ℝ) : fail lower r y z
 theorem xi_le_of_le {y Y : ℝ} (hy : 1 < y) (hyY : y ≤ Y) :
     xi y ≤ log Y / log (log 3) ^ (11 / 5 : ℝ) := by
   have hl3 : 1 < log 3 := by
-    rw [lt_log_iff_exp_lt (by norm_num)]; have := exp_one_lt_d9; linarith
+    rw [lt_log_iff_exp_lt (by norm_num)]; have := exp_one_lt_d9; linarith only [this]
   have hll : 0 < log (log 3) := log_pos hl3
   have hL : 0 < log y := log_pos hy
   have hP : 0 < log (log 3) ^ (11 / 5 : ℝ) := rpow_pos_of_pos hll _
   have hle : log (log 3) ^ (11 / 5 : ℝ) ≤ log (log (3 * y)) ^ (11 / 5 : ℝ) := by
-    refine rpow_le_rpow hll.le (log_le_log (by linarith) (log_le_log (by norm_num) ?_))
+    refine rpow_le_rpow hll.le (log_le_log (by linarith only [hl3]) (log_le_log (by norm_num) ?_))
       (by norm_num)
-    linarith
+    linarith only [hy]
   rw [xi]
   calc log y / log (log (3 * y)) ^ (11 / 5 : ℝ) ≤ log y / log (log 3) ^ (11 / 5 : ℝ) :=
         div_le_div_of_nonneg_left hL.le hP hle
-    _ ≤ _ := div_le_div_of_nonneg_right (log_le_log (by linarith) hyY) hP.le
+    _ ≤ _ := div_le_div_of_nonneg_right (log_le_log (by linarith only [hy]) hyY) hP.le
 
 /-- [I71, (4.8)]: for `1 < y ≤ Y` the claim at depth `r + 1` holds once `c₇` is large in terms
 of `Y`. -/
@@ -268,14 +268,14 @@ theorem small_y {cR c₇ Y : ℝ} (hcR : 0 < cR) (hY : 1 < Y)
   set Ξ := log Y / log (log 3) ^ (11 / 5 : ℝ)
   have hs1 : 1 ≤ s := (one_le_sMin lower).trans hs
   have hL : 0 < log y := log_pos hy
-  have hLY : log y ≤ log Y := log_le_log (by linarith) hyY
+  have hLY : log y ≤ log Y := log_le_log (by linarith only [hy]) hyY
   have hMΞ := bigM_pos Ξ
   have hG : bigM Ξ / 3 ≤ errMaj lower s :=
     le_trans (by gcongr; exact bigM_antitone (hsξ.trans (xi_le_of_le hy hyY)))
       (errMaj_mem lower s).1
   have hδ := one_le_delta hs1 y
   have hρ : (1 : ℝ) / 2 ≤ ((r + 1 : ℕ) : ℝ) / ((r + 1 : ℕ) + 1) := by
-    rw [div_le_div_iff₀ (by norm_num) (by positivity)]; push_cast; linarith
+    rw [div_le_div_iff₀ (by norm_num) (by positivity)]; push_cast; linarith only []
   have hz : y ^ (1 / s) ≤ Y := by
     refine le_trans ?_ hyY
     calc y ^ (1 / s) ≤ y ^ (1 / (1 : ℝ)) := rpow_one_div_le_rpow_one_div hy.le one_pos hs1
@@ -291,7 +291,7 @@ theorem small_y {cR c₇ Y : ℝ} (hcR : 0 < cR) (hY : 1 < Y)
       have hK : 6 * exp (SLT Y) * log Y ^ 2 ≤ c₇ * (cR * bigM Ξ) :=
         (div_le_iff₀ (mul_pos hcR hMΞ)).1 hc₇
       rw [le_div_iff₀ (by have := log_pos hY; positivity)]
-      linarith
+      linarith only [hK]
     have hnum : cR * c₇ * ((1 / 2) * (bigM Ξ / 3)) ≤
         cR * c₇ * ((((r + 1 : ℕ) : ℝ) / ((r + 1 : ℕ) + 1)) * delta s y * errMaj lower s) := by
       refine mul_le_mul_of_nonneg_left ?_ (mul_nonneg hcR.le hc₇0)
@@ -300,7 +300,7 @@ theorem small_y {cR c₇ Y : ℝ} (hcR : 0 < cR) (hY : 1 < Y)
       calc (1 / 2 : ℝ) * (bigM Ξ / 3) ≤ (((r + 1 : ℕ) : ℝ) / ((r + 1 : ℕ) + 1)) *
             (delta s y * errMaj lower s) := by
             refine mul_le_mul hρ ?_ (by positivity) (by positivity)
-            nlinarith
+            nlinarith only [hG, hMΞ, hδ]
         _ = _ := by ring
     have hc0 : 0 ≤ cR * c₇ * ((((r + 1 : ℕ) : ℝ) / ((r + 1 : ℕ) + 1)) * delta s y *
         errMaj lower s) := le_trans (by positivity) hnum
@@ -308,7 +308,7 @@ theorem small_y {cR c₇ Y : ℝ} (hcR : 0 < cR) (hY : 1 < Y)
     refine h1.trans ((div_le_div₀ hc0 hnum (by positivity) hLL).trans_eq (by ring))
   have : 0 ≤ cR * (mainMaj lower s / log y) := by positivity
   calc fail lower (r + 1) y (y ^ (1 / s)) ≤ exp (SLT Y) := hfail
-    _ ≤ _ := by rw [mul_add]; linarith
+    _ ≤ _ := by rw [mul_add]; linarith only [key, this]
 
 /-! ### The small primes: the crude bound against Lemma 9 -/
 
@@ -329,16 +329,16 @@ theorem crude_le : ∃ y₁ : ℝ, ∀ y ≥ y₁, ∀ (lower : Bool) (n : ℕ)
   set ξ := xi y
   set X := log (log (y ^ (1 / ξ))) + C'
   have hs1 : 1 ≤ s := (one_le_sMin lower).trans hs
-  have hξ4 : 6 ≤ ξ := by linarith [add_one_le_exp (32 : ℝ)]
+  have hξ4 : 6 ≤ ξ := by linarith only [add_one_le_exp (32 : ℝ), hξ32]
   have hL4 : 0 < log y ^ 4 := by have := log_pos hy1; positivity
   -- the crude bound
   have hfail : fail lower n y (y ^ (1 / ξ)) ≤
       2 * (exp 1 * X / (ξ - 2)) ^ (ξ - 2) := by
     rw [one_div]
-    refine fail_rpow_le_tail hy1 (by linarith) ?_ h2e
+    refine fail_rpow_le_tail hy1 (by linarith only [hξ4]) ?_ h2e
     rw [← one_div]
     have := hCS _ hw2
-    have : CS ≤ C' := by simp only [C']; linarith [le_abs_self CS]
+    have : CS ≤ C' := by simp only [C']; linarith only [le_abs_self CS]
     simp only [X]
     linarith
   -- Lemma 9
@@ -346,19 +346,19 @@ theorem crude_le : ∃ y₁ : ℝ, ∀ y ≥ y₁, ∀ (lower : Bool) (n : ℕ)
     intro t ht
     rw [errMaj_eq_majG_succ]
     refine le_trans (exp_le_exp.2 ?_) (hc _ t ht)
-    have : c * t ≤ c' * t := mul_le_mul_of_nonneg_right (le_max_left _ _) (by linarith)
-    linarith
+    have : c * t ≤ c' * t := mul_le_mul_of_nonneg_right (le_max_left _ _) (by linarith only [ht])
+    linarith only [this]
   have hGs := errMaj_pos lower s
   have hmain : 2 * (exp 1 * X / (ξ - 2)) ^ (ξ - 2) * log y ^ 4 ≤ delta s y * errMaj lower s := by
     rcases le_total s (ξ / 2) with h | h
-    · refine hA.trans ((hG _ (by linarith)).trans ?_)
+    · refine hA.trans ((hG _ (by linarith only [hξ4])).trans ?_)
       calc errMaj lower (ξ / 2) ≤ errMaj lower s := errMaj_antitone lower h
         _ ≤ delta s y * errMaj lower s := le_mul_of_one_le_left hGs.le (one_le_delta hs1 y)
     · refine hB.trans ?_
-      have hδ := delta_le_delta (by linarith : 1 ≤ ξ / 2) h y
+      have hδ := delta_le_delta (by linarith only [hξ4] : 1 ≤ ξ / 2) h y
       have hGG : exp (-(ξ * log ξ) - ξ * log (log ξ) - c' * ξ) ≤ errMaj lower s :=
-        (hG ξ (by linarith)).trans (errMaj_antitone lower hsξ)
-      exact mul_le_mul hδ hGG (exp_pos _).le (by linarith [one_le_delta hs1 y])
+        (hG ξ (by linarith only [hξ4])).trans (errMaj_antitone lower hsξ)
+      exact mul_le_mul hδ hGG (exp_pos _).le (by linarith only [one_le_delta hs1 y, hs1])
   rw [le_div_iff₀ hL4]
   calc fail lower n y (y ^ (1 / ξ)) * log y ^ 4
       ≤ 2 * (exp 1 * X / (ξ - 2)) ^ (ξ - 2) * log y ^ 4 := by gcongr
@@ -372,7 +372,7 @@ theorem ratio_le {r : ℕ} {ε : ℝ} (hε : ε * ((r : ℝ) + 1) ^ 2 ≤ 1) :
   rw [show ((r + 1 : ℕ) : ℝ) / ((r + 1 : ℕ) + 1) * (1 - ε) = ((r : ℝ) + 1) * (1 - ε) / (r + 2) by
     push_cast; ring]
   rw [div_le_div_iff₀ (by positivity) (by positivity)]
-  nlinarith
+  nlinarith only [hε]
 
 /-- The depth condition supplies the relative gain `(log L)²/(4L²)` used in [I71, (4.6)].
 Here `Λ` stands for `log L`; the estimate only needs `Λ > 0`. -/
@@ -398,15 +398,15 @@ theorem combine {cR c₇ L D M F cr E T ρ ρ' ε : ℝ}
     (hε0 : 0 ≤ ε) (hεL : 1 / (4 * L ^ 2) ≤ ε) (hρ' : 1 / 2 ≤ ρ') (hc : 32 ≤ cR * c₇)
     (hD : 0 ≤ D) (hL : 0 < L) :
     F ≤ cR * M / L + cR * c₇ * ρ' * D := by
-  have hcc : 0 ≤ cR * c₇ := by linarith
+  have hcc : 0 ≤ cR * c₇ := by linarith only [hc]
   have hD' : 0 ≤ D * (1 + ε / 2) := by positivity
   have h1 : cR * c₇ * ρ * T ≤ cR * c₇ * ρ' * D * ((1 - ε) * (1 + ε / 2)) := by
     calc cR * c₇ * ρ * T ≤ cR * c₇ * ρ * (D * (1 + ε / 2)) :=
           mul_le_mul_of_nonneg_left hT (by positivity)
       _ ≤ cR * c₇ * (ρ' * (1 - ε)) * (D * (1 + ε / 2)) := by gcongr
       _ = _ := by ring
-  have h2 : (1 - ε) * (1 + ε / 2) ≤ 1 - ε / 2 := by nlinarith
-  have hρ'0 : 0 ≤ ρ' := by linarith
+  have h2 : (1 - ε) * (1 + ε / 2) ≤ 1 - ε / 2 := by nlinarith only [hε0]
+  have hρ'0 : 0 ≤ ρ' := by linarith only [hρ']
   have h3 : cR * c₇ * ρ' * D * ((1 - ε) * (1 + ε / 2)) ≤ cR * c₇ * ρ' * D * (1 - ε / 2) :=
     mul_le_mul_of_nonneg_left h2 (by positivity)
   have hL2 : 0 < L ^ 2 := by positivity
@@ -417,9 +417,9 @@ theorem combine {cR c₇ L D M F cr E T ρ ρ' ε : ℝ}
   have h5 : 2 * (D / L ^ 2) ≤ cR * c₇ * ρ' * D * (ε / 2) := by
     have := mul_le_mul_of_nonneg_left h4 hD
     calc 2 * (D / L ^ 2) = D * (4 / L ^ 2) / 2 := by ring
-      _ ≤ D * (cR * c₇ * ρ' * ε) / 2 := by linarith
+      _ ≤ D * (cR * c₇ * ρ' * ε) / 2 := by linarith only [this]
       _ = _ := by ring
-  nlinarith
+  nlinarith only [hF, hcr, hE, h1, h3, h5]
 
 /-- The main case of the inductive step: `y` large and `r + 2 ≤ 2 L / log L`. All analytic
 inputs are hypotheses at the given `y`, `s`. -/
@@ -499,12 +499,12 @@ theorem main_step {cR c₇ CR C₁ C₃ : ℝ} {r : ℕ} (IH : Bound cR c₇ r)
     exact div_le_div_of_nonneg_right (by nlinarith only [hΛ]) (by positivity)
   have hρ' : 1 / 2 ≤ ρ' := by
     simp only [ρ']
-    rw [div_le_div_iff₀ (by norm_num) (by positivity)]; push_cast; linarith
+    rw [div_le_div_iff₀ (by norm_num) (by positivity)]; push_cast; linarith only []
   have hcr : fail lower (r + 1) y w ≤ D / L ^ 2 := by
     refine hcrude.trans_eq ?_
     rw [hD, div_div]; ring
   -- Split at `w`, apply the inner induction bounds, then combine the main sum and source.
-  have hwz : w ≤ y ^ (1 / s) := rpow_one_div_le_rpow_one_div hy.le (by linarith) hsξ
+  have hwz : w ≤ y ^ (1 / s) := rpow_one_div_le_rpow_one_div hy.le (by linarith only [hs1]) hsξ
   have hF : fail lower (r + 1) y (y ^ (1 / s)) ≤ fail lower (r + 1) y w +
       (cR * mainMaj lower s / L + K * s ^ 2 * G * pntE w / L) +
       cR * c₇ * ((r : ℝ) / (r + 1)) * T := by
@@ -558,7 +558,7 @@ theorem theorem4 {cR CR : ℝ} (hcR : 0 < cR) (hR : ∀ z ≥ 2, |R z * log z -
   have hc₇ : 32 ≤ cR * c₇ := by
     have := le_max_left (32 / cR) (6 * exp (SLT y₀) * log y₀ ^ 2 / (cR * bigM Ξ))
     rw [div_le_iff₀ hcR] at this
-    linarith
+    linarith only [this]
   refine ⟨c₇, hc₇0, fun r => ?_⟩
   change Bound cR c₇ r
   induction r with
@@ -584,14 +584,14 @@ theorem theorem4 {cR CR : ℝ} (hcR : 0 < cR) (hR : ∀ z ≥ 2, |R z * log z -
       rw [hyd y hyd' lower r (y ^ (1 / s)) hdeep 1]
       refine (IH lower y s hy hs hsξ).trans ?_
       have hab : (r : ℝ) / (r + 1) ≤ ((r + 1 : ℕ) : ℝ) / ((r + 1 : ℕ) + 1) := by
-        rw [div_le_div_iff₀ (by positivity) (by positivity)]; push_cast; nlinarith
+        rw [div_le_div_iff₀ (by positivity) (by positivity)]; push_cast; nlinarith only []
       have hL2 : 0 < log y ^ 2 := by have := log_pos hy; positivity
       refine mul_le_mul_of_nonneg_left (add_le_add_right (div_le_div_of_nonneg_right
         (mul_le_mul_of_nonneg_right (mul_le_mul_of_nonneg_right
           (mul_le_mul_of_nonneg_left hab hc₇0) (zero_le_one.trans (one_le_delta hs1 y)))
           (errMaj_pos lower s).le) hL2.le) _) hcR.le
     · obtain ⟨-, hξ32, -, hw2⟩ := hyx y hyx'
-      have hξ3 : 3 ≤ xi y := by linarith [add_one_le_exp (32 : ℝ)]
+      have hξ3 : 3 ≤ xi y := by linarith only [add_one_le_exp (32 : ℝ), hξ32]
       obtain ⟨⟨hΛ, hδ⟩, hK⟩ := hye y hye'
       exact main_step IH hcR hc₇ hCR hC₁0 hC₃0 hy hs hsξ (hC₁ lower y s hy hs hsξ hξ3 hw2)
         (src_le_of_le_xi hR hy hs hsξ hξ3 hw2) (hC₃ lower y s hy₃ hs)
diff --git a/LeanPool/IwaniecLinearSieve/LinearSieve/TheoremFourAsymp.lean b/LeanPool/IwaniecLinearSieve/LinearSieve/TheoremFourAsymp.lean
index 984ed68bc0..8c27d5277d 100644
--- a/LeanPool/IwaniecLinearSieve/LinearSieve/TheoremFourAsymp.lean
+++ b/LeanPool/IwaniecLinearSieve/LinearSieve/TheoremFourAsymp.lean
@@ -70,7 +70,7 @@ theorem tendsto_lin_sub_rpow :
   have h6 : 6 ≤ pntκ * ℓ ^ (1 / 10 : ℝ) := by
     rw [div_le_iff₀ pntκ_pos] at h; linarith
   rw [hsplit]
-  nlinarith
+  nlinarith only [hℓ, h6]
 
 theorem tendsto_log_pow_pntE :
     Tendsto (fun y : ℝ => log y ^ 5 * pntE (y ^ (1 / xi y))) atTop (𝓝 0) := by
@@ -85,7 +85,7 @@ theorem tendsto_log_pow_pntE :
   · filter_upwards [eventually_gt_atTop 1] with y hy
     have hL := log_pos hy
     have hLe : log y ≤ exp (log (log (3 * y))) := by
-      rw [← log_add_log_three hy]; linarith [log_pos (by norm_num : (1 : ℝ) < 3)]
+      rw [← log_add_log_three hy]; linarith only [log_pos (by norm_num : (1 : ℝ) < 3)]
     rw [pntE_rpow_one_div_xi hy, sub_eq_add_neg, exp_add, ← neg_mul]
     gcongr
     calc log y ^ 5 ≤ exp (log (log (3 * y))) ^ 5 := by gcongr
@@ -110,12 +110,12 @@ theorem eventually_mul_pntE_le (K : ℝ) : ∀ᶠ y : ℝ in atTop,
       _ = log y ^ 5 := by ring
   have h2 : |K| * (log y ^ 5 * pntE (y ^ (1 / xi y))) ≤ |K| * (1 / (|K| + 1)) := by gcongr
   have h3 : |K| * (1 / (|K| + 1)) ≤ 1 := by
-    rw [mul_one_div, div_le_one (by positivity)]; linarith
+    rw [mul_one_div, div_le_one (by positivity)]; linarith only []
   calc K * xi y ^ 2 * log y ^ 3 * pntE (y ^ (1 / xi y))
       ≤ |K| * (xi y ^ 2 * log y ^ 3) * pntE (y ^ (1 / xi y)) := by
         rw [mul_assoc K]; gcongr; exact le_abs_self K
     _ ≤ |K| * log y ^ 5 * pntE (y ^ (1 / xi y)) := by gcongr
-    _ ≤ 1 := by rw [mul_assoc]; linarith
+    _ ≤ 1 := by rw [mul_assoc]; linarith only [h2, h3]
 
 /-- On `[0, 1]`, the exponential is at most `1 + 2v`. -/
 theorem exp_le_one_add_two_mul {v : ℝ} (hv0 : 0 ≤ v) (hv1 : v ≤ 1) :
@@ -186,13 +186,13 @@ theorem eventually_delta_mul_le (C : ℝ) (hC : 0 ≤ C) : ∀ᶠ y : ℝ in atT
 /-- `ξ log ξ - (ξ - 2) log (ξ - 2) ≤ 2 log ξ + 2`. -/
 theorem mul_log_sub_le {ξ : ℝ} (hξ : 2 < ξ) :
     ξ * log ξ - (ξ - 2) * log (ξ - 2) ≤ 2 * log ξ + 2 := by
-  have hu : 0 < ξ - 2 := by linarith
-  have h := log_le_sub_one_of_pos (div_pos (by linarith : 0 < ξ) hu)
-  rw [log_div (by linarith) hu.ne'] at h
+  have hu : 0 < ξ - 2 := by linarith only [hξ]
+  have h := log_le_sub_one_of_pos (div_pos (by linarith only [hξ] : 0 < ξ) hu)
+  rw [log_div (by linarith only [hξ]) hu.ne'] at h
   have h' : (ξ - 2) * (log ξ - log (ξ - 2)) ≤ (ξ - 2) * (ξ / (ξ - 2) - 1) :=
     mul_le_mul_of_nonneg_left h hu.le
   have e : (ξ - 2) * (ξ / (ξ - 2) - 1) = 2 := by field_simp; ring
-  nlinarith
+  nlinarith only [h', e]
 
 /-- The exponent comparison for [I71, (4.4), (4.9)], after bounding the logarithms. -/
 theorem crude_half_exponent_le {c ℓ L ξ X : ℝ} (hℓ_large : 2 ≤ ℓ) (hxi_large : 8 * ℓ ≤ ξ)
@@ -358,15 +358,15 @@ theorem eventually_crude_hyp (c C' : ℝ) : ∀ᶠ ℓ : ℝ in atTop,
       (by norm_num : (0 : ℝ) < 1 / 4)).eventually (eventually_ge_atTop (2 * C')),
     tendsto_log_atTop.eventually (eventually_ge_atTop (4 * (2 + c + 18 * log 2))), hF6,
     eventually_ge_atTop (16 * (2 + |c|))] with ℓ h1 h2 h3 h4 h4' h5 h6 h6'
-  have hℓ0 : 0 < ℓ := by linarith
-  have hlℓ : 0 ≤ log ℓ := log_nonneg (by linarith)
-  refine ⟨h1, h2, ?_, ?_, by linarith, ?_⟩
+  have hℓ0 : 0 < ℓ := by linarith only [h1]
+  have hlℓ : 0 ≤ log ℓ := log_nonneg (by linarith only [h1])
+  refine ⟨h1, h2, ?_, ?_, by linarith only [h5], ?_⟩
   · have := mul_le_mul_of_nonneg_right h3 (exp_pos (ℓ / 2)).le
     rw [mul_assoc, ← exp_add, show -(1 / 2) * ℓ + ℓ / 2 = 0 by ring, exp_zero, mul_one] at this
-    linarith
+    linarith only [this]
   · have hq := rpow_nonneg hℓ0.le (1 / 4 : ℝ)
     rw [norm_of_nonneg hlℓ, norm_of_nonneg hq] at h4
-    linarith
+    linarith only [h4, h4', hlℓ]
   · rw [norm_of_nonneg hlℓ, id, norm_of_nonneg hℓ0.le] at h6
     have := le_abs_self c
     have := abs_nonneg c
diff --git a/LeanPool/IwaniecLinearSieve/LinearSieve/TheoremFourAux.lean b/LeanPool/IwaniecLinearSieve/LinearSieve/TheoremFourAux.lean
index 1cf36d8606..b1b2fa6ad5 100644
--- a/LeanPool/IwaniecLinearSieve/LinearSieve/TheoremFourAux.lean
+++ b/LeanPool/IwaniecLinearSieve/LinearSieve/TheoremFourAux.lean
@@ -48,7 +48,7 @@ theorem sum_R_div_eq {a b : ℝ} (hab : a ≤ b) :
   rw [hs] at h
   have ha := R_eq a
   have hb := R_eq b
-  linarith
+  linarith only [h, ha, hb]
 
 /-- The depth-one source term of `fail false`: the primes `p < z` with `p³ ≥ y` (none for the
 lower sieve). -/
@@ -83,7 +83,7 @@ theorem src_le {cR CR : ℝ} (hR : ∀ z ≥ 2, |R z * log z - cR| ≤ CR * pntE
     src lower y (y ^ (1 / s)) ≤
       (if lower then 0 else cR * max (3 - s) 0 / log y) + 6 * CR * pntE w / log y := by
   have hL : 0 < log y := log_pos hy
-  have hy0 : 0 < y := by linarith
+  have hy0 : 0 < y := by linarith only [hy]
   have hCR : 0 ≤ CR := by
     have h := (abs_nonneg _).trans (hR 2 le_rfl)
     exact nonneg_of_mul_nonneg_left h (pntE_pos 2)
@@ -100,32 +100,32 @@ theorem src_le {cR CR : ℝ} (hR : ∀ z ≥ 2, |R z * log z - cR| ≤ CR * pntE
         refine eq_empty_of_forall_notMem fun p hp ↦ ?_
         rw [mem_filter, mem_primesLT] at hp
         have := rpow_one_div_le_rpow_one_div hy.le (by norm_num) h3
-        linarith [hp.1.2]
-      rw [this, sum_empty, max_eq_right (by linarith)]
+        linarith only [hp.1.2, hp, this]
+      rw [this, sum_empty, max_eq_right (by linarith only [h3])]
       simpa using hE
-    · rw [sum_R_div_eq (rpow_one_div_le_rpow_one_div hy.le (by linarith) h3),
-        max_eq_left (by linarith)]
+    · rw [sum_R_div_eq (rpow_one_div_le_rpow_one_div hy.le (by linarith only [hs]) h3),
+        max_eq_left (by linarith only [h3])]
       have h1 := (abs_le.1 (hR _ (hw.trans hw3))).2
       have h2 := (abs_le.1 (hR _ (hw.trans hwz))).1
       rw [log_rpow_one_div hy0] at h1 h2
-      have e1 : pntE (y ^ (1 / 3 : ℝ)) ≤ pntE w := pntE_le_pntE (by linarith) hw3
-      have e2 : pntE (y ^ (1 / s)) ≤ pntE w := pntE_le_pntE (by linarith) hwz
+      have e1 : pntE (y ^ (1 / 3 : ℝ)) ≤ pntE w := pntE_le_pntE (by linarith only [hw]) hw3
+      have e2 : pntE (y ^ (1 / s)) ≤ pntE w := pntE_le_pntE (by linarith only [hw]) hwz
       have hR1 : R (y ^ (1 / 3 : ℝ)) ≤ 3 * (cR + CR * pntE w) / log y := by
         rw [le_div_iff₀ hL]
-        nlinarith
+        nlinarith only [h1, hCR, e1]
       have hR2 : s * (cR - CR * pntE w) / log y ≤ R (y ^ (1 / s)) := by
         rw [div_le_iff₀ hL]
         have : R (y ^ (1 / s)) * (log y / s) * s = R (y ^ (1 / s)) * log y := by
           field_simp
         have h2' : cR - CR * pntE w ≤ R (y ^ (1 / s)) * (log y / s) := by nlinarith
-        nlinarith [mul_le_mul_of_nonneg_left h2' (by linarith : (0 : ℝ) ≤ s)]
+        nlinarith [mul_le_mul_of_nonneg_left h2' (by linarith only [hs] : (0 : ℝ) ≤ s)]
       have : 3 * (cR + CR * pntE w) / log y - s * (cR - CR * pntE w) / log y ≤
           cR * (3 - s) / log y + 6 * CR * pntE w / log y := by
         rw [← sub_div, ← add_div]
         apply div_le_div_of_nonneg_right _ hL.le
         have := pntE_pos w
-        nlinarith [mul_nonneg (mul_nonneg hCR this.le) (by linarith : (0 : ℝ) ≤ 3 - s)]
-      linarith
+        nlinarith [mul_nonneg (mul_nonneg hCR this.le) (by linarith only [h3] : (0 : ℝ) ≤ 3 - s)]
+      linarith only [hR1, hR2, this]
   · simp only [src, ite_true]
     simpa using hE
 
@@ -137,7 +137,7 @@ theorem one_le_delta {s : ℝ} (hs : 1 ≤ s) (y : ℝ) : 1 ≤ delta s y := by
 theorem delta_le_delta {s s' : ℝ} (hs : 1 ≤ s) (hss' : s ≤ s') (y : ℝ) :
     delta s y ≤ delta s' y := by
   have hl := log_nonneg hs
-  have hll : log s ≤ log s' := log_le_log (by linarith) hss'
+  have hll : log s ≤ log s' := log_le_log (by linarith only [hs]) hss'
   have hx0 := lsx_nonneg (log y) hs
   have hx : s ^ 2 * log s ^ 5 / log y ^ 2 ≤ s' ^ 2 * log s' ^ 5 / log y ^ 2 := by gcongr
   rw [delta, delta]
@@ -150,9 +150,9 @@ theorem delta_max_le {s a : ℝ} (hs : 1 ≤ s) (ha : 1 ≤ a) (y : ℝ) :
     delta (max s a) y ≤ delta a y * delta s y := by
   rcases le_total s a with h | h
   · rw [max_eq_right h]
-    exact le_mul_of_one_le_right (by linarith [one_le_delta ha y]) (one_le_delta hs y)
+    exact le_mul_of_one_le_right (by linarith only [one_le_delta ha y, ha]) (one_le_delta hs y)
   · rw [max_eq_left h]
-    exact le_mul_of_one_le_left (by linarith [one_le_delta hs y]) (one_le_delta ha y)
+    exact le_mul_of_one_le_left (by linarith only [one_le_delta hs y, hs]) (one_le_delta ha y)
 
 /-! ### The inner level of the recursion -/
 
@@ -172,8 +172,8 @@ theorem lt_div_log_of_lt_rpow {y s : ℝ} {p : ℕ} (hy : 1 < y) (hs : 0 < s) (h
     (hpz : (p : ℝ) < y ^ (1 / s)) : s < log y / log p := by
   have hlp : 0 < log (p : ℝ) := log_pos (by exact_mod_cast hp)
   have h := log_lt_log (by positivity) hpz
-  rw [log_rpow_one_div (by linarith)] at h
-  rw [lt_div_iff₀ hlp]; rw [lt_div_iff₀ hs] at h; linarith
+  rw [log_rpow_one_div (by linarith only [hy])] at h
+  rw [lt_div_iff₀ hlp]; rw [lt_div_iff₀ hs] at h; linarith only [h]
 
 theorem prime_lt_of_mem_rosserPrimes {lower : Bool} {y s : ℝ} {p : ℕ} (hy : 1 < y) (hs : 1 ≤ s)
     (hp : p ∈ rosserPrimes lower y (y ^ (1 / s))) : (p : ℝ) < y := by
@@ -192,19 +192,19 @@ theorem sMin_le_inner {lower : Bool} {y s : ℝ} {p : ℕ} (hy : 1 < y) (hs : sM
     have h3 := ((mem_rosserPrimes.1 hp).2.resolve_left (by simp))
     have h := log_lt_log (by have := hpP.pos; positivity) h3
     rw [log_pow] at h
-    have : 3 < log y / log p := by rw [lt_div_iff₀ hlp]; push_cast at h; linarith
+    have : 3 < log y / log p := by rw [lt_div_iff₀ hlp]; push_cast at h; linarith only [h]
     simp only [Bool.not_false, sMin]
-    linarith
+    linarith only [this]
   · have hs2 : (2 : ℝ) ≤ s := hs
-    have := lt_div_log_of_lt_rpow hy (by linarith) hpP.one_lt
+    have := lt_div_log_of_lt_rpow hy (by linarith only [hs2]) hpP.one_lt
       (lt_of_mem_primesLT (rosserPrimes_subset hp))
     simp only [Bool.not_true, sMin]
-    linarith
+    linarith only [hs2, this]
 
 theorem one_lt_log_three_mul {x : ℝ} (hx : 1 ≤ x) : 1 < log (3 * x) := by
-  rw [lt_log_iff_exp_lt (by linarith)]
+  rw [lt_log_iff_exp_lt (by linarith only [hx])]
   have := exp_one_lt_d9
-  linarith
+  linarith only [hx, this]
 
 /-- `log (y^{1/ξ(y)}) = (log log 3y)^{11/5}`. -/
 theorem log_rpow_one_div_xi {y : ℝ} (hy : 1 < y) :
@@ -212,19 +212,19 @@ theorem log_rpow_one_div_xi {y : ℝ} (hy : 1 < y) :
   have hL : 0 < log y := log_pos hy
   have hℓ : 0 < log (log (3 * y)) := log_pos (one_lt_log_three_mul hy.le)
   have hP : 0 < log (log (3 * y)) ^ (11 / 5 : ℝ) := rpow_pos_of_pos hℓ _
-  rw [log_rpow_one_div (by linarith), xi, div_div_cancel₀ hL.ne']
+  rw [log_rpow_one_div (by linarith only [hy]), xi, div_div_cancel₀ hL.ne']
 
 /-- For `y^{1/ξ(y)} ≤ p < y`, the inner parameter satisfies `t_p - 1 ≤ ξ(y/p)`. -/
 theorem inner_le_xi {y : ℝ} {p : ℕ} (hy : 1 < y) (hp : 1 < p) (hpy : (p : ℝ) < y)
     (hw : y ^ (1 / xi y) ≤ p) : log y / log p - 1 ≤ xi (y / p) := by
   have hp0 : (0 : ℝ) < p := by positivity
-  have hy0 : 0 < y := by linarith
+  have hy0 : 0 < y := by linarith only [hy]
   have hlp : 0 < log (p : ℝ) := log_pos (by exact_mod_cast hp)
   have hℓ : 0 < log (log (3 * y)) := log_pos (one_lt_log_three_mul hy.le)
   have hyp1 : 1 < y / p := by rw [one_lt_div hp0]; exact hpy
   have hℓ' : 0 < log (log (3 * (y / p))) := log_pos (one_lt_log_three_mul hyp1.le)
   have hℓℓ' : log (log (3 * (y / p))) ≤ log (log (3 * y)) := by
-    refine log_le_log (log_pos (by linarith)) (log_le_log (by positivity) ?_)
+    refine log_le_log (log_pos (by linarith only [hyp1])) (log_le_log (by positivity) ?_)
     gcongr
     exact div_le_self hy0.le (by exact_mod_cast hp.le)
   have hP' : 0 < log (log (3 * (y / p))) ^ (11 / 5 : ℝ) := rpow_pos_of_pos hℓ' _
@@ -259,6 +259,6 @@ theorem fail_succ_le_split (lower : Bool) (r : ℕ) {y z w : ℝ} (hwz : w ≤ z
   rw [fail_succ_eq, fail_succ_eq lower r y w,
     ← sum_filter_add_sum_filter_not (rosserPrimes lower y z) (fun p : ℕ ↦ w ≤ (p : ℝ)),
     rosserPrimes_filter_lt hwz]
-  linarith [src_nonneg lower y w]
+  linarith only [src_nonneg lower y w]
 
 end IwaniecLinearSieve.TheoremFour
diff --git a/LeanPool/IwaniecLinearSieve/PrimeSums/Error.lean b/LeanPool/IwaniecLinearSieve/PrimeSums/Error.lean
index 340f2aa723..f6bc56b185 100644
--- a/LeanPool/IwaniecLinearSieve/PrimeSums/Error.lean
+++ b/LeanPool/IwaniecLinearSieve/PrimeSums/Error.lean
@@ -72,7 +72,7 @@ theorem tendsto_pntE : Tendsto pntE atTop (𝓝 0) := by
 
 /-- `pntE` dominates `1 / x`. -/
 theorem inv_le_pntE {x : ℝ} (hx : 2 ≤ x) : x⁻¹ ≤ pntE x := by
-  have hx0 : 0 < x := by linarith
+  have hx0 : 0 < x := by linarith only [hx]
   have hL : 1 / 4 ≤ log x := by
     have := log_two_gt_d9
     have := log_le_log (by norm_num) hx
@@ -85,25 +85,25 @@ theorem inv_le_pntE {x : ℝ} (hx : 2 ≤ x) : x⁻¹ ≤ pntE x := by
     have := pntκ_le_half
     have := sqrt_nonneg (log x)
     nlinarith
-  rw [mul_self_sqrt (by linarith)] at h1
-  linarith
+  rw [mul_self_sqrt (by linarith only [hL])] at h1
+  linarith only [h1]
 
 theorem one_div_mul_log_le_pntE {x : ℝ} (hx : 2 ≤ x) : 1 / (x * log x) ≤ 2 * pntE x := by
-  have hx0 : 0 < x := by linarith
+  have hx0 : 0 < x := by linarith only [hx]
   have hL : 1 / 2 ≤ log x := by
     have := log_two_gt_d9
     have := log_le_log (by norm_num) hx
     linarith
   calc 1 / (x * log x) = x⁻¹ * (log x)⁻¹ := by rw [one_div, mul_inv]
     _ ≤ pntE x * 2 := by
-      refine mul_le_mul (inv_le_pntE hx) ?_ (inv_nonneg.2 (by linarith)) (pntE_nonneg _)
-      rw [inv_le_comm₀ (by linarith) (by norm_num)]
-      linarith
+      refine mul_le_mul (inv_le_pntE hx) ?_ (inv_nonneg.2 (by linarith only [hL])) (pntE_nonneg _)
+      rw [inv_le_comm₀ (by linarith only [hL]) (by norm_num)]
+      linarith only [hL]
     _ = 2 * pntE x := mul_comm _ _
 
 /-- `pntE` dominates `x ^ (-1/2) * log x`. -/
 theorem sqrt_mul_log_le {x : ℝ} (hx : 1 ≤ x) : √x * log x ≤ 12 * x * pntE x := by
-  have hx0 : 0 < x := by linarith
+  have hx0 : 0 < x := by linarith only [hx]
   set L := log x with hLdef
   have hL : 0 ≤ L := log_nonneg hx
   have hsx : √x = exp (L / 2) := by
@@ -113,19 +113,19 @@ theorem sqrt_mul_log_le {x : ℝ} (hx : 1 ≤ x) : √x * log x ≤ 12 * x * pnt
     rw [← exp_add, add_halves, hLdef, exp_log hx0]
   clear_value L
   -- `L ≤ 4 exp (L / 4)` and `κ √L ≤ (L + 1) / 4`.
-  have h1 : L ≤ 4 * exp (L / 4) := by linarith [add_one_le_exp (L / 4)]
+  have h1 : L ≤ 4 * exp (L / 4) := by linarith only [add_one_le_exp (L / 4)]
   have h2 : pntκ * √L ≤ L / 4 + 1 / 4 := by
     have hκ := pntκ_le_half
     have hs := sqrt_nonneg L
     have hsq := mul_self_sqrt hL
-    nlinarith [sq_nonneg (√L - 1)]
+    nlinarith only [sq_nonneg (√L - 1), hsq, hκ, hs]
   have h3 : exp (pntκ * √L) ≤ 3 * exp (L / 4) := by
     calc exp (pntκ * √L) ≤ exp (L / 4 + 1 / 4) := exp_le_exp.2 h2
       _ = exp (L / 4) * exp (1 / 4) := exp_add _ _
       _ ≤ exp (L / 4) * 3 := by
         gcongr
         calc exp (1 / 4 : ℝ) ≤ exp 1 := exp_le_exp.2 (by norm_num)
-          _ ≤ 3 := by have := exp_one_lt_d9; linarith
+          _ ≤ 3 := by have := exp_one_lt_d9; linarith only [this]
       _ = 3 * exp (L / 4) := mul_comm _ _
   have h4 : L * exp (pntκ * √L) ≤ 12 * exp (L / 2) := by
     calc L * exp (pntκ * √L) ≤ (4 * exp (L / 4)) * (3 * exp (L / 4)) := by
@@ -146,7 +146,7 @@ theorem sqrt_mul_log_le {x : ℝ} (hx : 1 ≤ x) : √x * log x ≤ 12 * x * pnt
 
 theorem hasDerivAt_pntE {x : ℝ} (hx : 1 < x) :
     HasDerivAt pntE (pntE x * (-pntκ * (x⁻¹ / (2 * √(log x))))) x := by
-  have hlog : HasDerivAt log x⁻¹ x := hasDerivAt_log (by linarith)
+  have hlog : HasDerivAt log x⁻¹ x := hasDerivAt_log (by linarith only [hx])
   have h := ((hlog.sqrt (log_pos hx).ne').const_mul (-pntκ)).exp
   exact h
 
@@ -157,7 +157,7 @@ theorem exists_abs_psi_sub_le :
   obtain ⟨X, hX⟩ := eventually_atTop.1 hC
   refine ⟨max C 0, max X 1, le_max_right _ _, fun x hx ↦ ?_⟩
   have hx1 : 1 ≤ x := (le_max_right _ _).trans hx
-  have hx0 : 0 < x := by linarith
+  have hx0 : 0 < x := by linarith only [hx1]
   have h := hX x ((le_max_left _ _).trans hx)
   simp only [Pi.sub_apply, id, norm_eq_abs, norm_mul, abs_of_pos hx0, abs_exp] at h
   have hexp : exp (-StrongPNT.choose * log x ^ ((1 : ℝ) / 2)) ≤ pntE x := by
@@ -176,22 +176,22 @@ theorem exists_abs_psi_sub_le :
 theorem theta_asymp : ∃ C : ℝ, 0 ≤ C ∧ ∀ x ≥ 2, |Chebyshev.theta x - x| ≤ C * x * pntE x := by
   obtain ⟨C, X, hC, hX⟩ := exists_abs_psi_sub_le
   set X' := max X 2
-  refine ⟨max (C + 24) (pntE X')⁻¹, (hC.trans (by linarith)).trans (le_max_left _ _),
+  refine ⟨max (C + 24) (pntE X')⁻¹, (hC.trans (by linarith only [])).trans (le_max_left _ _),
     fun x hx ↦ ?_⟩
-  have hx0 : 0 < x := by linarith
+  have hx0 : 0 < x := by linarith only [hx]
   have hE := pntE_pos x
   rcases le_or_gt X' x with hxX | hxX
   · -- large `x`: use the PNT for `ψ` and `ψ - θ = O(√x log x)`.
     have h1 := hX x ((le_max_left _ _).trans hxX)
-    have h2 := Chebyshev.psi_sub_theta_le (x := x) (by linarith)
+    have h2 := Chebyshev.psi_sub_theta_le (x := x) (by linarith only [hx])
     have h3 := Chebyshev.theta_le_psi x
-    have h4 := sqrt_mul_log_le (x := x) (by linarith)
+    have h4 := sqrt_mul_log_le (x := x) (by linarith only [hx])
     calc |Chebyshev.theta x - x|
         ≤ |Chebyshev.psi x - x| + (Chebyshev.psi x - Chebyshev.theta x) := by
           have h5 := le_abs_self (Chebyshev.psi x - x)
           have h6 := neg_abs_le (Chebyshev.psi x - x)
           rw [abs_le]; constructor <;> linarith
-      _ ≤ C * x * pntE x + 2 * (12 * x * pntE x) := by linarith
+      _ ≤ C * x * pntE x + 2 * (12 * x * pntE x) := by linarith only [h1, h2, h4]
       _ = (C + 24) * x * pntE x := by ring
       _ ≤ max (C + 24) (pntE X')⁻¹ * x * pntE x := by gcongr; exact le_max_left _ _
   · -- small `x`: `0 ≤ θ x ≤ log 4 * x ≤ 2 x` and `pntE x ≥ pntE X'`.
@@ -201,7 +201,7 @@ theorem theta_asymp : ∃ C : ℝ, 0 ≤ C ∧ ∀ x ≥ 2, |Chebyshev.theta x -
       rw [show (4 : ℝ) = 2 ^ 2 by norm_num, log_pow]
       have := log_two_lt_d9
       push_cast
-      linarith
+      linarith only [this]
     have h3 : |Chebyshev.theta x - x| ≤ x := by
       rw [abs_le]; constructor <;> nlinarith
     have h4 : pntE X' ≤ pntE x := pntE_le_pntE hx0 hxX.le
diff --git a/LeanPool/IwaniecLinearSieve/PrimeSums/Lemma13.lean b/LeanPool/IwaniecLinearSieve/PrimeSums/Lemma13.lean
index 987b9b1a35..e471b4bf47 100644
--- a/LeanPool/IwaniecLinearSieve/PrimeSums/Lemma13.lean
+++ b/LeanPool/IwaniecLinearSieve/PrimeSums/Lemma13.lean
@@ -30,10 +30,10 @@ namespace IwaniecLinearSieve
 /-! ### Elementary facts about `log ∘ log` -/
 theorem continuousOn_inv_mul_log {u v : ℝ} (hu : 1 < u) :
     ContinuousOn (fun x ↦ (x * log x)⁻¹) (Set.Icc u v) := by
-  have hpos : ∀ x ∈ Set.Icc u v, 1 < x := fun x hx ↦ by linarith [hx.1]
+  have hpos : ∀ x ∈ Set.Icc u v, 1 < x := fun x hx ↦ by linarith only [hx.1, hu, hx]
   refine ContinuousOn.inv₀ (ContinuousOn.mul continuousOn_id ?_) fun x hx ↦ ?_
   · exact continuousOn_log.mono fun x hx ↦ by
-      simp only [Set.mem_compl_iff, Set.mem_singleton_iff]; linarith [hpos x hx]
+      simp only [Set.mem_compl_iff, Set.mem_singleton_iff]; linarith only [hpos x hx, hpos, hx]
   · have := hpos x hx
     have := log_pos this
     positivity
@@ -41,7 +41,7 @@ theorem continuousOn_inv_mul_log {u v : ℝ} (hu : 1 < u) :
 theorem integral_inv_mul_log {u v : ℝ} (hu : 1 < u) (huv : u ≤ v) :
     ∫ x in u..v, (x * log x)⁻¹ = log (log v) - log (log u) := by
   have hpos : ∀ x ∈ Set.uIcc u v, 1 < x := fun x hx ↦ by
-    rw [Set.uIcc_of_le huv] at hx; linarith [hx.1]
+    rw [Set.uIcc_of_le huv] at hx; linarith only [hx.1, hu, hx]
   refine integral_eq_sub_of_hasDerivAt (f := fun x ↦ log (log x)) (fun x hx ↦ ?_) ?_
   · have hx := hpos x hx
     have h := (hasDerivAt_log (by linarith : x ≠ 0)).log (log_pos hx).ne'
@@ -53,15 +53,15 @@ theorem integral_inv_mul_log {u v : ℝ} (hu : 1 < u) (huv : u ≤ v) :
 
 theorem log_log_sub_log_log_le {u v : ℝ} (hu : 1 < u) (huv : u ≤ v) :
     log (log v) - log (log u) ≤ (v - u) / (u * log u) := by
-  have hu0 : 0 < u := by linarith
+  have hu0 : 0 < u := by linarith only [hu]
   have hlu : 0 < log u := log_pos hu
-  have hlv : 0 < log v := log_pos (by linarith)
+  have hlv : 0 < log v := log_pos (by linarith only [hu, huv])
   have h1 : log (log v) - log (log u) ≤ log v / log u - 1 := by
     rw [← log_div hlv.ne' hlu.ne']
     exact log_le_sub_one_of_pos (div_pos hlv hlu)
   have h2 : log v - log u ≤ v / u - 1 := by
-    rw [← log_div (by linarith) hu0.ne']
-    exact log_le_sub_one_of_pos (div_pos (by linarith) hu0)
+    rw [← log_div (by linarith only [hu, huv]) hu0.ne']
+    exact log_le_sub_one_of_pos (div_pos (by linarith only [hu, huv]) hu0)
   calc log (log v) - log (log u) ≤ log v / log u - 1 := h1
     _ = (log v - log u) / log u := by field_simp
     _ ≤ (v / u - 1) / log u := by gcongr
@@ -146,14 +146,14 @@ theorem le_floor_iff_of_prime {p : ℕ} (hp : p.Prime) {A : ℝ} : p ≤ ⌊A⌋
     have : (0 : ℝ) < p := by exact_mod_cast hp.pos
     constructor <;> intro h
     · exact absurd h (by have := hp.pos; omega)
-    · linarith
+    · linarith only [hA, this, h]
 
 theorem floor_lt_iff_of_prime {p : ℕ} (hp : p.Prime) {B : ℝ} : ⌊B⌋₊ < p ↔ B < p := by
   rcases le_or_gt 0 B with hB | hB
   · exact Nat.floor_lt hB
   · rw [Nat.floor_of_nonpos hB.le]
     have : (0 : ℝ) < p := by exact_mod_cast hp.pos
-    exact ⟨fun _ ↦ by linarith, fun _ ↦ hp.pos⟩
+    exact ⟨fun _ ↦ by linarith only [hB, this], fun _ ↦ hp.pos⟩
 
 theorem mem_primesIoc {B A : ℝ} {p : ℕ} : p ∈ primesIoc B A ↔ p.Prime ∧ B < p ∧ (p : ℝ) ≤ A := by
   simp only [primesIoc, mem_filter, mem_Ioc]
@@ -215,47 +215,47 @@ theorem lemma13_Ioc : ∃ C, 0 ≤ C ∧ ∀ (b : ℝ → ℝ) (A B : ℝ), 2 
     MonotoneOn b (Set.Icc B A) → (∀ x ∈ Set.Icc B A, 0 ≤ b x) →
     |∑ p ∈ primesIoc B A, b p / p - ∫ x in B..A, b x / (x * log x)| ≤ C * b A * pntE B := by
   obtain ⟨c₅, C, hC0, hC⟩ := S_asymp_nonneg
-  refine ⟨2 + 2 * C, by linarith, fun b A B hB hBA hb hb0 ↦ ?_⟩
+  refine ⟨2 + 2 * C, by linarith only [hC0], fun b A B hB hBA hb hb0 ↦ ?_⟩
   set n := ⌊A⌋₊ - ⌊B⌋₊ + 1
-  have h0 : clampPt B A 0 = B := clampPt_zero (by linarith)
+  have h0 : clampPt B A 0 = B := clampPt_zero (by linarith only [hB])
   have hn : clampPt B A n = A := clampPt_last hBA
   have h2 : ∀ j, 2 ≤ clampPt B A j := fun j ↦ hB.trans (le_clampPt B A j)
   have hE : ∀ j, pntE (clampPt B A j) ≤ pntE B := fun j ↦
-    pntE_le_pntE (by linarith) (le_clampPt B A j)
+    pntE_le_pntE (by linarith only [hB]) (le_clampPt B A j)
   have hFf : ∀ j < n, ∫ x in clampPt B A j..clampPt B A (j + 1), (x * log x)⁻¹ =
       (log (log (clampPt B A (j + 1))) + c₅) - (log (log (clampPt B A j)) + c₅) := by
     intro j _
-    rw [integral_inv_mul_log (by linarith [h2 j]) (clampPt_mono B A (Nat.le_succ j))]
+    rw [integral_inv_mul_log (by linarith only [h2 j, h2]) (clampPt_mono B A (Nat.le_succ j))]
     ring
   have hδ : ∀ j < n, (log (log (clampPt B A (j + 1))) + c₅) - (log (log (clampPt B A j)) + c₅) ≤
       2 * pntE B := by
     intro j _
     have hj := h2 j
-    have hlog : 0 < log (clampPt B A j) := log_pos (by linarith)
+    have hlog : 0 < log (clampPt B A j) := log_pos (by linarith only [hj])
     calc _ = log (log (clampPt B A (j + 1))) - log (log (clampPt B A j)) := by ring
       _ ≤ (clampPt B A (j + 1) - clampPt B A j) / (clampPt B A j * log (clampPt B A j)) :=
-          log_log_sub_log_log_le (by linarith) (clampPt_mono B A (Nat.le_succ j))
+          log_log_sub_log_log_le (by linarith only [hj]) (clampPt_mono B A (Nat.le_succ j))
       _ ≤ 1 / (clampPt B A j * log (clampPt B A j)) := by
           gcongr
-          linarith [clampPt_succ_le B A j]
+          linarith only [clampPt_succ_le B A j]
       _ ≤ 2 * pntE (clampPt B A j) := one_div_mul_log_le_pntE hj
-      _ ≤ 2 * pntE B := by linarith [hE j]
+      _ ≤ 2 * pntE B := by linarith only [hE j, hE]
   have hε : ∀ j ≤ n, |S (clampPt B A j) - (log (log (clampPt B A j)) + c₅)| ≤ C * pntE B := by
     intro j _
     rw [← sub_sub]
     exact (hC _ (h2 j)).trans (mul_le_mul_of_nonneg_left (hE j) hC0)
   have key := abs_sum_sub_integral_le (n := n) (a := clampPt B A) (clampPt_mono B A)
     (b := b) (f := fun x ↦ (x * log x)⁻¹) (F := fun x ↦ log (log x) + c₅)
-    (g := fun j ↦ S (clampPt B A j)) (by linarith [pntE_pos B]) (by rw [h0, hn]; exact hb)
+    (g := fun j ↦ S (clampPt B A j)) (by linarith only [pntE_pos B]) (by rw [h0, hn]; exact hb)
     (by rw [h0]; exact hb0 B ⟨le_rfl, hBA⟩)
     (by
       rw [h0, hn]
       intro x hx
-      have : 0 < log x := log_pos (by linarith [hx.1])
-      have : 0 < x := by linarith [hx.1]
+      have : 0 < log x := log_pos (by linarith only [hx.1, hB, hx])
+      have : 0 < x := by linarith only [hx.1, hB, hx]
       positivity)
-    (by rw [h0, hn]; exact continuousOn_inv_mul_log (by linarith)) hFf hδ hε
-  rw [h0, hn, sum_clampPt_eq b (by linarith) hBA] at key
+    (by rw [h0, hn]; exact continuousOn_inv_mul_log (by linarith only [hB])) hFf hδ hε
+  rw [h0, hn, sum_clampPt_eq b (by linarith only [hB]) hBA] at key
   simp_rw [div_eq_mul_inv (b _)]
   calc _ ≤ (2 * pntE B + 2 * (C * pntE B)) * b A := key
     _ = (2 + 2 * C) * b A * pntE B := by ring
@@ -266,7 +266,7 @@ theorem sum_of_forall_cast_eq {t : Finset ℕ} {v : ℝ} (h : ∀ p ∈ t, (p :
     exact_mod_cast (h a ha).trans (h b hb).symm
   have hcard' : (t.card : ℝ) ≤ 1 := by exact_mod_cast hcard
   rw [sum_congr rfl fun p hp ↦ by rw [h p hp], sum_const, nsmul_eq_mul]
-  exact ⟨by positivity, by nlinarith⟩
+  exact ⟨by positivity, by nlinarith only [hφ, hcard']⟩
 
 /-- [I71, Lemma 13], increasing case, for any set of primes between those in `(B, A)` and
 those in `[B, A]`. -/
@@ -275,8 +275,8 @@ theorem lemma13_mono_of_subset : ∃ C, 0 ≤ C ∧ ∀ (b : ℝ → ℝ) (A B :
     (∀ p ∈ s, p.Prime ∧ B ≤ p ∧ (p : ℝ) ≤ A) → (∀ p : ℕ, p.Prime → B < p → (p : ℝ) < A → p ∈ s) →
     |∑ p ∈ s, b p / p - ∫ x in B..A, b x / (x * log x)| ≤ C * b A * pntE B := by
   obtain ⟨C, hC0, hC⟩ := lemma13_Ioc
-  refine ⟨C + 1, by linarith, fun b A B s hB hBA hb hb0 hs1 hs2 ↦ ?_⟩
-  have hB0 : 0 < B := by linarith
+  refine ⟨C + 1, by linarith only [hC0], fun b A B s hB hBA hb hb0 hs1 hs2 ↦ ?_⟩
+  have hB0 : 0 < B := by linarith only [hB]
   have hbA : 0 ≤ b A := hb0 A ⟨hBA, le_rfl⟩
   have hbB : 0 ≤ b B := hb0 B ⟨le_rfl, hBA⟩
   have hbBA : b B ≤ b A := hb ⟨le_rfl, hBA⟩ ⟨hBA, le_rfl⟩ hBA
@@ -290,7 +290,7 @@ theorem lemma13_mono_of_subset : ∃ C, 0 ≤ C ∧ ∀ (b : ℝ → ℝ) (A B :
       rw [Finset.mem_sdiff, mem_primesIoc] at hp
       obtain ⟨⟨hpp, hBp, hpA⟩, hp2⟩ := hp
       exact le_antisymm hpA (not_lt.1 fun h ↦ hp2 (hs2 p hpp hBp h)))
-    (fun x ↦ b x / x) (div_nonneg hbA (by linarith))
+    (fun x ↦ b x / x) (div_nonneg hbA (by linarith only [hB, hBA]))
   have h3 : b B / B ≤ b A * pntE B := by
     calc b B / B ≤ b A / B := by gcongr
       _ = b A * B⁻¹ := div_eq_mul_inv _ _
@@ -330,29 +330,29 @@ theorem lemma13_anti_of_subset : ∃ C, 0 ≤ C ∧ ∀ (b : ℝ → ℝ) (A B :
     (∀ p ∈ s, p.Prime ∧ B ≤ p ∧ (p : ℝ) ≤ A) → (∀ p : ℕ, p.Prime → B < p → (p : ℝ) < A → p ∈ s) →
     |∑ p ∈ s, b p / p - ∫ x in B..A, b x / (x * log x)| ≤ C * b B * pntE B := by
   obtain ⟨C, hC0, hC⟩ := lemma13_mono_of_subset
-  refine ⟨2 * C, by linarith, fun b A B s hB hBA hb hb0 hs1 hs2 ↦ ?_⟩
+  refine ⟨2 * C, by linarith only [hC0], fun b A B s hB hBA hb hb0 hs1 hs2 ↦ ?_⟩
   set c := b B
   have hc : 0 ≤ c := hb0 B ⟨le_rfl, hBA⟩
   have hbA : 0 ≤ b A := hb0 A ⟨hBA, le_rfl⟩
   have hbA' : b A ≤ c := hb ⟨le_rfl, hBA⟩ ⟨hBA, le_rfl⟩ hBA
   have hb' : MonotoneOn (fun x ↦ c - b x) (Set.Icc B A) := fun x hx y hy hxy ↦ by
-    simp only; linarith [hb hx hy hxy]
+    simp only; linarith only [hb hx hy hxy, hb, hx, hy, hxy]
   have hb'0 : ∀ x ∈ Set.Icc B A, 0 ≤ c - b x := fun x hx ↦ by
-    simp only [c]; linarith [hb ⟨le_rfl, hBA⟩ hx hx.1]
+    simp only [c]; linarith only [hb ⟨le_rfl, hBA⟩ hx hx.1, hb, hBA, hx]
   have e1 := hC (fun _ ↦ c) A B s hB hBA (fun _ _ _ _ _ ↦ le_rfl) (fun _ _ ↦ hc) hs1 hs2
   have e2 := hC (fun x ↦ c - b x) A B s hB hBA hb' hb'0 hs1 hs2
   have hsum : ∑ p ∈ s, b p / p = ∑ p ∈ s, c / p - ∑ p ∈ s, (c - b p) / p := by
     rw [← sum_sub_distrib]; exact sum_congr rfl fun p _ ↦ by ring
   have hint : ∫ x in B..A, b x / (x * log x) =
       (∫ x in B..A, c / (x * log x)) - ∫ x in B..A, (c - b x) / (x * log x) := by
-    rw [← integral_sub (intervalIntegrable_div_mul_log (by linarith) hBA
-      (Or.inl fun _ _ _ _ _ ↦ le_rfl)) (intervalIntegrable_div_mul_log (by linarith) hBA
+    rw [← integral_sub (intervalIntegrable_div_mul_log (by linarith only [hB]) hBA
+      (Or.inl fun _ _ _ _ _ ↦ le_rfl)) (intervalIntegrable_div_mul_log (by linarith only [hB]) hBA
       (Or.inl hb'))]
     exact integral_congr fun x _ ↦ by ring
   rw [hsum, hint]
   have h5 : 0 ≤ C * b A * pntE B := mul_nonneg (mul_nonneg hC0 hbA) (pntE_pos B).le
   rw [abs_le] at e1 e2 ⊢
-  constructor <;> linarith
+  constructor <;> linarith only [e1, e2, h5]
 
 /-- [I71, Lemma 13], decreasing case: for `b ≥ 0` decreasing on `[B, A]`, `2 ≤ B ≤ A`,
 `|∑_{B ≤ p ≤ A} b(p)/p - ∫_B^A b(x)/(x log x) dx| ≤ C b(B) exp(-κ √(log B))`. -/
@@ -367,7 +367,7 @@ theorem lemma13_anti : ∃ C, ∀ (b : ℝ → ℝ) (A B : ℝ), 2 ≤ B → B 
 theorem integral_inv_log_div_mul_log {u v : ℝ} (hu : 1 < u) (huv : u ≤ v) :
     ∫ x in u..v, (log x)⁻¹ / (x * log x) = 1 / log u - 1 / log v := by
   have hpos : ∀ x ∈ Set.uIcc u v, 1 < x := fun x hx ↦ by
-    rw [Set.uIcc_of_le huv] at hx; linarith [hx.1]
+    rw [Set.uIcc_of_le huv] at hx; linarith only [hx.1, hu, hx]
   have hderiv : ∀ x ∈ Set.uIcc u v,
       HasDerivAt (fun x ↦ -(log x)⁻¹) ((log x)⁻¹ / (x * log x)) x := fun x hx ↦ by
     have hx := hpos x hx
@@ -378,8 +378,8 @@ theorem integral_inv_log_div_mul_log {u v : ℝ} (hu : 1 < u) (huv : u ≤ v) :
     have hc := continuousOn_inv_mul_log (v := v) hu
     have hl : ContinuousOn (fun x ↦ (log x)⁻¹) (Set.Icc u v) :=
       ContinuousOn.inv₀ (continuousOn_log.mono fun x hx ↦ by
-        simp only [Set.mem_compl_iff, Set.mem_singleton_iff]; linarith [hx.1])
-        fun x hx ↦ (log_pos (by linarith [hx.1])).ne'
+        simp only [Set.mem_compl_iff, Set.mem_singleton_iff]; linarith only [hx.1, hu, hx])
+        fun x hx ↦ (log_pos (by linarith only [hx.1, hu, hx])).ne'
     simp_rw [div_eq_mul_inv ((log _)⁻¹)]
     exact (hl.mul hc).intervalIntegrable_of_Icc huv
   rw [integral_eq_sub_of_hasDerivAt hderiv hint]
@@ -394,12 +394,12 @@ theorem lemma14_of_subset : ∃ C, ∀ (A B : ℝ) (s : Finset ℕ), 2 ≤ B →
   refine ⟨2 * C, fun A B s hB hBA hs1 hs2 ↦ ?_⟩
   have hlogB : 1 / 2 ≤ log B := half_le_log hB
   have hb : AntitoneOn (fun x ↦ (log x)⁻¹) (Set.Icc B A) := fun x hx y hy hxy ↦ by
-    have hx0 : 0 < log x := log_pos (by linarith [hx.1])
-    exact inv_anti₀ hx0 (log_le_log (by linarith [hx.1]) hxy)
+    have hx0 : 0 < log x := log_pos (by linarith only [hx.1, hB, hx])
+    exact inv_anti₀ hx0 (log_le_log (by linarith only [hx.1, hB, hx]) hxy)
   have hb0 : ∀ x ∈ Set.Icc B A, 0 ≤ (log x)⁻¹ := fun x hx ↦
-    inv_nonneg.2 (log_nonneg (by linarith [hx.1]))
+    inv_nonneg.2 (log_nonneg (by linarith only [hx.1, hB, hx]))
   have h := hC _ A B s hB hBA hb hb0 hs1 hs2
-  rw [integral_inv_log_div_mul_log (by linarith) hBA] at h
+  rw [integral_inv_log_div_mul_log (by linarith only [hB]) hBA] at h
   have hsum : ∑ p ∈ s, (log (p : ℝ))⁻¹ / p = ∑ p ∈ s, 1 / (p * log p) :=
     sum_congr rfl fun p _ ↦ by ring
   rw [hsum] at h
diff --git a/LeanPool/IwaniecLinearSieve/PrimeSums/Mertens.lean b/LeanPool/IwaniecLinearSieve/PrimeSums/Mertens.lean
index b0dce2ebd1..8e857d8dad 100644
--- a/LeanPool/IwaniecLinearSieve/PrimeSums/Mertens.lean
+++ b/LeanPool/IwaniecLinearSieve/PrimeSums/Mertens.lean
@@ -38,8 +38,8 @@ theorem exists_abs_sub_le_of_cauchy {T g : ℝ → ℝ} {a : ℝ}
     refine ⟨N, fun n hn ↦ ?_⟩
     rw [Real.dist_eq]
     have hNn : (N : ℝ) ≤ n := by exact_mod_cast hn
-    calc |u n - u N| ≤ g (a + N) := h _ _ (by simp) (by linarith)
-      _ < ε := hX _ (by linarith)
+    calc |u n - u N| ≤ g (a + N) := h _ _ (by simp) (by linarith only [hNn])
+      _ < ε := hX _ (by linarith only [hN])
   obtain ⟨c, hc⟩ := cauchySeq_tendsto_of_complete hu
   refine ⟨c, fun x hx ↦ ?_⟩
   have h1 : Tendsto (fun n : ℕ ↦ |u n - T x|) atTop (𝓝 |c - T x|) := (hc.sub_const _).abs
@@ -47,7 +47,7 @@ theorem exists_abs_sub_le_of_cauchy {T g : ℝ → ℝ} {a : ℝ}
     obtain ⟨N, hN⟩ := exists_nat_ge (x - a)
     filter_upwards [eventually_ge_atTop N] with n hn
     have hNn : (N : ℝ) ≤ n := by exact_mod_cast hn
-    exact h x (a + n) hx (by linarith)
+    exact h x (a + n) hx (by linarith only [hN, hNn])
   rw [abs_sub_comm]
   exact le_of_tendsto h1 h2
 
@@ -79,7 +79,7 @@ theorem S_sub_S {x y : ℝ} (hxy : x ≤ y) :
 
 theorem hasDerivAt_inv_mul_log {t : ℝ} (ht : 1 < t) :
     HasDerivAt (fun t ↦ (t * log t)⁻¹) (-((log t + 1) / (t * log t) ^ 2)) t := by
-  have h0 : t ≠ 0 := by linarith
+  have h0 : t ≠ 0 := by linarith only [ht]
   have h1 : HasDerivAt (fun t ↦ t * log t) (1 * log t + t * t⁻¹) t :=
     (hasDerivAt_id t).mul (hasDerivAt_log h0)
   convert h1.inv (mul_ne_zero h0 (log_pos ht).ne') using 1
@@ -88,7 +88,7 @@ theorem hasDerivAt_inv_mul_log {t : ℝ} (ht : 1 < t) :
 
 theorem hasDerivAt_log_log_sub_inv_log {t : ℝ} (ht : 1 < t) :
     HasDerivAt (fun t ↦ log (log t) - (log t)⁻¹) ((log t + 1) / (t * log t) ^ 2 * t) t := by
-  have h0 : t ≠ 0 := by linarith
+  have h0 : t ≠ 0 := by linarith only [ht]
   have hl : log t ≠ 0 := (log_pos ht).ne'
   convert ((hasDerivAt_log h0).log hl).sub ((hasDerivAt_log h0).inv hl) using 1
   field_simp
@@ -98,9 +98,9 @@ theorem continuousOn_log_add_one_div {x y : ℝ} (hx : 1 < x) :
     ContinuousOn (fun t ↦ (log t + 1) / (t * log t) ^ 2) (Set.Icc x y) := by
   have hlog : ContinuousOn log (Set.Icc x y) :=
     continuousOn_log.mono fun t ht ↦ by
-      simp only [Set.mem_compl_iff, Set.mem_singleton_iff]; linarith [ht.1]
+      simp only [Set.mem_compl_iff, Set.mem_singleton_iff]; linarith only [ht.1, hx, ht]
   refine ContinuousOn.div (by fun_prop) (by fun_prop) fun t ht ↦ ?_
-  have : 1 < t := by linarith [ht.1]
+  have : 1 < t := by linarith only [ht.1, hx, ht]
   have := log_pos this
   positivity
 
@@ -109,16 +109,16 @@ theorem S_sub_loglog_eq {x y : ℝ} (hx : 2 ≤ x) (hxy : x ≤ y) :
     (S y - log (log y)) - (S x - log (log x)) =
       (y * log y)⁻¹ * (θ y - y) - (x * log x)⁻¹ * (θ x - x) +
         ∫ t in x..y, (log t + 1) / (t * log t) ^ 2 * (θ t - t) := by
-  have hpos : ∀ t ∈ Set.Icc x y, 1 < t := fun t ht ↦ by linarith [ht.1]
+  have hpos : ∀ t ∈ Set.Icc x y, 1 < t := fun t ht ↦ by linarith only [ht.1, hx, ht]
   have hderiv : ∀ t ∈ Set.Icc x y,
       HasDerivAt (fun t ↦ (t * log t)⁻¹) (-((log t + 1) / (t * log t) ^ 2)) t :=
     fun t ht ↦ hasDerivAt_inv_mul_log (hpos t ht)
-  have hcont := continuousOn_log_add_one_div (y := y) (show 1 < x by linarith)
+  have hcont := continuousOn_log_add_one_div (y := y) (show 1 < x by linarith only [hx])
   have hint : IntegrableOn (deriv fun t ↦ (t * log t)⁻¹) (Set.Icc x y) :=
     hcont.neg.integrableOn_Icc.congr_fun (fun t ht ↦ ((hderiv t ht).deriv).symm)
       measurableSet_Icc
   have habel := sum_mul_eq_sub_sub_integral_mul logPrime (f := fun t ↦ (t * log t)⁻¹)
-    (by linarith) hxy (fun t ht ↦ (hderiv t ht).differentiableAt) hint
+    (by linarith only [hx]) hxy (fun t ht ↦ (hderiv t ht).differentiableAt) hint
   rw [← S_sub_S hxy] at habel
   simp only [sum_logPrime_eq_theta] at habel
   rw [setIntegral_congr_fun measurableSet_Ioc
@@ -149,8 +149,8 @@ theorem S_sub_loglog_eq {x y : ℝ} (hx : 2 ≤ x) (hxy : x ≤ y) :
     integral_eq_sub_of_hasDerivAt
       (fun t ht ↦ hasDerivAt_log_log_sub_inv_log (hpos t (by rwa [Set.uIcc_of_le hxy] at ht)))
       hi2
-  have hy0 : y ≠ 0 := by linarith
-  have hx0 : x ≠ 0 := by linarith
+  have hy0 : y ≠ 0 := by linarith only [hx, hxy]
+  have hx0 : x ≠ 0 := by linarith only [hx]
   have hfy : (y * log y)⁻¹ * y = (log y)⁻¹ := by field_simp
   have hfx : (x * log x)⁻¹ * x = (log x)⁻¹ := by field_simp
   rw [hneg] at habel
@@ -164,14 +164,14 @@ theorem half_le_log {t : ℝ} (ht : 2 ≤ t) : 1 / 2 ≤ log t := by
 
 theorem continuousOn_deriv_pntE {x y : ℝ} (hx : 1 < x) :
     ContinuousOn (fun t ↦ pntE t * (-pntκ * (t⁻¹ / (2 * √(log t))))) (Set.Icc x y) := by
-  have hpos : ∀ t ∈ Set.Icc x y, 1 < t := fun t ht ↦ by linarith [ht.1]
+  have hpos : ∀ t ∈ Set.Icc x y, 1 < t := fun t ht ↦ by linarith only [ht.1, hx, ht]
   have hlog : ContinuousOn log (Set.Icc x y) :=
     continuousOn_log.mono fun t ht ↦ by
-      simp only [Set.mem_compl_iff, Set.mem_singleton_iff]; linarith [hpos t ht]
+      simp only [Set.mem_compl_iff, Set.mem_singleton_iff]; linarith only [hpos t ht, hpos, ht]
   unfold pntE
   refine ContinuousOn.mul (by fun_prop) (ContinuousOn.mul (by fun_prop) ?_)
   refine ContinuousOn.div (continuousOn_inv₀.mono fun t ht ↦ ?_) (by fun_prop) fun t ht ↦ ?_
-  · simp only [Set.mem_compl_iff, Set.mem_singleton_iff]; linarith [hpos t ht]
+  · simp only [Set.mem_compl_iff, Set.mem_singleton_iff]; linarith only [hpos t ht, hpos, ht]
   · have := sqrt_pos.2 (log_pos (hpos t ht))
     positivity
 
@@ -180,15 +180,15 @@ theorem abs_integrand_le {C t : ℝ} (hC : 0 ≤ C) (ht : 2 ≤ t)
     (hθ : |θ t - t| ≤ C * t * pntE t) :
     |(log t + 1) / (t * log t) ^ 2 * (θ t - t)| ≤
       -(12 * C / pntκ) * (pntE t * (-pntκ * (t⁻¹ / (2 * √(log t))))) := by
-  have ht0 : 0 < t := by linarith
+  have ht0 : 0 < t := by linarith only [ht]
   have hL := half_le_log ht
-  have hL0 : 0 < log t := by linarith
-  have hs : 1 / 2 ≤ √(log t) := (le_sqrt (by norm_num) hL0.le).2 (by linarith)
-  have hs0 : 0 < √(log t) := by linarith
+  have hL0 : 0 < log t := by linarith only [hL]
+  have hs : 1 / 2 ≤ √(log t) := (le_sqrt (by norm_num) hL0.le).2 (by linarith only [hL, hL0])
+  have hs0 : 0 < √(log t) := by linarith only [hs]
   have hss := mul_self_sqrt hL0.le
   have hE := pntE_pos t
   have hκ := pntκ_pos
-  have key : (log t + 1) * √(log t) ≤ 6 * log t ^ 2 := by nlinarith
+  have key : (log t + 1) * √(log t) ≤ 6 * log t ^ 2 := by nlinarith only [hL, hss, hs]
   calc |(log t + 1) / (t * log t) ^ 2 * (θ t - t)|
       = (log t + 1) / (t * log t) ^ 2 * |θ t - t| := by
         rw [abs_mul, abs_of_nonneg (by positivity)]
@@ -197,7 +197,7 @@ theorem abs_integrand_le {C t : ℝ} (hC : 0 ≤ C) (ht : 2 ≤ t)
     _ ≤ C * pntE t * (6 / (t * √(log t))) := by
         refine mul_le_mul_of_nonneg_left ?_ (by positivity)
         rw [div_le_div_iff₀ (by positivity) (by positivity)]
-        nlinarith
+        nlinarith only [key, ht]
     _ = -(12 * C / pntκ) * (pntE t * (-pntκ * (t⁻¹ / (2 * √(log t))))) := by
         field_simp
         ring
@@ -213,7 +213,7 @@ theorem exists_abs_S_sub_loglog_sub_le :
   have hbd : ∀ t, x ≤ t → |(t * log t)⁻¹ * (θ t - t)| ≤ 2 * C * pntE x := by
     intro t hxt
     have ht : 2 ≤ t := hx.trans hxt
-    have ht0 : 0 < t := by linarith
+    have ht0 : 0 < t := by linarith only [hx, hxt]
     have hL := half_le_log ht
     have hE := pntE_pos t
     calc |(t * log t)⁻¹ * (θ t - t)| = (t * log t)⁻¹ * |θ t - t| := by
@@ -221,13 +221,13 @@ theorem exists_abs_S_sub_loglog_sub_le :
       _ ≤ (t * log t)⁻¹ * (C * t * pntE t) := by gcongr; exact hC t ht
       _ = C * pntE t / log t := by field_simp
       _ ≤ 2 * C * pntE t := by
-          rw [div_le_iff₀ (by linarith)]
-          nlinarith [mul_nonneg hC0 hE.le]
-      _ ≤ 2 * C * pntE x := by gcongr; exact pntE_le_pntE (by linarith) hxt
+          rw [div_le_iff₀ (by linarith only [hL])]
+          nlinarith only [mul_nonneg hC0 hE.le, hL, hC0, hE]
+      _ ≤ 2 * C * pntE x := by gcongr; exact pntE_le_pntE (by linarith only [hx]) hxt
   have hderivE : ∀ t ∈ Set.uIcc x y,
       HasDerivAt pntE (pntE t * (-pntκ * (t⁻¹ / (2 * √(log t))))) t := fun t ht ↦
-    hasDerivAt_pntE (by rw [Set.uIcc_of_le hxy] at ht; linarith [ht.1])
-  have hcontE := continuousOn_deriv_pntE (y := y) (show 1 < x by linarith)
+    hasDerivAt_pntE (by rw [Set.uIcc_of_le hxy] at ht; linarith only [ht.1, hx, ht])
+  have hcontE := continuousOn_deriv_pntE (y := y) (show 1 < x by linarith only [hx])
   rw [← Set.uIcc_of_le hxy] at hcontE
   have hintE := hcontE.intervalIntegrable (μ := volume)
   have hftc : ∫ t in x..y, -(12 * C / pntκ) * (pntE t * (-pntκ * (t⁻¹ / (2 * √(log t))))) =
@@ -240,7 +240,7 @@ theorem exists_abs_S_sub_loglog_sub_le :
     refine (norm_integral_le_of_norm_le hxy (ae_of_all _ fun t ht ↦ ?_)
       (hintE.const_mul (-(12 * C / pntκ)))).trans ?_
     · rw [norm_eq_abs]
-      have ht2 : 2 ≤ t := by linarith [ht.1]
+      have ht2 : 2 ≤ t := by linarith only [ht.1, hx, ht]
       exact abs_integrand_le hC0 ht2 (hC t ht2)
     · rw [hftc]
       have := pntE_pos y
@@ -251,7 +251,7 @@ theorem exists_abs_S_sub_loglog_sub_le :
   calc _ ≤ |(y * log y)⁻¹ * (θ y - y)| + |(x * log x)⁻¹ * (θ x - x)| +
         |∫ t in x..y, (log t + 1) / (t * log t) ^ 2 * (θ t - t)| :=
         (abs_add_le _ _).trans (add_le_add_left (abs_sub _ _) _)
-    _ ≤ (4 * C + 12 * C / pntκ) * pntE x := by linarith
+    _ ≤ (4 * C + 12 * C / pntκ) * pntE x := by linarith only [hint, h1, h2]
 
 /-- Mertens' second theorem with the de la Vallée Poussin error term. -/
 theorem S_asymp : ∃ c₅ C : ℝ, ∀ x ≥ 2, |S x - log (log x) - c₅| ≤ C * pntE x := by
diff --git a/LeanPool/IwaniecLinearSieve/PrimeSums/NthPrime.lean b/LeanPool/IwaniecLinearSieve/PrimeSums/NthPrime.lean
index 5b092e1d6c..209f17c7fb 100644
--- a/LeanPool/IwaniecLinearSieve/PrimeSums/NthPrime.lean
+++ b/LeanPool/IwaniecLinearSieve/PrimeSums/NthPrime.lean
@@ -25,12 +25,12 @@ open Real Filter Topology
 namespace IwaniecLinearSieve
 
 theorem log_le_div_eight {K : ℝ} (hK : 256 ≤ K) : log K ≤ K / 8 := by
-  have hK0 : 0 < K := by linarith
-  have hs : 16 ≤ √K := (le_sqrt (by norm_num) hK0.le).2 (by linarith)
+  have hK0 : 0 < K := by linarith only [hK]
+  have hs : 16 ≤ √K := (le_sqrt (by norm_num) hK0.le).2 (by linarith only [hK])
   have h1 : log K = 2 * log √K := by rw [log_sqrt hK0.le]; ring
   have h2 := log_le_sub_one_of_pos (sqrt_pos.2 hK0)
   have h3 := sq_sqrt hK0.le
-  nlinarith
+  nlinarith only [hK, h1, h2, h3, hs]
 
 /-- The `r`-th prime `p_r = Nat.nth Nat.Prime (r - 1)` satisfies `p_r ≤ C r log r`. -/
 theorem nth_prime_le : ∃ C, ∀ r : ℕ, 2 ≤ r → (Nat.nth Nat.Prime (r - 1) : ℝ) ≤ C * r * log r := by
diff --git a/LeanPool/IwaniecLinearSieve/PrimeSums/Product.lean b/LeanPool/IwaniecLinearSieve/PrimeSums/Product.lean
index b359526d52..7206d2507a 100644
--- a/LeanPool/IwaniecLinearSieve/PrimeSums/Product.lean
+++ b/LeanPool/IwaniecLinearSieve/PrimeSums/Product.lean
@@ -30,7 +30,7 @@ theorem one_sub_inv_pos {p : ℕ} (hp : p.Prime) : 0 < 1 - (p : ℝ)⁻¹ := by
 
 theorem one_sub_inv_le_one (p : ℕ) : 1 - (p : ℝ)⁻¹ ≤ 1 := by
   have : (0 : ℝ) ≤ (p : ℝ)⁻¹ := by positivity
-  linarith
+  linarith only [this]
 
 theorem primesLT_mono {z w : ℝ} (hzw : z ≤ w) : primesLT z ⊆ primesLT w := fun p hp ↦ by
   rw [mem_primesLT] at hp ⊢
@@ -81,20 +81,20 @@ theorem S_sub_SLT {z : ℝ} (hz : 0 < z) : 0 ≤ S z - SLT z ∧ S z - SLT z ≤
 /-- `0 ≤ -log (1 - 1/p) - 1/p ≤ 1/(p-1) - 1/p`. -/
 theorem abs_log_one_sub_inv_add_inv_le {p : ℝ} (hp : 2 ≤ p) :
     |log (1 - p⁻¹) + p⁻¹| ≤ (p - 1)⁻¹ - p⁻¹ := by
-  have hp0 : 0 < p := by linarith
+  have hp0 : 0 < p := by linarith only [hp]
   have hq : 0 < 1 - p⁻¹ := by
-    rw [sub_pos]; exact inv_lt_one_of_one_lt₀ (by linarith)
-  have h1 : log (1 - p⁻¹) ≤ -p⁻¹ := by linarith [log_le_sub_one_of_pos hq]
+    rw [sub_pos]; exact inv_lt_one_of_one_lt₀ (by linarith only [hp])
+  have h1 : log (1 - p⁻¹) ≤ -p⁻¹ := by linarith only [log_le_sub_one_of_pos hq, hq]
   have h2 : -((1 - p⁻¹)⁻¹ - 1) ≤ log (1 - p⁻¹) := by
     have := log_le_sub_one_of_pos (inv_pos.2 hq)
     rw [log_inv] at this
-    linarith
+    linarith only [this]
   have h3 : (1 - p⁻¹)⁻¹ - 1 = (p - 1)⁻¹ := by
-    have : p - 1 ≠ 0 := by linarith
+    have : p - 1 ≠ 0 := by linarith only [hp]
     field_simp
     ring
-  rw [abs_of_nonpos (by linarith)]
-  linarith
+  rw [abs_of_nonpos (by linarith only [h1])]
+  linarith only [h2, h3]
 
 theorem sum_Ico_inv_sub_inv {m M : ℕ} (hmM : m ≤ M) :
     ∑ n ∈ Ico m M, (((n : ℝ) - 1)⁻¹ - (n : ℝ)⁻¹) = ((m : ℝ) - 1)⁻¹ - ((M : ℝ) - 1)⁻¹ := by
@@ -127,27 +127,27 @@ theorem abs_sum_log_one_sub_inv_add_inv_le {z w : ℝ} (hz : 2 ≤ z) (hzw : z 
         sum_le_sum_of_subset_of_nonneg hsub fun n hn _ ↦ hnn n hn
     _ = ((⌈z⌉₊ : ℝ) - 1)⁻¹ - ((⌈w⌉₊ : ℝ) - 1)⁻¹ := sum_Ico_inv_sub_inv (Nat.ceil_mono hzw)
     _ ≤ (z - 1)⁻¹ := by
-        have : 0 ≤ ((⌈w⌉₊ : ℝ) - 1)⁻¹ := inv_nonneg.2 (by linarith)
+        have : 0 ≤ ((⌈w⌉₊ : ℝ) - 1)⁻¹ := inv_nonneg.2 (by linarith only [hw1])
         have : ((⌈z⌉₊ : ℝ) - 1)⁻¹ ≤ (z - 1)⁻¹ :=
           inv_anti₀ (by linarith) (by linarith [Nat.le_ceil z])
         linarith
     _ ≤ 2 * z⁻¹ := by
         rw [← div_eq_mul_inv, inv_eq_one_div, div_le_div_iff₀ (by linarith) (by linarith)]
-        linarith
+        linarith only [hz]
 
 theorem log_R_eq (z : ℝ) : log (R z) = ∑ p ∈ primesLT z, log (1 - (p : ℝ)⁻¹) :=
   log_prod fun _ hp ↦ (one_sub_inv_pos (mem_primesLT.1 hp).1).ne'
 
 theorem abs_exp_sub_one_le_mul_exp (d : ℝ) : |exp d - 1| ≤ |d| * exp |d| := by
   rcases le_total 0 d with hd | hd
-  · rw [abs_of_nonneg hd, abs_of_nonneg (by linarith [add_one_le_exp d])]
+  · rw [abs_of_nonneg hd, abs_of_nonneg (by linarith only [add_one_le_exp d, hd])]
     have h1 := add_one_le_exp (-d)
     have h2 : exp d * exp (-d) = 1 := by rw [← exp_add]; simp
-    nlinarith [exp_pos d]
-  · rw [abs_of_nonpos hd, abs_of_nonpos (by linarith [exp_le_one_iff.2 hd])]
+    nlinarith only [exp_pos d, h2, h1]
+  · rw [abs_of_nonpos hd, abs_of_nonpos (by linarith only [exp_le_one_iff.2 hd, hd])]
     have h1 := add_one_le_exp d
-    have h2 : 1 ≤ exp (-d) := one_le_exp_iff.2 (by linarith)
-    nlinarith
+    have h2 : 1 ≤ exp (-d) := one_le_exp_iff.2 (by linarith only [hd])
+    nlinarith only [h1, hd, h2]
 
 theorem exists_abs_log_R_add_loglog_sub_le :
     ∃ K, 0 ≤ K ∧ ∀ z w, 2 ≤ z → z ≤ w →
@@ -170,13 +170,13 @@ theorem exists_abs_log_R_add_loglog_sub_le :
     ring
   have h1 := abs_sum_log_one_sub_inv_add_inv_le hz hzw
   rw [sum_add_distrib, ← hR, ← hS] at h1
-  have h2 := S_sub_SLT (z := z) (by linarith)
-  have h3 := S_sub_SLT (z := w) (by linarith)
+  have h2 := S_sub_SLT (z := z) (by linarith only [hz])
+  have h3 := S_sub_SLT (z := w) (by linarith only [hz, hzw])
   have h4 := hC z hz
   have h5 := hC w hw
-  have hE : pntE w ≤ pntE z := pntE_le_pntE (by linarith) hzw
+  have hE : pntE w ≤ pntE z := pntE_le_pntE (by linarith only [hz]) hzw
   have hiz := inv_le_pntE hz
-  have hiw : w⁻¹ ≤ z⁻¹ := inv_anti₀ (by linarith) hzw
+  have hiw : w⁻¹ ≤ z⁻¹ := inv_anti₀ (by linarith only [hz]) hzw
   rw [abs_le] at h1 h4 h5 ⊢
   constructor <;> nlinarith
 
@@ -186,13 +186,13 @@ theorem R_asymp : ∃ cR > 0, ∃ C, ∀ z ≥ 2, |R z * log z - cR| ≤ C * pnt
   obtain ⟨L, hL⟩ := exists_abs_sub_le_of_cauchy (T := fun z ↦ log (R z) + log (log z))
     (g := fun z ↦ K * pntE z) (a := 2) hK (by simpa using tendsto_pntE.const_mul K)
   refine ⟨exp L, exp_pos L, exp L * (K * exp K), fun z hz ↦ ?_⟩
-  have hlog : 0 < log z := log_pos (by linarith)
+  have hlog : 0 < log z := log_pos (by linarith only [hz])
   have hRz : R z * log z = exp (log (R z) + log (log z)) := by
     rw [exp_add, exp_log (R_pos z), exp_log hlog]
   have hd := hL z hz
   have hdK : |log (R z) + log (log z) - L| ≤ K := by
     have := pntE_le_one z
-    nlinarith
+    nlinarith only [hd, hK0, this]
   rw [hRz, show exp (log (R z) + log (log z)) - exp L =
       exp L * (exp (log (R z) + log (log z) - L) - 1) by rw [mul_sub, ← exp_add]; ring_nf,
     abs_mul, abs_of_pos (exp_pos L)]
@@ -214,13 +214,13 @@ theorem R_lower : ∃ c > 0, ∀ z ≥ 2, c / log z ≤ R z := by
   have hlog2 : 0 < log 2 := log_pos one_lt_two
   refine ⟨min (cR / 2) (R Z' * log 2), lt_min (half_pos hcR) (mul_pos (R_pos _) hlog2),
     fun z hz ↦ ?_⟩
-  have hlog : 0 < log z := log_pos (by linarith)
+  have hlog : 0 < log z := log_pos (by linarith only [hz])
   rw [div_le_iff₀ hlog]
   rcases le_or_gt Z' z with hzZ | hzZ
   · have h1 := hC z hz
     have h2 := hZ z ((le_max_left _ _).trans hzZ)
     rw [abs_le] at h1
-    exact (min_le_left _ _).trans (by linarith)
+    exact (min_le_left _ _).trans (by linarith only [h1, h2])
   · refine (min_le_right _ _).trans ?_
     exact mul_le_mul (R_antitone hzZ.le) (log_le_log (by norm_num) hz) hlog2.le (R_pos z).le
 
@@ -228,7 +228,7 @@ theorem R_lower : ∃ c > 0, ∀ z ≥ 2, c / log z ≤ R z := by
 theorem R_upper : ∃ C > 0, ∀ z ≥ 2, R z ≤ C / log z := by
   obtain ⟨cR, hcR, C, hC⟩ := R_asymp
   refine ⟨cR + |C|, by positivity, fun z hz ↦ ?_⟩
-  have hlog : 0 < log z := log_pos (by linarith)
+  have hlog : 0 < log z := log_pos (by linarith only [hz])
   rw [le_div_iff₀ hlog]
   have h1 := hC z hz
   have h2 : C * pntE z ≤ |C| :=
@@ -236,6 +236,6 @@ theorem R_upper : ∃ C > 0, ∀ z ≥ 2, R z ≤ C / log z := by
       rw [abs_mul, abs_of_pos (pntE_pos z)]
       exact mul_le_of_le_one_right (abs_nonneg _) (pntE_le_one z))
   rw [abs_le] at h1
-  linarith
+  linarith only [h1, h2]
 
 end IwaniecLinearSieve
diff --git a/LeanPool/IwaniecLinearSieve/PrimeSums/SummationByParts.lean b/LeanPool/IwaniecLinearSieve/PrimeSums/SummationByParts.lean
index 4e7e53c5bf..10f016926a 100644
--- a/LeanPool/IwaniecLinearSieve/PrimeSums/SummationByParts.lean
+++ b/LeanPool/IwaniecLinearSieve/PrimeSums/SummationByParts.lean
@@ -129,9 +129,9 @@ theorem abs_sum_sub_integral_le {n : ℕ} {a : ℕ → ℝ} (ha : Monotone a) {b
           have h2 : (b (a (j + 1)) - b (a j)) * (F (a (j + 1)) - F (a j)) ≤
               (b (a (j + 1)) - b (a j)) * δ :=
             mul_le_mul_of_nonneg_left (hδ j hj) (sub_nonneg.2 (hβ j hj))
-          linarith
+          linarith only [h1, h2]
       _ = (b (a n) - b (a 0)) * δ := by rw [← sum_mul, sum_range_sub (fun j ↦ b (a j))]
-      _ ≤ δ * b (a n) := by nlinarith
+      _ ≤ δ * b (a n) := by nlinarith only [hδ0, hb0]
   have herr := abs_sum_mul_sub_le (β := fun j ↦ b (a j)) (e := fun j ↦ g j - F (a j)) hβ hb0 hε
   rw [abs_le] at herr ⊢
   constructor <;> linarith
diff --git a/LeanPool/IwaniecLinearSieve/Rosser.lean b/LeanPool/IwaniecLinearSieve/Rosser.lean
index 1cd66330b6..06771699a4 100644
--- a/LeanPool/IwaniecLinearSieve/Rosser.lean
+++ b/LeanPool/IwaniecLinearSieve/Rosser.lean
@@ -508,10 +508,10 @@ theorem rosserMain_false_eq {r : ℕ} (hr : #(primesLT z) < r) (y : ℝ) :
 
 theorem rosserMain_true_le_R (y z : ℝ) : rosserMain true y z ≤ R z := by
   rw [rosserMain_true_eq (Nat.lt_succ_self _) y]
-  linarith [fail_nonneg true (#(primesLT z) + 1) y z]
+  linarith only [fail_nonneg true (#(primesLT z) + 1) y z]
 
 theorem R_le_rosserMain_false (y z : ℝ) : R z ≤ rosserMain false y z := by
   rw [rosserMain_false_eq (Nat.lt_succ_self _) y]
-  linarith [fail_nonneg false (#(primesLT z) + 1) y z]
+  linarith only [fail_nonneg false (#(primesLT z) + 1) y z]
 
 end IwaniecLinearSieve
diff --git a/LeanPool/IwaniecLinearSieve/SieveFunctions/Bounds.lean b/LeanPool/IwaniecLinearSieve/SieveFunctions/Bounds.lean
index a4ef49e792..82de2226fe 100644
--- a/LeanPool/IwaniecLinearSieve/SieveFunctions/Bounds.lean
+++ b/LeanPool/IwaniecLinearSieve/SieveFunctions/Bounds.lean
@@ -37,28 +37,28 @@ theorem log_three_sub_log_two_lt : log 3 - log 2 < 5 / 12 := by
   have h1 := log_three_lt_d9
   have h2 := log_two_gt_d9
   norm_num at h1 h2 ⊢
-  linarith
+  linarith only [h1, h2]
 
 theorem one_lt_log_three : 1 < log 3 := by
-  have := log_three_gt_d9; norm_num at this ⊢; linarith
+  have := log_three_gt_d9; norm_num at this ⊢; linarith only [this]
 
 theorem exp_one_sq_lt : exp 1 ^ 2 < 2 + 6 * log 3 := by
   have h1 := exp_one_lt_d9
   have h0 := exp_pos 1
   have h3 := one_lt_log_three
   norm_num at h1
-  nlinarith
+  nlinarith only [h3, h1, h0]
 
 /-- `s e^{-s}` is decreasing for `s ≥ 1`. -/
 theorem mul_exp_neg_le_of_one_le {u v : ℝ} (hu : 1 ≤ u) (huv : u ≤ v) :
     v * exp (-v) ≤ u * exp (-u) := by
   have h1 : v ≤ u * exp (v - u) := by
     have := add_one_le_exp (v - u)
-    nlinarith
+    nlinarith only [this, hu, huv]
   have h2 : exp (-u) = exp (v - u) * exp (-v) := by rw [← exp_add]; ring_nf
   rw [h2]
   have := exp_pos (-v)
-  nlinarith
+  nlinarith only [h1, this]
 
 /-! ### Lemma 3 -/
 
@@ -73,7 +73,7 @@ theorem psi_two : psi 2 = (1 + 3 * log 3) / (2 * exp 1) := by
 theorem psi_deriv_aux {x : ℝ} (hx : 2 < x) :
     (x - 1) * (1 + 3 * log (3 / (x - 1))) ≤ 3 * x / (x - 1) := by
   set y := x - 1 with hy
-  have hy0 : 0 < y := by linarith
+  have hy0 : 0 < y := by linarith only [hx]
   have hx' : x = y + 1 := by ring
   rw [hx']
   have hlog : log (2 / y) ≤ 2 / y - 1 := log_le_sub_one_of_pos (by positivity)
@@ -81,20 +81,20 @@ theorem psi_deriv_aux {x : ℝ} (hx : 2 < x) :
   have hL : 1 + 3 * log (3 / y) ≤ -3 / 4 + 6 / y := by
     rw [log_div (by norm_num) hy0.ne']
     have : 6 / y = 3 * (2 / y) := by ring
-    linarith [log_three_sub_log_two_lt]
+    linarith only [log_three_sub_log_two_lt, hlog, this]
   have h6 : y * (6 / y) = 6 := by field_simp
   have : y * (1 + 3 * log (3 / y)) ≤ -3 / 4 * y + 6 := by
     have := mul_le_mul_of_nonneg_left hL hy0.le
-    rw [mul_add y (-3 / 4), h6] at this; linarith
+    rw [mul_add y (-3 / 4), h6] at this; linarith only [this]
   rw [le_div_iff₀ hy0]
-  nlinarith [sq_nonneg (y - 2)]
+  nlinarith only [sq_nonneg (y - 2), h6, hL, hx]
 
 theorem hasDerivAt_psi {x : ℝ} (hx : 1 < x) :
     HasDerivAt psi
       (exp (x - 3) * ((x - 1) * (1 + 3 * log (3 / (x - 1))) - 3 * x / (x - 1)) /
         x ^ 2) x := by
   have hx0 : x ≠ 0 := by positivity
-  have hx1 : x - 1 ≠ 0 := by linarith
+  have hx1 : x - 1 ≠ 0 := by linarith only [hx]
   have h3 : (3 : ℝ) / (x - 1) ≠ 0 := div_ne_zero (by norm_num) hx1
   have h := (((hasDerivAt_id' x).inv hx0).mul ((hasDerivAt_id' x).sub_const 3).exp).mul
     ((((hasDerivAt_const x (3 : ℝ)).div ((hasDerivAt_id' x).sub_const 1) hx1).log h3).const_mul
@@ -112,13 +112,13 @@ theorem psi_le_psi_two {s : ℝ} (hs : s ∈ Icc (2 : ℝ) 4) : psi s ≤ psi 2
       (f' := fun x => exp (x - 3) * ((x - 1) * (1 + 3 * log (3 / (x - 1))) - 3 * x / (x - 1)) /
         x ^ 2) ?_ ?_ ?_
     · intro x hx
-      exact (hasDerivAt_psi (by linarith [hx.1])).continuousAt.continuousWithinAt
+      exact (hasDerivAt_psi (by linarith only [hx.1, hx])).continuousAt.continuousWithinAt
     · intro x hx
       rw [interior_Icc] at hx
-      exact (hasDerivAt_psi (by linarith [hx.1])).hasDerivWithinAt
+      exact (hasDerivAt_psi (by linarith only [hx.1, hx])).hasDerivWithinAt
     · intro x hx
       rw [interior_Icc] at hx
-      have hx1 : 0 < x - 1 := by linarith [hx.1]
+      have hx1 : 0 < x - 1 := by linarith only [hx.1, hx]
       refine div_nonpos_of_nonpos_of_nonneg
         (mul_nonpos_of_nonneg_of_nonpos (exp_pos _).le (sub_nonpos.2 (psi_deriv_aux hx.1)))
         (by positivity)
@@ -137,7 +137,7 @@ theorem gRatio_eq : gRatio = exp 1 / 3 * psi 2 := by
 
 theorem gRatio_lt : gRatio < 0.72 := by
   have := log_three_lt_d9
-  rw [gRatio]; norm_num at this ⊢; linarith
+  rw [gRatio]; norm_num at this ⊢; linarith only [this]
 
 theorem gRatio_pos : 0 < gRatio := by
   rw [gRatio]; have := one_lt_log_three; positivity
@@ -147,7 +147,7 @@ theorem gRatio_lt_one : gRatio < 1 := gRatio_lt.trans (by norm_num)
 theorem bddAbove_gLead : BddAbove ((fun s => g 2 s * s⁻¹ * exp s) '' Icc 2 4) :=
   isCompact_Icc.bddAbove_image <|
     (((continuous_g 2).continuousOn.mul (continuousOn_inv₀.mono fun x hx => by
-      simp only [mem_compl_iff, mem_singleton_iff]; linarith [hx.1])).mul
+      simp only [mem_compl_iff, mem_singleton_iff]; linarith only [hx.1, hx])).mul
       continuous_exp.continuousOn)
 
 theorem le_gLead {s : ℝ} (hs : s ∈ Icc (2 : ℝ) 4) : g 2 s * s⁻¹ * exp s ≤ gLead :=
@@ -166,16 +166,16 @@ theorem integral_shift_le {h : ℝ → ℝ} (hh : Continuous h) {C s b : ℝ} (h
     refine ContinuousOn.intervalIntegrable ?_
     rw [uIcc_of_le hsb]
     exact (hh.comp (continuous_sub_right 1)).continuousOn.div
-      (continuous_sub_right 1).continuousOn fun t ht => by linarith [ht.1]
+      (continuous_sub_right 1).continuousOn fun t ht => by linarith only [ht.1, hs, ht]
   have hcont : Continuous fun t : ℝ => C * exp (1 - t) :=
     continuous_const.mul (continuous_exp.comp (continuous_const.sub continuous_id))
   calc ∫ t in s..b, h (t - 1) / (t - 1) ≤ ∫ t in s..b, C * exp (1 - t) := by
         refine integral_mono_on hsb hint1 (hcont.intervalIntegrable _ _) fun t ht => ?_
-        have ht1 : 0 < t - 1 := by linarith [ht.1]
+        have ht1 : 0 < t - 1 := by linarith only [ht.1, hs, ht]
         rw [div_le_iff₀ ht1]
-        have := hb (t - 1) (by linarith [ht.1])
+        have := hb (t - 1) (by linarith only [ht.1, ht])
         have e : exp (-(t - 1)) = exp (1 - t) := by ring_nf
-        rw [e] at this; linarith
+        rw [e] at this; linarith only [this]
     _ = C * exp (1 - s) - C * exp (1 - b) := by
         rw [integral_eq_sub_of_hasDerivAt (f := fun t => -(C * exp (1 - t))) (fun t _ => ?_)
           (hcont.intervalIntegrable _ _)]
@@ -184,7 +184,7 @@ theorem integral_shift_le {h : ℝ → ℝ} (hh : Continuous h) {C s b : ℝ} (h
           convert this using 1; ring
     _ ≤ C * exp (1 - s) := by
         have := mul_nonneg hC (exp_pos (1 - b)).le
-        linarith
+        linarith only [this]
 
 /-- The inductive step of [I71, Lemma 4] in uniform form. -/
 theorem g_add_three_le {n : ℕ} {C s : ℝ} (hC : 0 ≤ C) (hs : gLower (n + 3) ≤ s)
@@ -192,7 +192,7 @@ theorem g_add_three_le {n : ℕ} {C s : ℝ} (hC : 0 ≤ C) (hs : gLower (n + 3)
   rcases le_or_gt s ((n : ℝ) + 5) with hsb | hsb
   · rw [g_add_three_eq n hs]
     exact integral_shift_le (continuous_g _) hC ((two_le_gLower _).trans hs) hsb hb
-  · rw [g_eq_zero_of_le (n + 3) (by push_cast; linarith)]
+  · rw [g_eq_zero_of_le (n + 3) (by push_cast; linarith only [hsb])]
     positivity
 
 theorem gLower_two_mul_add_three (n : ℕ) : gLower (2 * n + 3) = 3 :=
@@ -213,13 +213,13 @@ theorem g_even_eq_on_Icc (n : ℕ) {s : ℝ} (hs : s ∈ Icc (2 : ℝ) 4) :
     refine integral_congr fun t ht => ?_
     rw [uIcc_of_le hs.2] at ht
     rw [shiftKernel_of_two_le _ (by linarith [ht.1, hs.1]), show 2 * n + 1 + 2 = 2 * n + 3 by ring,
-      g_eq_of_le_gLower _ (s := t - 1) (by rw [gLower_two_mul_add_three]; linarith [ht.2]),
+      g_eq_of_le_gLower _ (s := t - 1) (by rw [gLower_two_mul_add_three]; linarith only [ht.2, ht]),
       gLower_two_mul_add_three, mul_one_div]
-  have hs1 : 0 < s - 1 := by linarith [hs.1]
+  have hs1 : 0 < s - 1 := by linarith only [hs.1, hs]
   rw [hc, intervalIntegral.integral_const_mul,
     integral_comp_sub_right (fun x => 1 / x), integral_one_div_of_pos hs1 (by norm_num)] at h
   norm_num at h
-  linarith
+  linarith only [h]
 
 private theorem g_odd_le_of_even (n : ℕ)
     (H : ∀ s, 2 ≤ s → g (2 * n + 2) s ≤ gLead * gRatio ^ n * s * exp (-s)) {s : ℝ} (hs : 1 ≤ s) :
@@ -234,7 +234,7 @@ private theorem g_odd_le_of_even (n : ℕ)
     rw [e]
     have := mul_nonneg (mul_nonneg (mul_nonneg hC (exp_pos (-s)).le) (exp_pos 1).le)
       (sub_nonneg.2 hs)
-    nlinarith
+    nlinarith only [this]
   rcases le_total 3 s with hs3 | hs3
   · exact (h3 s hs3).trans (key s hs3)
   · have e : g (2 * n + 3) s = g (2 * n + 3) 3 := by
@@ -265,11 +265,11 @@ private theorem g_even_le_of_odd (n : ℕ)
     have e : exp (1 - s) = exp 1 * exp (-s) := by rw [← exp_add]; ring_nf
     rw [e, pow_succ]
     have h1 : exp 1 ^ 2 / 3 ≤ gRatio * s := by
-      rw [gRatio]; nlinarith
+      rw [gRatio]; nlinarith only [he, hs4, hs]
     have h0 : 0 ≤ gLead * gRatio ^ n * exp (-s) :=
       mul_nonneg (mul_nonneg gLead_nonneg (pow_nonneg hA.le _)) (exp_pos _).le
     have := mul_le_mul_of_nonneg_left h1 h0
-    nlinarith
+    nlinarith only [this]
   · rw [g_even_eq_on_Icc n ⟨hs, hs4⟩]
     have hg4 := h4 4 (by norm_num)
     have hg3 := H 3 (by norm_num)
@@ -287,7 +287,7 @@ private theorem g_even_le_of_odd (n : ℕ)
       rw [hpsi']
       rw [e4] at hg4
       have := mul_le_mul_of_nonneg_right hg3 hlog
-      nlinarith
+      nlinarith only [hg4, this]
     have hs0 : 0 ≤ s * exp (-s) := by positivity
     have := mul_le_mul_of_nonneg_left (mul_le_mul_of_nonneg_right hpsi hs0) hC
     calc _ ≤ gLead * (exp 1 / 3) * gRatio ^ n * (psi 2 * (s * exp (-s))) := by
@@ -302,7 +302,7 @@ theorem g_even_le (n : ℕ) {s : ℝ} (hs : 2 ≤ s) :
     simp only [mul_zero, zero_add, pow_zero, mul_one]
     rcases le_total s 4 with hs4 | hs4
     · have := le_gLead ⟨hs, hs4⟩
-      have hs0 : 0 < s := by linarith
+      have hs0 : 0 < s := by linarith only [hs]
       have e : g 2 s = g 2 s * s⁻¹ * exp s * (s * exp (-s)) := by
         rw [exp_neg]; field_simp
       rw [e]
@@ -310,7 +310,7 @@ theorem g_even_le (n : ℕ) {s : ℝ} (hs : 2 ≤ s) :
         (by ring)
     · rw [g_two_of_four_le hs4]
       have := gLead_nonneg
-      have : 0 ≤ s := by linarith
+      have : 0 ≤ s := by linarith only [hs4]
       positivity
   | succ n ih =>
     rw [show 2 * (n + 1) + 2 = 2 * n + 4 by ring]
diff --git a/LeanPool/IwaniecLinearSieve/SieveFunctions/LemmaFive.lean b/LeanPool/IwaniecLinearSieve/SieveFunctions/LemmaFive.lean
index b1d9489d81..e28dd9d0e7 100644
--- a/LeanPool/IwaniecLinearSieve/SieveFunctions/LemmaFive.lean
+++ b/LeanPool/IwaniecLinearSieve/SieveFunctions/LemmaFive.lean
@@ -67,12 +67,12 @@ theorem hasDerivAt_integral_Ioi {k : ℝ → ℝ} {a s : ℝ} (hint : Integrable
   refine hd.congr_of_eventuallyEq ?_
   filter_upwards [Ioi_mem_nhds has] with u hu
   have := integral_Ioi_sub_Ioi hint (le_of_lt hu)
-  linarith
+  linarith only [this]
 
 theorem continuousOn_shift {h : ℝ → ℝ} (hh : Continuous h) :
     ContinuousOn (fun t => h (t - 1) / (t - 1)) (Ioi 1) :=
   (hh.comp (continuous_sub_right 1)).continuousOn.div (continuous_sub_right 1).continuousOn
-    fun t ht => by have : (1 : ℝ) < t := ht; linarith
+    fun t ht => by have : (1 : ℝ) < t := ht; linarith only [this]
 
 /-- `F'(s) = -f(s-1)/(s-1)` for `s > 3`. -/
 theorem hasDerivAt_FSieve {s : ℝ} (hs : 3 < s) :
@@ -91,12 +91,12 @@ theorem hasDerivAt_fSieve_of_four_lt {s : ℝ} (hs : 4 < s) :
   refine hd.congr_of_eventuallyEq ?_
   filter_upwards [Ioi_mem_nhds hs] with u hu
   have hu' : (4 : ℝ) < u := hu
-  rw [fSieve_eq_integral (by linarith), g_two_of_four_le hu'.le, add_zero]
+  rw [fSieve_eq_integral (by linarith only [hu']), g_two_of_four_le hu'.le, add_zero]
 
 /-- `f'(s) = 1 - (F(3) + 3)/(s-1)` for `2 < s < 4`. -/
 theorem hasDerivAt_fSieve_of_lt_four {s : ℝ} (hs2 : 2 < s) (hs4 : s < 4) :
     HasDerivAt fSieve (1 - (FSieve 3 + 3) / (s - 1)) s := by
-  have hne : s - 1 ≠ 0 := by linarith
+  have hne : s - 1 ≠ 0 := by linarith only [hs2]
   have hd : HasDerivAt
       (fun u => fSieve 4 + (FSieve 3 + 3) * (log 3 - log (u - 1)) + u - 4)
       (1 - (FSieve 3 + 3) / (s - 1)) s := by
@@ -107,7 +107,7 @@ theorem hasDerivAt_fSieve_of_lt_four {s : ℝ} (hs2 : 2 < s) (hs4 : s < 4) :
     ring
   refine hd.congr_of_eventuallyEq ?_
   filter_upwards [Ioo_mem_nhds hs2 hs4] with u hu
-  rw [fSieve_eq_on_Icc' ⟨hu.1.le, hu.2.le⟩, log_div (by norm_num) (by linarith [hu.1])]
+  rw [fSieve_eq_on_Icc' ⟨hu.1.le, hu.2.le⟩, log_div (by norm_num) (by linarith only [hu.1, hu])]
 
 /-! ### Iwaniec's `M` -/
 
@@ -116,10 +116,10 @@ theorem hasDerivAt_fSieve_of_lt_four {s : ℝ} (hs2 : 2 < s) (hs4 : s < 4) :
 noncomputable def MSieve (s : ℝ) : ℝ := fSieve s + FSieve s + max (3 - s) 0
 
 theorem MSieve_of_three_le {s : ℝ} (hs : 3 ≤ s) : MSieve s = fSieve s + FSieve s := by
-  rw [MSieve, max_eq_right (by linarith), add_zero]
+  rw [MSieve, max_eq_right (by linarith only [hs]), add_zero]
 
 theorem MSieve_of_le_three {s : ℝ} (hs : s ≤ 3) : MSieve s = 3 + FSieve 3 - s + fSieve s := by
-  rw [MSieve, max_eq_left (by linarith), FSieve_of_le_three hs]; ring
+  rw [MSieve, max_eq_left (by linarith only [hs]), FSieve_of_le_three hs]; ring
 
 theorem continuous_MSieve : Continuous MSieve :=
   (continuous_fSieve.add continuous_FSieve).add ((continuous_const.sub continuous_id).max
@@ -131,7 +131,7 @@ theorem MSieve_nonneg (s : ℝ) : 0 ≤ MSieve s := by
 
 theorem MSieve_antitone : Antitone MSieve := fun u v h => by
   have := fSieve_antitone h; have := FSieve_antitone h
-  have : max (3 - v) 0 ≤ max (3 - u) 0 := max_le_max (by linarith) le_rfl
+  have : max (3 - v) 0 ≤ max (3 - u) 0 := max_le_max (by linarith only [h]) le_rfl
   rw [MSieve, MSieve]; linarith
 
 /-- `Σ_{k ≥ 2} g_k(s) = M(s)` for `s ≥ 3`. -/
@@ -147,26 +147,26 @@ theorem fr_lt_MSieve (r : ℕ) (s : ℝ) : fr r s < MSieve s := by
 theorem MSieve_le {s : ℝ} (hs : 3 ≤ s) :
     MSieve s ≤ (gLead * (1 - gRatio)⁻¹ + gLead * (exp 1 / 3) * (1 - gRatio)⁻¹) * s * exp (-s) := by
   rw [MSieve_of_three_le hs]
-  have := fSieve_le (by linarith : (2 : ℝ) ≤ s)
-  have := FSieve_le (by linarith : (1 : ℝ) ≤ s)
+  have := fSieve_le (by linarith only [hs] : (2 : ℝ) ≤ s)
+  have := FSieve_le (by linarith only [hs] : (1 : ℝ) ≤ s)
   linarith
 
 /-- The derivative of `M` for `s > 3`, `s ≠ 4`: `(s - 1) M'(s) = -M(s - 1)`. -/
 theorem hasDerivAt_MSieve {s : ℝ} (hs3 : 3 < s) (hs4 : s ≠ 4) :
     HasDerivAt MSieve (-(MSieve (s - 1) / (s - 1))) s := by
-  have hne : s - 1 ≠ 0 := by linarith
+  have hne : s - 1 ≠ 0 := by linarith only [hs3]
   have hev : MSieve =ᶠ[𝓝 s] fun u => fSieve u + FSieve u := by
     filter_upwards [Ioi_mem_nhds hs3] with u hu
     exact MSieve_of_three_le (le_of_lt hu)
   rcases lt_or_gt_of_ne hs4 with h4 | h4
   · have hd := (hasDerivAt_fSieve_of_lt_four (by linarith) h4).add (hasDerivAt_FSieve hs3)
     refine (hd.congr_of_eventuallyEq hev).congr_deriv ?_
-    rw [MSieve_of_le_three (by linarith)]
+    rw [MSieve_of_le_three (by linarith only [h4])]
     field_simp
     ring
   · have hd := (hasDerivAt_fSieve_of_four_lt h4).add (hasDerivAt_FSieve hs3)
     refine (hd.congr_of_eventuallyEq hev).congr_deriv ?_
-    rw [MSieve_of_three_le (by linarith)]
+    rw [MSieve_of_three_le (by linarith only [h4])]
     field_simp
     ring
 
@@ -196,7 +196,7 @@ theorem hasDerivAt_lemma5Q {s : ℝ} (hs3 : 3 < s) (hs4 : s ≠ 4) : HasDerivAt
   have hd := (((hasDerivAt_id' s).sub_const 1).mul hM).sub ((hP s).sub hP1)
   rw [funext lemma5Q_eq]
   refine hd.congr_deriv ?_
-  have hne : s - 1 ≠ 0 := by linarith
+  have hne : s - 1 ≠ 0 := by linarith only [hs3]
   field_simp
   ring
 
@@ -206,15 +206,15 @@ theorem lemma5Q_eq_of_deriv {a b : ℝ} (hab : a ≤ b) (hd : ∀ x ∈ Ioo a b,
   · rw [h]
   · obtain ⟨c, _, hc⟩ := exists_hasDerivAt_eq_slope lemma5Q (fun _ => (0 : ℝ)) h
       continuous_lemma5Q.continuousOn hd
-    have hba : b - a ≠ 0 := by linarith
+    have hba : b - a ≠ 0 := by linarith only [h]
     rw [eq_div_iff hba, zero_mul] at hc
-    linarith
+    linarith only [hc]
 
 theorem lemma5Q_const {b : ℝ} (hb : 3 ≤ b) : lemma5Q b = lemma5Q 3 := by
   rcases le_total b 4 with h4 | h4
   · exact lemma5Q_eq_of_deriv hb fun x hx => hasDerivAt_lemma5Q hx.1 (by linarith [hx.2])
-  · rw [lemma5Q_eq_of_deriv h4 fun x hx => hasDerivAt_lemma5Q (by linarith [hx.1])
-      (by linarith [hx.1]),
+  · rw [lemma5Q_eq_of_deriv h4 fun x hx => hasDerivAt_lemma5Q (by linarith only [hx.1, hx])
+      (by linarith only [hx.1, hx]),
       lemma5Q_eq_of_deriv (by norm_num) fun x hx => hasDerivAt_lemma5Q hx.1 (by linarith [hx.2])]
 
 theorem abs_lemma5Q_le {b : ℝ} (hb : 4 ≤ b) :
@@ -222,11 +222,11 @@ theorem abs_lemma5Q_le {b : ℝ} (hb : 4 ≤ b) :
       (b ^ 2 * exp (-b)) := by
   set C := gLead * (1 - gRatio)⁻¹ + gLead * (exp 1 / 3) * (1 - gRatio)⁻¹
   have hM1 : MSieve (b - 1) ≤ C * (b - 1) * exp (-(b - 1)) := MSieve_le (s := b - 1) (by linarith)
-  have hMb : MSieve b ≤ MSieve (b - 1) := MSieve_antitone (by linarith)
+  have hMb : MSieve b ≤ MSieve (b - 1) := MSieve_antitone (by linarith only [])
   have hI0 : 0 ≤ ∫ x in (b - 1)..b, MSieve x :=
-    integral_nonneg (by linarith) fun x _ => MSieve_nonneg x
+    integral_nonneg (by linarith only []) fun x _ => MSieve_nonneg x
   have hI1 : ∫ x in (b - 1)..b, MSieve x ≤ MSieve (b - 1) := by
-    have := integral_mono_on (μ := volume) (by linarith : b - 1 ≤ b)
+    have := integral_mono_on (μ := volume) (by linarith only [] : b - 1 ≤ b)
       (continuous_MSieve.intervalIntegrable _ _)
       (intervalIntegrable_const (c := MSieve (b - 1))) fun x hx => MSieve_antitone hx.1
     simpa using this
@@ -237,14 +237,14 @@ theorem abs_lemma5Q_le {b : ℝ} (hb : 4 ≤ b) :
   have he : exp (-(b - 1)) = exp 1 * exp (-b) := by rw [← exp_add]; ring_nf
   rw [he] at hM1
   refine hQ.trans ?_
-  have := mul_le_mul_of_nonneg_left hM1 (by linarith : (0 : ℝ) ≤ b)
+  have := mul_le_mul_of_nonneg_left hM1 (by linarith only [hb] : (0 : ℝ) ≤ b)
   have hb' : 0 ≤ C * exp 1 * exp (-b) * b := by
     have : 0 ≤ C := by
       have := gLead_nonneg; have := gRatio_lt_one; have := exp_pos 1
       have : 0 ≤ (1 - gRatio)⁻¹ := inv_nonneg.2 (by linarith)
       positivity
     have := exp_pos 1; have := exp_pos (-b); positivity
-  nlinarith
+  nlinarith only [this, hb']
 
 theorem lemma5Q_three : lemma5Q 3 = 0 := by
   set C := (gLead * (1 - gRatio)⁻¹ + gLead * (exp 1 / 3) * (1 - gRatio)⁻¹) * exp 1
@@ -271,8 +271,8 @@ theorem integral_MSieve_two_three :
       ∫ x in (2 : ℝ)..3, MSieve x = ∫ x in (2 : ℝ)..3, (c + K * (log 3 - log (x - 1))) := by
     refine integral_congr fun x hx => ?_
     rw [uIcc_of_le (by norm_num)] at hx
-    rw [MSieve_of_le_three hx.2, fSieve_eq_on_Icc' ⟨hx.1, by linarith [hx.2]⟩,
-      log_div (by norm_num) (by linarith [hx.1])]
+    rw [MSieve_of_le_three hx.2, fSieve_eq_on_Icc' ⟨hx.1, by linarith only [hx.2, hx]⟩,
+      log_div (by norm_num) (by linarith only [hx.1, hx])]
     ring
   rw [hcongr, integral_eq_sub_of_hasDerivAt
     (f := fun x => c * x + K * ((x - 1) * (log 3 - log (x - 1)) + x))]
@@ -280,7 +280,7 @@ theorem integral_MSieve_two_three :
     ring
   · intro x hx
     rw [uIcc_of_le (by norm_num)] at hx
-    have hne : x - 1 ≠ 0 := by linarith [hx.1]
+    have hne : x - 1 ≠ 0 := by linarith only [hx.1, hx]
     have := ((hasDerivAt_id' x).const_mul c).add
       (((((hasDerivAt_id' x).sub_const 1).mul
         ((((hasDerivAt_id' x).sub_const 1).log hne).const_sub (log 3))).add
@@ -292,7 +292,7 @@ theorem integral_MSieve_two_three :
     refine continuousOn_const.add (continuousOn_const.mul (continuousOn_const.sub ?_))
     refine ((continuous_sub_right 1).continuousOn).log fun x hx => ?_
     rw [uIcc_of_le (by norm_num)] at hx
-    linarith [hx.1]
+    linarith only [hx.1, hx]
 
 /-- The key identity `f(4) + (F(3) + 3) log 3 = 4`. -/
 theorem fSieve_four_add : fSieve 4 + (FSieve 3 + 3) * log 3 = 4 := by
@@ -300,14 +300,14 @@ theorem fSieve_four_add : fSieve 4 + (FSieve 3 + 3) * log 3 = 4 := by
   rw [lemma5Q, show (3 : ℝ) - 1 = 2 by norm_num, integral_MSieve_two_three,
     MSieve_of_three_le le_rfl, fSieve_eq_on_Icc' ⟨by norm_num, by norm_num⟩,
     show (3 : ℝ) / (3 - 1) = 3 / 2 by norm_num, log_div (by norm_num) (by norm_num)] at h
-  linarith
+  linarith only [h]
 
 /-- [I71, Lemma 5] in the form we need: `f(s) = s - (F(3) + 3) log (s - 1)` for `2 ≤ s ≤ 4`
 (Iwaniec: `F(3) + 3 = 2e^γ`). -/
 theorem fSieve_eq_on_Icc {s : ℝ} (hs : s ∈ Icc (2 : ℝ) 4) :
     fSieve s = s - (FSieve 3 + 3) * log (s - 1) := by
-  rw [fSieve_eq_on_Icc' hs, log_div (by norm_num) (by linarith [hs.1])]
-  linarith [fSieve_four_add]
+  rw [fSieve_eq_on_Icc' hs, log_div (by norm_num) (by linarith only [hs.1, hs])]
+  linarith only [fSieve_four_add]
 
 /-- [I71, (3.10)]: `f(2) = 2`. -/
 theorem fSieve_two : fSieve 2 = 2 := by
@@ -316,11 +316,11 @@ theorem fSieve_two : fSieve 2 = 2 := by
 /-- The consequence of Lemma 5 used for the sieve: `1 - f(s)/s ≥ 3 log (s - 1) / s` on `[2, 4]`. -/
 theorem le_one_sub_fSieve_div {s : ℝ} (hs : s ∈ Icc (2 : ℝ) 4) :
     3 * log (s - 1) / s ≤ 1 - fSieve s / s := by
-  have hs0 : 0 < s := by linarith [hs.1]
-  have hlog : 0 ≤ log (s - 1) := log_nonneg (by linarith [hs.1])
+  have hs0 : 0 < s := by linarith only [hs.1, hs]
+  have hlog : 0 ≤ log (s - 1) := log_nonneg (by linarith only [hs.1, hs])
   have hF := FSieve_nonneg 3
   rw [fSieve_eq_on_Icc hs, div_le_iff₀ hs0, sub_mul, div_mul_cancel₀ _ hs0.ne']
-  nlinarith
+  nlinarith only [hlog, hF]
 
 /-- `le_one_sub_fSieve_div` in the form used by the linear-sieve modules. -/
 theorem one_sub_fSieve_div_ge : ∀ s ∈ Icc (2 : ℝ) 4, 1 - fSieve s / s ≥ 3 * Real.log (s - 1) / s :=
diff --git a/LeanPool/IwaniecLinearSieve/SieveFunctions/Series.lean b/LeanPool/IwaniecLinearSieve/SieveFunctions/Series.lean
index eace69efe9..fd934b2616 100644
--- a/LeanPool/IwaniecLinearSieve/SieveFunctions/Series.lean
+++ b/LeanPool/IwaniecLinearSieve/SieveFunctions/Series.lean
@@ -130,7 +130,7 @@ theorem FSieve_isBigO : FSieve =O[atTop] fun s => s * exp (-s) := by
   refine Asymptotics.IsBigO.of_bound (gLead * (exp 1 / 3) * (1 - gRatio)⁻¹) ?_
   filter_upwards [eventually_ge_atTop 2] with s hs
   rw [norm_of_nonneg (FSieve_nonneg s), norm_of_nonneg (by positivity)]
-  exact (FSieve_le (by linarith)).trans_eq (by ring)
+  exact (FSieve_le (by linarith only [hs])).trans_eq (by ring)
 
 theorem g_even_le_fSieve (n : ℕ) (s : ℝ) : g (2 * n + 2) s ≤ fSieve s :=
   (summable_g_even s).le_tsum n fun _ _ => g_nonneg _ _
@@ -166,10 +166,10 @@ theorem fr_of_odd {r : ℕ} (hr : ¬ Even r) : fr r = FSieve := funext fun _ =>
 theorem shift_div_le {h : ℝ → ℝ} {C t : ℝ} (ht : 1 < t)
     (hb : h (t - 1) ≤ C * (t - 1) * exp (-(t - 1))) :
     h (t - 1) / (t - 1) ≤ C * exp 1 * exp (-t) := by
-  have ht1 : 0 < t - 1 := by linarith
+  have ht1 : 0 < t - 1 := by linarith only [ht]
   rw [div_le_iff₀ ht1]
   have e : exp (-(t - 1)) = exp 1 * exp (-t) := by rw [← exp_add]; ring_nf
-  rw [e] at hb; linarith
+  rw [e] at hb; linarith only [hb]
 
 /-- An exponentially decaying `h` gives an integrable kernel `h(t-1)/(t-1)` on `(s, ∞)`. -/
 theorem integrableOn_shift {h : ℝ → ℝ} (hh : Continuous h) {C s : ℝ} (hs : 2 ≤ s)
@@ -179,10 +179,10 @@ theorem integrableOn_shift {h : ℝ → ℝ} (hh : Continuous h) {C s : ℝ} (hs
   · refine ContinuousOn.aestronglyMeasurable ?_ measurableSet_Ioi
     exact (hh.comp (continuous_sub_right 1)).continuousOn.div
       (continuous_sub_right 1).continuousOn fun t ht => by
-        have : s < t := ht; linarith
+        have : s < t := ht; linarith only [hs, this]
   · filter_upwards [ae_restrict_mem measurableSet_Ioi] with t ht
     have ht' : s < t := ht
-    rw [norm_of_nonneg (div_nonneg (hnn _) (by linarith))]
+    rw [norm_of_nonneg (div_nonneg (hnn _) (by linarith only [hs, ht']))]
     have := shift_div_le (C := C) (by linarith) (hb (t - 1) (by linarith))
     simpa using this
 
@@ -195,19 +195,19 @@ theorem tsum_integral_Ioi_shift {φ : ℕ → ℝ → ℝ} {s : ℝ} (hs : 2 ≤
   · congr 1; funext t; exact tsum_div_const
   · refine hsum.congr fun n => setIntegral_congr_fun measurableSet_Ioi fun t ht => ?_
     have : s < t := ht
-    exact (norm_of_nonneg (div_nonneg (hnn _ _) (by linarith))).symm
+    exact (norm_of_nonneg (div_nonneg (hnn _ _) (by linarith only [hs, this]))).symm
 
 theorem integrableOn_FSieve_shift {s : ℝ} (hs : 2 ≤ s) :
     IntegrableOn (fun t => FSieve (t - 1) / (t - 1)) (Ioi s) :=
   integrableOn_shift (C := gLead * (exp 1 / 3) * (1 - gRatio)⁻¹) continuous_FSieve hs
     FSieve_nonneg fun u hu =>
-    (FSieve_le (by linarith)).trans_eq (by ring)
+    (FSieve_le (by linarith only [hs, hu])).trans_eq (by ring)
 
 theorem integrableOn_fSieve_shift {s : ℝ} (hs : 3 ≤ s) :
     IntegrableOn (fun t => fSieve (t - 1) / (t - 1)) (Ioi s) :=
-  integrableOn_shift (C := gLead * (1 - gRatio)⁻¹) continuous_fSieve (by linarith)
+  integrableOn_shift (C := gLead * (1 - gRatio)⁻¹) continuous_fSieve (by linarith only [hs])
     fSieve_nonneg fun u hu =>
-    (fSieve_le (by linarith)).trans_eq (by ring)
+    (fSieve_le (by linarith only [hs, hu])).trans_eq (by ring)
 
 theorem g_even_add_four_eq_Ioi (n : ℕ) {s : ℝ} (hs : 2 ≤ s) :
     IntegrableOn (fun t => g (2 * n + 3) (t - 1) / (t - 1)) (Ioi s) ∧
diff --git a/LeanPool/IwaniecLinearSieve/SieveMajorants/Defs.lean b/LeanPool/IwaniecLinearSieve/SieveMajorants/Defs.lean
index 47b1859ebd..b7602b5cb0 100644
--- a/LeanPool/IwaniecLinearSieve/SieveMajorants/Defs.lean
+++ b/LeanPool/IwaniecLinearSieve/SieveMajorants/Defs.lean
@@ -42,7 +42,7 @@ theorem continuous_delayKer : Continuous delayKer := by
   refine (continuous_id.max continuous_const).div
     (((continuous_id.max continuous_const).sub continuous_const).pow 2) fun x => ?_
   have : (3 : ℝ) ≤ max x 3 := le_max_right _ _
-  have : (0 : ℝ) < max x 3 - 1 := by linarith
+  have : (0 : ℝ) < max x 3 - 1 := by linarith only [this]
   positivity
 
 theorem continuous_initW : Continuous initW := by
@@ -51,7 +51,7 @@ theorem continuous_initW : Continuous initW := by
     (continuous_id.max continuous_const).sub continuous_const
   have hne : ∀ s : ℝ, max s 2 - 1 ≠ 0 := fun s => by
     have : (2 : ℝ) ≤ max s 2 := le_max_right _ _
-    linarith
+    linarith only [this]
   exact (continuous_const.div h1 hne).sub (h1.log hne)
 
 theorem initW_of_le {s : ℝ} (hs : s ≤ 2) : initW s = 1 := by
@@ -77,10 +77,10 @@ theorem bigM_of_le_three {s : ℝ} (hs : s ≤ 3) : bigM s = 2 + initW s :=
   Delay.sol_of_le hs
 
 theorem bigW_of_le_two {s : ℝ} (hs : s ≤ 2) : bigW s = 1 := by
-  rw [bigW_of_le_three (by linarith), initW_of_le hs]
+  rw [bigW_of_le_three (by linarith only [hs]), initW_of_le hs]
 
 theorem bigM_of_le_two {s : ℝ} (hs : s ≤ 2) : bigM s = 3 := by
-  rw [bigM_of_le_three (by linarith), initW_of_le hs]; norm_num
+  rw [bigM_of_le_three (by linarith only [hs]), initW_of_le hs]; norm_num
 
 theorem bigW_eq {s : ℝ} (hs : 2 ≤ s) (hs' : s ≤ 3) : bigW s = 1 / (s - 1) - log (s - 1) := by
   rw [bigW_of_le_three hs', initW_of_ge hs]
@@ -102,7 +102,7 @@ theorem bigM_three : bigM 3 = 5 / 2 - log 2 := by
 /-- The derivative of `1/(x-1) - log(x-1)` is `-x/(x-1)²`. -/
 theorem hasDerivAt_initForm {x : ℝ} (hx : 1 < x) :
     HasDerivAt (fun x => 1 / (x - 1) - log (x - 1)) (-(x / (x - 1) ^ 2)) x := by
-  have h0 : x - 1 ≠ 0 := by linarith
+  have h0 : x - 1 ≠ 0 := by linarith only [hx]
   have h1 : HasDerivAt (fun x : ℝ => x - 1) 1 x := (hasDerivAt_id x).sub_const 1
   have := (h1.inv h0).sub (h1.log h0)
   convert this using 1
@@ -175,7 +175,7 @@ theorem eq_of_hasDerivAt_zero {g : ℝ → ℝ} {a : ℝ} (hg : ContinuousOn g (
     (hg.mono Icc_subset_Ici_self) fun x hx => hd x hx.1
   have : s - a ≠ 0 := by linarith
   field_simp at hc'
-  linarith
+  linarith only [hc']
 
 /-! ### (3.11) -/
 
@@ -197,14 +197,14 @@ theorem integral_wIntegrand_two_three :
       ∫ x in (2 : ℝ)..3, (1 / (x - 1) - log (x - 1)) / x ^ 2 := by
     refine intervalIntegral.integral_congr fun x hx => ?_
     rw [uIcc_of_le (by norm_num)] at hx
-    rw [wIntegrand_of_ge (by linarith [hx.1]), bigW_eq hx.1 hx.2]
+    rw [wIntegrand_of_ge (by linarith only [hx.1, hx]), bigW_eq hx.1 hx.2]
   rw [hcongr]
   have hderiv : ∀ x ∈ uIcc (2 : ℝ) 3, HasDerivAt (fun x => (1 + log (x - 1)) / x)
       ((1 / (x - 1) - log (x - 1)) / x ^ 2) x := by
     intro x hx
     rw [uIcc_of_le (by norm_num)] at hx
-    have hx1 : x - 1 ≠ 0 := by linarith [hx.1]
-    have hx0 : x ≠ 0 := by linarith [hx.1]
+    have hx1 : x - 1 ≠ 0 := by linarith only [hx.1, hx]
+    have hx0 : x ≠ 0 := by linarith only [hx.1, hx]
     have h1 : HasDerivAt (fun x : ℝ => x - 1) 1 x := (hasDerivAt_id x).sub_const 1
     have := ((h1.log hx1).const_add 1).div (hasDerivAt_id x) hx0
     refine this.congr_deriv ?_
@@ -214,8 +214,8 @@ theorem integral_wIntegrand_two_three :
   have hcont : ContinuousOn (fun x : ℝ => (1 / (x - 1) - log (x - 1)) / x ^ 2) (uIcc 2 3) := by
     rw [uIcc_of_le (by norm_num)]
     intro x hx
-    have hx1 : x - 1 ≠ 0 := by linarith [hx.1]
-    have hx0 : x ^ 2 ≠ 0 := pow_ne_zero 2 (by linarith [hx.1])
+    have hx1 : x - 1 ≠ 0 := by linarith only [hx.1, hx]
+    have hx0 : x ^ 2 ≠ 0 := pow_ne_zero 2 (by linarith only [hx.1, hx])
     exact (((continuousAt_const.div (continuousAt_id.sub continuousAt_const) hx1).sub
       ((continuousAt_id.sub continuousAt_const).log hx1)).div
       (continuousAt_id.pow 2) hx0).continuousWithinAt
@@ -229,13 +229,13 @@ theorem bigW_eq_neg_mul_integral {s : ℝ} (hs : 3 ≤ s) :
   have hgc : ContinuousOn g (Ici 3) := by
     refine ContinuousOn.add ?_ ?_
     · exact continuous_bigW.continuousOn.div continuousOn_id fun x hx => by
-        linarith [hx.out]
+        linarith only [hx.out, hx]
     · exact fun t _ => (hasDerivAt_integral_unit continuous_wIntegrand t).continuousAt
         |>.continuousWithinAt
   have hgd : ∀ t, 3 < t → HasDerivAt g 0 t := by
     intro t ht
-    have ht0 : t ≠ 0 := by linarith
-    have ht1 : t - 1 ≠ 0 := by linarith
+    have ht0 : t ≠ 0 := by linarith only [ht]
+    have ht1 : t - 1 ≠ 0 := by linarith only [ht]
     have := ((hasDerivAt_bigW ht).div (hasDerivAt_id t) ht0).add
       (hasDerivAt_integral_unit continuous_wIntegrand t)
     refine this.congr_deriv ?_
@@ -251,12 +251,12 @@ theorem bigW_eq_neg_mul_integral {s : ℝ} (hs : 3 ≤ s) :
   have hgs : g s = 0 := (eq_of_hasDerivAt_zero hgc hgd hs).trans h3
   have hint : ∫ x in (s - 1)..s, wIntegrand x = ∫ x in (s - 1)..s, bigW x / x ^ 2 := by
     refine intervalIntegral.integral_congr fun x hx => ?_
-    rw [uIcc_of_le (by linarith)] at hx
-    exact wIntegrand_of_ge (by linarith [hx.1])
+    rw [uIcc_of_le (by linarith only [])] at hx
+    exact wIntegrand_of_ge (by linarith only [hx.1, hs, hx])
   simp only [g, hint] at hgs
-  have hs0 : s ≠ 0 := by linarith
+  have hs0 : s ≠ 0 := by linarith only [hs]
   field_simp at hgs
-  linarith
+  linarith only [hgs]
 
 /-! ### (3.12) -/
 
@@ -280,7 +280,7 @@ theorem integral_mIntegrand_two_three :
       ∫ x in (2 : ℝ)..3, (1 - 1 / (2 * x ^ 2)) * (2 + (1 / (x - 1) - log (x - 1))) := by
     refine intervalIntegral.integral_congr fun x hx => ?_
     rw [uIcc_of_le (by norm_num)] at hx
-    rw [mIntegrand_of_ge (by linarith [hx.1]), bigM_eq hx.1 hx.2]
+    rw [mIntegrand_of_ge (by linarith only [hx.1, hx]), bigM_eq hx.1 hx.2]
     ring
   rw [hcongr]
   have hderiv : ∀ x ∈ uIcc (2 : ℝ) 3, HasDerivAt
@@ -289,12 +289,12 @@ theorem integral_mIntegrand_two_three :
       ((1 - 1 / (2 * x ^ 2)) * (2 + (1 / (x - 1) - log (x - 1)))) x := by
     intro x hx
     rw [uIcc_of_le (by norm_num)] at hx
-    have hx1 : x - 1 ≠ 0 := by linarith [hx.1]
-    have hx0 : x ≠ 0 := by linarith [hx.1]
+    have hx1 : x - 1 ≠ 0 := by linarith only [hx.1, hx]
+    have hx0 : x ≠ 0 := by linarith only [hx.1, hx]
     have h1 : HasDerivAt (fun x : ℝ => x - 1) 1 x := (hasDerivAt_id x).sub_const 1
     have hr : HasDerivAt (fun x : ℝ => (x - 1) ^ 2 - 1 / 2) (2 * (x - 1)) x := by
       convert (h1.pow 2).sub_const (1 / 2) using 1; ring
-    have hm := (hasDerivAt_initForm (x := x) (by linarith [hx.1])).const_add 2
+    have hm := (hasDerivAt_initForm (x := x) (by linarith only [hx.1, hx])).const_add 2
     have hq : HasDerivAt (fun x : ℝ => 2 * (x - 1)) 2 x := by
       convert h1.const_mul 2 using 1; ring
     have := (((hr.mul hm).div (hasDerivAt_id x) hx0).add (hasDerivAt_id x)).add
@@ -307,8 +307,8 @@ theorem integral_mIntegrand_two_three :
       (fun x : ℝ => (1 - 1 / (2 * x ^ 2)) * (2 + (1 / (x - 1) - log (x - 1)))) (uIcc 2 3) := by
     rw [uIcc_of_le (by norm_num)]
     intro x hx
-    have hx1 : x - 1 ≠ 0 := by linarith [hx.1]
-    have hx0 : 2 * x ^ 2 ≠ 0 := by have : x ≠ 0 := by linarith [hx.1]
+    have hx1 : x - 1 ≠ 0 := by linarith only [hx.1, hx]
+    have hx0 : 2 * x ^ 2 ≠ 0 := by have : x ≠ 0 := by linarith only [hx.1, hx]
                                    positivity
     exact ((continuousAt_const.sub (continuousAt_const.div
       (continuousAt_const.mul (continuousAt_id.pow 2)) hx0)).mul
@@ -324,15 +324,15 @@ theorem bigM_integral_identity {s : ℝ} (hs : 3 ≤ s) :
   set g : ℝ → ℝ := fun t => ((t - 1) ^ 2 - 1 / 2) * bigM t / t - ∫ x in (t - 1)..t, mIntegrand x
   have hgc : ContinuousOn g (Ici 3) := by
     refine ContinuousOn.sub ?_ ?_
-    · refine ContinuousOn.div ?_ continuousOn_id fun x hx => by linarith [hx.out]
+    · refine ContinuousOn.div ?_ continuousOn_id fun x hx => by linarith only [hx.out, hx]
       exact (((continuous_id.sub continuous_const).pow 2).sub continuous_const).continuousOn.mul
         continuous_bigM.continuousOn
     · exact fun t _ => (hasDerivAt_integral_unit continuous_mIntegrand t).continuousAt
         |>.continuousWithinAt
   have hgd : ∀ t, 3 < t → HasDerivAt g 0 t := by
     intro t ht
-    have ht0 : t ≠ 0 := by linarith
-    have ht1 : t - 1 ≠ 0 := by linarith
+    have ht0 : t ≠ 0 := by linarith only [ht]
+    have ht1 : t - 1 ≠ 0 := by linarith only [ht]
     have h1 : HasDerivAt (fun x : ℝ => x - 1) 1 t := (hasDerivAt_id t).sub_const 1
     have hr : HasDerivAt (fun x : ℝ => (x - 1) ^ 2 - 1 / 2) (2 * (t - 1)) t := by
       convert (h1.pow 2).sub_const (1 / 2) using 1; ring
@@ -352,9 +352,9 @@ theorem bigM_integral_identity {s : ℝ} (hs : 3 ≤ s) :
   have hint : ∫ x in (s - 1)..s, mIntegrand x =
       ∫ x in (s - 1)..s, (1 - 1 / (2 * x ^ 2)) * bigM x := by
     refine intervalIntegral.integral_congr fun x hx => ?_
-    rw [uIcc_of_le (by linarith)] at hx
-    exact mIntegrand_of_ge (by linarith [hx.1])
+    rw [uIcc_of_le (by linarith only [])] at hx
+    exact mIntegrand_of_ge (by linarith only [hx.1, hs, hx])
   simp only [g, hint] at hgs
-  linarith
+  linarith only [hgs]
 
 end IwaniecLinearSieve
diff --git a/LeanPool/IwaniecLinearSieve/SieveMajorants/Delay.lean b/LeanPool/IwaniecLinearSieve/SieveMajorants/Delay.lean
index d4cc5d6abd..1cb7fb9bb7 100644
--- a/LeanPool/IwaniecLinearSieve/SieveMajorants/Delay.lean
+++ b/LeanPool/IwaniecLinearSieve/SieveMajorants/Delay.lean
@@ -52,7 +52,7 @@ theorem step_congr {y y' : ℝ → ℝ} {m : ℝ} (h : ∀ x ≤ m, y x = y' x)
     congr 1
     refine intervalIntegral.integral_congr fun x hx => ?_
     rw [uIcc_of_le h3] at hx
-    rw [h (x - 1) (by linarith [hx.2])]
+    rw [h (x - 1) (by linarith only [hx.2, hs, hx])]
 
 theorem iter_succ_eq (n : ℕ) {s : ℝ} (hs : s ≤ n + 3) :
     iter k y₀ (n + 1) s = iter k y₀ n s := by
@@ -64,14 +64,14 @@ theorem iter_succ_eq (n : ℕ) {s : ℝ} (hs : s ≤ n + 3) :
     change step k y₀ (iter k y₀ (n + 1)) s = step k y₀ (iter k y₀ n) s
     refine step_congr (m := n + 3) (fun x hx => ih hx) ?_
     push_cast at hs
-    linarith
+    linarith only [hs]
 
 theorem iter_add_eq (n j : ℕ) {s : ℝ} (hs : s ≤ n + 3) :
     iter k y₀ (n + j) s = iter k y₀ n s := by
   induction j with
   | zero => rfl
   | succ j ih =>
-    rw [← add_assoc, iter_succ_eq _ (by push_cast; linarith), ih]
+    rw [← add_assoc, iter_succ_eq _ (by push_cast; linarith only [hs]), ih]
 
 theorem iter_eq_of_le {m n : ℕ} (hmn : m ≤ n) {s : ℝ} (hs : s ≤ m + 3) :
     iter k y₀ n s = iter k y₀ m s := by
@@ -82,15 +82,15 @@ theorem sol_eq_iter {n : ℕ} {s : ℝ} (hs : s ≤ n + 3) : sol k y₀ s = iter
   unfold sol
   rcases le_total n ⌈s⌉₊ with h | h
   · exact iter_eq_of_le h hs
-  · exact (iter_eq_of_le h (by linarith [Nat.le_ceil s])).symm
+  · exact (iter_eq_of_le h (by linarith only [Nat.le_ceil s])).symm
 
 /-- `sol` is a fixed point of `step`. -/
 theorem sol_eq_step (s : ℝ) : sol k y₀ s = step k y₀ (sol k y₀) s := by
   set n := ⌈s⌉₊
   have hn : s ≤ n := Nat.le_ceil s
-  rw [sol_eq_iter (n := n + 1) (by push_cast; linarith)]
+  rw [sol_eq_iter (n := n + 1) (by push_cast; linarith only [hn])]
   change step k y₀ (iter k y₀ n) s = _
-  exact step_congr (m := n + 3) (fun x hx => (sol_eq_iter hx).symm) (by linarith)
+  exact step_congr (m := n + 3) (fun x hx => (sol_eq_iter hx).symm) (by linarith only [hn])
 
 theorem sol_of_le {s : ℝ} (hs : s ≤ 3) : sol k y₀ s = y₀ s := by
   rw [sol_eq_step, step_of_le hs]
@@ -119,7 +119,7 @@ theorem continuous_sol (hk : Continuous k) (hy₀ : Continuous y₀) : Continuou
   set n := ⌈s⌉₊
   have hn : s ≤ n := Nat.le_ceil s
   have hev : iter k y₀ n =ᶠ[𝓝 s] sol k y₀ := by
-    filter_upwards [Iio_mem_nhds (show s < n + 3 by linarith)] with x hx
+    filter_upwards [Iio_mem_nhds (show s < n + 3 by linarith only [hn])] with x hx
     exact (sol_eq_iter hx.le).symm
   exact ((continuous_iter hk hy₀ n).continuousAt).congr hev
 
@@ -165,7 +165,7 @@ theorem pos_of_first_crossing {f : ℝ → ℝ} {a₀ a : ℝ} (hf : ContinuousO
   have htB : t ∈ B := hBc.csInf_mem hBne hBb
   have hat : a ≤ t := htB.1
   have hft : f t ≤ 0 := htB.2
-  have hat' : a < t := lt_of_le_of_ne hat fun h => by rw [← h] at hft; linarith
+  have hat' : a < t := lt_of_le_of_ne hat fun h => by rw [← h] at hft; linarith only [ha, hft]
   have hpos : ∀ x ∈ Ico a t, 0 < f x := by
     intro x hx
     by_contra hx'
@@ -184,6 +184,6 @@ theorem pos_of_first_crossing {f : ℝ → ℝ} {a₀ a : ℝ} (hf : ContinuousO
     rcases le_total x a with hxa | hxa
     · exact hinit x ⟨hx.1, hxa⟩
     · exact hnn x ⟨hxa, hx.2⟩
-  linarith [hstep t hat' hall hpos]
+  linarith only [hstep t hat' hall hpos, hft, hstep, hat', hall, hpos]
 
 end IwaniecLinearSieve
diff --git a/LeanPool/IwaniecLinearSieve/SieveMajorants/Lemmas.lean b/LeanPool/IwaniecLinearSieve/SieveMajorants/Lemmas.lean
index 3d9a83b4b8..30d69993df 100644
--- a/LeanPool/IwaniecLinearSieve/SieveMajorants/Lemmas.lean
+++ b/LeanPool/IwaniecLinearSieve/SieveMajorants/Lemmas.lean
@@ -39,10 +39,10 @@ namespace IwaniecLinearSieve
 /-- From (3.12): `𝔐(s - 1/2) ≤ 2(s-1)²/s 𝔐(s)` for `s ≥ 3`. -/
 theorem bigM_sub_half_le {s : ℝ} (hs : 3 ≤ s) :
     bigM (s - 1 / 2) ≤ 2 * (s - 1) ^ 2 / s * bigM s := by
-  have hs0 : 0 < s := by linarith
-  have hy : 0 < (s - 1) ^ 2 := by nlinarith
-  have hs1 : s - 1 ≠ 0 := by linarith
-  have hwc := continuousOn_weight_mul continuous_bigM (a := s - 1) (b := s) (by linarith)
+  have hs0 : 0 < s := by linarith only [hs]
+  have hy : 0 < (s - 1) ^ 2 := by nlinarith only [hs]
+  have hs1 : s - 1 ≠ 0 := by linarith only [hs]
+  have hwc := continuousOn_weight_mul continuous_bigM (a := s - 1) (b := s) (by linarith only [hs])
   have hI : ∀ a b, s - 1 ≤ a → a ≤ b → b ≤ s →
       IntervalIntegrable (fun x => (1 - 1 / (2 * x ^ 2)) * bigM x) volume a b :=
     fun a b ha hab hb => (hwc.mono (Icc_subset_Icc ha hb)).intervalIntegrable_of_Icc hab
@@ -50,56 +50,57 @@ theorem bigM_sub_half_le {s : ℝ} (hs : 3 ≤ s) :
     (hI (s - 1) (s - 1 / 2) le_rfl (by linarith) (by linarith))
     (hI (s - 1 / 2) s (by linarith) (by linarith) le_rfl)
   have h2 : 0 ≤ ∫ x in (s - 1 / 2)..s, (1 - 1 / (2 * x ^ 2)) * bigM x :=
-    intervalIntegral.integral_nonneg (by linarith) fun x hx =>
-      (mul_pos (weight_mem (by linarith [hx.1])).1 (bigM_pos x)).le
+    intervalIntegral.integral_nonneg (by linarith only []) fun x hx =>
+      (mul_pos (weight_mem (by linarith only [hx.1, hs, hx])).1 (bigM_pos x)).le
   have h1 : ∫ _ in (s - 1)..(s - 1 / 2), (1 - 1 / (2 * (s - 1) ^ 2)) * bigM (s - 1 / 2) ≤
       ∫ x in (s - 1)..(s - 1 / 2), (1 - 1 / (2 * x ^ 2)) * bigM x := by
-    refine intervalIntegral.integral_mono_on (by linarith) intervalIntegrable_const
+    refine intervalIntegral.integral_mono_on (by linarith only []) intervalIntegrable_const
       (hI _ _ le_rfl (by linarith) (by linarith)) fun x hx => ?_
     have hw : 1 - 1 / (2 * (s - 1) ^ 2) ≤ 1 - 1 / (2 * x ^ 2) := by
       have : 1 / (2 * x ^ 2) ≤ 1 / (2 * (s - 1) ^ 2) :=
-        one_div_le_one_div_of_le (by positivity) (by nlinarith [hx.1])
-      linarith
+        one_div_le_one_div_of_le (by positivity) (by nlinarith only [hx.1, hx, hs])
+      linarith only [this]
     exact mul_le_mul hw (bigM_antitone hx.2) (bigM_pos _).le
-      (weight_mem (by linarith [hx.1])).1.le
+      (weight_mem (by linarith only [hx.1, hs, hx])).1.le
   rw [intervalIntegral.integral_const, smul_eq_mul] at h1
   have key := bigM_integral_identity hs
   rw [← hsplit] at key
   have : (s - 1 / 2 - (s - 1)) * ((1 - 1 / (2 * (s - 1) ^ 2)) * bigM (s - 1 / 2)) ≤
-      ((s - 1) ^ 2 - 1 / 2) * bigM s / s := by linarith
+      ((s - 1) ^ 2 - 1 / 2) * bigM s / s := by linarith only [h2, h1, key]
   have e1 : (s - 1 / 2 - (s - 1)) * ((1 - 1 / (2 * (s - 1) ^ 2)) * bigM (s - 1 / 2)) =
       ((s - 1) ^ 2 - 1 / 2) * bigM (s - 1 / 2) / (2 * (s - 1) ^ 2) := by
     field_simp; ring
   rw [e1, div_le_div_iff₀ (by positivity) hs0] at this
-  have hr : 0 < (s - 1) ^ 2 - 1 / 2 := by nlinarith
+  have hr : 0 < (s - 1) ^ 2 - 1 / 2 := by nlinarith only [hs, hy]
   rw [div_mul_eq_mul_div, le_div_iff₀ hs0]
-  nlinarith
+  nlinarith only [this, hr]
 
 /-- [I71, Lemma 8]: `𝔐(s-1) < 4 s² 𝔐(s)` for `s ≥ 3`. -/
 theorem bigM_sub_one_lt {s : ℝ} (hs : 3 ≤ s) : bigM (s - 1) < 4 * s ^ 2 * bigM s := by
-  have hs0 : 0 < s := by linarith
+  have hs0 : 0 < s := by linarith only [hs]
   have hB := bigM_sub_half_le hs
   have hMs := bigM_pos s
   rcases le_total s (7 / 2) with h | h
   · have h1 : bigM (s - 1) ≤ 3 := bigM_le_three _
-    have h2 : bigM 3 ≤ bigM (s - 1 / 2) := bigM_antitone (by linarith)
+    have h2 : bigM 3 ≤ bigM (s - 1 / 2) := bigM_antitone (by linarith only [h])
     rw [bigM_three] at h2
     have h3 : 2 * (s - 1) ^ 2 / s ≤ s ^ 2 := by
-      rw [div_le_iff₀ hs0]; nlinarith
+      rw [div_le_iff₀ hs0]; nlinarith only [hs]
     have := mul_le_mul_of_nonneg_right h3 hMs.le
-    nlinarith [log_two_lt_d9]
-  · have hA := bigM_sub_half_le (s := s - 1 / 2) (by linarith)
+    nlinarith only [log_two_lt_d9, hB, h1, h2, this]
+  · have hA := bigM_sub_half_le (s := s - 1 / 2) (by linarith only [h])
     rw [show s - 1 / 2 - 1 / 2 = s - 1 by ring] at hA
     have h3 : 2 * (s - 1 / 2 - 1) ^ 2 / (s - 1 / 2) < 2 * s := by
-      rw [div_lt_iff₀ (by linarith)]; nlinarith
+      rw [div_lt_iff₀ (by linarith only [h])]; nlinarith
     have h4 : 2 * (s - 1) ^ 2 / s < 2 * s := by
-      rw [div_lt_iff₀ hs0]; nlinarith
-    have h5 : 0 < 2 * (s - 1) ^ 2 / s := div_pos (by nlinarith) hs0
+      rw [div_lt_iff₀ hs0]; nlinarith only [h]
+    have h5 : 0 < 2 * (s - 1) ^ 2 / s := div_pos (by nlinarith only [h, hs]) hs0
     calc bigM (s - 1) ≤ 2 * (s - 1 / 2 - 1) ^ 2 / (s - 1 / 2) * bigM (s - 1 / 2) := hA
       _ ≤ 2 * (s - 1 / 2 - 1) ^ 2 / (s - 1 / 2) * (2 * (s - 1) ^ 2 / s * bigM s) :=
-        mul_le_mul_of_nonneg_left hB (div_nonneg (by positivity) (by linarith))
+        mul_le_mul_of_nonneg_left hB (div_nonneg (by positivity) (by linarith only [h]))
       _ < 2 * s * (2 * s * bigM s) := by
-        apply mul_lt_mul' h3.le (mul_lt_mul_of_pos_right h4 hMs) (by positivity) (by linarith)
+        apply mul_lt_mul' h3.le (mul_lt_mul_of_pos_right h4 hMs) (by positivity) (by
+          linarith only [h])
       _ = 4 * s ^ 2 * bigM s := by ring
 
 /-- [I71, Lemma 8] in ratio form. -/
@@ -127,7 +128,7 @@ theorem log_four_lt : log 4 < 1.3863 := by
   rw [show (4 : ℝ) = 2 ^ 2 by norm_num, log_pow]
   have := log_two_lt_d9
   push_cast
-  linarith
+  linarith only [this]
 
 /-- The numerical comparison in the main range of Lemma 10. With `q² = t - 1`, the
 logarithmic bound makes the integrated exponential estimate smaller than `2t/(t-1)²`. -/
@@ -136,8 +137,7 @@ theorem log_mul_ratio_lt {t q L : ℝ} (ht0 : 0 < t) (hq1 : 1 < q)
     log t * (t / ((t - 1) ^ 2 - 1 / 2) * ((1 - q⁻¹) / (L / 2))) <
       2 * (t / (t - 1) ^ 2) := by
   have hq0 : 0 < q := by linarith only [hq1]
-  have hq4 : 0 < q ^ 4 - 1 / 2 := by
-    linarith only [one_lt_pow₀ hq1 (by decide : 4 ≠ 0)]
+  have hq4 : 0 < q ^ 4 - 1 / 2 := by linarith only [one_lt_pow₀ hq1 (by decide : 4 ≠ 0)]
   have hL0 : 0 < L := by linarith only [hL]
   have hD : 0 < L * q * (q ^ 4 - 1 / 2) := by positivity
   have hy : (t - 1) ^ 2 = q ^ 4 := by rw [← hq2]; ring
@@ -153,7 +153,7 @@ theorem log_mul_ratio_lt {t q L : ℝ} (ht0 : 0 < t) (hq1 : 1 < q)
   -- `log t (q-1) q⁴ < L q (q⁴ - 1/2)` using `log t ≤ L + 1/q²`
   have hLt' : log t ≤ L + 1 / q ^ 2 := by rwa [hq2]
   have h1 := mul_le_mul_of_nonneg_right hLt'
-    (show 0 ≤ (q - 1) * q ^ 4 by have : 0 ≤ q - 1 := by linarith
+    (show 0 ≤ (q - 1) * q ^ 4 by have : 0 ≤ q - 1 := by linarith only [hq1]
                                  positivity)
   have h2 : (L + 1 / q ^ 2) * ((q - 1) * q ^ 4) = L * (q - 1) * q ^ 4 + (q - 1) * q ^ 2 := by
     field_simp
@@ -162,11 +162,11 @@ theorem log_mul_ratio_lt {t q L : ℝ} (ht0 : 0 < t) (hq1 : 1 < q)
       have hcube := mul_lt_mul_of_pos_right (one_lt_pow₀ hq1 (by decide : 3 ≠ 0)) hq0
       nlinarith only [hcube, hq0]
     have hB' : 0 < q ^ 2 * q * (q - 1) + q * (q - 1 / 2) := by
-      have : 0 < q - 1 := by linarith
-      have : 0 < q - 1 / 2 := by linarith
+      have : 0 < q - 1 := by linarith only [hq1]
+      have : 0 < q - 1 / 2 := by linarith only [hq1]
       positivity
-    nlinarith [mul_lt_mul_of_pos_right hL hA]
-  nlinarith
+    nlinarith only [mul_lt_mul_of_pos_right hL hA, hB', hL, hA]
+  nlinarith only [h1, h2, h3]
 
 /-- The inequality behind [I71, Lemma 10]: `log t · 𝔐(t) < 2 t/(t-1)² · 𝔐(t-1)` for
 `t ≥ 2`. -/
@@ -179,15 +179,15 @@ theorem log_mul_bigM_lt {t : ℝ} (ht : 2 ≤ t) :
       (continuousOn_id.div ((continuousOn_id.sub continuousOn_const).pow 2) fun x hx => ?_))
       (continuous_bigM.comp (continuous_sub_right 1)).continuousOn)
       ((continuousOn_log.mono fun x hx => ?_).mul continuous_bigM.continuousOn)
-    · have : 0 < x - 1 := by linarith [hx.out]
+    · have : 0 < x - 1 := by linarith only [hx.out, hx]
       positivity
-    · simp only [mem_compl_iff, mem_singleton_iff]; linarith [hx.out]
+    · simp only [mem_compl_iff, mem_singleton_iff]; linarith only [hx.out, hx]
   · intro x hx
     obtain rfl : x = 2 := le_antisymm hx.2 hx.1
     rw [show (2 : ℝ) - 1 = 1 by norm_num, bigM_of_le_two (by norm_num), bigM_two]
-    linarith [log_two_lt_d9]
+    linarith only [log_two_lt_d9]
   · rw [show (2 : ℝ) - 1 = 1 by norm_num, bigM_of_le_two (by norm_num), bigM_two]
-    linarith [log_two_lt_d9]
+    linarith only [log_two_lt_d9]
   intro t ht _ hpos
   show 0 < 2 * (t / (t - 1) ^ 2) * bigM (t - 1) - log t * bigM t
   rw [sub_pos]
@@ -196,24 +196,24 @@ theorem log_mul_bigM_lt {t : ℝ} (ht : 2 ≤ t) :
   have hlog0 : 0 ≤ log t := log_nonneg (by linarith)
   rcases le_total t 3 with h3 | h3
   · -- explicit range `2 < t ≤ 3`
-    rw [bigM_of_le_two (show t - 1 ≤ 2 by linarith)]
-    have hl : log t < 1.3863 := (log_le_log ht0 (by linarith)).trans_lt log_four_lt
+    rw [bigM_of_le_two (show t - 1 ≤ 2 by linarith only [h3])]
+    have hl : log t < 1.3863 := (log_le_log ht0 (by linarith only [h3])).trans_lt log_four_lt
     have hk : 3 / 4 ≤ t / (t - 1) ^ 2 := by
       rw [le_div_iff₀ (by have : 0 < t - 1 := by linarith
                           positivity)]
       nlinarith
     have := bigM_le_three t
-    nlinarith
+    nlinarith only [hl, hk, hlog0, this]
   rcases le_total t 4 with h4 | h4
   · -- crude range `3 ≤ t ≤ 4`, from `𝔐(t) ≤ t/((t-1)² - 1/2) 𝔐(t-1)`
     have hl : log t < 1.3863 := (log_le_log ht0 h4).trans_lt log_four_lt
     have hR := bigM_le_ratio h3
     have hy : 4 ≤ (t - 1) ^ 2 := by nlinarith
-    have hr : 0 < (t - 1) ^ 2 - 1 / 2 := by linarith
+    have hr : 0 < (t - 1) ^ 2 - 1 / 2 := by linarith only [hy]
     have key : log t * (t / ((t - 1) ^ 2 - 1 / 2)) < 2 * (t / (t - 1) ^ 2) := by
-      rw [mul_div_assoc', mul_div_assoc', div_lt_div_iff₀ hr (by linarith)]
-      have : 1 < (2 - log t) * (t - 1) ^ 2 := by nlinarith
-      nlinarith [mul_lt_mul_of_pos_left this ht0]
+      rw [mul_div_assoc', mul_div_assoc', div_lt_div_iff₀ hr (by linarith only [hy])]
+      have : 1 < (2 - log t) * (t - 1) ^ 2 := by nlinarith only [hy, hl]
+      nlinarith only [mul_lt_mul_of_pos_left this ht0, this, ht0]
     calc log t * bigM t ≤ log t * (t / ((t - 1) ^ 2 - 1 / 2) * bigM (t - 1)) :=
           mul_le_mul_of_nonneg_left hR hlog0
       _ = log t * (t / ((t - 1) ^ 2 - 1 / 2)) * bigM (t - 1) := by ring
@@ -222,9 +222,9 @@ theorem log_mul_bigM_lt {t : ℝ} (ht : 2 ≤ t) :
   set L₁ := log (t - 1) with hL₁
   set l := L₁ / 2 with hl
   have hL₁1 : 1 < L₁ := by
-    rw [hL₁, lt_log_iff_exp_lt (by linarith)]
-    linarith [exp_one_lt_d9]
-  have hl0 : 0 < l := by linarith
+    rw [hL₁, lt_log_iff_exp_lt (by linarith only [h4])]
+    linarith only [exp_one_lt_d9, h4]
+  have hl0 : 0 < l := by linarith only [hl, hL₁1]
   -- `𝔐(x) ≤ 𝔐(t-1) exp(-l(x - (t-1)))` on `[t-1, t]`
   have hanti : AntitoneOn (fun x => bigM x * exp (l * x)) (Icc (t - 1) t) := by
     have hd : ∀ x, 3 < x → HasDerivAt (fun x => bigM x * exp (l * x))
@@ -234,20 +234,20 @@ theorem log_mul_bigM_lt {t : ℝ} (ht : 2 ≤ t) :
     refine antitoneOn_of_deriv_nonpos (convex_Icc _ _)
       (continuous_bigM.mul (continuous_const.mul continuous_id).rexp).continuousOn
       (fun x hx => ?_) (fun x hx => ?_) <;> rw [interior_Icc] at hx
-    · exact (hd x (by linarith [hx.1])).differentiableAt.differentiableWithinAt
-    · rw [(hd x (by linarith [hx.1])).deriv]
-      have hfx := hpos x ⟨by linarith [hx.1], hx.2⟩
-      have hlx : L₁ ≤ log x := log_le_log (by linarith) hx.1.le
+    · exact (hd x (by linarith only [hx.1, h4, hx])).differentiableAt.differentiableWithinAt
+    · rw [(hd x (by linarith only [hx.1, h4, hx])).deriv]
+      have hfx := hpos x ⟨by linarith only [hx.1, h4, hx], hx.2⟩
+      have hlx : L₁ ≤ log x := log_le_log (by linarith only [h4]) hx.1.le
       have hMx := bigM_pos x
-      have : l * bigM x < x / (x - 1) ^ 2 * bigM (x - 1) := by nlinarith
+      have : l * bigM x < x / (x - 1) ^ 2 * bigM (x - 1) := by nlinarith only [hfx, hl, hMx, hlx]
       have he := exp_pos (l * x)
-      nlinarith
+      nlinarith only [this, he]
   have hbound : ∀ x ∈ Icc (t - 1) t,
       (1 - 1 / (2 * x ^ 2)) * bigM x ≤ bigM (t - 1) * exp (-(l * (x - (t - 1)))) := by
     intro x hx
-    have h := hanti ⟨le_rfl, by linarith⟩ hx hx.1
+    have h := hanti ⟨le_rfl, by linarith only []⟩ hx hx.1
     simp only at h
-    have hw := weight_mem (x := x) (by linarith [hx.1])
+    have hw := weight_mem (x := x) (by linarith only [hx.1, h4, hx])
     have hMx := bigM_pos x
     have e : bigM (t - 1) * exp (-(l * (x - (t - 1)))) =
         bigM (t - 1) * exp (l * (t - 1)) / exp (l * x) := by
@@ -259,20 +259,20 @@ theorem log_mul_bigM_lt {t : ℝ} (ht : 2 ≤ t) :
   have hint : ((t - 1) ^ 2 - 1 / 2) * bigM t / t ≤ bigM (t - 1) * ((1 - exp (-l)) / l) := by
     rw [bigM_integral_identity h3, ← integral_exp_neg_mul_unit (t - 1) hl0.ne',
       sub_add_cancel, ← intervalIntegral.integral_const_mul]
-    refine intervalIntegral.integral_mono_on (by linarith)
-      ((continuousOn_weight_mul continuous_bigM (by linarith)).intervalIntegrable_of_Icc
-        (by linarith)) ((by fun_prop : Continuous fun x =>
+    refine intervalIntegral.integral_mono_on (by linarith only [])
+      ((continuousOn_weight_mul continuous_bigM (by linarith only [h4])).intervalIntegrable_of_Icc
+        (by linarith only [])) ((by fun_prop : Continuous fun x =>
           bigM (t - 1) * exp (-(l * (x - (t - 1))))).intervalIntegrable _ _) hbound
   -- the numerical inequality, with `q = exp l = √(t-1)`
   set q := exp l with hq
   have hq2 : q ^ 2 = t - 1 := by
-    rw [hq, sq, ← exp_add, show l + l = L₁ by rw [hl]; ring, hL₁, exp_log (by linarith)]
+    rw [hq, sq, ← exp_add, show l + l = L₁ by rw [hl]; ring, hL₁, exp_log (by linarith only [h4])]
   have hq1 : 1 < q := one_lt_exp_iff.2 hl0
   have hel : exp (-l) = q⁻¹ := by rw [exp_neg]
   have hLt : log t ≤ L₁ + 1 / (t - 1) := by
-    have := log_le_sub_one_of_pos (div_pos ht0 (by linarith : (0 : ℝ) < t - 1))
+    have := log_le_sub_one_of_pos (div_pos ht0 (by linarith only [h4] : (0 : ℝ) < t - 1))
     rw [log_div (by linarith) (by linarith)] at this
-    have : t - 1 ≠ 0 := by linarith
+    have : t - 1 ≠ 0 := by linarith only [h4]
     have e : t / (t - 1) - 1 = 1 / (t - 1) := by field_simp; ring
     linarith
   rw [hel] at hint
@@ -280,7 +280,7 @@ theorem log_mul_bigM_lt {t : ℝ} (ht : 2 ≤ t) :
   have hMt : bigM t ≤ t / ((t - 1) ^ 2 - 1 / 2) * (bigM (t - 1) * ((1 - q⁻¹) / l)) := by
     rw [div_mul_eq_mul_div, le_div_iff₀ hr]
     rw [div_le_iff₀ ht0] at hint
-    linarith
+    linarith only [hint]
   have key := log_mul_ratio_lt ht0 hq1 hq2 hL₁1 hLt
   calc log t * bigM t ≤ log t * (t / ((t - 1) ^ 2 - 1 / 2) * (bigM (t - 1) * ((1 - q⁻¹) / l))) :=
         mul_le_mul_of_nonneg_left hMt hlog0
@@ -290,25 +290,25 @@ theorem log_mul_bigM_lt {t : ℝ} (ht : 2 ≤ t) :
 /-- [I71, Lemma 10]: `𝔐(t) t log t / 𝔐(t-1) < 9/2` for `t ≥ 3` (so it is `O(1)`). -/
 theorem bigM_mul_log_div_lt {t : ℝ} (ht : 3 ≤ t) :
     bigM t * t * log t / bigM (t - 1) < 9 / 2 := by
-  have h := log_mul_bigM_lt (t := t) (by linarith)
+  have h := log_mul_bigM_lt (t := t) (by linarith only [ht])
   have hB := bigM_pos (t - 1)
-  have ht0 : 0 < t := by linarith
-  have hy : 0 < (t - 1) ^ 2 := by nlinarith
+  have ht0 : 0 < t := by linarith only [ht]
+  have hy : 0 < (t - 1) ^ 2 := by nlinarith only [ht]
   rw [div_lt_iff₀ hB]
   have h' : log t * bigM t * t ≤ 2 * (t / (t - 1) ^ 2) * bigM (t - 1) * t :=
     mul_le_mul_of_nonneg_right h.le ht0.le
   have hk : 2 * (t / (t - 1) ^ 2) * t ≤ 9 / 2 := by
-    rw [mul_div_assoc', div_mul_eq_mul_div, div_le_iff₀ hy]; nlinarith
-  nlinarith
+    rw [mul_div_assoc', div_mul_eq_mul_div, div_le_iff₀ hy]; nlinarith only [ht]
+  nlinarith only [h, ht, hB, hk]
 
 /-- Corollary to [I71, Lemma 10]: `G_{r+1}(t) (t-1)² log t / (G_r(t-1) t) < 4` for `t ≥ 2`
 (and all `r`; [I71] states it for `t > (5 + (-1)^r)/2`). -/
 theorem majG_succ_mul_log_div_lt (r : ℕ) {t : ℝ} (ht : 2 ≤ t) :
     majG (r + 1) t * (t - 1) ^ 2 * log t / (majG r (t - 1) * t) < 4 := by
   have h := log_mul_bigM_lt ht
-  have ht0 : 0 < t := by linarith
-  have hy : 0 < (t - 1) ^ 2 := by nlinarith
-  have hlog : 0 ≤ log t := log_nonneg (by linarith)
+  have ht0 : 0 < t := by linarith only [ht]
+  have hy : 0 < (t - 1) ^ 2 := by nlinarith only [ht]
+  have hlog : 0 ≤ log t := log_nonneg (by linarith only [ht])
   have hG := majG_mem (r + 1) t
   have hG' := majG_mem r (t - 1)
   have hGpos := majG_pos r (t - 1)
@@ -316,11 +316,11 @@ theorem majG_succ_mul_log_div_lt (r : ℕ) {t : ℝ} (ht : 2 ≤ t) :
   have h1 : majG (r + 1) t * (t - 1) ^ 2 * log t ≤ 2 * bigM t / 3 * (t - 1) ^ 2 * log t :=
     mul_le_mul_of_nonneg_right (mul_le_mul_of_nonneg_right hG.2 hy.le) hlog
   have h2 : log t * bigM t * (t - 1) ^ 2 < 2 * t * bigM (t - 1) := by
-    have ht1 : t - 1 ≠ 0 := by linarith
+    have ht1 : t - 1 ≠ 0 := by linarith only [ht]
     have := mul_lt_mul_of_pos_right h hy
     rwa [show 2 * (t / (t - 1) ^ 2) * bigM (t - 1) * (t - 1) ^ 2 = 2 * t * bigM (t - 1) by
       field_simp] at this
-  nlinarith
+  nlinarith only [hG', h1, h2, ht]
 
 /-! ### Lemma 9 (lower bound) -/
 
@@ -330,22 +330,22 @@ noncomputable def lemma9Fun (s : ℝ) : ℝ := exp (-(s * log s + s * log (log s
 theorem continuousOn_lemma9Fun : ContinuousOn lemma9Fun (Ici 3) := by
   unfold lemma9Fun
   have hlog : ContinuousOn log (Ici 3) := continuousOn_log.mono fun x hx => by
-    simp only [mem_compl_iff, mem_singleton_iff]; linarith [hx.out]
+    simp only [mem_compl_iff, mem_singleton_iff]; linarith only [hx.out, hx]
   have hloglog : ContinuousOn (fun x => log (log x)) (Ici 3) :=
-    ContinuousOn.log hlog fun x hx => (log_pos (by linarith [hx.out])).ne'
+    ContinuousOn.log hlog fun x hx => (log_pos (by linarith only [hx.out, hx])).ne'
   exact ((((continuousOn_id.mul hlog).add (continuousOn_id.mul hloglog)).add
     (continuousOn_const.mul continuousOn_id)).neg).rexp
 
 theorem one_le_log_of_three_le {x : ℝ} (hx : 3 ≤ x) : 1 ≤ log x := by
-  rw [le_log_iff_exp_le (by linarith)]
-  linarith [exp_one_lt_d9]
+  rw [le_log_iff_exp_le (by linarith only [hx])]
+  linarith only [exp_one_lt_d9, hx]
 
 theorem lemma9Fun_le_one {x : ℝ} (hx : 3 ≤ x) : lemma9Fun x ≤ 1 := by
   unfold lemma9Fun
   rw [exp_le_one_iff, neg_nonpos]
   have h1 := log_nonneg (one_le_log_of_three_le hx)
-  have h2 := log_nonneg (show 1 ≤ x by linarith)
-  have : 0 ≤ x := by linarith
+  have h2 := log_nonneg (show 1 ≤ x by linarith only [hx])
+  have : 0 ≤ x := by linarith only [hx]
   positivity
 
 /-- Convexity estimate: `φ(s) - φ(x) ≥ λ (s - x)` for `3 ≤ s - 1 ≤ x ≤ s`, where
@@ -353,20 +353,21 @@ theorem lemma9Fun_le_one {x : ℝ} (hx : 3 ≤ x) : lemma9Fun x ≤ 1 := by
 theorem lemma9_phi_sub {s x : ℝ} (hs : 4 ≤ s) (hx : s - 1 ≤ x) (hxs : x ≤ s) :
     (log (s - 1) + log (log (s - 1)) + 3) * (s - x) ≤
       (s * log s + s * log (log s) + 2 * s) - (x * log x + x * log (log x) + 2 * x) := by
-  have hx0 : 0 < x := by linarith
-  have hs0 : 0 < s := by linarith
+  have hx0 : 0 < x := by linarith only [hs, hx]
+  have hs0 : 0 < s := by linarith only [hs]
   -- `s log s - x log x ≥ (s - x)(1 + log x)`
   have h1 : (s - x) * (1 + log x) ≤ s * log s - x * log x := by
     have := log_le_sub_one_of_pos (div_pos hx0 hs0)
     rw [log_div hx0.ne' hs0.ne'] at this
     have e : s * (x / s - 1) = x - s := by field_simp
-    nlinarith
-  have h2 : log (s - 1) ≤ log x := log_le_log (by linarith) hx
-  have hl1 : 1 ≤ log (s - 1) := one_le_log_of_three_le (by linarith)
-  have h3 : log (log (s - 1)) ≤ log (log x) := log_le_log (by linarith) h2
-  have h4 : log (log x) ≤ log (log s) := log_le_log (by linarith) (log_le_log hx0 hxs)
+    nlinarith only [this, e, hs]
+  have h2 : log (s - 1) ≤ log x := log_le_log (by linarith only [hs]) hx
+  have hl1 : 1 ≤ log (s - 1) := one_le_log_of_three_le (by linarith only [hs])
+  have h3 : log (log (s - 1)) ≤ log (log x) := log_le_log (by linarith only [hl1]) h2
+  have h4 : log (log x) ≤ log (log s) := log_le_log (by
+    linarith only [h2, hl1]) (log_le_log hx0 hxs)
   have h5 : 0 ≤ log (log (s - 1)) := log_nonneg hl1
-  have hsx : 0 ≤ s - x := by linarith
+  have hsx : 0 ≤ s - x := by linarith only [hxs]
   nlinarith [mul_le_mul_of_nonneg_left h2 hsx, mul_le_mul_of_nonneg_left h3 hsx,
     mul_le_mul_of_nonneg_left h4 hs0.le]
 
@@ -402,8 +403,8 @@ theorem lemma9_integral_factor_ge_one {s : ℝ} (hs : 4 ≤ s) :
   set L := log (s - 1) with hL
   set l := L + log L + 3 with hl
   set w₀ := 1 - 1 / (2 * (s - 1) ^ 2) with hw₀
-  have hL1 : 1 ≤ L := one_le_log_of_three_le (by linarith)
-  have hlogL : log L ≤ L - 1 := log_le_sub_one_of_pos (by linarith)
+  have hL1 : 1 ≤ L := one_le_log_of_three_le (by linarith only [hs])
+  have hlogL : log L ≤ L - 1 := log_le_sub_one_of_pos (by linarith only [hL1])
   have hlogL0 : 0 ≤ log L := log_nonneg hL1
   have hl0 : 0 < l := by linarith only [hL1, hlogL0, hl]
   have hr : 0 < (s - 1) ^ 2 - 1 / 2 := by nlinarith only [hs]
@@ -415,18 +416,18 @@ theorem lemma9_integral_factor_ge_one {s : ℝ} (hs : 4 ≤ s) :
     rw [this]
     have h := pow_le_pow_left₀ (by norm_num) exp_one_gt_d9.le 3
     norm_num at h
-    linarith
+    linarith only [this, h]
   have hexp_gain : l * (s - 1) ^ 2 ≤ s * (exp l - 1) := by
     rw [hel]
-    have hy : 3 ≤ s - 1 := by linarith
+    have hy : 3 ≤ s - 1 := by linarith only [hs]
     have h0 : 0 ≤ (s - 1) * L := by positivity
     have : 20 * ((s - 1) * L) ≤ (s - 1) * L * exp 3 := by
-      nlinarith [mul_le_mul_of_nonneg_left he3 h0]
+      nlinarith only [mul_le_mul_of_nonneg_left he3 h0, he3, h0]
     nlinarith [mul_le_mul_of_nonneg_left hL1 (by nlinarith : (0 : ℝ) ≤ (s - 1) ^ 2)]
   have hexp_cancel : exp l * (1 - exp (-l)) = exp l - 1 := by
     rw [mul_sub, mul_one, ← exp_add]; simp
   have hweight_cancel : w₀ / ((s - 1) ^ 2 - 1 / 2) = 1 / (s - 1) ^ 2 := by
-    have : s - 1 ≠ 0 := by linarith
+    have : s - 1 ≠ 0 := by linarith only [hs]
     rw [hw₀, div_eq_div_iff hr.ne' (by positivity)]
     field_simp
   have hfactor : w₀ * (exp l * ((1 - exp (-l)) / l)) * (s / ((s - 1) ^ 2 - 1 / 2)) =
@@ -435,7 +436,7 @@ theorem lemma9_integral_factor_ge_one {s : ℝ} (hs : 4 ≤ s) :
     calc w₀ * (exp l * ((1 - exp (-l)) / l)) * (s / ((s - 1) ^ 2 - 1 / 2))
         = w₀ / ((s - 1) ^ 2 - 1 / 2) * (s * (exp l * (1 - exp (-l))) / l) := by ring
       _ = _ := by rw [hweight_cancel]; field_simp
-  rw [hfactor, le_div_iff₀ (mul_pos hl0 (by nlinarith)), one_mul]
+  rw [hfactor, le_div_iff₀ (mul_pos hl0 (by nlinarith only [hr])), one_mul]
   exact hexp_gain
 
 /-- `lemma9Fun` is a subsolution of (3.12) for `s ≥ 4`. -/
@@ -487,43 +488,44 @@ theorem bigM_gt_lemma9Fun {s : ℝ} (hs : 3 ≤ s) : bigM 4 / 2 * lemma9Fun s <
     have h2 : bigM 4 ≤ bigM x := bigM_antitone hx.2
     have h3 : κ * lemma9Fun x ≤ κ := by
       have : 0 ≤ κ := by positivity
-      nlinarith
-    linarith
+      nlinarith only [hκ, h1, hM4]
+    linarith only [hκ, hM4, h2, h3]
   rcases le_total s 4 with h4 | h4
   · exact sub_pos.1 (hinit s ⟨hs, h4⟩)
   refine sub_pos.1 <| pos_of_first_crossing (f := fun s => bigM s - κ * lemma9Fun s) (a₀ := 3)
     (a := 4) (continuous_bigM.continuousOn.sub (continuousOn_const.mul
-      (continuousOn_lemma9Fun.mono fun x hx => by simp only [mem_Ici] at hx ⊢; linarith)))
+      (continuousOn_lemma9Fun.mono fun x hx => by simp only [mem_Ici] at hx ⊢; linarith only [hx])))
     (fun x hx => (hinit x hx).le) (hinit 4 ⟨by norm_num, le_rfl⟩) ?_ s h4
   intro t ht hall hpos
   show 0 < bigM t - κ * lemma9Fun t
   have hpos' : ∀ x ∈ Ioo (t - 1) t, 0 < bigM x - κ * lemma9Fun x := by
     intro x hx
     rcases le_total x 4 with h | h
-    · exact hinit x ⟨by linarith [hx.1], h⟩
+    · exact hinit x ⟨by linarith only [hx.1, ht, hx], h⟩
     · exact hpos x ⟨h, hx.2⟩
-  have ht0 : 0 < t := by linarith
-  have hr : 0 < (t - 1) ^ 2 - 1 / 2 := by nlinarith
+  have ht0 : 0 < t := by linarith only [ht]
+  have hr : 0 < (t - 1) ^ 2 - 1 / 2 := by nlinarith only [ht]
   have hcw : ContinuousOn (fun x => (1 - 1 / (2 * x ^ 2)) * (κ * lemma9Fun x)) (Icc (t - 1) t) := by
     refine ContinuousOn.mul (continuousOn_const.sub (continuousOn_const.div
       (continuousOn_const.mul (continuousOn_id.pow 2)) fun x hx => ?_))
       (continuousOn_const.mul (continuousOn_lemma9Fun.mono fun x hx => by
-        simp only [mem_Ici]; linarith [hx.1]))
-    have : 0 < x := by linarith [hx.1]
+        simp only [mem_Ici]; linarith only [hx.1, ht, hx]))
+    have : 0 < x := by linarith only [hx.1, ht, hx]
     positivity
   have hlt : ∫ x in (t - 1)..t, (1 - 1 / (2 * x ^ 2)) * (κ * lemma9Fun x) <
       ∫ x in (t - 1)..t, (1 - 1 / (2 * x ^ 2)) * bigM x := by
     refine intervalIntegral.integral_lt_integral_of_continuousOn_of_le_of_exists_lt
       (by linarith) hcw (continuousOn_weight_mul continuous_bigM (by linarith)) ?_ ?_
     · intro x hx
-      have hw := (weight_mem (x := x) (by linarith [hx.1])).1
+      have hw := (weight_mem (x := x) (by linarith only [hx.1, ht, hx])).1
       rcases hx.2.lt_or_eq with h | rfl
       · exact mul_le_mul_of_nonneg_left (sub_pos.1 (hpos' x ⟨hx.1, h⟩)).le hw.le
-      · exact mul_le_mul_of_nonneg_left (sub_nonneg.1 (hall x ⟨by linarith, le_rfl⟩)) hw.le
+      · exact mul_le_mul_of_nonneg_left (sub_nonneg.1 (hall x ⟨by
+        linarith only [ht], le_rfl⟩)) hw.le
     · refine ⟨t - 1 / 2, ⟨by linarith, by linarith⟩, ?_⟩
       exact mul_lt_mul_of_pos_left (sub_pos.1 (hpos' _ ⟨by linarith, by linarith⟩))
-        (weight_mem (by linarith)).1
-  rw [← bigM_integral_identity (by linarith), intervalIntegral.integral_congr
+        (weight_mem (by linarith only [ht])).1
+  rw [← bigM_integral_identity (by linarith only [ht]), intervalIntegral.integral_congr
     (g := fun x => κ * ((1 - 1 / (2 * x ^ 2)) * lemma9Fun x)) (fun x _ => by simp only; ring),
     intervalIntegral.integral_const_mul] at hlt
   have hsub := lemma9Fun_le_integral ht.le
@@ -539,13 +541,13 @@ theorem bigM_gt_lemma9Fun {s : ℝ} (hs : 3 ≤ s) : bigM 4 / 2 * lemma9Fun s <
     generalize (t - 1) ^ 2 - 1 / 2 = r at hr ⊢
     field_simp
   rw [e] at h2
-  linarith
+  linarith only [h1, h2]
 
 /-- [I71, Lemma 9], lower bound for `𝔐`: there is `κ > 0` with
 `𝔐(s) ≥ κ exp(-(s log s + s log log s + 2 s))` for `s ≥ 3`. -/
 theorem bigM_ge_exp : ∃ κ > 0, ∀ s ≥ 3,
     κ * exp (-(s * log s + s * log (log s) + 2 * s)) ≤ bigM s :=
-  ⟨bigM 4 / 2, by linarith [bigM_pos 4], fun _ hs => (bigM_gt_lemma9Fun hs).le⟩
+  ⟨bigM 4 / 2, by linarith only [bigM_pos 4], fun _ hs => (bigM_gt_lemma9Fun hs).le⟩
 
 /-- [I71, Lemma 9], lower bound: there is `c` with
 `G_r(s) ≥ exp(-s log s - s log log s - c s)` for all `r` and `s ≥ 3`. -/
@@ -561,7 +563,7 @@ theorem majG_ge_exp : ∃ c : ℝ, ∀ (r : ℕ) (s : ℝ), 3 ≤ s →
     calc exp (-(K * s)) ≤ exp (log (κ / 3)) := by
           rw [exp_le_exp]
           have : -log (κ / 3) ≤ |log (κ / 3)| := neg_le_abs _
-          nlinarith
+          nlinarith only [hK, this, hK0, hs]
       _ = κ / 3 := exp_log (by positivity)
   have e : exp (-(s * log s) - s * log (log s) - (2 + K) * s) =
       exp (-(K * s)) * exp (-(s * log s + s * log (log s) + 2 * s)) := by
@@ -570,7 +572,7 @@ theorem majG_ge_exp : ∃ c : ℝ, ∀ (r : ℕ) (s : ℝ), 3 ≤ s →
   calc exp (-(K * s)) * exp (-(s * log s + s * log (log s) + 2 * s))
       ≤ κ / 3 * exp (-(s * log s + s * log (log s) + 2 * s)) :=
         mul_le_mul_of_nonneg_right hexp (exp_pos _).le
-    _ ≤ bigM s / 3 := by linarith
+    _ ≤ bigM s / 3 := by linarith only [h1]
     _ ≤ majG r s := hG
 
 end IwaniecLinearSieve
diff --git a/LeanPool/IwaniecLinearSieve/SieveMajorants/Majorants.lean b/LeanPool/IwaniecLinearSieve/SieveMajorants/Majorants.lean
index 51a4973987..3789b0eec4 100644
--- a/LeanPool/IwaniecLinearSieve/SieveMajorants/Majorants.lean
+++ b/LeanPool/IwaniecLinearSieve/SieveMajorants/Majorants.lean
@@ -68,12 +68,12 @@ theorem majf_of_le_two {s : ℝ} (hs : s ≤ 2) : majf s = 2 := by
 /-- Corollary to [I71, Lemma 6]: `𝔐/3 ≤ 𝔣 ≤ 2𝔐/3`. -/
 theorem majf_mem (s : ℝ) : bigM s / 3 ≤ majf s ∧ majf s ≤ 2 * bigM s / 3 := by
   have := abs_le.1 (abs_bigW_le s)
-  unfold majf; constructor <;> linarith [this.1, this.2]
+  unfold majf; constructor <;> linarith only [this.1, this.2, this]
 
 /-- Corollary to [I71, Lemma 6]: `𝔐/3 ≤ 𝔉 ≤ 2𝔐/3`. -/
 theorem majF_mem (s : ℝ) : bigM s / 3 ≤ majF s ∧ majF s ≤ 2 * bigM s / 3 := by
   have := abs_le.1 (abs_bigW_le s)
-  unfold majF; constructor <;> linarith [this.1, this.2]
+  unfold majF; constructor <;> linarith only [this.1, this.2, this]
 
 /-- Corollary to [I71, Lemma 6] for `G_r`. -/
 theorem majG_mem (r : ℕ) (s : ℝ) : bigM s / 3 ≤ majG r s ∧ majG r s ≤ 2 * bigM s / 3 := by
@@ -82,10 +82,10 @@ theorem majG_mem (r : ℕ) (s : ℝ) : bigM s / 3 ≤ majG r s ∧ majG r s ≤
   · exact majF_mem s
 
 theorem majG_le_two (r : ℕ) (s : ℝ) : majG r s ≤ 2 := by
-  linarith [(majG_mem r s).2, bigM_le_three s]
+  linarith only [(majG_mem r s).2, bigM_le_three s]
 
 theorem majG_pos (r : ℕ) (s : ℝ) : 0 < majG r s :=
-  lt_of_lt_of_le (by linarith [bigM_pos s]) (majG_mem r s).1
+  lt_of_lt_of_le (by linarith only [bigM_pos s]) (majG_mem r s).1
 
 theorem majf_pos (s : ℝ) : 0 < majf s := by
   simpa [majG_of_even (⟨0, rfl⟩ : Even 0)] using majG_pos 0 s
@@ -111,12 +111,12 @@ theorem hasDerivAt_majf {s : ℝ} (hs : 2 < s) :
   have hexp : ∀ x, 2 < x → x ≤ 4 → HasDerivAt (fun x => 1 + (1 / (x - 1) - log (x - 1)))
       (-(x / (x - 1) ^ 2 * majF (x - 1))) x := by
     intro x hx hx4
-    rw [majF_of_le_three (by linarith), mul_one]
-    exact (hasDerivAt_initForm (by linarith)).const_add 1
+    rw [majF_of_le_three (by linarith only [hx4]), mul_one]
+    exact (hasDerivAt_initForm (by linarith only [hx])).const_add 1
   have heq : ∀ x, 2 ≤ x → x ≤ 3 → majf x = 1 + (1 / (x - 1) - log (x - 1)) := by
     intro x hx hx3; rw [majf_eq hx hx3]; ring
   rcases lt_trichotomy s 3 with h3 | rfl | h3
-  · refine (hexp s hs (by linarith)).congr_of_eventuallyEq ?_
+  · refine (hexp s hs (by linarith only [hs, h3])).congr_of_eventuallyEq ?_
     filter_upwards [Ioo_mem_nhds hs h3] with x hx
     exact heq x hx.1.le hx.2.le
   · have hl : HasDerivWithinAt majf (-(3 / (3 - 1) ^ 2 * majF (3 - 1))) (Iic 3) 3 := by
@@ -137,10 +137,10 @@ theorem hasDerivAt_majG_succ (r : ℕ) {t : ℝ} (ht : (5 + (-1) ^ r) / 2 < t) :
   rcases Nat.even_or_odd r with hr | hr
   · rw [majG_of_odd hr.add_one, majG_of_even hr]
     rw [hr.neg_one_pow] at ht
-    exact (hasDerivAt_majF (by linarith)).congr_deriv (by ring)
+    exact (hasDerivAt_majF (by linarith only [ht])).congr_deriv (by ring)
   · rw [majG_of_even hr.add_one, majG_of_odd hr]
     rw [hr.neg_one_pow] at ht
-    exact (hasDerivAt_majf (by linarith)).congr_deriv (by ring)
+    exact (hasDerivAt_majf (by linarith only [ht])).congr_deriv (by ring)
 
 /-! ### Monotonicity -/
 theorem majF_antitone : Antitone majF := by
@@ -151,8 +151,8 @@ theorem majF_antitone : Antitone majF := by
       (fun x hx => ?_) (fun x hx => ?_) <;> rw [interior_Ici] at hx
     · exact (hasDerivAt_majF hx).differentiableAt.differentiableWithinAt
     · rw [(hasDerivAt_majF hx).deriv]
-      have := mul_pos (kernel_pos (by linarith [hx.out] : (1 : ℝ) < x)) (majf_pos (x - 1))
-      linarith
+      have := mul_pos (kernel_pos (by linarith only [hx.out, hx] : (1 : ℝ) < x)) (majf_pos (x - 1))
+      linarith only [this]
 
 theorem majf_antitone : Antitone majf := by
   refine antitone_of_antitoneOn_Iic_Ici (a := 2) ?_ ?_
@@ -162,8 +162,8 @@ theorem majf_antitone : Antitone majf := by
       (fun x hx => ?_) (fun x hx => ?_) <;> rw [interior_Ici] at hx
     · exact (hasDerivAt_majf hx).differentiableAt.differentiableWithinAt
     · rw [(hasDerivAt_majf hx).deriv]
-      have := mul_pos (kernel_pos (by linarith [hx.out] : (1 : ℝ) < x)) (majF_pos (x - 1))
-      linarith
+      have := mul_pos (kernel_pos (by linarith only [hx.out, hx] : (1 : ℝ) < x)) (majF_pos (x - 1))
+      linarith only [this]
 
 /-- [I71, Remark after Lemma 6]: `G_r` is decreasing. -/
 theorem majG_antitone (r : ℕ) : Antitone (majG r) := by
@@ -192,9 +192,9 @@ theorem majF_eq_integral {s : ℝ} (hs : 3 ≤ s) :
     continuous_majF.neg.continuousWithinAt
     (fun t ht => (hasDerivAt_majF (hs.trans_lt ht)).neg.congr_deriv (by ring))
     (fun t ht => by
-      have h1 : 0 < t - 1 := by linarith [ht.out]
+      have h1 : 0 < t - 1 := by linarith only [ht.out, hs, ht]
       have := majf_pos (t - 1)
-      have : 0 < t := by linarith
+      have : 0 < t := by linarith only [h1]
       positivity)
     (by simpa using tendsto_majF_atTop.neg)
   rw [this]; ring
@@ -207,9 +207,9 @@ theorem majf_eq_integral {s : ℝ} (hs : 2 ≤ s) :
     continuous_majf.neg.continuousWithinAt
     (fun t ht => (hasDerivAt_majf (hs.trans_lt ht)).neg.congr_deriv (by ring))
     (fun t ht => by
-      have h1 : 0 < t - 1 := by linarith [ht.out]
+      have h1 : 0 < t - 1 := by linarith only [ht.out, hs, ht]
       have := majF_pos (t - 1)
-      have : 0 < t := by linarith
+      have : 0 < t := by linarith only [h1]
       positivity)
     (by simpa using tendsto_majf_atTop.neg)
   rw [this]; ring
diff --git a/LeanPool/IwaniecLinearSieve/SieveMajorants/Properties.lean b/LeanPool/IwaniecLinearSieve/SieveMajorants/Properties.lean
index d58a76b33b..5b2faa4b96 100644
--- a/LeanPool/IwaniecLinearSieve/SieveMajorants/Properties.lean
+++ b/LeanPool/IwaniecLinearSieve/SieveMajorants/Properties.lean
@@ -29,16 +29,16 @@ namespace IwaniecLinearSieve
 theorem initW_mem {s : ℝ} (hs : s ≤ 3) : -(1 / 2) ≤ initW s ∧ initW s ≤ 1 := by
   unfold initW
   set y := max s 2 - 1 with hy
-  have hy1 : 1 ≤ y := by have := le_max_right s 2; linarith
-  have hy2 : y ≤ 2 := by have : max s 2 ≤ 3 := max_le hs (by norm_num); linarith
+  have hy1 : 1 ≤ y := by have := le_max_right s 2; linarith only [this]
+  have hy2 : y ≤ 2 := by have : max s 2 ≤ 3 := max_le hs (by norm_num); linarith only [this]
   have hlog0 : 0 ≤ log y := log_nonneg hy1
-  have hlog1 : log y ≤ y - 1 := log_le_sub_one_of_pos (by linarith)
-  have h1 : 1 / y ≤ 1 := by rw [div_le_one (by linarith)]; exact hy1
-  have h2 : 1 / 2 ≤ 1 / y := one_div_le_one_div_of_le (by linarith) hy2
+  have hlog1 : log y ≤ y - 1 := log_le_sub_one_of_pos (by linarith only [hy1])
+  have h1 : 1 / y ≤ 1 := by rw [div_le_one (by linarith only [hy1])]; exact hy1
+  have h2 : 1 / 2 ≤ 1 / y := one_div_le_one_div_of_le (by linarith only [hy1]) hy2
   constructor <;> linarith
 
 theorem bigM_pos_of_le_three {s : ℝ} (hs : s ≤ 3) : 0 < bigM s := by
-  rw [bigM_of_le_three hs]; linarith [(initW_mem hs).1]
+  rw [bigM_of_le_three hs]; linarith only [(initW_mem hs).1, hs]
 
 theorem abs_bigW_le_of_le_three {s : ℝ} (hs : s ≤ 3) : |bigW s| ≤ bigM s / 3 := by
   rw [bigW_of_le_three hs, bigM_of_le_three hs, abs_le]
@@ -49,7 +49,7 @@ theorem abs_bigW_le_of_le_three {s : ℝ} (hs : s ≤ 3) : |bigW s| ≤ bigM s /
 theorem weight_mem {x : ℝ} (hx : 1 ≤ x) : 0 < 1 - 1 / (2 * x ^ 2) ∧ 1 - 1 / (2 * x ^ 2) ≤ 1 := by
   have : 1 / (2 * x ^ 2) ≤ 1 / 2 := by
     apply one_div_le_one_div_of_le (by norm_num)
-    nlinarith
+    nlinarith only [hx]
   have : 0 < 1 / (2 * x ^ 2) := by positivity
   constructor <;> linarith
 
@@ -73,18 +73,18 @@ theorem bigM_pos (s : ℝ) : 0 < bigM s := by
     · exact bigM_pos_of_le_three h
     · exact hpos x ⟨h, hx⟩
   have hI : 0 < ∫ x in (t - 1)..t, (1 - 1 / (2 * x ^ 2)) * bigM x := by
-    refine intervalIntegral.intervalIntegral_pos_of_pos_on ?_ (fun x hx => ?_) (by linarith)
+    refine intervalIntegral.intervalIntegral_pos_of_pos_on ?_ (fun x hx => ?_) (by linarith only [])
     · exact (continuousOn_weight_mul continuous_bigM (by linarith)).intervalIntegrable_of_Icc
-        (by linarith)
-    · exact mul_pos (weight_mem (by linarith [hx.1])).1 (hpos' x hx.2)
+        (by linarith only [])
+    · exact mul_pos (weight_mem (by linarith only [hx.1, ht, hx])).1 (hpos' x hx.2)
   rw [← bigM_integral_identity ht.le] at hI
-  have hr : 0 < (t - 1) ^ 2 - 1 / 2 := by nlinarith
-  have ht0 : 0 < t := by linarith
+  have hr : 0 < (t - 1) ^ 2 - 1 / 2 := by nlinarith only [ht]
+  have ht0 : 0 < t := by linarith only [ht]
   by_contra h
   push Not at h
   have : ((t - 1) ^ 2 - 1 / 2) * bigM t / t ≤ 0 :=
     div_nonpos_of_nonpos_of_nonneg (mul_nonpos_of_nonneg_of_nonpos hr.le h) ht0.le
-  linarith
+  linarith only [hI, this]
 
 /-- An antitone function on `(-∞, a]` and on `[a, ∞)` is antitone. -/
 theorem antitone_of_antitoneOn_Iic_Ici {f : ℝ → ℝ} {a : ℝ} (h₁ : AntitoneOn f (Iic a))
@@ -99,19 +99,19 @@ theorem antitone_of_antitoneOn_Iic_Ici {f : ℝ → ℝ} {a : ℝ} (h₁ : Antit
 theorem antitoneOn_initW : AntitoneOn initW (Iic 3) := by
   intro s _ t _ hst
   unfold initW
-  have h1 : 1 ≤ max s 2 - 1 := by have := le_max_right s 2; linarith
+  have h1 : 1 ≤ max s 2 - 1 := by have := le_max_right s 2; linarith only [this]
   have h2 : max s 2 ≤ max t 2 := max_le_max hst le_rfl
   have h3 : log (max s 2 - 1) ≤ log (max t 2 - 1) := log_le_log (by linarith) (by linarith)
   have h4 : 1 / (max t 2 - 1) ≤ 1 / (max s 2 - 1) :=
     one_div_le_one_div_of_le (by linarith) (by linarith)
-  linarith
+  linarith only [h3, h4]
 
 theorem continuousOn_kernel_mul {g : ℝ → ℝ} (hg : Continuous g) :
     ContinuousOn (fun x => x / (x - 1) ^ 2 * g (x - 1)) (Ici 2) := by
   refine ContinuousOn.mul (continuousOn_id.div ((continuousOn_id.sub continuousOn_const).pow 2)
     fun x hx => ?_) (hg.comp (continuous_sub_right 1)).continuousOn
   have : (2 : ℝ) ≤ x := hx
-  have : 0 < x - 1 := by linarith
+  have : 0 < x - 1 := by linarith only [this]
   positivity
 
 theorem intervalIntegrable_kernel_mul {g : ℝ → ℝ} (hg : Continuous g) {a b : ℝ} (ha : 2 ≤ a)
@@ -122,7 +122,7 @@ theorem intervalIntegrable_kernel_mul {g : ℝ → ℝ} (hg : Continuous g) {a b
   · rw [uIcc_of_ge h] at hx; exact hb.trans hx.1
 
 theorem kernel_pos {x : ℝ} (hx : 1 < x) : 0 < x / (x - 1) ^ 2 := by
-  have : 0 < x - 1 := by linarith
+  have : 0 < x - 1 := by linarith only [hx]
   positivity
 
 /-- `𝔐` is antitone (on all of `ℝ`). -/
@@ -130,7 +130,7 @@ theorem bigM_antitone : Antitone bigM := by
   refine antitone_of_antitoneOn_Iic_Ici (a := 3) ?_ ?_
   · intro s hs t ht hst
     rw [bigM_of_le_three hs, bigM_of_le_three ht]
-    linarith [antitoneOn_initW hs ht hst]
+    linarith only [antitoneOn_initW hs ht hst, hs, ht, hst]
   · intro s hs t ht hst
     have hs' : (3 : ℝ) ≤ s := hs
     have ht' : (3 : ℝ) ≤ t := ht
@@ -140,8 +140,8 @@ theorem bigM_antitone : Antitone bigM := by
         (intervalIntegrable_kernel_mul continuous_bigM (by linarith) (by linarith))]
     have : 0 ≤ ∫ x in s..t, x / (x - 1) ^ 2 * bigM (x - 1) :=
       intervalIntegral.integral_nonneg hst fun x hx =>
-        (mul_pos (kernel_pos (by linarith [hx.1])) (bigM_pos _)).le
-    linarith
+        (mul_pos (kernel_pos (by linarith only [hx.1, hs', hx])) (bigM_pos _)).le
+    linarith only [this]
 
 theorem bigM_le_three (s : ℝ) : bigM s ≤ 3 := by
   rcases le_total s 2 with h | h
@@ -151,15 +151,15 @@ theorem bigM_le_three (s : ℝ) : bigM s ≤ 3 := by
 /-- From (3.12) and monotonicity: `𝔐(s) ≤ s/((s-1)² - 1/2) 𝔐(s-1)` for `s ≥ 3`. -/
 theorem bigM_le_ratio {s : ℝ} (hs : 3 ≤ s) :
     bigM s ≤ s / ((s - 1) ^ 2 - 1 / 2) * bigM (s - 1) := by
-  have hr : 0 < (s - 1) ^ 2 - 1 / 2 := by nlinarith
-  have hs0 : 0 < s := by linarith
+  have hr : 0 < (s - 1) ^ 2 - 1 / 2 := by nlinarith only [hs]
+  have hs0 : 0 < s := by linarith only [hs]
   have h := bigM_integral_identity hs
   have hle : ∫ x in (s - 1)..s, (1 - 1 / (2 * x ^ 2)) * bigM x ≤
       ∫ _ in (s - 1)..s, bigM (s - 1) := by
-    refine intervalIntegral.integral_mono_on (by linarith)
-      ((continuousOn_weight_mul continuous_bigM (by linarith)).intervalIntegrable_of_Icc
-        (by linarith)) intervalIntegrable_const fun x hx => ?_
-    obtain ⟨h0, h1⟩ := weight_mem (x := x) (by linarith [hx.1])
+    refine intervalIntegral.integral_mono_on (by linarith only [])
+      ((continuousOn_weight_mul continuous_bigM (by linarith only [hs])).intervalIntegrable_of_Icc
+        (by linarith only [])) intervalIntegrable_const fun x hx => ?_
+    obtain ⟨h0, h1⟩ := weight_mem (x := x) (by linarith only [hx.1, hs, hx])
     calc (1 - 1 / (2 * x ^ 2)) * bigM x ≤ 1 * bigM x :=
           mul_le_mul_of_nonneg_right h1 (bigM_pos x).le
       _ ≤ bigM (s - 1) := by rw [one_mul]; exact bigM_antitone hx.1
@@ -167,29 +167,29 @@ theorem bigM_le_ratio {s : ℝ} (hs : 3 ≤ s) :
   simp only [sub_sub_cancel, smul_eq_mul, one_mul] at hle
   rw [div_mul_eq_mul_div, le_div_iff₀ hr]
   rw [div_le_iff₀ hs0] at hle
-  linarith
+  linarith only [hle]
 
 /-- `𝔐(s) = O(e^{-s})`. -/
 theorem bigM_le_exp (s : ℝ) : bigM s ≤ 3 * exp 5 * exp (-s) := by
   have base : ∀ s : ℝ, s ≤ 5 → bigM s ≤ 3 * exp 5 * exp (-s) := by
     intro s hs
     have : 1 ≤ exp 5 * exp (-s) := by
-      rw [← exp_add]; exact one_le_exp (by linarith)
-    nlinarith [bigM_le_three s]
+      rw [← exp_add]; exact one_le_exp (by linarith only [hs])
+    nlinarith only [bigM_le_three s, this]
   have key : ∀ n : ℕ, ∀ s : ℝ, s ≤ n → bigM s ≤ 3 * exp 5 * exp (-s) := by
     intro n
     induction n with
-    | zero => intro s hs; exact base s (by simp at hs; linarith)
+    | zero => intro s hs; exact base s (by simp at hs; linarith only [hs])
     | succ n ih =>
       intro s hs
       rcases le_total s 5 with h5 | h5
       · exact base s h5
-      have h1 := bigM_le_ratio (s := s) (by linarith)
-      have h2 := ih (s - 1) (by push_cast at hs; linarith)
-      have hr : 0 < (s - 1) ^ 2 - 1 / 2 := by nlinarith
+      have h1 := bigM_le_ratio (s := s) (by linarith only [h5])
+      have h2 := ih (s - 1) (by push_cast at hs; linarith only [hs])
+      have hr : 0 < (s - 1) ^ 2 - 1 / 2 := by nlinarith only [h5]
       have hc : s / ((s - 1) ^ 2 - 1 / 2) ≤ exp (-1) := by
         rw [div_le_iff₀ hr, exp_neg, ← div_eq_inv_mul, le_div_iff₀ (exp_pos 1)]
-        nlinarith [exp_one_lt_d9]
+        nlinarith only [exp_one_lt_d9, hr, h5]
       calc bigM s ≤ s / ((s - 1) ^ 2 - 1 / 2) * bigM (s - 1) := h1
         _ ≤ exp (-1) * (3 * exp 5 * exp (-(s - 1))) :=
           mul_le_mul hc h2 (bigM_pos _).le (exp_pos _).le
@@ -213,43 +213,43 @@ theorem abs_bigW_lt {s : ℝ} (hs : 3 ≤ s) : |bigW s| < bigM s / 3 := by
   refine sub_pos.1 <| pos_of_first_crossing (f := fun s => bigM s / 3 - |bigW s|) (a₀ := 2)
     (a := 3) ((continuous_bigM.div_const 3).sub continuous_bigW.abs).continuousOn
     (fun x hx => sub_nonneg.2 (abs_bigW_le_of_le_three hx.2)) ?_ ?_ s hs
-  · rw [bigM_three, bigW_three, abs_of_neg (by linarith [log_two_gt_d9])]
-    linarith [log_two_lt_d9]
+  · rw [bigM_three, bigW_three, abs_of_neg (by linarith only [log_two_gt_d9])]
+    linarith only [log_two_lt_d9]
   intro t ht hall _
-  have ht0 : 0 < t := by linarith
-  have hr : 0 < (t - 1) ^ 2 - 1 / 2 := by nlinarith
+  have ht0 : 0 < t := by linarith only [ht]
+  have hr : 0 < (t - 1) ^ 2 - 1 / 2 := by nlinarith only [ht]
   have hx0 : ∀ x ∈ Icc (t - 1) t, x ^ 2 ≠ 0 := fun x hx =>
-    pow_ne_zero 2 (by linarith [hx.1])
+    pow_ne_zero 2 (by linarith only [hx.1, ht, hx])
   have hcW : ContinuousOn (fun x => |bigW x / x ^ 2|) (Icc (t - 1) t) :=
     (continuous_bigW.continuousOn.div (continuousOn_id.pow 2) hx0).abs
   have hcM : ContinuousOn (fun x => bigM x / 3 / x ^ 2) (Icc (t - 1) t) :=
     (continuous_bigM.div_const 3).continuousOn.div (continuousOn_id.pow 2) hx0
   have hcM' : ContinuousOn (fun x => 1 / (3 * ((t - 1) ^ 2 - 1 / 2)) *
       ((1 - 1 / (2 * x ^ 2)) * bigM x)) (Icc (t - 1) t) :=
-    continuousOn_const.mul (continuousOn_weight_mul continuous_bigM (by linarith))
+    continuousOn_const.mul (continuousOn_weight_mul continuous_bigM (by linarith only [ht]))
   have h1 : |bigW t| ≤ t * ∫ x in (t - 1)..t, |bigW x / x ^ 2| := by
     rw [bigW_eq_neg_mul_integral ht.le, abs_mul, abs_neg, abs_of_pos ht0]
     exact mul_le_mul_of_nonneg_left (intervalIntegral.abs_integral_le_integral_abs
-      (by linarith)) ht0.le
+      (by linarith only [])) ht0.le
   have h2 : ∫ x in (t - 1)..t, |bigW x / x ^ 2| ≤ ∫ x in (t - 1)..t, bigM x / 3 / x ^ 2 := by
-    refine intervalIntegral.integral_mono_on (by linarith) (hcW.intervalIntegrable_of_Icc
+    refine intervalIntegral.integral_mono_on (by linarith only []) (hcW.intervalIntegrable_of_Icc
       (by linarith)) (hcM.intervalIntegrable_of_Icc (by linarith)) fun x hx => ?_
-    have hx2 : 0 < x ^ 2 := pow_pos (by linarith [hx.1]) 2
+    have hx2 : 0 < x ^ 2 := pow_pos (by linarith only [hx.1, ht, hx]) 2
     rw [abs_div, abs_of_pos hx2]
-    have := hall x ⟨by linarith [hx.1], hx.2⟩
-    exact div_le_div_of_nonneg_right (by linarith) hx2.le
+    have := hall x ⟨by linarith only [hx.1, ht, hx], hx.2⟩
+    exact div_le_div_of_nonneg_right (by linarith only [this]) hx2.le
   have hpt : ∀ x, t - 1 < x → 0 < 1 / (3 * ((t - 1) ^ 2 - 1 / 2)) *
       ((1 - 1 / (2 * x ^ 2)) * bigM x) - bigM x / 3 / x ^ 2 := by
     intro x hx
-    have hx' : 0 < x := by linarith
+    have hx' : 0 < x := by linarith only [ht, hx]
     rw [lemma6_aux hr.ne' hx'.ne']
-    have : 0 < x ^ 2 - 1 / 2 - ((t - 1) ^ 2 - 1 / 2) := by nlinarith
+    have : 0 < x ^ 2 - 1 / 2 - ((t - 1) ^ 2 - 1 / 2) := by nlinarith only [hx, ht]
     have := bigM_pos x
     positivity
   have h3 : ∫ x in (t - 1)..t, bigM x / 3 / x ^ 2 < ∫ x in (t - 1)..t,
       1 / (3 * ((t - 1) ^ 2 - 1 / 2)) * ((1 - 1 / (2 * x ^ 2)) * bigM x) := by
     refine intervalIntegral.integral_lt_integral_of_continuousOn_of_le_of_exists_lt
-      (by linarith) hcM hcM' (fun x hx => (sub_pos.1 (hpt x hx.1)).le)
+      (by linarith only []) hcM hcM' (fun x hx => (sub_pos.1 (hpt x hx.1)).le)
       ⟨t, ⟨by linarith, le_rfl⟩, sub_pos.1 (hpt t (by linarith))⟩
   rw [intervalIntegral.integral_const_mul, ← bigM_integral_identity ht.le] at h3
   have h4 : t * (1 / (3 * ((t - 1) ^ 2 - 1 / 2)) * (((t - 1) ^ 2 - 1 / 2) * bigM t / t)) =
@@ -270,6 +270,6 @@ theorem abs_bigW_le (s : ℝ) : |bigW s| ≤ bigM s / 3 := by
 /-- `𝔚(s) = O(e^{-s})`. -/
 theorem abs_bigW_le_exp (s : ℝ) : |bigW s| ≤ exp 5 * exp (-s) := by
   have := bigM_le_exp s
-  linarith [abs_bigW_le s]
+  linarith only [abs_bigW_le s, this]
 
 end IwaniecLinearSieve
diff --git a/LeanPool/IwaniecLinearSieve/Vendor/PrimeNumberTheoremAnd/EulerMaclaurin.lean b/LeanPool/IwaniecLinearSieve/Vendor/PrimeNumberTheoremAnd/EulerMaclaurin.lean
index 4375c423cb..a7565f0a29 100644
--- a/LeanPool/IwaniecLinearSieve/Vendor/PrimeNumberTheoremAnd/EulerMaclaurin.lean
+++ b/LeanPool/IwaniecLinearSieve/Vendor/PrimeNumberTheoremAnd/EulerMaclaurin.lean
@@ -70,7 +70,7 @@ lemma intervalIntegrable_deriv_mul_B1 (ha : 0 ≤ a) (hab : a ≤ b) (h_cont : C
   filter_upwards [self_mem_ae_restrict (by measurability)] with x hx
   rw [Set.uIcc_of_le hab, Set.mem_Icc] at hx
   norm_cast
-  exact abs_B1_le_half (by linarith)
+  exact abs_B1_le_half (by linarith only [ha, hx])
 
 lemma integral_deriv_mul_floor_add_one (ha : 0 ≤ a) (hab : a ≤ b)
     (hf_diff : ∀ t ∈ Set.Icc a b, DifferentiableAt ℝ f t) (h_cont : ContinuousOn (deriv f) [[a,
diff --git a/LeanPool/IwaniecLinearSieve/Vendor/PrimeNumberTheoremAnd/MediumPNT.lean b/LeanPool/IwaniecLinearSieve/Vendor/PrimeNumberTheoremAnd/MediumPNT.lean
index 72c402315b..f2ade4d339 100644
--- a/LeanPool/IwaniecLinearSieve/Vendor/PrimeNumberTheoremAnd/MediumPNT.lean
+++ b/LeanPool/IwaniecLinearSieve/Vendor/PrimeNumberTheoremAnd/MediumPNT.lean
@@ -167,21 +167,25 @@ lemma SmoothedChebyshevDirichlet_aux_integrable {SmoothingF : ℝ → ℝ}
     apply continuous_iff_continuousAt.mpr
     intro x
     have := Smooth1MellinDifferentiable diffSmoothingF suppSmoothingF ⟨εpos, ε_lt_one⟩
-      SmoothingFpos mass_one (s := σ + x * I) (by simp only [add_re, ofReal_re, mul_re, I_re,
-        mul_zero, ofReal_im, I_im, mul_one, sub_self, add_zero]; linarith) |>.continuousAt
+      SmoothingFpos mass_one (s := σ + x * I) (by
+        simp only [add_re, ofReal_re, mul_re, I_re, mul_zero, ofReal_im, I_im, mul_one,
+          sub_self, add_zero]
+        linarith only [εpos, ε_lt_one, σ_gt]) |>.continuousAt
     fun_prop
   · filter_upwards [] with t
     calc
       _≤ c / ε * 1 / (σ^2 + t^2) := by
-        convert hc (σ / 2) (by linarith) (σ + t * I) (by simp only [add_re, ofReal_re, mul_re,
-          I_re, mul_zero, ofReal_im, I_im, mul_one, sub_self, add_zero, half_le_self_iff]; linarith)
+        convert hc (σ / 2) (by linarith only [εpos, ε_lt_one, σ_gt]) (σ + t * I) (by
+            simp only [add_re, ofReal_re, mul_re, I_re, mul_zero, ofReal_im, I_im, mul_one,
+              sub_self, add_zero, half_le_self_iff]
+            linarith only [εpos, ε_lt_one, σ_gt])
           (by simp only [add_re, ofReal_re, mul_re, I_re, mul_zero, ofReal_im, I_im, mul_one,
-            sub_self, add_zero]; linarith) ε εpos  ε_lt_one using 1
+            sub_self, add_zero]; linarith only [σ_le]) ε εpos  ε_lt_one using 1
         simp only [mul_one, Complex.sq_norm, normSq_apply, add_re, ofReal_re, mul_re, I_re,
           mul_zero, ofReal_im, I_im, sub_self, add_zero, add_im, mul_im, zero_add, mul_inv_rev]
         ring_nf
       _ ≤ _ := by
-        gcongr; nlinarith
+        gcongr; nlinarith only [εpos, σ_gt, ε_lt_one]
 
 -- TODO: add to mathlib
 attribute [fun_prop] Continuous.const_cpow
@@ -219,17 +223,18 @@ lemma SmoothedChebyshevDirichlet_aux_tsum_integral {SmoothingF : ℝ → ℝ}
         SmoothingFpos mass_one hz).continuousAt
     · fun_prop
     · simp only [mapsTo_univ_iff, mem_ofPred_eq, add_re, ofReal_re, mul_re, I_re, mul_zero,
-        ofReal_im, I_im, mul_one, sub_self, add_zero, forall_const]; linarith
+        ofReal_im, I_im, mul_one, sub_self, add_zero, forall_const];
+          linarith only [εpos, ε_lt_one, σ_gt]
   have abs_two : ∀ a : ℝ, ∀ i : ℕ, ‖(i : ℂ) ^ ((σ : ℂ) + ↑a * I)‖₊ = i ^ σ := by
     intro a i
     simp_rw [← norm_toNNReal]
     rw [norm_natCast_cpow_of_re_ne_zero _ (by simp only [add_re, ofReal_re, mul_re, I_re, mul_zero,
-      ofReal_im, I_im, mul_one, sub_self, add_zero, ne_eq]; linarith)]
+      ofReal_im, I_im, mul_one, sub_self, add_zero, ne_eq]; linarith only [εpos, ε_lt_one, σ_gt])]
     simp only [add_re, ofReal_re, mul_re, I_re, mul_zero, ofReal_im, I_im, mul_one, sub_self,
-      add_zero, Real.toNNReal_of_nonneg <| rpow_nonneg (y := σ) (x := i) (by linarith)]
+      add_zero, Real.toNNReal_of_nonneg <| rpow_nonneg (y := σ) (x := i) (by linarith only [])]
     norm_cast
   rw [MeasureTheory.integral_tsum]
-  · have x_neq_zero : X ≠ 0 := by linarith
+  · have x_neq_zero : X ≠ 0 := by linarith only [X_pos]
     intro i
     by_cases i_eq_zero : i = 0
     · simpa [i_eq_zero] using aestronglyMeasurable_const
@@ -253,7 +258,7 @@ lemma SmoothedChebyshevDirichlet_aux_tsum_integral {SmoothingF : ℝ → ℝ}
     · rw [lt_top_iff_ne_top, ENNReal.tsum_coe_ne_top_iff_summable_coe]
       push_cast
       convert (ArithmeticFunction.LSeriesSummable_vonMangoldt (s := σ)
-        (by simp only [ofReal_re]; linarith)).norm
+        (by simp only [ofReal_re]; linarith only [σ_gt])).norm
       rw [LSeries.term_def]
       split_ifs with h <;> simp[h]
     · simp_rw [← enorm_eq_nnnorm]
@@ -293,12 +298,12 @@ theorem SmoothedChebyshevDirichlet {SmoothingF : ℝ → ℝ}
     simp only [σ]
     have : 0 < (Real.log X)⁻¹ := by
       simp only [inv_pos]
-      linarith
-    linarith
+      linarith only [εpos, ε_lt_one, log_gt]
+    linarith only [this]
   have σ_le : σ ≤ 2 := by
     simp only [σ]
     have : (Real.log X)⁻¹ < 1 := inv_lt_one_of_one_lt₀ log_gt
-    linarith
+    linarith only [this]
   calc
     _ = 1 / (2 * π * I) * (I * ∫ (t : ℝ), ∑' n, Λ n / (n : ℂ) ^ (σ + ↑t * I) *
       mellin (fun x ↦ ↑(Smooth1 SmoothingF ε x)) (σ + ↑t * I) * X ^ (σ + ↑t * I)) := ?_
@@ -323,7 +328,7 @@ theorem SmoothedChebyshevDirichlet {SmoothingF : ℝ → ℝ}
     · simp [σ_gt]
   · congr
     exact SmoothedChebyshevDirichlet_aux_tsum_integral diffSmoothingF SmoothingFpos
-      suppSmoothingF mass_one (by linarith) εpos ε_lt_one σ_gt σ_le
+      suppSmoothingF mass_one (by linarith only [X_gt, εpos, ε_lt_one]) εpos ε_lt_one σ_gt σ_le
   · field_simp; congr; ext n; rw [← MeasureTheory.integral_const_mul]; congr; ext t
     by_cases n_ne_zero : n = 0
     · simp [n_ne_zero]
@@ -334,7 +339,7 @@ theorem SmoothedChebyshevDirichlet {SmoothingF : ℝ → ℝ}
       · push_cast at this ⊢
         rw [← this, div_mul_cancel₀]
         · simp only [ne_eq, Nat.cast_eq_zero, n_ne_zero, not_false_eq_true]
-      · apply div_nonneg (by linarith : 0 ≤ X); simp
+      · apply div_nonneg (by linarith only [X_gt, εpos, ε_lt_one] : 0 ≤ X); simp
       · simp
     · simp only [ne_eq, cpow_eq_zero_iff, Nat.cast_eq_zero, n_ne_zero, false_and,
         not_false_eq_true]
@@ -343,7 +348,8 @@ theorem SmoothedChebyshevDirichlet {SmoothingF : ℝ → ℝ}
   · have ht (t : ℝ) : -(σ + t * I) = (-1) * (σ + t * I) := by simp
     have hn (n : ℂ) : (n / X) ^ (-1 : ℂ) = X / n := by simp [cpow_neg_one]
     have (n : ℕ) : (log ((n : ℂ) / (X : ℂ)) * -1).im = 0 := by
-      simp [Complex.log_im, arg_eq_zero_iff, div_nonneg (Nat.cast_nonneg _) (by linarith : 0 ≤ X)]
+      simp [Complex.log_im, arg_eq_zero_iff, div_nonneg (Nat.cast_nonneg _) (by
+        linarith only [X_gt, εpos, ε_lt_one] : 0 ≤ X)]
     have h (n : ℕ) (t : ℝ) : ((n : ℂ) / X) ^ ((-1 : ℂ) * (σ + t * I)) =
         ((n / X) ^ (-1 : ℂ)) ^ (σ + ↑t * I) := by
       rw [cpow_mul] <;> {rw [this n]; simp [Real.pi_pos, Real.pi_nonneg]}
@@ -364,11 +370,11 @@ theorem SmoothedChebyshevDirichlet {SmoothingF : ℝ → ℝ}
       · norm_cast
       · rw [mul_comm]
         norm_cast
-    · exact div_pos (by exact_mod_cast n_pos) (by linarith : 0 < X)
+    · exact div_pos (by exact_mod_cast n_pos) (by linarith only [X_gt, εpos, ε_lt_one] : 0 < X)
     · apply Smooth1MellinConvergent diffSmoothingF suppSmoothingF ⟨εpos, ε_lt_one⟩
         SmoothingFpos mass_one
       simp only [ofReal_re]
-      linarith
+      linarith only [εpos, ε_lt_one, σ_gt]
     · dsimp [VerticalIntegrable]
       apply SmoothedChebyshevDirichlet_aux_integrable diffSmoothingF SmoothingFpos
         suppSmoothingF mass_one εpos ε_lt_one σ_gt σ_le
@@ -658,7 +664,7 @@ theorem SmoothedChebyshevClose {SmoothingF : ℝ → ℝ}
     rw [C_eq]
     positivity
   refine ⟨C, Cpos, fun X X_ge_C ε εpos ε_lt_one ↦ ?_⟩
-  have X_gt_zero : (0 : ℝ) < X := by linarith
+  have X_gt_zero : (0 : ℝ) < X := by linarith only [c₁_pos, c₁_lt, X_ge_C]
   have n_on_X_pos {n : ℕ} (npos : 0 < n) :
       0 < n / X := by
     have : (0 : ℝ) < n := by exact_mod_cast npos
@@ -675,9 +681,9 @@ theorem SmoothedChebyshevClose {SmoothingF : ℝ → ℝ}
     exact (div_le_iff₀' X_gt_zero).mpr n_le
   have smoothIs0 (n : ℕ) (n_le : (1 + c₂ * ε) ≤ n / X) :=
     hc₂ (ε := ε) (n / X) ⟨εpos, ε_lt_one⟩ n_le
-  have ε_pos: ε > 0 := by linarith
-  have X_pos: X > 0 := by linarith
-  have X_gt_three : 3 < X := by linarith
+  have ε_pos: ε > 0 := by linarith only [εpos]
+  have X_pos: X > 0 := by linarith only [c₁_pos, c₁_lt, X_ge_C]
+  have X_gt_three : 3 < X := by linarith only [X_ge_C]
   intro X_bound
   have X_bound_1 : 1 ≤ X * ε * c₁ := by
     rw[c₁_eq, ← div_le_iff₀]
@@ -706,7 +712,7 @@ theorem SmoothedChebyshevClose {SmoothingF : ℝ → ℝ}
     norm_num
     exact Real.log_pos (by norm_num)
   rw [SmoothedChebyshevDirichlet diffSmoothingF SmoothingFnonneg suppSmoothingF
-    mass_one (by linarith) εpos ε_lt_one]
+    mass_one (by linarith only [X_ge_C]) εpos ε_lt_one]
   convert SmoothedChebyshevClose_aux SmoothingF c₁ c₁_pos c₁_lt c₂ c₂_pos c₂_lt hc₂ C C_eq ε
     ε_pos ε_lt_one X X_pos X_gt_three X_bound_1 X_bound_2 smooth1BddAbove smooth1BddBelow
     smoothIs1 smoothIs0
@@ -953,10 +959,10 @@ theorem SmoothedChebyshevPull1_aux_integrable {SmoothingF : ℝ → ℝ} {ε : 
       simp
     · rw [Complex.norm_cpow_eq_rpow_re_of_nonneg]
       · simp
-      · linarith
+      · linarith only [ε_pos, ε_lt_one, X_gt]
       · simp only [add_re, ofReal_re, mul_re, I_re, mul_zero, ofReal_im, I_im, mul_one, sub_self,
           add_zero, ne_eq]
-        linarith
+        linarith only [ε_pos, ε_lt_one, σ₀_gt]
   convert (SmoothedChebyshevDirichlet_aux_integrable ContDiffSmoothingF SmoothingFnonneg
     suppSmoothingF mass_one ε_pos ε_lt_one σ₀_gt σ₀_le_2).bdd_mul
       (c := c) ?_ (ae_of_all _ this) using 2
@@ -990,7 +996,7 @@ theorem SmoothedChebyshevPull1_aux_integrable {SmoothingF : ℝ → ℝ} {ε : 
     · apply ContinuousAt.comp _ (by fun_prop)
       apply continuousAt_const_cpow
       norm_cast
-      linarith
+      linarith only [ε_pos, ε_lt_one, X_gt]
 
 /-
 Let $g : \C \to \C$ be a holomorphic function on a rectangle, then $g$ is bounded above on the
@@ -1108,13 +1114,13 @@ theorem SmoothedChebyshevPull1 {SmoothingF : ℝ → ℝ} {ε : ℝ} (ε_pos : 0
       constructor
       · unfold uIoo
         rw [min_eq_left (by linarith), max_eq_right (by linarith)]
-        exact mem_Ioo.mpr ⟨σ₁_lt_one, (by linarith)⟩
+        exact mem_Ioo.mpr ⟨σ₁_lt_one, (by linarith only [X_eq_gt_one])⟩
       · unfold uIoo
         rw [min_eq_left (by linarith), max_eq_right (by linarith)]
         exact mem_Ioo.mpr ⟨(by linarith), (by linarith)⟩
     apply ResidueTheoremOnRectangleWithSimplePole'
-    · simp; linarith
-    · simp; linarith
+    · simp; linarith only [σ₁_lt_one, X_eq_gt_one]
+    · simp; linarith only [T_pos]
     · simp only [one_div]
       exact pInRectangleInterior
     · apply DifferentiableOn.mul
@@ -1141,7 +1147,7 @@ theorem SmoothedChebyshevPull1 {SmoothingF : ℝ → ℝ} {ε : ℝ} (ε_pos : 0
           simp only [sub_re, ofReal_re, mul_re, I_re, mul_zero, ofReal_im, I_im, mul_one, sub_self,
             sub_zero, one_div, ofReal_inv, add_re, one_re, inv_re, normSq_ofReal,
             div_self_mul_self', add_zero] at this
-          rw [uIcc_of_le (by linarith)] at this
+          rw [uIcc_of_le (by linarith only [σ₁_lt_one, X_eq_gt_one])] at this
           linarith [this.1]
       · intro s hs
         apply DifferentiableAt.differentiableWithinAt
@@ -1149,7 +1155,7 @@ theorem SmoothedChebyshevPull1 {SmoothingF : ℝ → ℝ} {ε : ℝ} (ε_pos : 0
         apply DifferentiableAt.const_cpow (by fun_prop)
         left
         norm_cast
-        linarith
+        linarith only [ε_pos, ε_lt_one, X_gt]
     · let U : Set ℂ := Rectangle (σ₁ - ↑T * I) (1 + (Real.log X)⁻¹ + T * I)
       let f : ℂ → ℂ := fun z ↦ -ζ' z / ζ z
       let g : ℂ → ℂ := fun z ↦ 𝓜 (fun x ↦ ↑(Smooth1 SmoothingF ε x)) z * ↑X ^ z
@@ -1168,13 +1174,13 @@ theorem SmoothedChebyshevPull1 {SmoothingF : ℝ → ℝ} {ε : ℝ} (ε_pos : 0
           have := uInU.1
           simp only [sub_re, ofReal_re, mul_re, I_re, mul_zero, ofReal_im, I_im, mul_one, sub_self,
             sub_zero, add_re, one_re, inv_re, normSq_ofReal, div_self_mul_self', add_zero] at this
-          rw [uIcc_of_le (by linarith)] at this
+          rw [uIcc_of_le (by linarith only [σ₁_lt_one, X_eq_gt_one])] at this
           linarith [this.1]
         · unfold HPow.hPow instHPow
           apply DifferentiableAt.const_cpow differentiableAt_fun_id
           left
           norm_cast
-          linarith
+          linarith only [ε_pos, ε_lt_one, X_gt]
       have f_near_p : (f - fun (z : ℂ) => 1 * (z - 1)⁻¹) =O[nhdsWithin 1 {1}ᶜ] (1 : ℂ → ℂ) := by
         simp only [one_mul, f]
         exact riemannZetaLogDerivResidueBigO
@@ -1200,7 +1206,7 @@ lemma verticalIntegral_split_three_finite {s a b e σ : ℝ} {f : ℂ → ℂ}
     VIntegral f σ a b +
     VIntegral f σ b e := by
   dsimp [VIntegral]
-  rw [← intervalIntegrable_iff_integrableOn_Icc_of_le (by linarith)] at hf
+  rw [← intervalIntegrable_iff_integrableOn_Icc_of_le (by linarith only [hab])] at hf
   rw [← intervalIntegral.integral_add_adjacent_intervals (b := a),
     ← intervalIntegral.integral_add_adjacent_intervals (a := a) (b := b)]
   · ring
@@ -1238,11 +1244,11 @@ theorem SmoothedChebyshevPull2_aux1 {T σ₁ : ℝ} (σ₁lt : σ₁ < 1)
   · apply mem_reProdIm.mpr
     simp only [add_re, ofReal_re, mul_re, I_re, mul_zero, ofReal_im, I_im, mul_one, sub_self,
       add_zero, add_im, mul_im, zero_add, left_mem_Icc, ht, and_true]
-    linarith
+    linarith only [σ₁lt]
   · intro h
     replace h := congr_arg re h
     simp at h
-    linarith
+    linarith only [σ₁lt, h]
 
 /-
 Next pull contours to another box.
@@ -1559,7 +1565,7 @@ theorem integral_evaluation (x : ℝ) (T : ℝ) (T_large : 3 < T) :
         exact ae_volume_of_contains_compl_singleton_zero _ U
   have T3 : Integrable (fun (t : ℝ) ↦ (t^2)⁻¹) (volume.restrict (Iic (-T))) := by
     have D3 := integrableOn_Ioi_rpow_of_lt (by norm_num : (-2 : ℝ) < -1)
-      (by linarith : 0 < T) |>.comp_neg
+      (by linarith only [T_large] : 0 < T) |>.comp_neg
     simp only [rpow_neg_ofNat, Int.reduceNeg, zpow_neg, neg_Ioi] at D3
     have D4 :=
       (integrableOn_Iic_iff_integrableOn_Iio'
@@ -1584,7 +1590,7 @@ theorem integral_evaluation (x : ℝ) (T : ℝ) (T_large : 3 < T) :
     _ = _ := by
       rw [← integral_comp_neg_Ioi]
       conv => lhs; arg 2; ext x; rw [show ((-x) ^ 2)⁻¹ = x ^ (-2 : ℝ) by simp [zpow_ofNat]]
-      rw[integral_Ioi_rpow_of_lt (by norm_num) (by linarith)]
+      rw[integral_Ioi_rpow_of_lt (by norm_num) (by linarith only [T_large])]
       ring_nf
       rw [rpow_neg_one]
 
@@ -1632,7 +1638,7 @@ lemma IBound_aux1 (X₀ : ℝ) (X₀pos : X₀ > 0) {k : ℝ} (k_pos : 0 < k) :
       _ ≤ max C₁ 1 := le_max_left C₁ 1
   · calc
       Real.log X ^ k ≤ ‖Real.log X ^ k‖ := le_norm_self _
-      _ ≤ ‖X ^ 1‖ := by exact_mod_cast hM X (by linarith[hXM])
+      _ ≤ ‖X ^ 1‖ := by exact_mod_cast hM X (by linarith only [hXM])
       _ = 1 * X := by
         rw[pow_one, one_mul]
         apply norm_of_nonneg
@@ -1727,12 +1733,12 @@ theorem I1Bound
   have pts_re_ge_one : 1 < pts_re := by
     unfold pts_re
     simp only [lt_add_iff_pos_right, inv_pos]
-    have U : 1 < X := by linarith
+    have U : 1 < X := by linarith only [eps_pos, eps_less_one, X_large]
     exact Real.log_pos U
   have pts_re_le_one : pts_re < 2 := by
     have := inv_lt_one_of_one_lt₀ (logt_gt_one X_large.le)
     dsimp [pts_re]
-    linarith
+    linarith only [this]
   have inve : (pts_re - 1)⁻¹ = Real.log X := by
     unfold pts_re
     simp_all only [one_div, support_subset_iff, ne_eq, mem_Icc, mul_inv_rev, gt_iff_lt,
@@ -1873,7 +1879,7 @@ theorem I1Bound
                 · refine Left.mul_nonneg ?_ ?_
                   · exact Left.mul_nonneg (by positivity) (by positivity)
                   · refine log_nonneg ?_
-                    · linarith
+                    · linarith only [eps_pos, eps_less_one, X_large]
                 · refine Left.mul_nonneg ?_ ?_
                   · exact exp_nonneg 1
                   · exact le_of_lt X_pos_triv
@@ -1939,7 +1945,7 @@ theorem I9Bound
   refine ⟨C, Cpos, ?_⟩
   intro ε εpos ε_lt_one X X_gt T T_gt
   specialize bound ε εpos ε_lt_one X X_gt T_gt
-  rwa [I9I1 (by linarith), norm_conj]
+  rwa [I9I1 (by linarith only [εpos, ε_lt_one, X_gt]), norm_conj]
 
 lemma one_add_inv_log {X : ℝ} (X_ge : 3 ≤ X) : (1 + (Real.log X)⁻¹) < 2 := by
   rw[← one_add_one_eq_two]
@@ -2030,7 +2036,7 @@ lemma I2GenBound {SmoothingF : ℝ → ℝ}
       _ ≤ 1 / 2 / 1 := by
         refine div_le_div_of_nonneg_left (by norm_num) (by norm_num) (Real.one_le_rpow ?_ n₁_pos.le)
         rw[Real.le_log_iff_exp_le Tpos]
-        linarith [Real.exp_one_lt_d9]
+        linarith only [Real.exp_one_lt_d9, ε_pos, ε_lt_one, T_gt]
       _ < 1 := by norm_num
   suffices ∀ σ ∈ Ioc σ₁ (1 + (Real.log X)⁻¹),
       ‖SmoothedChebyshevIntegrand SmoothingF ε X (↑σ - ↑T * I)‖ ≤ C' * X / (ε * T) by
@@ -2045,7 +2051,7 @@ lemma I2GenBound {SmoothingF : ℝ → ℝ}
         apply mul_le_mul_of_nonneg_left
         · rw[abs_of_nonneg (sub_nonneg.mpr interval_length_nonneg)]
           calc
-            1 + (Real.log X)⁻¹ - σ₁ ≤ 1 + (Real.log X)⁻¹ := by linarith
+            1 + (Real.log X)⁻¹ - σ₁ ≤ 1 + (Real.log X)⁻¹ := by linarith only [σ₁pos]
             _ ≤ 2 := (one_add_inv_log X_gt.le).le
         positivity
       _ = 2 * C' * X / (ε * T) := by ring
@@ -2060,9 +2066,9 @@ lemma I2GenBound {SmoothingF : ℝ → ℝ}
       _ ≤ C₂ * Real.log |-T| ^ n₂ := has_bound σ (-T)
           (by simp only [abs_neg]; rw [abs_of_pos Tpos]; exact T_gt)
           (by unfold σ₁ at hσ; simp only [mem_Ioc, abs_neg, log_abs, mem_Ici,
-            tsub_le_iff_right] at hσ ⊢; replace hσ := hσ.1; linarith)
+            tsub_le_iff_right] at hσ ⊢; replace hσ := hσ.1; linarith only [hσ])
       _ ≤ C₂ * Real.log T ^ n₂ := by simp
-      _ ≤ C₂ * (C₃ * T) := by gcongr; exact hC₃ T (by linarith)
+      _ ≤ C₂ * (C₃ * T) := by gcongr; exact hC₃ T (by linarith only [T_gt])
   calc
     ‖-ζ' (σ - T * I) / ζ (σ - T * I) * 𝓜 (fun x ↦ (Smooth1 SmoothingF ε x : ℂ))
         (σ - T * I) * X ^ (σ - T * I)‖ =
@@ -2076,10 +2082,10 @@ lemma I2GenBound {SmoothingF : ℝ → ℝ}
       · refine Mbd σ₁ σ₁pos _ ?_ ?_ ε ε_pos ε_lt_one
         · simp only [mem_Ioc, sub_re, ofReal_re, mul_re, I_re, mul_zero, ofReal_im, I_im, mul_one,
             sub_self, sub_zero, σ₁] at hσ ⊢
-          linarith
+          linarith only [hσ]
         · simp only [mem_Ioc, sub_re, ofReal_re, mul_re, I_re, mul_zero, ofReal_im, I_im, mul_one,
             sub_self, sub_zero, σ₁] at hσ ⊢
-          linarith[one_add_inv_log X_gt.le]
+          linarith only [one_add_inv_log X_gt.le, hσ, X_gt]
       · rw[cpow_def_of_ne_zero]
         · rw[norm_exp,← ofReal_log, re_ofReal_mul]
           · simp only [sub_re, ofReal_re, mul_re, I_re, mul_zero, ofReal_im, I_im, mul_one,
@@ -2089,10 +2095,10 @@ lemma I2GenBound {SmoothingF : ℝ → ℝ}
               add_comm, add_div, div_self, one_div]
             · exact hσ.2
             · refine (Real.log_pos ?_).ne.symm
-              linarith
+              linarith only [X_gt, ε_pos, ε_lt_one]
             · apply Real.log_pos
-              linarith
-            · linarith
+              linarith only [X_gt, ε_pos, ε_lt_one]
+            · linarith only [X_gt, ε_pos, ε_lt_one]
             · positivity
           · positivity
         · exact_mod_cast Xpos.ne.symm
@@ -2191,7 +2197,7 @@ lemma _root_.Real.log_le_const_mul_rpow {c x : ℝ} (hc : 0 < c) (hx : 0 < x) :
     Real.log x ≤ c * x ^ (1 / c) := by
   have h := Real.log_le_sub_one_of_pos (Real.rpow_pos_of_pos hx (1 / c)); rw [Real.log_rpow hx] at h
   have h' := mul_le_mul_of_nonneg_left h hc.le; field_simp at h'
-  nlinarith [Real.rpow_pos_of_pos hx (1 / c)]
+  nlinarith only [Real.rpow_pos_of_pos hx (1 / c), hc, h']
 
 /-
 For every $0<n$ there exists a constant $C>0$ (depending on $n$) such that
@@ -2209,7 +2215,7 @@ lemma log_pow_over_xsq_integral_bounded :
     ∃ C : ℝ, 0 < C ∧ ∀ T > 3, ∫ x in Ioo 3 T, (Real.log x) ^ n / x ^ 2 < C := by
   intro n n_pos
   set c : ℝ := 2 * n with cDef
-  have cpos : 0 < c := by linarith
+  have cpos : 0 < c := by linarith only [n_pos]
   set g : ℝ → ℝ := fun x => c ^ n * x ^ (-(3 / 2) : ℝ) with gDef
   have g_nonneg : ∀ x ∈ Ioi (3 : ℝ), 0 ≤ g x := by
     intro x hx; simp only [mem_Ioi] at hx
@@ -2219,17 +2225,17 @@ lemma log_pow_over_xsq_integral_bounded :
     Integrable.const_mul (integrableOn_Ioi_rpow_of_lt (by linarith) (by linarith)) _
   have g_mono : ∀ x ∈ Ioi (3 : ℝ), Real.log x ^ n / x ^ 2 ≤ g x := by
     intro x hx; simp only [mem_Ioi] at hx
-    have xpos : 0 < x := by linarith
+    have xpos : 0 < x := by linarith only [hx]
     have logxPos : 0 < Real.log x := by
       rw [Real.log_pos_iff xpos.le]
-      linarith
+      linarith only [hx]
     have logBnd := Real.rpow_le_rpow logxPos.le (Real.log_le_const_mul_rpow cpos xpos) n_pos.le
     rw [Real.mul_rpow cpos.le (Real.rpow_nonneg xpos.le _), ← Real.rpow_mul xpos.le, cDef] at logBnd
     field_simp at logBnd
     have : - ((3 : ℝ) / 2) = (1 / 2) - 2 := by norm_num
     simp only [cDef, gDef, this, Real.rpow_sub xpos, ← mul_div_assoc, rpow_ofNat]
     exact (div_le_div_iff_of_pos_right (sq_pos_iff.mpr (ne_of_gt xpos))).mpr logBnd
-  refine ⟨1 + (∫ x in Ioi (3 : ℝ), g x), by linarith, fun T _ => ?_⟩
+  refine ⟨1 + (∫ x in Ioi (3 : ℝ), g x), by linarith only [gInt_nonneg], fun T _ => ?_⟩
   calc
     _ ≤ ∫ (x : ℝ) in Ioo 3 T, g x := by
       refine setIntegral_mono_on (IntegrableOn.mono_set (ContinuousOn.integrableOn_Icc
@@ -2238,13 +2244,13 @@ lemma log_pow_over_xsq_integral_bounded :
         (fun x hx ↦ pow_ne_zero _ ?_))) Ioo_subset_Icc_self)
         (IntegrableOn.mono_set g_integrable Ioo_subset_Ioi_self) measurableSet_Ioo
         (fun x hx ↦ g_mono x hx.1)
-      · linarith [hx.1]
+      · linarith only [hx.1, hx]
       · simp only [mem_Icc, ne_eq, log_eq_zero, not_or, n_pos.le, or_true, implies_true]
-      · linarith [hx.1]
+      · linarith only [hx.1, hx]
     _ ≤ ∫ (x : ℝ) in Ioi 3, g x := by
       refine setIntegral_mono_set g_integrable ?_ (LE.le.eventuallyLE Ioo_subset_Ioi_self)
       exact MeasureTheory.ae_restrict_of_forall_mem measurableSet_Ioi (fun x hx ↦ g_nonneg x hx)
-  linarith
+  linarith only []
 
 /-- The uniform estimate for contour segment `I₃` used in the PNT argument. -/
 def I3BoundGenProp (n : ℝ) (SmoothingF : ℝ → ℝ) (A : ℝ) : Prop := ∃ (C : ℝ) (_ : 0 < C),
@@ -2309,8 +2315,8 @@ theorem I3GenBound {SmoothingF : ℝ → ℝ}
     intro t ht
     apply Real.one_lt_rpow _ n₂_pos
     apply logt_gt_one
-    rw [abs_of_neg (by linarith [ht.2])]
-    linarith [ht.2]
+    rw [abs_of_neg (by linarith only [ht.2, εgt0, εlt1, ht])]
+    linarith only [ht.2, ht]
   have Aoverlogt2gtAoverlogT2_bounds : ∀ t, 3 < |t| ∧ |t| < T →
         A / Real.log |t| ^ n₁ > A / Real.log T ^ n₁ := by
     intro t ht
@@ -2323,16 +2329,16 @@ theorem I3GenBound {SmoothingF : ℝ → ℝ}
   have hlogT : 1 < Real.log T ^ n₁ :=
     Real.one_lt_rpow (logt_gt_one Tgt3.le) n₁_pos
   have AoverlogT1in0half : A / Real.log T ^ n₁ ∈ Ioo 0 (1 / 2) := by
-    refine ⟨div_pos hA.1 (by linarith), ?_⟩
+    refine ⟨div_pos hA.1 (by linarith only [εgt0, εlt1, hlogT]), ?_⟩
     exact (div_lt_self hA.1 hlogT).trans_le hA.2
-  have σ₁lt1 : σ₁ < 1 := by dsimp [σ₁]; linarith [AoverlogT1in0half.1]
+  have σ₁lt1 : σ₁ < 1 := by dsimp [σ₁]; linarith only [AoverlogT1in0half.1, AoverlogT1in0half]
   have σ₁pos : 0 < σ₁ := by dsimp [σ₁]; linarith [AoverlogT1in0half.2]
   have quotient_bound : ∀ t ∈ Ioo (-T) (-3),
       Real.log |t| ^ n₂ / (σ₁ ^ 2 + t ^ 2) ≤ Real.log |t| ^ n₂ / t ^ 2 := by
     intro t ht
     exact div_le_div_of_nonneg_left (Real.rpow_nonneg (by
-      have := (t_bounds t ht).1; apply Real.log_nonneg; linarith) _)
-      (sq_pos_of_ne_zero (by have := ht.2; linarith)) (by nlinarith [sq_nonneg σ₁])
+      have := (t_bounds t ht).1; apply Real.log_nonneg; linarith only [εgt0, εlt1, this]) _)
+      (sq_pos_of_ne_zero (by linarith only [ht.2])) (by nlinarith [sq_nonneg σ₁])
   have MellinBound : ∀ (t : ℝ),
       ‖𝓜 (fun x ↦ (Smooth1 SmoothingF ε x : ℂ)) (σ₁ + t * I)‖ ≤
         CM * (ε * ‖(σ₁ + t * I)‖ ^ 2)⁻¹ := by
@@ -2400,7 +2406,7 @@ theorem I3GenBound {SmoothingF : ℝ → ℝ}
   have ne_zero_of_mem_uIcc (x) (hx : x ∈ uIcc (-T) (-3)) : x ≠ 0 := by
     rintro rfl
     norm_num [mem_uIcc] at hx
-    linarith
+    linarith only [εgt0, εlt1, Tgt3, hx]
   have cont1 : ContinuousOn (fun t ↦ Real.log |t| ^ n₂) (uIcc (-T) (-3)) := by
     exact ContinuousOn.rpow (ContinuousOn.log continuous_abs.continuousOn (fun x hx ↦
       abs_ne_zero.mpr (ne_zero_of_mem_uIcc x hx))) continuousOn_const (fun _ _ ↦ Or.inr n₂_pos)
@@ -2529,7 +2535,7 @@ theorem I7GenBound {SmoothingF : ℝ → ℝ}
   refine ⟨C, Cpos, fun X X_gt ε εpos ε_lt_one T T_gt ↦ ?_⟩
   specialize bound X X_gt εpos ε_lt_one T_gt
   intro σ₁
-  rwa [I7I3 (by linarith), norm_conj]
+  rwa [I7I3 (by linarith only [X_gt, εpos, ε_lt_one]), norm_conj]
 
 /-- The uniform estimate for contour segment `I₄` used in the PNT argument. -/
 def I4BoundGenProp (n : ℝ) (SmoothingF : ℝ → ℝ) (A σ₂ : ℝ) : Prop := ∃ (C : ℝ) (_ : 0 ≤ C) (Tlb :
@@ -2594,7 +2600,7 @@ private lemma logDeriv_horizontal_bddAbove {σ₂ : ℝ}
       repeat rw[ofReal_im] at h
       ring_nf at h
       obtain ⟨_, ripGoal⟩ := h
-      linarith
+      linarith only [ripGoal]
     refine ⟨?_, this⟩
     rw [mem_reProdIm]
     simp only [sub_re, add_re, ofReal_re, mul_re, one_re, ofReal_im, sub_im, one_im, sub_self,
@@ -2606,7 +2612,7 @@ private lemma logDeriv_horizontal_bddAbove {σ₂ : ℝ}
       · simp only [le_add_iff_nonneg_right]
         apply mul_nonneg
         · exact xInIcc.1
-        · linarith [hσ₂.2]
+        · linarith only [hσ₂.2, hσ₂]
       · have : σ₂ + x * (1 - σ₂) = σ₂ * (1 - x) + x := by ring
         rw [this]
         clear this
@@ -2614,11 +2620,11 @@ private lemma logDeriv_horizontal_bddAbove {σ₂ : ℝ}
         rw [this]
         clear this
         gcongr
-        · linarith [xInIcc.2]
+        · linarith only [xInIcc.2, xInIcc]
         · exact hσ₂.2.le
-        · linarith [xInIcc.1]
+        · linarith only [xInIcc.1, xInIcc]
         · exact xInIcc.2
-    · linarith [hσ₂.2]
+    · linarith only [hσ₂.2, hσ₂]
 
 /-- The horizontal contour stays a positive distance from the origin. -/
 private lemma horizontal_norm_sInf_pos (σ₂ : ℝ) : 0 < sInf ((fun (t : ℝ) ↦ ‖↑σ₂ + ↑t * (1 - ↑σ₂) -
@@ -2670,11 +2676,11 @@ private lemma horizontal_contour_endpoint_le {n A σ₂ T : ℝ}
   change σ₂ ≤ σ₁
   have logTlb_pos : 0 < Real.log Tlb := by
     rw[← Real.log_one]
-    exact log_lt_log (by norm_num) (by linarith [hTlb])
+    exact log_lt_log (by norm_num) (by linarith only [hTlb])
   have logTlb_nonneg : 0 ≤ Real.log Tlb := le_of_lt (by exact logTlb_pos)
   have expr_nonneg : 0 ≤ A / (1 - σ₂) := by
     apply div_nonneg
-    · linarith [hA.1]
+    · linarith only [hA.1, hA]
     · rw[sub_nonneg]
       exact le_of_lt hσ₂.2
   have temp : σ₂ ≤ 1 - A / Real.log Tlb ^ n := by
@@ -2690,7 +2696,7 @@ private lemma horizontal_contour_endpoint_le {n A σ₂ T : ℝ}
         apply rpow_inv_rpow (by exact expr_nonneg)
         exact Ne.symm (Std.ne_of_lt n_pos)
       rw[h, div_le_iff₀, mul_comm, ← div_le_iff₀] at this
-      · linarith
+      · linarith only [this]
       · exact rpow_pos_of_pos (by exact logTlb_pos) _
       · rw[sub_pos]
         exact hσ₂.2
@@ -2702,7 +2708,7 @@ private lemma horizontal_contour_endpoint_le {n A σ₂ T : ℝ}
     · rfl
     · apply Real.rpow_pos_of_pos
       apply Real.log_pos
-      linarith
+      linarith only [hTlb]
     · exact Real.rpow_le_rpow logTlb_nonneg (log_le_log (by linarith [hTlb]) T_gt_Tlb.le) n_pos.le
   exact le_trans temp this
 
@@ -2748,7 +2754,7 @@ lemma I4GenBound {SmoothingF : ℝ → ℝ}
   have maxσ₂σ₁ : max σ₂ σ₁ = σ₁ := max_eq_right (by exact σ₂_le_σ₁)
   have σ₁_lt_one : σ₁ < 1 :=
     sub_lt_self _ (div_pos hA.1
-      (Real.rpow_pos_of_pos (Real.log_pos (by linarith)) _))
+      (Real.rpow_pos_of_pos (Real.log_pos (by linarith only [this, ε_pos, ε_lt_one, T_gt_Tlb])) _))
   rw[norm_mul, ← one_mul C]
   have : 1 * C * X * X ^ (-A / Real.log T ^ n) / ε = 1 * (C * X * X ^ (-A / Real.log T ^ n) / ε)
     := by ring
@@ -2756,7 +2762,7 @@ lemma I4GenBound {SmoothingF : ℝ → ℝ}
   apply mul_le_mul
   · simp only [norm_div, norm_one, norm_mul, Complex.norm_two, Complex.norm_real,
       Real.norm_of_nonneg pi_nonneg, Complex.norm_I, mul_one]
-    exact (div_le_one (by positivity)).2 (by nlinarith [Real.pi_gt_three])
+    exact (div_le_one (by positivity)).2 (by nlinarith only [Real.pi_gt_three, ε_pos, ε_lt_one])
   · let f : ℝ → ℂ := fun σ ↦ (-ζ' (↑σ - 3 * I) / ζ (↑σ - 3 * I) * 𝓜 (fun x ↦ ↑(Smooth1 SmoothingF
     ε x)) (↑σ - 3 * I) * ↑X ^ (↑σ - 3 * I))
     have temp : ‖∫ (σ : ℝ) in σ₂..σ₁, -ζ' (↑σ - 3 * I) / ζ (↑σ - 3 * I) * 𝓜 (fun x ↦ ↑(Smooth1
@@ -2871,7 +2877,8 @@ lemma I4GenBound {SmoothingF : ℝ → ℝ}
             exact le_trans this (by refine Complex.abs_re_le_norm ?_)
           · exact CPrimeNonneg
         have : ‖(X : ℂ) ^ (↑x - 3 * I)‖ ≤ X * X ^ (-A / Real.log T ^ n) := by
-          rw [Complex.norm_cpow_eq_rpow_re_of_pos (by linarith : 0 < X)]
+          rw [Complex.norm_cpow_eq_rpow_re_of_pos (by
+            linarith only [X_gt_three, ε_pos, ε_lt_one] : 0 < X)]
           simp only [sub_re, ofReal_re, mul_re, I_re, I_im, reThree, imThree,
             mul_zero, zero_mul, sub_zero]
           have hx : x ≤ σ₁ := by
@@ -2879,10 +2886,12 @@ lemma I4GenBound {SmoothingF : ℝ → ℝ}
             rw [maxσ₂σ₁] at xInIoc
             exact xInIoc.2
           calc
-            X ^ x ≤ X ^ σ₁ := Real.rpow_le_rpow_of_exponent_le (by linarith) hx
+            X ^ x ≤ X ^ σ₁ := Real.rpow_le_rpow_of_exponent_le (by
+              linarith only [X_gt_three, ε_pos, ε_lt_one]) hx
             _ = X * X ^ (-A / Real.log T ^ n) := by
               dsimp [σ₁]
-              rw [sub_eq_add_neg, Real.rpow_add (by linarith : 0 < X),
+              rw [sub_eq_add_neg, Real.rpow_add (by
+                linarith only [X_gt_three, ε_pos, ε_lt_one] : 0 < X),
                 Real.rpow_one, neg_div]
         apply mul_le_mul
         · exact temp
@@ -2950,7 +2959,7 @@ lemma I6GenBound {SmoothingF : ℝ → ℝ}
   refine ⟨C, Cpos, Tlb, Tlb_gt, fun X X_gt ε εpos ε_lt_one T T_gt ↦ ?_⟩
   specialize bound X X_gt εpos ε_lt_one T_gt
   intro σ₁
-  rwa [I6I4 (by linarith), norm_neg, norm_conj]
+  rwa [I6I4 (by linarith only [X_gt, εpos, ε_lt_one]), norm_neg, norm_conj]
 
 /-- The uniform estimate for contour segment `I₅` used in the PNT argument. -/
 def I5BoundGenProp (SmoothingF : ℝ → ℝ) (σ₂ : ℝ) : Prop := ∃ (C : ℝ) (_ : 0 < C),
@@ -3244,18 +3253,18 @@ private lemma eventual_exp_log_rpow_mul_log_le {const1 const2 : ℝ} (const1pos
       filter_upwards [this, eventually_gt_atTop 10] with x hx x_gt
       convert hx using 1
       · rw [Real.norm_of_nonneg]
-        exact Real.log_nonneg (logt_gt_one (by linarith)).le
+        exact Real.log_nonneg (logt_gt_one (by linarith only [x_gt])).le
       · congr! 1
         rw [Real.norm_of_nonneg]
         apply Real.rpow_nonneg
         apply Real.log_nonneg
-        linarith
+        linarith only [x_gt]
     have loglogx :  ∀ᶠ (x : ℝ) in atTop,
         Real.log x = rexp (Real.log (Real.log x)) := by
       filter_upwards [eventually_gt_atTop 3] with x hx
       rw [Real.exp_log]
       apply Real.log_pos
-      linarith
+      linarith only [hx]
     filter_upwards [loglogx, this] with x loglogx hx
     conv =>
       enter [1, 2]
@@ -3271,7 +3280,7 @@ private lemma eventual_exp_log_rpow_mul_log_le_exp {const1 const1' const2 : ℝ}
   ∀ᶠ (x : ℝ) in atTop,
   rexp (-const1 * Real.log x ^ const2) * Real.log x ≤
   rexp (-const1' * Real.log x ^ const2) := by
-    have : 0 < const1 - const1' := by linarith
+    have : 0 < const1 - const1' := by linarith only [const1bnds]
     filter_upwards [eventual_exp_log_rpow_mul_log_le this const2pos] with x hx
     have : rexp (-const1 * Real.log x ^ const2) * Real.log x
       = rexp (-(const1') * Real.log x ^ const2)
@@ -3297,7 +3306,7 @@ private lemma balanced_rpow_exp_le {n₁ A : ℝ} (n₁_pos : 0 < n₁)
     filter_upwards [eventually_gt_atTop 0] with x hx
     rw [Real.exp_log hx]
   filter_upwards [this, eventually_gt_atTop 3] with x hx x_gt_3
-  have logxpos : 0 < Real.log x := by apply Real.log_pos; linarith
+  have logxpos : 0 < Real.log x := by apply Real.log_pos; linarith only [x_gt_3]
   conv =>
     enter [1, 1, 1]
     rw [hx]
@@ -3330,13 +3339,13 @@ private lemma balanced_rpow_exp_le {n₁ A : ℝ} (n₁_pos : 0 < n₁)
     positivity
   · apply Real.rpow_nonneg
     apply Real.log_nonneg
-    linarith
+    linarith only [x_gt_3]
 
 private lemma tendsto_const_mul_log_rpow_neg {pow2 : ℝ} (pow2_neg : pow2 < 0) (c' : ℝ) :
     Tendsto (fun x ↦ c' * Real.log x ^ pow2) atTop (𝓝 0) := by
   rw [← mul_zero c']
   apply Tendsto.const_mul
-  have := tendsto_rpow_neg_atTop (y := -pow2) (by linarith)
+  have := tendsto_rpow_neg_atTop (y := -pow2) (by linarith only [pow2_neg])
   rw [neg_neg] at this
   apply this.comp
   exact Real.tendsto_log_atTop
@@ -3350,21 +3359,23 @@ private lemma eventual_const_mul_log_rpow_lt {pow2 : ℝ} (pow2_neg : pow2 < 0)
 private lemma eventual_log_linear_nonnegative {c1 : ℝ} (c1pos : 0 < c1) (c2 : ℝ) {pow1 : ℝ}
   (pow1_lt : pow1 < 1) :
     ∀ᶠ (x : ℝ) in atTop, 0 ≤ Real.log x * (c1 - c2 * (Real.log x) ^ (pow1 - 1)) := by
-  filter_upwards [eventually_gt_atTop 3 , eventual_const_mul_log_rpow_lt (by linarith : pow1 - 1 <
+  filter_upwards [eventually_gt_atTop 3 , eventual_const_mul_log_rpow_lt (by
+    linarith only [pow1_lt] : pow1 - 1 <
     0)
-    (by linarith : 0 < c1 / 2) c2] with x x_gt hx
+    (by linarith only [c1pos] : 0 < c1 / 2) c2] with x x_gt hx
   have : 0 ≤ Real.log x := by
     apply Real.log_nonneg
-    linarith
+    linarith only [x_gt]
   apply mul_nonneg this
-  linarith
+  linarith only [c1pos, hx]
 
 private lemma eventual_log_linear_domination {const1 : ℝ} (const1_lt : const1 < 1) (const2 const3
   : ℝ)
     {pow1 : ℝ} (pow1_lt : pow1 < 1) : ∀ᶠ (x : ℝ) in atTop,
     const1 * Real.log x + const2 * Real.log x ^ pow1
       ≤ Real.log x - const3 * Real.log x ^ pow1 := by
-  filter_upwards [eventual_log_linear_nonnegative (by linarith : 0 < 1 - const1) (const2 + const3)
+  filter_upwards [eventual_log_linear_nonnegative (by
+    linarith only [const1_lt] : 0 < 1 - const1) (const2 + const3)
     pow1_lt,
     eventually_gt_atTop 3] with x hx x_gt
   have :
@@ -3381,7 +3392,7 @@ private lemma eventual_log_linear_domination {const1 : ℝ} (const1_lt : const1
       conv =>
         enter [1, 2]
         rw [← Real.rpow_one (Real.log x)]
-      rw [← Real.rpow_add (Real.log_pos (by linarith))]
+      rw [← Real.rpow_add (Real.log_pos (by linarith only [x_gt]))]
       ring_nf
     rw [this]
   have : Real.log x * const3 * Real.log x ^ (-1 + pow1)
@@ -3391,7 +3402,7 @@ private lemma eventual_log_linear_domination {const1 : ℝ} (const1_lt : const1
     conv =>
       enter [1, 2]
       rw [← Real.rpow_one (Real.log x)]
-    rw [← Real.rpow_add (Real.log_pos (by linarith))]
+    rw [← Real.rpow_add (Real.log_pos (by linarith only [x_gt]))]
     ring_nf
   rw [this]
 
@@ -3526,21 +3537,22 @@ private theorem pnt_from_contour_estimates {n₁ : ℝ} (n₁_pos : 0 < n₁) (
       · intro s hs
         apply DifferentiableAt.differentiableWithinAt
         apply Smooth1MellinDifferentiable ContDiff1ν ν_supp ⟨ε_pos, ε_lt_one⟩ ν_nonneg ν_massOne
-        linarith [mem_reProdIm.mp hs.1 |>.1.1, σ₂InIoo.1]
+        linarith only [mem_reProdIm.mp hs.1 |>.1.1, σ₂InIoo.1, hs, σ₂InIoo]
     · intro s hs
       apply DifferentiableAt.differentiableWithinAt
       apply DifferentiableAt.const_cpow (by fun_prop)
       left
       norm_cast
-      linarith
+      linarith only [X_gt_3, ε_lt_one, εx_pos]
   have ψ_ε_diff : ‖ψ_ε_of_X - 𝓜 (fun x ↦ (Smooth1 ν ε x : ℂ)) 1 * X‖ ≤ ‖I₁ ν ε X T‖ + ‖I₂ ν ε T X
     σ₁‖
     + ‖I₃ ν ε T X σ₁‖ + ‖I₄ ν ε X σ₁ σ₂‖ + ‖I₅ ν ε X σ₂‖ + ‖I₆ ν ε X σ₁ σ₂‖ + ‖I₇ ν ε T X σ₁‖
     + ‖I₈ ν ε T X σ₁‖ + ‖I₉ ν ε X T‖ := by
     unfold ψ_ε_of_X
-    rw [SmoothedChebyshevPull1 ε_pos ε_lt_one X X_gt_3 (T := T) (by linarith)
+    rw [SmoothedChebyshevPull1 ε_pos ε_lt_one X X_gt_3 (T := T) (by
+      linarith only [ε_lt_one, T_gt_3, εx_pos])
       σ₁pos σ₁_lt_one holo1 ν_supp ν_nonneg ν_massOne ContDiff1ν]
-    rw [SmoothedChebyshevPull2 ε_pos ε_lt_one X X_gt_3 (T := T) (by linarith)
+    rw [SmoothedChebyshevPull2 ε_pos ε_lt_one X X_gt_3 (T := T) (by linarith only [T_gt_3])
       σ₂InIoo.1 σ₁_lt_one σ₂_lt_σ₁ holo1 holo2a ν_supp ν_nonneg ν_massOne ContDiff1ν]
     ring_nf
     iterate 5
@@ -3558,7 +3570,7 @@ private theorem pnt_from_contour_estimates {n₁ : ℝ} (n₁_pos : 0 < n₁) (
     push_cast
     rw [← sub_mul, norm_mul]
     gcongr
-    rw [norm_real, norm_of_nonneg (by linarith)]
+    rw [norm_real, norm_of_nonneg (by linarith only [X_gt_3, ε_lt_one, εx_pos])]
   specialize hc₁ ε ε_pos ε_lt_one X X_gt_3 T_gt_3
   specialize hc₂ X X_gt_3 ε_pos ε_lt_one T_gt_3
   specialize hc₃ X X_gt_3 ε_pos ε_lt_one T_gt_3
@@ -3572,7 +3584,7 @@ private theorem pnt_from_contour_estimates {n₁ : ℝ} (n₁_pos : 0 < n₁) (
   have C'bnd : c_close * ε * X * Real.log X + C_main * ε * X ≤ C' * ε * X * Real.log X := by
     have : C_main * ε * X * 1 ≤ C_main * ε * X * Real.log X := by
       gcongr
-    linarith
+    linarith only [this]
   have C''bnd : c₁ * X * Real.log X / (ε * T) + c₂ * X / (ε * T) + c₈ * X / (ε * T)
     + c₉ * X * Real.log X / (ε * T) ≤ C'' * X * Real.log X / (ε * T) := by
     unfold C''
@@ -3583,7 +3595,7 @@ private theorem pnt_from_contour_estimates {n₁ : ℝ} (n₁_pos : 0 < n₁) (
       gcongr
     have : c₂ * X / (ε * T) ≤ c₂ * X * Real.log X / (ε * T) := by
       ring_nf at this ⊢
-      linarith
+      linarith only [this]
     grw [this]
     have : c₈ * X / (ε * T) * 1 ≤ c₈ * X / (ε * T) * Real.log X := by
       gcongr
@@ -3716,7 +3728,7 @@ lemma GenStrengthPNT {n₁ n₂ : ℝ}
   let Tx := (fun x ↦ Real.exp (c_Tx * (Real.log x) ^ ((1 : ℝ) / (1 + n₁))))
   have one_div_succ_n₁_pos : 0 < (1 : ℝ) / (1 + n₁) := by
     simp only [one_div, inv_pos]
-    linarith
+    linarith only [n₁_pos]
   have one_div_succ_n₁_lt_one : (1 : ℝ) / (1 + n₁) < 1 := by
     rw [one_div, inv_lt_one₀ (one_div_pos.mp one_div_succ_n₁_pos)]
     norm_num [n₁_pos]
@@ -3765,7 +3777,7 @@ lemma GenStrengthPNT {n₁ n₂ : ℝ}
       C' * x * rexp (-c * Real.log x ^ ((1 : ℝ) / (1 + n₁))) := by
     unfold c εx c_εx
     have const1bnd : (A ^ ((1 : ℝ) / (1 + n₁)) / 4) < (A ^ ((1 : ℝ) / (1 + n₁)) / 2) := by
-        linarith
+        linarith only [c_Tx_pos]
     have this (x) :
       C' * rexp (-(A ^ ((1 : ℝ) / (1 + n₁)) / 2) * Real.log x ^ ((1 : ℝ) / (1 + n₁))) * x *
         Real.log x =
@@ -3787,7 +3799,7 @@ lemma GenStrengthPNT {n₁ n₂ : ℝ}
     simp_rw [← Real.exp_add, div_eq_mul_inv, ← Real.exp_neg, this]
     have const1bnd : const1' < (A ^ const2 - const1) := by
       unfold const1' const1
-      linarith
+      linarith only [c_Tx_pos]
     filter_upwards [eventual_exp_log_rpow_mul_log_le_exp const1bnd const2bnd, eventually_gt_atTop
       3] with x x_bnd x_gt
     rw [mul_assoc]
diff --git a/LeanPool/IwaniecLinearSieve/Vendor/PrimeNumberTheoremAnd/MellinCalculus.lean b/LeanPool/IwaniecLinearSieve/Vendor/PrimeNumberTheoremAnd/MellinCalculus.lean
index df8f6f6da3..de7b3ad783 100644
--- a/LeanPool/IwaniecLinearSieve/Vendor/PrimeNumberTheoremAnd/MellinCalculus.lean
+++ b/LeanPool/IwaniecLinearSieve/Vendor/PrimeNumberTheoremAnd/MellinCalculus.lean
@@ -181,7 +181,7 @@ lemma _root_.Filter.TendstoAtZero_of_support_in_Icc {a b : ℝ} (f : ℝ → 
     Tendsto f (𝓝[>]0) (𝓝 0) := by
   apply Tendsto.comp (tendsto_nhds_of_eventually_eq ?_) tendsto_id
   filter_upwards [Ioo_mem_nhdsGT ha] with c hc; replace hc := (mem_Ioo.mp hc).2
-  have h : c ∉ Icc a b := fun h ↦ by linarith [mem_Icc.mp h]
+  have h : c ∉ Icc a b := fun h ↦ by linarith only [mem_Icc.mp h, hc, h]
   convert mt (Function.support_subset_iff.mp fSupp c) h; simp
 
 lemma _root_.Filter.TendstoAtTop_of_support_in_Icc {a b : ℝ} (f : ℝ → 𝕂)
@@ -189,16 +189,16 @@ lemma _root_.Filter.TendstoAtTop_of_support_in_Icc {a b : ℝ} (f : ℝ → 𝕂
     Tendsto f atTop (𝓝 0) := by
   apply Tendsto.comp (tendsto_nhds_of_eventually_eq ?_) tendsto_id
   filter_upwards [Ioi_mem_atTop b] with c hc; rw [mem_Ioi] at hc
-  have h : c ∉ Icc a b := fun h ↦ by linarith [mem_Icc.mp h]
+  have h : c ∉ Icc a b := fun h ↦ by linarith only [mem_Icc.mp h, hc, h]
   convert mt (Function.support_subset_iff.mp fSupp c) h; simp
 
 lemma _root_.Filter.BigO_zero_atZero_of_support_in_Icc {a b : ℝ} (f : ℝ → 𝕂) (ha : 0 < a)
     (fSupp : f.support ⊆ Set.Icc a b) :
     f =O[𝓝[>] 0] fun _ ↦ (0 : ℝ) := by
   refine Eventually.isBigO ?_
-  filter_upwards [Ioo_mem_nhdsGT (by linarith : (0 : ℝ) < a)] with c hc
+  filter_upwards [Ioo_mem_nhdsGT (by linarith only [ha] : (0 : ℝ) < a)] with c hc
   refine norm_le_zero_iff.mpr <| Function.support_subset_iff'.mp fSupp c ?_
-  exact fun h ↦ by linarith [mem_Icc.mp h, (mem_Ioo.mp hc).2]
+  exact fun h ↦ by linarith only [mem_Icc.mp h, (mem_Ioo.mp hc).2, h, hc]
 
 lemma _root_.Filter.BigO_zero_atTop_of_support_in_Icc {a b : ℝ} (f : ℝ → 𝕂)
     (fSupp : f.support ⊆ Set.Icc a b) :
@@ -206,7 +206,7 @@ lemma _root_.Filter.BigO_zero_atTop_of_support_in_Icc {a b : ℝ} (f : ℝ → 
   refine Eventually.isBigO ?_
   filter_upwards [Ioi_mem_atTop b] with c hc; replace hc := mem_Ioi.mp hc
   refine norm_le_zero_iff.mpr <| Function.support_subset_iff'.mp fSupp c ?_
-  exact fun h ↦ by linarith [mem_Icc.mp h]
+  exact fun h ↦ by linarith only [mem_Icc.mp h, hc, h]
 
 lemma _root_.deriv.ofReal_comp' {f : ℝ → ℝ} :
     deriv (fun x : ℝ ↦ (f x : ℂ)) = (fun x ↦ ((deriv f) x : ℂ)) :=
@@ -523,7 +523,7 @@ lemma MellinOfPsi {ν : ℝ → ℝ} (diffν : ContDiff ℝ 1 ν)
   have mainBnd : ∀ (σ₁ : ℝ), 0 < σ₁ → ∀ (s : ℂ), σ₁ ≤ s.re → s.re ≤ 2 →
       ‖𝓜 (fun x ↦ (ν x : ℂ)) s‖ ≤ C * ‖s‖⁻¹ := by
     intro σ₁ σ₁pos s hs₁ hs₂
-    have s_ne_zero: s ≠ 0 := fun h ↦ by linarith [zero_re ▸ h ▸ hs₁]
+    have s_ne_zero: s ≠ 0 := fun h ↦ by linarith only [zero_re ▸ h ▸ hs₁, σ₁pos, hs₁, h]
     simp only [mellin, f, MellinOfPsi_aux diffν suppν s_ne_zero, norm_mul, smul_eq_mul, mul_comm]
     gcongr
     · simp
@@ -546,9 +546,9 @@ lemma MellinOfPsi {ν : ℝ → ℝ} (diffν : ContDiff ℝ 1 ν)
       · intro x hx;
         have f_bound := isMaxOn_iff.mp max x hx
         have pow_bound : ‖(x : ℂ) ^ s‖ ≤ 2 ^ σ₂ := by
-          rw [norm_cpow_eq_rpow_re_of_pos (by linarith [mem_Icc.mp hx])]
-          have xpos : 0 ≤ x := by linarith [(mem_Icc.mp hx).1]
-          have h := rpow_le_rpow xpos (mem_Icc.mp hx).2 (by linarith : 0 ≤ s.re)
+          rw [norm_cpow_eq_rpow_re_of_pos (by linarith only [mem_Icc.mp hx, hx])]
+          have xpos : 0 ≤ x := by linarith only [(mem_Icc.mp hx).1, hx]
+          have h := rpow_le_rpow xpos (mem_Icc.mp hx).2 (by linarith only [σ₁pos, hs₁] : 0 ≤ s.re)
           exact le_trans h <| rpow_le_rpow_of_exponent_le (by norm_num) hs₂
         convert! mul_le_mul f_bound pow_bound (norm_nonneg _) ?_ using 1 <;> simp [f]
   have Cnonneg : 0 ≤ C := by
@@ -558,7 +558,7 @@ lemma MellinOfPsi {ν : ℝ → ℝ} (diffν : ContDiff ℝ 1 ν)
     have := hhh.trans hh
     exact (mul_nonneg_iff_of_pos_right hhhh).mp this
   by_cases CeqZero : C = 0
-  · refine ⟨1, by linarith, ?_⟩
+  · refine ⟨1, by linarith only [], ?_⟩
     intro ε εpos s hs₁ hs₂
     have := mainBnd ε εpos s hs₁ hs₂
     rw [CeqZero, zero_mul] at this
@@ -623,7 +623,7 @@ lemma DeltaSpikeSupport_aux {ν : ℝ → ℝ} {ε : ℝ} (εpos : 0 < ε)
   have hl := (le_rpow_inv_iff_of_pos (by norm_num) hx εpos).mp this.1
   rw [inv_rpow (by norm_num) ε, ← rpow_neg (by norm_num)] at hl
   refine ⟨hl, (rpow_inv_le_iff_of_pos ?_ (by norm_num) εpos).mp this.2⟩
-  linarith [(by apply rpow_nonneg (by norm_num) : 0 ≤ (2 : ℝ) ^ (-ε))]
+  linarith only [(by apply rpow_nonneg (by norm_num) : 0 ≤ (2 : ℝ) ^ (-ε)), hx]
 
 lemma DeltaSpikeSupport' {ν : ℝ → ℝ} {ε x : ℝ} (εpos : 0 < ε) (xnonneg : 0 ≤ x)
     (suppν : ν.support ⊆ Icc (1 / 2) 2) :
@@ -832,15 +832,15 @@ lemma Smooth1Properties_estimate {ε : ℝ} (εpos : 0 < ε) :
   have mono: StrictMonoOn f <| Ici 1 := by
     refine strictMonoOn_of_deriv_pos (convex_Ici _) ?_ ?_
     · apply continuousOn_id.mul (continuousOn_id.log ?_) |>.sub continuousOn_id
-      intro x hx; simp only [mem_Ici] at hx; simp only [id_eq, ne_eq]; linarith
+      intro x hx; simp only [mem_Ici] at hx; simp only [id_eq, ne_eq]; linarith only [hx]
     · intro x hx; simp only [nonempty_Iio, interior_Ici', mem_Ioi] at hx
       dsimp only [f]
       rw [deriv_fun_sub, deriv_fun_mul, Real.deriv_log, deriv_id'', one_mul, mul_inv_cancel₀]
       · simp [log_pos hx]
-      · linarith
+      · linarith only [hx]
       · simp only [differentiableAt_fun_id]
-      · simp only [differentiableAt_log_iff, ne_eq]; linarith
-      · exact differentiableAt_fun_id.mul <| differentiableAt_fun_id.log (by linarith)
+      · simp only [differentiableAt_log_iff, ne_eq]; linarith only [hx]
+      · exact differentiableAt_fun_id.mul <| differentiableAt_fun_id.log (by linarith only [hx])
       · simp only [differentiableAt_fun_id]
   exact mono (by rw [mem_Ici]) (mem_Ici.mpr <| le_of_lt hc) hc
 
@@ -923,7 +923,7 @@ lemma Smooth1Properties_below {ν : ℝ → ℝ} (suppν : ν.support ⊆ Icc (1
     apply DeltaSpikeSupport εpos ?_ suppν
     · simp only [mem_Icc, not_and, not_le]; intro
       linarith [(by apply (div_lt_iff₀ (by linarith)).mpr; nlinarith : x / y < 2 ^ (-ε))]
-    · rw [le_div_iff₀ (by linarith), zero_mul]; exact xpos.le
+    · rw [le_div_iff₀ (by linarith only [hy2]), zero_mul]; exact xpos.le
 
 
 
@@ -1025,7 +1025,7 @@ lemma Smooth1Properties_above {ν : ℝ → ℝ} (suppν : ν.support ⊆ Icc (1
     simp only [mem_Icc, not_and, not_le]
   on_goal 2 =>
     suffices h : 2 ^ ε < x / y by
-      linarith [(by apply rpow_pos_of_pos (by norm_num) : 0 < (2 : ℝ) ^ ε)]
+      linarith only [(by apply rpow_pos_of_pos (by norm_num) : 0 < (2 : ℝ) ^ ε), h]
   all_goals
   try intro
   have : x / y = ((x / y) ^ (1 / ε)) ^ ε := by
@@ -1253,7 +1253,7 @@ lemma MellinOfSmooth1a {ν : ℝ → ℝ} (diffν : ContDiff ℝ 1 ν)
         · exact (DeltaSpikeOfRealContinuous εpos diffν).continuousOn
         · exact continuous_ofReal.continuousOn
         · intro x hx; simp only [mem_Icc] at hx; simp only [ofReal_ne_zero]
-          linarith [(by apply rpow_pos_of_pos (by norm_num) : (0 : ℝ) < 2 ^ (-ε))]
+          linarith only [(by apply rpow_pos_of_pos (by norm_num) : (0 : ℝ) < 2 ^ (-ε)), hx]
   have : 𝓜 (MellinConvolution g f') s = 𝓜 g s * 𝓜 f' s := by
     rw [mul_comm, ← MellinConvolutionTransform f' g s
       (by convert int_F using 1; simp only [f', F, f]; field_simp)]
@@ -1285,10 +1285,10 @@ lemma MellinOfSmooth1b {ν : ℝ → ℝ} (diffν : ContDiff ℝ 1 ν)
   rw [MellinOfSmooth1a diffν suppν εpos <| lt_of_le_of_lt' hs1 σ₁pos]
   have hh1 : ε * σ₁ ≤ (ε * s).re := by
     simp only [mul_re, ofReal_re, ofReal_im, zero_mul, sub_zero]
-    nlinarith
+    nlinarith only [hs1, εpos]
   have hh2 : (ε * s).re ≤ 2 := by
     simp only [mul_re, ofReal_re, ofReal_im, zero_mul, sub_zero]
-    nlinarith
+    nlinarith only [hs2, σ₁pos, ε_lt_one, hs1]
   calc
     ‖s⁻¹ * 𝓜 (fun x ↦ (ν x : ℂ)) (ε * s)‖ =
         ‖s⁻¹‖ * ‖𝓜 (fun x ↦ (ν x : ℂ)) (ε * s)‖ := by simp
@@ -1317,7 +1317,7 @@ lemma MellinOfSmooth1c {ν : ℝ → ℝ} (diffν : ContDiff ℝ 1 ν)
   rw [Asymptotics.isBigO_iff] at h ⊢
   obtain ⟨c, hc⟩ := h
   use c
-  filter_upwards [hc, Ioo_mem_nhdsGT (by linarith : (0 : ℝ) < 1)] with ε hε hε'
+  filter_upwards [hc, Ioo_mem_nhdsGT (by linarith only [] : (0 : ℝ) < 1)] with ε hε hε'
   rw [MellinOfSmooth1a diffν suppν hε'.1 (s := 1) (by norm_num)]
   simp only [inv_one, mul_one, one_mul, id_eq, Real.norm_eq_abs]
   exact hε
diff --git a/LeanPool/IwaniecLinearSieve/Vendor/PrimeNumberTheoremAnd/ResidueCalcOnRectangles.lean b/LeanPool/IwaniecLinearSieve/Vendor/PrimeNumberTheoremAnd/ResidueCalcOnRectangles.lean
index 812fa9f8b0..892105f64b 100644
--- a/LeanPool/IwaniecLinearSieve/Vendor/PrimeNumberTheoremAnd/ResidueCalcOnRectangles.lean
+++ b/LeanPool/IwaniecLinearSieve/Vendor/PrimeNumberTheoremAnd/ResidueCalcOnRectangles.lean
@@ -491,7 +491,7 @@ lemma _root_.Complex.inv_re_add_im : (x + y * I)⁻¹ = (x - I * y) / (x ^ 2 + y
   congr <;> simp [conj_ofReal, normSq] <;> ring
 
 lemma sq_add_sq_ne_zero (hy : y ≠ 0) : x ^ 2 + y ^ 2 ≠ 0 := by
-  linarith [sq_nonneg x, sq_pos_iff.mpr hy]
+  linarith only [sq_nonneg x, sq_pos_iff.mpr hy, hy]
 
 lemma continuous_self_div_sq_add_sq (hy : y ≠ 0) :
     Continuous fun x => x / (x ^ 2 + y ^ 2) :=
diff --git a/LeanPool/IwaniecLinearSieve/Vendor/PrimeNumberTheoremAnd/StrongPNT.lean b/LeanPool/IwaniecLinearSieve/Vendor/PrimeNumberTheoremAnd/StrongPNT.lean
index 0583fdb737..0cefccd5f1 100644
--- a/LeanPool/IwaniecLinearSieve/Vendor/PrimeNumberTheoremAnd/StrongPNT.lean
+++ b/LeanPool/IwaniecLinearSieve/Vendor/PrimeNumberTheoremAnd/StrongPNT.lean
@@ -91,7 +91,7 @@ theorem borelCaratheodory' {M r R : ℝ} {f : ℂ → ℂ} {z : ℂ}
   have h_borelCaratheodory : ∀ ε > 0, ‖f z‖ ≤ (2 * (M + ε) * ‖z‖) / (R - ‖z‖) := by
     intro ε εpos;
     apply Complex.borelCaratheodory_zero;
-    exacts [by linarith, analytic.differentiableOn,
+    exacts [by linarith only [Mpos, εpos], analytic.differentiableOn,
       fun z hz => by rw [Set.mem_ofPred_eq]; linarith [realPartBounded z hz],
       Rpos, by exact Metric.mem_ball.mpr (lt_of_le_of_lt (Metric.mem_closedBall.mp hyp_z) hyp_r),
       zeroAtZero]
@@ -165,7 +165,8 @@ lemma DerivativeBound {M r r' R : ℝ} {f : ℂ → ℂ} {z : ℂ}
     (z_in_r : z ∈ Metric.closedBall 0 r) :
     ‖(deriv f) z‖ ≤ 2 * M * (r') ^ 2 / ((R - r') * (r' - r) ^ 2) := by
   rw [cauchy_formula_deriv r_lt_r' r'_lt_R analytic_f.differentiableOn  z_in_r, one_div]
-  grw [circleIntegral.norm_two_pi_i_inv_smul_integral_le_of_norm_le_const (by linarith)
+  grw [circleIntegral.norm_two_pi_i_inv_smul_integral_le_of_norm_le_const (by
+    linarith only [pos_r, r_lt_r'])
     (C := 2 * M * r' / ((R - r') * (r' - r) ^ 2))]
   · exact le_of_eq (by ring)
   · intro z' hz'
@@ -180,7 +181,7 @@ lemma DerivativeBound {M r r' R : ℝ} {f : ℂ → ℂ} {z : ℂ}
       simp only [mem_sphere_iff_norm, sub_zero, Metric.mem_closedBall,
         dist_zero_right] at hz' z_in_r
       rw [← hz']
-      exact le_trans (by linarith) (norm_sub_norm_le z' z)
+      exact le_trans (by linarith only [z_in_r]) (norm_sub_norm_le z' z)
     rw [norm_pow, norm_inv, one_div, inv_pow]
     gcongr
 
@@ -205,7 +206,7 @@ theorem BorelCaratheodoryDeriv {M r R : ℝ} {f : ℂ → ℂ} {z : ℂ}
   have hr' : 2 * M * ((R + r) / 2) ^ 2 / ((R - (R + r) / 2) * ((R + r) / 2 - r) ^ 2) =
       4 * M * (R + r) ^ 2 / (R - r) ^ 3 := by
     rw [div_eq_div_iff (mul_ne_zero (by linarith) (pow_ne_zero _ (by linarith)))
-      (pow_ne_zero _ (by linarith))]
+      (pow_ne_zero _ (by linarith only [hyp_r]))]
     ring
   calc ‖deriv f z‖
     _ ≤ 4 * M * (R + r) ^ 2 / (R - r) ^ 3 := hr' ▸
@@ -213,7 +214,8 @@ theorem BorelCaratheodoryDeriv {M r R : ℝ} {f : ℂ → ℂ} {z : ℂ}
         analytic_f zeroAtZero realPartBounded hyp_z
     _ ≤ 16 * M * R ^ 2 / (R - r) ^ 3 := by
       have : 16 * M * R ^ 2 = 4 * M * (2 * R) ^ 2 := by ring_nf
-      rw [this]; bound
+      rw [this]
+      gcongr <;> linarith only [rpos, hyp_r]
 
 
 
@@ -296,14 +298,14 @@ theorem LogOfAnalyticFunction {r R : ℝ} {B : ℂ → ℂ}
       exact enorm_eq_iff_norm_eq.mp (congrArg enorm hc)
     intro z hz
     have hBz := Bnonzero z (Metric.ball_subset_closedBall hz)
-    have hB0 := Bnonzero 0 (by norm_num; linarith)
+    have hB0 := Bnonzero 0 (by norm_num; linarith only [zero_lt_r, r_lt_R])
     rw [← Real.log_div (norm_ne_zero_iff.mpr hBz) (norm_ne_zero_iff.mpr hB0),
       ← h_exp_re z hz, Real.log_exp]
   have hmem : ∀ z, z ∈ Metric.ball (0 : ℂ) r → z ∈ Metric.closedBall (0 : ℂ) R := by
     intro z hz
     apply Metric.mem_closedBall.mpr
     rw [Metric.mem_ball] at hz
-    linarith
+    linarith only [r_lt_R, hz]
   refine ⟨J_B, fun z hz => ?_, hJB.2.1, fun z hz => ?_, hJB.2.2⟩
   · exact DifferentiableOn.analyticAt
       (fun w hw ↦ (hJB.1 w hw).differentiableAt.differentiableWithinAt)
@@ -347,7 +349,7 @@ lemma finiteSetOfZeros_mono {r : ℝ} {f : ℂ → ℂ}
   unfold SetOfZeros
   refine ofPred_subset_ofPred.mpr ?_
   intro z hz
-  exact ⟨by linarith, hz.2⟩
+  exact ⟨by linarith only [r_lt_one, hz], hz.2⟩
 
 
 
@@ -405,7 +407,7 @@ lemma ZeroFactorization {R : ℝ} {f : ℂ → ℂ} {ρ : ℂ}
     exact zero_le_one
   have ρ_mem_closedBall : ρ ∈ Metric.closedBall (0 : ℂ) 1 := by
     rw[mem_closedBall_iff_norm, sub_zero]
-    linarith[hρ.1]
+    linarith only [hρ.1, RleOne, hρ]
   have orderAtZeroIsZero : analyticOrderAt f 0 = 0 := by
     rw[analyticOrderAt_eq_zero]
     exact Or.symm (Decidable.not_or_of_imp fun a a_1 ↦ hf_neq_zero_at_zero a)
@@ -481,8 +483,9 @@ lemma CfAnalytic {r R : ℝ} {f : ℂ → ℂ}
   · simp only [finite_zeros_mono, ↓reduceDIte]
     by_cases w_in_zeros : w ∈ SetOfZeros r f
     · obtain ⟨hW, hhWanalytic, hhWne_zero, hhWeq⟩ :=
-        ZeroFactorization (by linarith)
-          (hfAnalytic.mono (Metric.closedBall_subset_closedBall (by linarith))) hf_neq_zero_at_zero
+        ZeroFactorization (by linarith only [r_lt_R, R_lt_one])
+          (hfAnalytic.mono (Metric.closedBall_subset_closedBall (by
+            linarith only []))) hf_neq_zero_at_zero
           w_in_zeros
       have h_eq : ∀ᶠ z in nhds w,
           (if h : z ∈ SetOfZeros r f then ZeroFactor f z / ∏ ρ ∈ finite_zeros_mono.toFinset \ {z},
@@ -518,7 +521,8 @@ lemma CfAnalytic {r R : ℝ} {f : ℂ → ℂ}
     · apply AnalyticAt.congr _ _
       · exact fun z => f z / ∏ ρ ∈ finite_zeros_mono.toFinset, ( z - ρ ) ^ analyticOrderNatAt f ρ
       · refine AnalyticAt.div ?_ ?_ ?_
-        · exact hfAnalytic w ( Metric.mem_closedBall.mpr <| le_trans hw.out <| by linarith )
+        · exact hfAnalytic w ( Metric.mem_closedBall.mpr <| le_trans hw.out <| by
+          linarith only [R_lt_one] )
         · exact analyticAt_finset_prod_sub_pow _ _ _
         · simp only [ ne_eq, Finset.prod_eq_zero_iff, Finite.mem_toFinset, pow_eq_zero_iff',
           sub_eq_zero, ↓existsAndEq, true_and, not_and, Decidable.not_not]
@@ -605,7 +609,7 @@ lemma BlaschkeOfZero {r R : ℝ} {f : ℂ → ℂ}
   simp only [finiteSetOfZeros_mono r_lt_one finiteZeros, zero_not_zero, ↓reduceDIte, zero_sub,
     zero_mul, zero_div, sub_zero, Complex.norm_mul, Complex.norm_div, norm_prod, norm_pow, norm_neg,
     norm_real, norm_eq_abs]
-  rw[div_eq_mul_inv, mul_assoc, abs_of_pos (by linarith)]
+  rw[div_eq_mul_inv, mul_assoc, abs_of_pos (by linarith only [r_pos, r_lt_R])]
   refine (mul_right_inj' (norm_ne_zero_iff.mpr hf_neq_zero_at_zero)).mpr ?_
   rw[← Finset.prod_inv_distrib, ← Finset.prod_mul_distrib]
   simp only [div_eq_inv_mul, mul_pow, inv_pow]
@@ -638,7 +642,7 @@ lemma norm_fOfZero_le_norm_BlaschkeOfZero {r R : ℝ} {f : ℂ → ℂ}
     simp only [SetOfZeros, Finite.mem_toFinset, mem_ofPred_eq] at hρ
     apply one_le_pow₀
     rw[one_le_div]
-    · linarith
+    · linarith only [r_lt_R, hρ]
     · rw [norm_pos_iff]
       by_contra h
       rw [h] at hρ
@@ -679,7 +683,7 @@ lemma DiskBound {B r R : ℝ} {f : ℂ → ℂ} {z : ℂ}
   have hw_not_in : ¬(w ∈ SetOfZeros r f) := by
     apply notMem_ofPred_iff.mpr
     intro le_r
-    linarith
+    linarith only [r_lt_R, hw, le_r]
   have Bf_eq_f_at_w : ‖BlaschkeB r R f w‖ = ‖f w‖ := by
     unfold BlaschkeB Cf
     simp only [finiteSetOfZeros_mono r_lt_one finiteZeros, hw_not_in, ↓reduceDIte, Complex.norm_mul,
@@ -761,7 +765,7 @@ lemma BlaschkeNonzero {r R : ℝ} {f : ℂ → ℂ}
   have R_pos : 0 < R := lt_trans r_pos r_lt_R
   intro z hz
   have hz_norm_le_r : ‖z‖ ≤ r := by rwa [mem_closedBall_iff_norm, sub_zero] at hz
-  have hz_norm_lt_R : ‖z‖ < R := by linarith
+  have hz_norm_lt_R : ‖z‖ < R := by linarith only [r_lt_R, hz_norm_le_r]
   let hFin := finiteSetOfZeros_mono r_lt_one finiteZeros
   have hBProd : ∏ ρ ∈ hFin.toFinset,
       (↑R - z * (starRingEnd ℂ) ρ / ↑R) ^ analyticOrderNatAt f ρ ≠ 0 := by
@@ -771,17 +775,18 @@ lemma BlaschkeNonzero {r R : ℝ} {f : ℂ → ℂ}
     norm_num [ sub_eq_zero, Complex.ext_iff ];
     simp only [SetOfZeros, Finite.mem_toFinset, mem_ofPred_eq] at hρ
     rw [ eq_div_iff ] <;> norm_num [ Complex.normSq, Complex.norm_def ] at *;
-    · rw [Real.sqrt_lt' (by linarith)] at hz_norm_lt_R
+    · rw [Real.sqrt_lt' (by linarith only [r_pos, r_lt_R])] at hz_norm_lt_R
       rw [ Real.sqrt_le_iff ] at hρ
       refine fun h => absurd h ?_
       nlinarith [sq_nonneg ( z.re - ρ.re ), sq_nonneg ( z.im - ρ.im ),
         mul_lt_mul_of_pos_left r_lt_R R_pos]
-    · linarith
+    · linarith only [r_pos, r_lt_R]
   unfold BlaschkeB Cf
   by_cases z_in_zeros : z ∈ SetOfZeros r f
   · simp only [hFin, z_in_zeros, ↓reduceDIte]
-    obtain ⟨_, _, hne, heq⟩ := ZeroFactorization (by linarith)
-      (hfAnalytic.mono (Metric.closedBall_subset_closedBall (by linarith))) hf_neq_zero_at_zero
+    obtain ⟨_, _, hne, heq⟩ := ZeroFactorization (by linarith only [r_lt_R, R_lt_one])
+      (hfAnalytic.mono (Metric.closedBall_subset_closedBall (by
+        linarith only []))) hf_neq_zero_at_zero
       z_in_zeros
     rw [heq.1]
     refine mul_ne_zero (div_ne_zero hne (Finset.prod_ne_zero_iff.mpr fun ρ hρ =>
@@ -915,7 +920,7 @@ theorem JBlaschkeDerivBound {B r' r R : ℝ} {f : ℂ → ℂ} {z : ℂ}
     rw [← norm_one (α := ℂ), ← hf0_eq_one]
     exact norm_fOfZero_le_norm_BlaschkeOfZero r_pos r_lt_R R_lt_one finiteZeros
       (hf0_eq_one ▸ one_ne_zero)
-  suffices h : Real.log ‖BlaschkeB r R f w‖ ≤ Real.log B by linarith
+  suffices h : Real.log ‖BlaschkeB r R f w‖ ≤ Real.log B by linarith only [hlog, h]
   exact Real.log_le_log (norm_pos_iff.mpr (blaschkeNonzero w hwr))
     (DiskBound r_pos r_lt_R R_lt_one finiteZeros hfAnalytic (hf0_eq_one ▸ one_ne_zero) fz_bound
       (Metric.closedBall_subset_closedBall r_lt_R.le hwr))
@@ -1050,7 +1055,7 @@ theorem FinalBound {B r' r R' R : ℝ} {f : ℂ → ℂ} {z : ℂ}
           apply div_le_div_of_nonneg_left (sq_nonneg R)
             (norm_pos_iff.mpr (star_ne_zero.mpr (fun h => one_ne_zero (hf0_eq_one ▸ h ▸ hρ.2))))
           rw [norm_star]
-          linarith [hρ.1]
+          linarith only [hρ.1, r_lt_R', hρ]
       _ ≤ ‖↑R ^ 2 / conj ρ - z‖ := norm_sub_norm_le _ _
   suffices h3 : deriv (BlaschkeB r R f) z / BlaschkeB r R f z = deriv f z / f z
     + ∑ ρ ∈ (finiteSetOfZeros_mono r_lt_one finiteZeros).toFinset,
@@ -1203,7 +1208,7 @@ lemma ZetaFixedLowerBound (t : ℝ) :
           rw [← Complex.norm_of_nonneg zero_le_one]; exact norm_sub_le _ _
       _ = ‖1 + (p : ℂ) ^ (-(3 : ℂ) / 2)‖ := by
           have : 0 ≤ 1 + (p : ℝ) ^ (-(3 : ℝ) / 2) :=
-            by linarith [Real.rpow_nonneg (cast_nonneg' ↑p) (-3 / 2)]
+            by linarith only [Real.rpow_nonneg (cast_nonneg' ↑p) (-3 / 2)]
           simp only [Complex.norm_natCast_cpow_of_pos (Nat.Prime.pos p.2), add_re, neg_re, mul_re,
             I_re, ofReal_re, zero_mul, I_im, ofReal_im, mul_zero, sub_self, div_ofNat_re, re_ofNat,
             neg_div', add_zero]
@@ -1260,7 +1265,7 @@ lemma Zeta1AltFormula {s : ℂ} (hs : 0 < s.re) :
       neg_div_neg_eq, one_div, mul_add, ← mul_assoc, mul_right_comm, mul_inv_cancel₀ s_ne_zero]
     norm_num
   · simp only [neg_re, one_re, sub_re]
-    linarith
+    linarith only [hs]
   · refine MeasureTheory.Integrable.mono' (integrableOn_Ioi_rpow_of_lt (by linarith) (by linarith))
       ?_ ?_ (g := fun u => u ^ ( -s.re - 1 ))
     · apply Measurable.aestronglyMeasurable
@@ -1268,7 +1273,7 @@ lemma Zeta1AltFormula {s : ℂ} (hs : 0 < s.re) :
       exact (Measurable.of_discrete.comp Int.measurable_floor).sub Complex.measurable_ofReal
     · filter_upwards [MeasureTheory.ae_restrict_mem measurableSet_Ioi] with x hx
       norm_num [Complex.norm_cpow_eq_rpow_re_of_pos ( zero_lt_one.trans hx )]
-      apply mul_le_of_le_one_left (Real.rpow_nonneg (by linarith [hx.out]) _)
+      apply mul_le_of_le_one_left (Real.rpow_nonneg (by linarith only [hx.out, hx]) _)
       norm_cast; rw [← norm_neg, neg_sub, ← Int.fract, Real.norm_of_nonneg (Int.fract_nonneg _)]
       exact (Int.fract_lt_one _).le
   · refine MeasureTheory.Integrable.mono' (integrableOn_Ioi_rpow_of_lt (by linarith) (by linarith))
@@ -1312,12 +1317,12 @@ For the sake of clearer proof writing let $z=s+3/2+it$. Since $|s|\leq 1$ we kno
 theorem GlobalBound
     {s : ℂ} (hs : ‖s‖ ≤ 1) {t : ℝ} (ht : |t| ≥ 2) :
     ‖ζ (s + 3 / 2 + I * t)‖ ≤ 7 + 2 * |t| := by
-  have sReLB : -1 ≤ s.re := by linarith [abs_le.mp ((Complex.abs_re_le_norm s).trans hs)]
+  have sReLB : -1 ≤ s.re := by linarith only [abs_le.mp ((Complex.abs_re_le_norm s).trans hs), hs]
   have hz : s + 3 / 2 + I * ↑t ∈ {s | 0 < s.re ∧ s ≠ 1} := by
     simp only [ne_eq, Complex.ext_iff, one_re, one_im, not_and, mem_ofPred_eq, add_re, div_ofNat_re,
       re_ofNat, mul_re, I_re, ofReal_re, zero_mul, I_im, ofReal_im, mul_zero, sub_self, add_zero,
       add_im, div_ofNat_im, im_ofNat, zero_div, mul_im, one_mul, zero_add]
-    refine ⟨by linarith, fun hs => ?_⟩
+    refine ⟨by linarith only [sReLB], fun hs => ?_⟩
     cases abs_cases t <;>  linarith [abs_le.mp (Complex.abs_re_le_norm s),
       abs_le.mp (Complex.abs_im_le_norm s)]
   have leadingTerms : ‖1 + 1 / (s + 3 / 2 + I * ↑t - 1)‖ ≤ 2 := by
@@ -1328,21 +1333,24 @@ theorem GlobalBound
       add_re, div_ofNat_re, re_ofNat, mul_re, I_re, ofReal_re, zero_mul, I_im, ofReal_im, mul_zero,
       sub_self, add_zero, one_re, sub_im, add_im, div_ofNat_im, im_ofNat, zero_div, mul_im, one_mul,
       zero_add, one_im, sub_zero, one_le_sqrt] at ⊢ hs
-    cases abs_cases t <;> nlinarith [sq_nonneg (s.re + 1 / 2), sq_nonneg (s.im + t - 1),
-      sq_nonneg (s.im + t + 1)]
+    rcases abs_cases t with ht0 | ht0 <;>
+      nlinarith only [hs, ht, ht0, sq_nonneg (s.re + 1 / 2), sq_nonneg (s.im + t - 1),
+        sq_nonneg (s.im + t + 1)]
   have domBound {x : ℝ} (hu : x ∈ Ioi 1) : |Int.fract x| * ‖(x : ℂ) ^ (-(s + 3 / 2 + I * ↑t) - 1)‖
     ≤ x ^ (-(s.re + 3 / 2) - 1) := by
     rw [mem_Ioi] at hu
-    rw [Complex.norm_cpow_eq_rpow_re_of_pos (by linarith)]
+    rw [Complex.norm_cpow_eq_rpow_re_of_pos (by linarith only [hu])]
     simp only [neg_add_rev, sub_re, add_re, neg_re, mul_re, I_re, ofReal_re, zero_mul, I_im, one_re,
       ofReal_im, mul_zero, sub_self, neg_zero, div_ofNat_re, re_ofNat, zero_add, Int.abs_fract]
-    refine mul_le_of_le_one_left (by apply Real.rpow_nonneg (by linarith)) ((Int.fract_lt_one x).le)
+    refine mul_le_of_le_one_left (by apply Real.rpow_nonneg (by
+      linarith only [hu])) ((Int.fract_lt_one x).le)
   have domIntegral : Integrable (fun x : ℝ => x ^ (-(s.re + 3 / 2) - 1))
-    (volume.restrict (Set.Ioi 1)) := integrableOn_Ioi_rpow_of_lt (by linarith) zero_lt_one
+    (volume.restrict (Set.Ioi 1)) := integrableOn_Ioi_rpow_of_lt (by
+      linarith only [sReLB]) zero_lt_one
   have hint : ‖∫ (u : ℝ) in Ioi 1, (↑(Int.fract u) : ℂ) * (u : ℂ) ^ (-(s + 3 / 2 + I * ↑t) - 1)‖
     ≤ 1 / (s.re + 3 / 2) := by
     refine (MeasureTheory.norm_integral_le_integral_norm _).trans ?_
-    have hI := integral_Ioi_rpow_of_lt (a := -(s.re + 3 / 2) - 1) (by linarith) one_pos
+    have hI := integral_Ioi_rpow_of_lt (a := -(s.re + 3 / 2) - 1) (by linarith only [sReLB]) one_pos
     simp only [sub_add_cancel, one_rpow, neg_div_neg_eq] at hI
     simp only [Complex.norm_mul, norm_real, norm_eq_abs, ← hI]
     refine integral_mono_ae (domIntegral.mono' (((measurable_fract.abs).mul
@@ -1358,16 +1366,16 @@ theorem GlobalBound
       by rw [norm_div, Complex.norm_ofNat, Complex.norm_ofNat]
     apply le_trans
       (norm_add_le_of_le (norm_add_le_of_le hs (le_of_eq threeHalves_norm)) (le_of_eq It_norm))
-    linarith
+    linarith only []
   have hmul : ‖(s + 3 / 2 + I * ↑t) * ∫ (u : ℝ) in Ioi 1,
     (↑(Int.fract u) : ℂ) * (u : ℂ) ^ (-(s + 3 / 2 + I * ↑t) - 1)‖ ≤ 5 + 2 * |t| := by
     rw [norm_mul]
     have hinv : (1 : ℝ) / (s.re + 3 / 2) ≤ 2 := by rw [div_le_iff₀ (by linarith)]; linarith
     apply le_trans
-      (mul_le_mul z_norm (hint.trans hinv) (norm_nonneg _) (by linarith [abs_nonneg t]))
-    linarith
+      (mul_le_mul z_norm (hint.trans hinv) (norm_nonneg _) (by linarith only [abs_nonneg t, ht]))
+    linarith only []
   rw [ZetaAltFormula hz.1 hz.2]
-  exact (norm_sub_le_of_le leadingTerms hmul).trans (by linarith)
+  exact (norm_sub_le_of_le leadingTerms hmul).trans (by linarith only [])
 
 
 
@@ -1383,7 +1391,7 @@ lemma norm_zeta_strict_mono_ofReal {a b : ℝ} (hb : 1 < b) (hab : b < a) :
     simp only [rpow_eq_pow]
     rw [zeta_eq_tsum_one_div_nat_add_one_cpow (by norm_num [hc])]
     push_cast; congr; funext n
-    rw [Complex.ofReal_cpow (by linarith)]
+    rw [Complex.ofReal_cpow (by linarith only [])]
     push_cast; rfl
   have hsum {c : ℝ} (hc : 1 < c) : Summable (fun n : ℕ => ((n + 2 : ℝ) ^ c)⁻¹) := by
     exact_mod_cast (summable_nat_add_iff 2).2 (Real.summable_nat_rpow_inv.2 hc)
@@ -1396,7 +1404,7 @@ lemma norm_zeta_strict_mono_ofReal {a b : ℝ} (hb : 1 < b) (hab : b < a) :
         add_lt_add_iff_left, add_assoc, one_add_one_eq_two]
       have h : ∀ n : ℕ, ((n + 2 : ℝ) ^ a)⁻¹ < ((n + 2 : ℝ) ^ b)⁻¹ := fun _ =>
         inv_strictAnti₀ (Real.rpow_pos_of_pos (by positivity) b)
-          (Real.rpow_lt_rpow_of_exponent_lt (by linarith) hab)
+          (Real.rpow_lt_rpow_of_exponent_lt (by linarith only []) hab)
       exact Summable.tsum_strict_mono (hsum (hb.trans hab)) (hsum hb)
         (Pi.lt_def.mpr ⟨fun n => (h n).le, 0, h 0⟩)
     · push_cast; simpa [add_assoc, one_add_one_eq_two] using hsum hb
@@ -1454,15 +1462,16 @@ theorem LogDerivZetaFinalBound {r' r R' R : ℝ} (r'_pos : 0 < r') (r'_lt_r : r'
     simpa only [ofReal_div, ofReal_ofNat] using one_lt_zeta_div
   set C : ℝ := 1 + Real.log (11 * (‖ζ (3 / 2)‖₊ / ‖ζ 3‖₊)) / Real.log 2 with C_def
   refine ⟨C, ?_, ?_⟩
-  · rw [C_def, Real.log_mul (Ne.symm (OfNat.zero_ne_ofNat 11)) (by linarith)]
+  · rw [C_def, Real.log_mul (Ne.symm (OfNat.zero_ne_ofNat 11)) (by linarith only [hzd])]
     exact add_pos zero_lt_one
       (div_pos (add_pos (Real.log_pos one_lt_ofNat) (Real.log_pos hzd)) (Real.log_pos one_lt_two))
   · intro t ht f finiteZeros z hz
     set g : ℂ → ℂ := f / (fun z ↦ f 0) with g_def
     have g_def' : g = fun z ↦ f z / f 0 := rfl
     set B : ℝ := (7 + 2 * |t|) * (‖ζ (3 / 2)‖₊ / ‖ζ 3‖₊) with B_def
-    have one_lt_B : 1 < B := one_lt_mul (by linarith) hzd
-    have one_le_C : (1 : ℝ) ≤ 11 * (‖ζ (3 / 2)‖₊ / ‖ζ 3‖₊) := (one_lt_mul (by linarith) hzd).le
+    have one_lt_B : 1 < B := one_lt_mul (by linarith only [ht]) hzd
+    have one_le_C : (1 : ℝ) ≤ 11 * (‖ζ (3 / 2)‖₊ / ‖ζ 3‖₊) := (one_lt_mul (by
+      linarith only []) hzd).le
     have f0nonzero : ¬f 0 = 0 := by
       simp only [f, zero_add]
       exact riemannZeta_ne_zero_of_one_lt_re (by norm_num)
@@ -1470,11 +1479,11 @@ theorem LogDerivZetaFinalBound {r' r R' R : ℝ} (r'_pos : 0 < r') (r'_lt_r : r'
       rw [← sq_le_one_iff₀ (norm_nonneg _), ← Complex.normSq_eq_norm_sq,
         Complex.normSq_apply] at hnorm
       intro hre him
-      have hre' : z.re = -(1/2 : ℝ) := by linarith
-      have him' : z.im = -t := by linarith
+      have hre' : z.re = -(1/2 : ℝ) := by linarith only [hre]
+      have him' : z.im = -t := by linarith only [him]
       simp only [hre', him', neg_mul_neg] at hnorm
       rw [← abs_two, ge_iff_le, ← sq_le_sq] at ht
-      nlinarith [hnorm, ht]
+      nlinarith only [hnorm, ht]
     have gAnalytic : AnalyticOnNhd ℂ g (Metric.closedBall (0 : ℂ) 1) := by
       simp only [g_def, f, zero_add]
       intro z hz; rw [Metric.mem_closedBall, _root_.dist_zero_right] at hz
@@ -1496,7 +1505,7 @@ theorem LogDerivZetaFinalBound {r' r R' R : ℝ} (r'_pos : 0 < r') (r'_lt_r : r'
       simp only [B_def, g_def, f, zero_add, Pi.div_apply, Complex.norm_div]
       rw [div_eq_mul_one_div]
       refine mul_le_mul (GlobalBound (le_trans hz' R_lt_one.le) ht) ?_
-        (one_div_nonneg.mpr (norm_nonneg _)) (by linarith)
+        (one_div_nonneg.mpr (norm_nonneg _)) (by linarith only [ht])
       rw [one_div_le (norm_pos_iff.mpr (riemannZeta_ne_zero_of_one_lt_re (by norm_num))), one_div,
         inv_div, ← toReal_coe_nnnorm, ENNReal.coe_toReal, ← NNReal.coe_div, ← nnnorm_div]
       · exact_mod_cast ZetaFixedLowerBound t
@@ -1537,8 +1546,10 @@ theorem LogDerivZetaFinalBound {r' r R' R : ℝ} (r'_pos : 0 < r') (r'_lt_r : r'
           (add_nonneg (div_nonneg (mul_nonneg (ofNat_nonneg' _) (sq_nonneg _))
               (pow_nonneg (sub_nonneg.mpr r'_lt_r.le) _))
             (div_nonneg zero_le_one (mul_nonneg (sub_nonneg.mpr ?_)
-                (Real.log_nonneg ((one_le_div (by linarith)).mpr R'_lt_R.le)))))
-        rw [le_div_iff₀ (by linarith)]; nlinarith
+                (Real.log_nonneg ((one_le_div (by
+                  linarith only [r'_pos, r'_lt_r, r_lt_R'])).mpr R'_lt_R.le)))))
+        rw [le_div_iff₀ (by linarith only [r'_pos, r'_lt_r, r_lt_R'])]
+        nlinarith only [r'_pos, r'_lt_r, r_lt_R', R'_lt_R]
     rw [add_mul, one_mul, div_mul_eq_mul_div, mul_div_assoc]
     suffices h2 : Real.log B ≤ Real.log |t| + Real.log (11 * (↑‖ζ (3 / 2)‖₊ / ↑‖ζ 3‖₊)) by
       exact le_trans h2 ((add_le_add_iff_left _).mpr (le_mul_of_one_le_right
@@ -1547,7 +1558,8 @@ theorem LogDerivZetaFinalBound {r' r R' R : ℝ} (r'_pos : 0 < r') (r'_lt_r : r'
     rw [← Real.log_mul (by linarith) (by linarith),
       log_le_log_iff (by linarith) (mul_pos (by linarith) (by linarith))]
     simp only [← mul_assoc, B_def, coe_nnnorm]
-    exact mul_le_mul_of_nonneg_right (by linarith) (div_nonneg (norm_nonneg _) (norm_nonneg _))
+    exact mul_le_mul_of_nonneg_right (by
+      linarith only [ht]) (div_nonneg (norm_nonneg _) (norm_nonneg _))
 
 
 
@@ -1572,21 +1584,21 @@ lemma ZetaShiftFiniteZeros {t : ℝ} (ht : |t| ≥ 2)
     have him : z.im = -t := by
       have := congr_arg Complex.im h; simp only [add_im, div_ofNat_im, im_ofNat, zero_div, mul_im,
         I_re, ofReal_im, mul_zero, I_im, ofReal_re, one_mul, zero_add, one_im] at this
-      linarith
+      linarith only [this]
     have abs_z_im := Complex.abs_im_le_norm z
     rw [him, abs_neg] at abs_z_im
-    linarith
+    linarith only [ht, hz, abs_z_im]
   have hfeq : Set.EqOn f 0 (Metric.ball (0 : ℂ) 2) := by
     refine AnalyticOnNhd.eqOn_zero_of_preconnected_of_mem_closure hfAnalytic
       Metric.isPreconnected_ball (z₀ := x) ?_ ?_
     · simp only [Metric.mem_ball, Metric.mem_closedBall, dist_zero_right] at hxK ⊢
-      linarith
+      linarith only [hxK]
     · simp only [mem_closure_iff_clusterPt, ← accPt_principal_iff_clusterPt]
       exact hacc.mono (principal_mono.mpr fun _ h => h.2)
   have hne : f 0 ≠ 0 := by
     simp only [hf, zero_add, ne_eq]
     exact riemannZeta_ne_zero_of_one_lt_re (by norm_num)
-  exact hne (hfeq (Metric.mem_ball_self (by linarith)))
+  exact hne (hfeq (Metric.mem_ball_self (by linarith only [])))
 
 
 
@@ -1677,10 +1689,11 @@ lemma SumBoundI :
   have hz' : z ∈ Metric.closedBall (0 : ℂ) r' \ SetOfZeros R' f := by
     simp only [SetOfZeros, f, Set.mem_sdiff, Metric.mem_closedBall, dist_zero_right, mem_ofPred_eq,
       not_and]
-    refine ⟨le_of_lt (lt_trans hd' (by linarith)), fun _ => riemannZeta_ne_zero_of_one_lt_re ?_⟩
+    refine ⟨le_of_lt (lt_trans hd' (by
+      linarith only [])), fun _ => riemannZeta_ne_zero_of_one_lt_re ?_⟩
     simp only [add_re, div_ofNat_re, re_ofNat, mul_re, I_re, ofReal_re, zero_mul, I_im, ofReal_im,
       mul_zero, sub_self, add_zero]
-    linarith [abs_lt.mp (lt_of_le_of_lt (Complex.abs_re_le_norm z) hd')]
+    linarith only [abs_lt.mp (lt_of_le_of_lt (Complex.abs_re_le_norm z) hd'), hd']
   have LogDerivBound := LogDerivBound finiteZeros' z hz'
   refine le_trans (le_of_eq ?_) (LogDerivBound.trans (by rw [mul_assoc]))
   apply congrArg norm
@@ -1752,12 +1765,12 @@ lemma ShiftTwoBound :
   intro δ hd t ht finiteZeros
   suffices h1 : -(ζ' (1 + δ + 2 * I * t) / ζ (1 + δ + 2 * I * t)).re ≤ C * log |2 * t| by
     refine le_trans h1 ?_
-    rw [mul_assoc C, abs_mul, Real.log_mul (by norm_num) (by linarith [ht]), two_mul]
+    rw [mul_assoc C, abs_mul, Real.log_mul (by norm_num) (by linarith only [ht]), two_mul]
     exact mul_le_mul (by rfl) (add_le_add (log_le_log (by norm_num) (by norm_num [ht])) (by rfl))
-      (add_nonneg (Real.log_nonneg (by norm_num)) (Real.log_nonneg (by linarith [ht]))) hC.le
+      (add_nonneg (Real.log_nonneg (by norm_num)) (Real.log_nonneg (by linarith only [ht]))) hC.le
   have ht' : |2 * t| ≥ 2 := by
     simp only [abs_mul, abs_ofNat, ofNat_pos, le_mul_iff_one_le_right]
-    linarith
+    linarith only [ht]
   have SumBound := SumBound δ hd _ ht' finiteZeros; rw [← Complex.norm_neg', neg_sub] at SumBound
   refine le_trans ?_ (le_trans (Complex.re_le_norm _) SumBound)
   simp only [ofReal_mul, ofReal_ofNat, sub_re, re_sum, ← mul_assoc, mul_comm]
@@ -1771,7 +1784,7 @@ lemma ShiftTwoBound :
     ofReal_im, mul_zero, sub_self, re_ofNat, mul_im, ← sq, ne_eq, OfNat.ofNat_ne_zero,
     not_false_eq_true, zero_pow, one_mul, zero_add, im_ofNat, add_zero, normSq_apply, sub_im,
     add_im, one_im, natCast_im, zero_div]
-  exact div_nonneg (mul_nonneg (cast_nonneg' _) (by linarith [hd.1]))
+  exact div_nonneg (mul_nonneg (cast_nonneg' _) (by linarith only [hd.1, hρ_re, hd]))
     (add_nonneg (sq_nonneg _) (sq_nonneg _))
 
 
@@ -1839,7 +1852,7 @@ lemma ShiftOneBound :
               t = ρ.im →
     -(ζ' (1 + δ + I * t) / ζ (1 + δ + I * t)).re ≤ C * Real.log |t| - 1 / (1 + δ - ρ.re) := by
   obtain ⟨C, hC, SumBound⟩ := SumBoundI
-  refine ⟨7 + C, by linarith, ?_⟩
+  refine ⟨7 + C, by linarith only [hC], ?_⟩
   intro δ hd t ht finiteZeros ρ hρzero hρim
   have SumBound := SumBound δ hd t ht finiteZeros; rw [← Complex.norm_neg', neg_sub] at SumBound
   have SumBound := le_trans (Complex.re_le_norm _) SumBound
@@ -1858,9 +1871,9 @@ lemma ShiftOneBound :
     refine div_nonneg (mul_nonneg (by positivity) ?_) (normSq_nonneg _)
     by_contra h; push Not at h
     simp only [ZeroWindow, Finite.mem_toFinset, mem_ofPred_eq] at hρ'
-    exact riemannZeta_ne_zero_of_one_le_re (by linarith [hd.1]) hρ'.1
+    exact riemannZeta_ne_zero_of_one_le_re (by linarith only [hd.1, h, hd]) hρ'.1
   by_cases hρZt : ρ ∈ finiteZeros.toFinset
-  · have obvious : C * log |t| ≤ (7 + C) * log |t| := mul_le_mul (by linarith) (by rfl)
+  · have obvious : C * log |t| ≤ (7 + C) * log |t| := mul_le_mul (by linarith only []) (by rfl)
       (Real.log_nonneg (by linarith)) (by linarith)
     have SumBound := le_trans SumBound obvious
     rw [← Finset.insert_erase hρZt, ← Finset.singleton_union, ← Finset.sdiff_singleton_eq_erase,
@@ -1873,7 +1886,7 @@ lemma ShiftOneBound :
       ← one_div] at SumBound
     refine le_sub_left_of_add_le (le_trans (add_le_add ?_ ?_) SumBound)
     · rw [← mul_div_assoc, mul_one]
-      refine div_le_div_of_nonneg_right ?_ (by linarith [hd.1])
+      refine div_le_div_of_nonneg_right ?_ (by linarith only [hd.1, hρre, hd])
       simp only [one_le_cast, Nat.one_le_iff_ne_zero, analyticOrderNatAt, ne_eq, ENat.toNat_eq_zero,
         analyticOrderAt_eq_zero, analyticOrderAt_eq_top, not_or, not_not]
       refine ⟨⟨DifferentiableOn.analyticAt (s := {z : ℂ | z ≠ 1})
@@ -1896,7 +1909,7 @@ lemma ShiftOneBound :
       exact Finset.sum_nonneg (fun ρ' hρ' => hTermNonneg hρ')
     have invBound : 1 / (1 + δ - ρ.re) ≤ 7 * Real.log |t| := by
       suffices h1 : 1 / (1 + δ - ρ.re) ≤ 4 by
-        have explicitEstimate : 4 ≤ 7 * Real.log 2 := by linarith [Real.log_two_gt_d9]
+        have explicitEstimate : 4 ≤ 7 * Real.log 2 := by linarith only [Real.log_two_gt_d9]
         exact le_trans h1 (le_trans explicitEstimate ((mul_le_mul_iff_of_pos_left ofNat_pos').mpr
           (Real.log_le_log ofNat_pos' ht)))
       simp only [ZeroWindow, Finite.mem_toFinset, mem_ofPred_eq, hρzero, true_and, not_le] at hρZt
@@ -1906,9 +1919,9 @@ lemma ShiftOneBound :
         simp only [ofReal_sub, ofReal_div, ofReal_ofNat, neg_add_eq_sub, neg_div, neg_add_eq_sub]
       rw [this, Complex.norm_real, Real.norm_eq_abs] at hρZt
       have hρreImproved : ρ.re < 3 / 4 := by rcases lt_abs.mp hρZt with _ | _ <;> linarith
-      rw [one_div_le (by linarith [hd.1]) four_pos]
-      linarith [hd.1]
-    linarith
+      rw [one_div_le (by linarith only [hd.1, hρre, hd]) four_pos]
+      linarith only [hd.1, hρreImproved, hd]
+    linarith only [logBound, invBound]
 
 
 
@@ -1942,7 +1955,7 @@ lemma ShiftZeroBound :
         simp only [mem_inter_iff, Metric.mem_ball, dist_self_add_left, norm_real, norm_eq_abs,
           mem_compl_iff, mem_singleton_iff, add_eq_left, ofReal_eq_zero, abs_lt]
         exact ⟨⟨by linarith [δrange.1], by linarith [δrange.2, min_le_left ε (1 / 2)]⟩,
-          by linarith [δrange.1]⟩
+          by linarith only [δrange.1, δrange]⟩
       have reBound := (Complex.re_le_norm _).trans (hε δin)
       simp only [Pi.sub_apply, Pi.div_apply, Pi.neg_apply, add_sub_cancel_left, sub_re, inv_re,
         ofReal_re, normSq_ofReal, div_self_mul_self', Pi.one_apply, norm_one, mul_one,
@@ -1964,14 +1977,14 @@ lemma ShiftZeroBound :
         (ContinuousOn.div continuousOn_const continuousOn_id ?_))
     · simp only [MapsTo, mem_Icc, mem_compl_iff, mem_singleton_iff, add_eq_left,
         ofReal_eq_zero, and_imp]
-      exact fun x hx _ => by linarith [rIn.1, hx]
+      exact fun x hx _ => by linarith only [rIn.1, hx, rIn]
     · simp only [MapsTo, mem_Icc, mem_compl_iff, mem_singleton_iff, add_eq_left,
         ofReal_eq_zero, and_imp]
-      exact fun x hx _ => by linarith [rIn.1, hx]
+      exact fun x hx _ => by linarith only [rIn.1, hx, rIn]
     · simp only [add_re, one_re, ofReal_re, lt_add_iff_pos_right]
-      linarith [rIn.1, hx.1]
+      linarith only [rIn.1, hx.1, rIn, hx]
     · simp only [ne_eq]
-      exact fun x hx => by linarith [rIn.1, hx.1]
+      exact fun x hx => by linarith only [rIn.1, hx.1, rIn, hx]
   obtain ⟨C₁, boundCompact⟩ := ShiftZeroBoundCompact
   refine ⟨1 + max |C₀| |C₁|, ?_, fun δ δrange => ?_⟩
   · simp only [ge_iff_le, le_add_iff_nonneg_right, le_sup_iff, abs_nonneg, or_self]
@@ -1979,12 +1992,12 @@ lemma ShiftZeroBound :
     · have δIn : δ ∈ Ioo 0 r := by simp only [mem_Ioo, δrange.1, δ_lt_r, and_self]
       apply le_trans (boundNear δ δIn)
       simp only [one_div, add_le_add_iff_left]
-      linarith [le_abs_self C₀, le_max_left |C₀| |C₁|]
+      linarith only [le_abs_self C₀, le_max_left |C₀| |C₁|]
     · have δIn : δ ∈ Icc r 1 := by
         simp only [mem_Icc, δrange.2.le, ← not_lt, δ_lt_r, not_false_eq_true, and_self]
       apply le_trans (boundCompact δ δIn)
       simp only [one_div, add_le_add_iff_left]
-      linarith [le_abs_self C₁, le_max_right |C₀| |C₁|]
+      linarith only [le_abs_self C₁, le_max_right |C₀| |C₁|]
 
 
 
@@ -2028,22 +2041,22 @@ lemma ZeroWindowFinite {t : ℝ} (ht : |t| ≥ 2) : (ZeroWindow t).Finite := by
       simp only [gt_iff_lt, lt_abs]
       by_cases tpos : 0 < t
       · rw [abs_of_pos tpos] at ht
-        exact Or.inl (by linarith)
+        exact Or.inl (by linarith only [ht, this])
       · rw [abs_of_nonpos (not_lt.mp tpos)] at ht
-        exact Or.inr (by linarith)
+        exact Or.inr (by linarith only [ht, this])
     refine analyticAt_riemannZeta (fun h => ?_)
     simp only [h, one_im, gt_iff_lt, abs_zero] at him
-    linarith
+    linarith only [him]
   have hfeq : Set.EqOn ζ 0 (Metric.ball (3 / 2 + I * t) 1) := by
     refine AnalyticOnNhd.eqOn_zero_of_preconnected_of_mem_closure hfAnalytic
       Metric.isPreconnected_ball (z₀ := x) ?_ ?_
     · simp only [Metric.mem_ball, Metric.mem_closedBall] at hxK ⊢
-      linarith
+      linarith only [hxK]
     · simp only [mem_closure_iff_clusterPt, ← accPt_principal_iff_clusterPt]
       refine hacc.mono (principal_mono.mpr fun _ h => h.1)
   have hne : ζ (3 / 2 + I * t) ≠ 0 := by
     exact riemannZeta_ne_zero_of_one_lt_re (by norm_num)
-  exact hne (hfeq (Metric.mem_ball_self (by linarith)))
+  exact hne (hfeq (Metric.mem_ball_self (by linarith only [])))
 
 
 
@@ -2093,18 +2106,20 @@ theorem ZeroInequality : ∃ (E : ℝ), E ∈ Ioo (0 : ℝ) (1 / 14 : ℝ) ∧
   obtain ⟨C, Cpos, ShiftTwo⟩ := ShiftTwoBound
   set D : ℝ := 5 * A + 4 * B + C with D_def
   set E : ℝ := (14 * D)⁻¹ with E_def
-  have Dge1 : 1 ≤ D := by linarith
+  have Dge1 : 1 ≤ D := by linarith only [Age, Bpos, Cpos]
   refine ⟨E, ⟨?_, ?_⟩, fun ρ hρzero σ ρre t ρim ht => ?_⟩
   · rw [E_def, mul_inv_rev, mul_pos_iff_of_pos_right (inv_pos.mpr ofNat_pos'), inv_pos]
-    linarith
+    linarith only [Age, Bpos, Cpos]
   · rw [E_def, one_div, inv_lt_inv₀ (by linarith) (by linarith)]
-    linarith
+    linarith only [Age, Bpos, Cpos]
   · set δ : ℝ := 1 / (2 * D * Real.log |t|) with δ_def
     have δrange : δ ∈ Ioo 0 1 := by
       simp only [mem_Ioo, δ_def, one_div_pos]
-      rw [div_lt_one (by nlinarith [Real.log_le_log zero_lt_two ht, Real.log_two_gt_d9])]
-      exact ⟨by nlinarith [Real.log_le_log zero_lt_two ht, Real.log_two_gt_d9],
-        by nlinarith [Real.log_le_log zero_lt_two ht, Real.log_two_gt_d9]⟩
+      rw [div_lt_one (by
+        nlinarith only [Dge1, Real.log_le_log zero_lt_two ht, Real.log_two_gt_d9])]
+      exact ⟨by
+        nlinarith only [Dge1, Real.log_le_log zero_lt_two ht, Real.log_two_gt_d9], by
+        nlinarith only [Dge1, Real.log_le_log zero_lt_two ht, Real.log_two_gt_d9]⟩
     have hugeEq :
         3 * (-ζ' (1 + δ) / ζ (1 + δ)) +
         4 * (-ζ' (1 + δ + I * t) / ζ (1 + δ + I * t)) +
@@ -2191,7 +2206,7 @@ theorem ZeroInequality : ∃ (E : ℝ), E ∈ Ioo (0 : ℝ) (1 / 14 : ℝ) ∧
     have ZeroWindowTwoFinite : (ZeroWindow (2 * t)).Finite := by
       apply ZeroWindowFinite
       simp only [abs_mul, abs_ofNat, ge_iff_le, ofNat_pos, le_mul_iff_one_le_right]
-      linarith
+      linarith only [ht]
     have ShiftZero := ShiftZero δ δrange
     have ShiftOne := ShiftOne δ δrange t ht ZeroWindowOneFinite ρ hρzero ρim
     have ShiftTwo := ShiftTwo δ δrange t ht ZeroWindowTwoFinite
@@ -2203,17 +2218,17 @@ theorem ZeroInequality : ∃ (E : ℝ), E ∈ Ioo (0 : ℝ) (1 / 14 : ℝ) ∧
           (Real.log_ne_zero_of_pos_of_ne_one (by linarith) (by linarith))] at h1
         rw [E_def, ← inv_mul', le_sub_comm,
           inv_le_iff_one_le_mul₀' (mul_pos (by linarith) (Real.log_pos (by linarith)))]
-        linarith
+        linarith only [h1]
       · rw [add_sub_right_comm]
         apply add_pos_of_nonneg_of_pos
         · by_contra hσ; simp only [sub_nonneg, not_le, ρre] at hσ
           exact (riemannZeta_ne_zero_of_one_lt_re hσ) hρzero
-        · exact mul_pos (inv_pos.mpr (Real.log_pos (by linarith))) (by positivity)
+        · exact mul_pos (inv_pos.mpr (Real.log_pos (by linarith only [ht]))) (by positivity)
     suffices h2 :  0 ≤ 3 / δ + 3 * A - 4 / (1 + δ - σ) + 4 * B * Real.log |t| + C * Real.log |t| by
       simp only [sub_eq_neg_add, add_assoc, le_neg_add_iff_add_le, add_zero, ge_iff_le] at ⊢ h2
       apply le_trans h2
       simp only [← add_assoc, D_def, add_mul, add_le_add_iff_right, add_le_add_iff_left]
-      nlinarith [Real.log_le_log zero_lt_two ht, Real.log_two_gt_d9]
+      nlinarith only [Age, Real.log_le_log zero_lt_two ht, Real.log_two_gt_d9]
     calc 0 ≤ 2 * ∑' (n : ℕ), Λ (n) * n ^ (-1 - δ) * (1 + Real.cos (-t * Real.log n)) ^ 2 := by
           rw [mul_nonneg_iff_of_pos_left two_pos]
           exact tsum_nonneg (fun n => mul_nonneg (mul_nonneg ArithmeticFunction.vonMangoldt_nonneg
@@ -2262,7 +2277,7 @@ lemma DeltaRange : ∀ (t : ℝ),
     |t| ≥ 2 →
       DeltaT t < (1 : ℝ) / 9 := by
   intro t ht
-  rw [DeltaT, div_lt_div_iff₀ (Real.log_pos (by linarith)) (ofNat_pos'), one_mul]
+  rw [DeltaT, div_lt_div_iff₀ (Real.log_pos (by linarith only [ht])) (ofNat_pos'), one_mul]
   exact lt_of_lt_of_le (by linarith [EinIoo.2, Real.log_two_gt_d9]) (Real.log_le_log zero_lt_two ht)
 
 
@@ -2336,7 +2351,8 @@ lemma SumBoundII :
       suffices h1 : 1 - E / Real.log |t| < 1 - DeltaT t / 3 by
         linarith [hzRe.1, ZeroInequalitySpec z zZetaZero z.re rfl t hzIm ht]
       simp only [DeltaT, sub_lt_sub_iff_left]
-      exact _root_.div_lt_self (_root_.div_pos EinIoo.1 (Real.log_pos (by linarith))) one_lt_ofNat
+      exact _root_.div_lt_self (_root_.div_pos EinIoo.1 (Real.log_pos (by
+        linarith only [ht]))) one_lt_ofNat
   have LogDerivBound := LogDerivBound finiteZeros' Z hZ'
   refine le_trans (le_of_eq ?_) (LogDerivBound.trans (by rw [mul_assoc]))
   apply congrArg norm
@@ -2393,18 +2409,19 @@ lemma GapSize (t : ℝ) (ht : |t| ≥ 3)
     exact h.trans hρ.2
   have ρImAbsUpperBound : Real.log |ρ.im| ≤ 2 * Real.log |t| := by
     have moveTwo : Real.log (2 * |t|) ≤ 2 * Real.log |t| := by
-      rw [← Real.log_rpow (by linarith)]
+      rw [← Real.log_rpow (by linarith only [ht])]
       have := mul_le_mul_of_nonneg_right ht (abs_nonneg t); rw [← sq, ← Real.rpow_two] at this
       exact Real.log_le_log (by linarith) (by linarith)
-    refine le_trans (Real.log_le_log (by linarith) ?_) moveTwo
-    linarith [abs_sub_abs_le_abs_sub ρ.im t]
+    refine le_trans (Real.log_le_log (by linarith only [ht, this, ρImDiffBound]) ?_) moveTwo
+    linarith only [abs_sub_abs_le_abs_sub ρ.im t, ht, ρImDiffBound]
   have deltaRelation : DeltaT t ≤ 2 * (DeltaT ρ.im) := by
     simp only [DeltaT, mul_div, mul_comm]
     rw [div_le_div_iff₀ (Real.log_pos (by linarith)) (Real.log_pos (by linarith)), mul_assoc]
-    nlinarith [EinIoo.1, EinIoo.2]
-  have hρRe := ZeroInequalitySpec ρ hρ.1 ρ.re rfl ρ.im rfl (by linarith); rw [← DeltaT] at hρRe
-  calc DeltaT t / 6 ≤ (1 - DeltaT t / 3) - (1 - DeltaT ρ.im) := by linarith
-    _ ≤ z.re - ρ.re := by linarith [hzRe.1, hρRe]
+    nlinarith only [EinIoo.1, EinIoo.2, ρImAbsUpperBound]
+  have hρRe := ZeroInequalitySpec ρ hρ.1 ρ.re rfl ρ.im rfl (by
+    linarith only [ht, this, ρImDiffBound]); rw [← DeltaT] at hρRe
+  calc DeltaT t / 6 ≤ (1 - DeltaT t / 3) - (1 - DeltaT ρ.im) := by linarith only [deltaRelation]
+    _ ≤ z.re - ρ.re := by linarith only [hzRe.1, hρRe, hzRe]
     _ = (z - ρ).re := by rw [Complex.sub_re]
     _ ≤ ‖z - ρ‖ := Complex.re_le_norm _
 
@@ -2461,10 +2478,10 @@ lemma LogDerivZetaUniformLogSquaredBoundStrip : ∃ (F : ℝ) (_ : F = E / 3)
   have d_gt_one : 1 < d := by
     simp only [hd, Complex.norm_div, Complex.norm_mul, Complex.norm_ofNat]
     rw [one_lt_div]
-    · refine mul_lt_mul (by linarith) ?_ ?_ (ofNat_nonneg' _)
+    · refine mul_lt_mul (by linarith only []) ?_ ?_ (ofNat_nonneg' _)
       · have ζNormLe := norm_zeta_strict_mono_ofReal (a := 3) (b := (3 / 2))
         simp only [half_lt_self_iff, ofNat_pos, ofReal_ofNat, ofReal_div, forall_const] at ζNormLe
-        refine le_of_lt (ζNormLe (by linarith))
+        refine le_of_lt (ζNormLe (by linarith only []))
       · simp only [norm_pos_iff, ne_eq]
         exact riemannZeta_ne_zero_of_one_lt_re (by norm_num)
     · simp only [ofNat_pos, mul_pos_iff_of_pos_left, norm_pos_iff, ne_eq]
@@ -2478,7 +2495,7 @@ lemma LogDerivZetaUniformLogSquaredBoundStrip : ∃ (F : ℝ) (_ : F = E / 3)
     · rw [one_div_pos]
       exact Real.log_pos (by norm_num)
     · rw [one_lt_div ofNat_pos']
-      linarith
+      linarith only []
   refine ⟨E / 3, rfl, ⟨6 * D / E + C,
     add_pos (mul_pos (mul_pos ofNat_pos' Dpos) (inv_pos.mpr EinIoo.1)) Cpos, ?_⟩⟩
   intro t ht σ hσ
@@ -2505,17 +2522,18 @@ lemma LogDerivZetaUniformLogSquaredBoundStrip : ∃ (F : ℝ) (_ : F = E / 3)
       I_re, ofReal_im, mul_zero, I_im, ofReal_re, one_mul, zero_add, one_im] at hIm
     rw [add_eq_zero_iff_eq_neg] at hIm
     have h := Complex.abs_im_le_norm z; rw [hIm, abs_neg] at h
-    linarith
+    linarith only [ht, hz, h]
   have zetaThreeHalfNonzero : ¬ζ (3 / 2 + I * ↑t) = 0 := by
     exact riemannZeta_ne_zero_of_one_lt_re (by norm_num)
   have f0_1 : f 0 = 1 := by
     simp only [hg, hf, zero_add, div_self_eq_one₀, ne_eq, zetaThreeHalfNonzero, not_false_eq_true]
   have finiteSetOf0s : (SetOfZeros 1 f).Finite := by
-    have gFiniteSetOf0s := ZetaShiftFiniteZeros (t := t) (by linarith) hg
+    have gFiniteSetOf0s := ZetaShiftFiniteZeros (t := t) (by
+      linarith only [ht, r_pos, r_lt_R, R_lt_one]) hg
     simp only [SetOfZeros, hf, div_eq_zero_iff, zetaThreeHalfNonzero, or_false] at gFiniteSetOf0s ⊢
     exact gFiniteSetOf0s
   have rFinite0s:= finiteSetOfZeros_mono r_lt_one finiteSetOf0s
-  have finite0s := ZeroWindowFinite (t := t) (by linarith)
+  have finite0s := ZeroWindowFinite (t := t) (by linarith only [ht, r_pos, r_lt_R, R_lt_one])
   have fz_bound : ∀ z : ℂ, ‖z‖ ≤ R → ‖f z‖ ≤ B := by
     intro z hz
     simp only [hf, hg, Complex.norm_div, hB, hd, Complex.norm_mul, Complex.norm_ofNat]
@@ -2569,7 +2587,7 @@ lemma LogDerivZetaUniformLogSquaredBoundStrip : ∃ (F : ℝ) (_ : F = E / 3)
         have h := Complex.abs_im_le_norm (-1 / 2 - I * t); simp only [sub_im, div_ofNat_im, neg_im,
           one_im, neg_zero, zero_div, mul_im, I_re, ofReal_im, mul_zero, I_im, ofReal_re, one_mul,
           zero_add, zero_sub, abs_neg] at h
-        linarith
+        linarith only [ht, hzBound, h]
   set z : ℂ := σ + t * I with hz
   have zIm : t = z.im := by
     simp only [hz, add_im, ofReal_im, mul_im, ofReal_re, I_im, mul_one, I_re, mul_zero, add_zero,
@@ -2580,7 +2598,7 @@ lemma LogDerivZetaUniformLogSquaredBoundStrip : ∃ (F : ℝ) (_ : F = E / 3)
   have one_le_logt : 1 ≤ Real.log |t| := by
     rw [← Real.log_exp 1]
     apply Real.log_le_log (Real.exp_pos _)
-    linarith [Real.exp_one_lt_three]
+    linarith only [Real.exp_one_lt_three, ht]
   calc ‖ζ' z / ζ z‖ ≤ _ := norm_le_norm_sub_add _ (∑ ρ ∈ finite0s.toFinset, analyticOrderNatAt ζ ρ
     / (z - ρ))
     _ ≤ ‖∑ ρ ∈ finite0s.toFinset, ↑(analyticOrderNatAt ζ ρ) / (z - ρ)‖ + C * Real.log |t| := by
@@ -2598,7 +2616,7 @@ lemma LogDerivZetaUniformLogSquaredBoundStrip : ∃ (F : ℝ) (_ : F = E / 3)
       refine div_le_div_of_nonneg_left (cast_nonneg' _) ?_ (GapSize t ht z zRe ρ hρ)
       simp only [DeltaT, ofNat_pos, div_pos_iff_of_pos_right]
       refine _root_.div_pos EinIoo.1 (Real.log_pos ?_)
-      linarith
+      linarith only [ht, r_pos, r_lt_R, R_lt_one]
     _ ≤ 6 * D / E * Real.log |t| ^ 2 + C * Real.log |t| := by
       simp only [DeltaT, add_le_add_iff_right, ← div_mul, mul_comm]
       field_simp
@@ -2606,7 +2624,7 @@ lemma LogDerivZetaUniformLogSquaredBoundStrip : ∃ (F : ℝ) (_ : F = E / 3)
     _ ≤ _ := by
       simp only [add_mul, add_le_add_iff_left]
       refine mul_le_mul_of_nonneg_left ?_ Cpos.le
-      nlinarith [one_le_logt]
+      nlinarith only [one_le_logt]
 
 
 
@@ -2615,7 +2633,7 @@ noncomputable def F : ℝ := LogDerivZetaUniformLogSquaredBoundStrip.choose
 lemma Fequ : F = E / 3 := LogDerivZetaUniformLogSquaredBoundStrip.choose_spec.1
 lemma FinIoo : F ∈ Ioo (0 : ℝ) (1 / 42 : ℝ) := by
   simp only [one_div, Fequ, mem_Ioo, EinIoo.1, div_pos_iff_of_pos_left, ofNat_pos, true_and]
-  linarith [EinIoo.2]
+  linarith only [EinIoo.2]
 lemma LogDerivZetaUniformLogSquaredBoundStripSpec : ∃ (C : ℝ) (_ : 0 < C),
     ∀ (t : ℝ), 3 ≤ |t| →
       ∀ (σ : ℝ), σ ∈ Set.Icc (1 - F / Real.log |t|) (3 / 2) →
@@ -2693,19 +2711,19 @@ theorem LogDerivZetaUniformLogSquaredBound : ∃ (C : ℝ) (_ : 0 < C),
     · exact le_max_left _ _
     · simp only [log_abs, rpow_ofNat, Std.le_refl]
   · refine (hC2 _ ?_).trans ?_
-    · norm_num; linarith
+    · norm_num; linarith only [hσ']
     · nth_rewrite 1 [← mul_one C2, ← mul_one 1, ← sq]
       refine mul_le_mul (le_max_right _ _) ?_ (sq_nonneg _) ?_
       · rw [one_pow, rpow_ofNat, one_le_sq_iff_one_le_abs, abs_of_pos (Real.log_pos (by
         linarith)), Real.le_log_iff_exp_le (by linarith)]
-        linarith [Real.exp_one_lt_d9]
-      · linarith [le_max_right C1 C2]
+        linarith only [Real.exp_one_lt_d9, ht]
+      · linarith only [le_max_right C1 C2, hC2pos]
 
 
 
 /-- A wrapper for the above theorem -/
 lemma LogDerivZetaBndUnif12 : LogDerivZetaBndUnifGenProp 1 2 := by
-  refine ⟨F, ⟨FinIoo.1, by linarith [FinIoo.2]⟩, ?_⟩
+  refine ⟨F, ⟨FinIoo.1, by linarith only [FinIoo.2]⟩, ?_⟩
   simp only [rpow_one]
   apply LogDerivZetaUniformLogSquaredBound
 
@@ -2714,15 +2732,15 @@ lemma LogDerivZetaBndUnif12 : LogDerivZetaBndUnifGenProp 1 2 := by
 -- analouge from ZetaBounds
 lemma ZetaZeroFree1 :
     ZetaZeroFreeGenProp 1 := by
-  refine ⟨F, ⟨FinIoo.1, by linarith [FinIoo.2]⟩, ?_⟩
+  refine ⟨F, ⟨FinIoo.1, by linarith only [FinIoo.2]⟩, ?_⟩
   intro σ t ht hσ
   by_contra h
   have ZeroInequalityThing := ZeroInequalitySpec (σ + t * I) h
   simp only [add_re, ofReal_re, mul_re, I_re, mul_zero, ofReal_im, I_im, mul_one, sub_self,
     add_zero, add_im, mul_im, zero_add, ge_iff_le, forall_eq] at ZeroInequalityThing
   have contra := hσ.1; rw [Fequ] at contra
-  have contra := le_trans contra (ZeroInequalityThing (by linarith))
-  have log_pos : 0 < Real.log |t| := by exact Real.log_pos (by linarith)
+  have contra := le_trans contra (ZeroInequalityThing (by linarith only [ht]))
+  have log_pos : 0 < Real.log |t| := by exact Real.log_pos (by linarith only [ht])
   rw [rpow_one, sub_le_sub_iff_left, div_div, div_le_div_iff_of_pos_left EinIoo.1 log_pos (mul_pos
     three_pos (Real.log_pos (lt_trans one_lt_ofNat ht)))] at contra
   linarith
diff --git a/LeanPool/IwaniecLinearSieve/Vendor/PrimeNumberTheoremAnd/ZetaBounds.lean b/LeanPool/IwaniecLinearSieve/Vendor/PrimeNumberTheoremAnd/ZetaBounds.lean
index a219171358..6234cfda7e 100644
--- a/LeanPool/IwaniecLinearSieve/Vendor/PrimeNumberTheoremAnd/ZetaBounds.lean
+++ b/LeanPool/IwaniecLinearSieve/Vendor/PrimeNumberTheoremAnd/ZetaBounds.lean
@@ -664,7 +664,7 @@ lemma sum_eq_int_deriv {φ : ℝ → ℂ} {a b : ℝ} (apos : 0 ≤ a) (a_lt_b :
   rw [← intervalIntegral.integral_neg]
   refine intervalIntegral.integral_congr fun x hx ↦ ?_
   rw [uIcc_of_le a_lt_b.le, mem_Icc] at hx
-  rw [← Int.natCast_floor_eq_floor (by linarith)]
+  rw [← Int.natCast_floor_eq_floor (by linarith only [apos, hx])]
   norm_cast
   push_cast
   ring
@@ -673,7 +673,7 @@ lemma sum_eq_int_deriv {φ : ℝ → ℂ} {a b : ℝ} (apos : 0 ≤ a) (a_lt_b :
 lemma xpos_of_uIcc {a b : ℕ} (ha : a ∈ Ioo 0 b) {x : ℝ} (x_in : x ∈ [[(a : ℝ), b]]) :
     0 < x := by
   rw [uIcc_of_le (by exact_mod_cast ha.2.le), mem_Icc] at x_in
-  linarith [(by exact_mod_cast ha.1 : (0 : ℝ) < a)]
+  linarith only [(by exact_mod_cast ha.1 : (0 : ℝ) < a), x_in, ha]
 
 lemma ZetaSum_aux1₁ {a b : ℕ} {s : ℂ} (s_ne_one : s ≠ 1) (ha : a ∈ Ioo 0 b) :
     (∫ (x : ℝ) in a..b, 1 / (x : ℂ) ^ s) =
@@ -737,7 +737,7 @@ lemma ZetaSum_aux1 {a b : ℕ} {s : ℂ} (s_ne_one : s ≠ 1) (s_ne_zero : s ≠
   have φderiv : ∀ x ∈ [[(a : ℝ), b]], deriv φ x = φ' x := by
     exact fun x hx ↦ ZetaSum_aux1φderiv s_ne_zero (xpos x hx)
   have derivφCont : ContinuousOn (deriv φ) [[a, b]] := ZetaSum_aux1derivφCont s_ne_zero ha
-  convert sum_eq_int_deriv (by linarith) (by exact_mod_cast ha.2) φDiff derivφCont using 1
+  convert sum_eq_int_deriv (by linarith only []) (by exact_mod_cast ha.2) φDiff derivφCont using 1
   · congr <;> simp only [Nat.floor_natCast]
   · rw [Nat.floor_natCast, Nat.floor_natCast, ← intervalIntegral.integral_const_mul]
     simp_rw [mul_div, ← mul_div, φ, ZetaSum_aux1₁ s_ne_one ha]
@@ -866,11 +866,11 @@ lemma finsetSum_tendsto_tsum {N : ℕ} {f : ℕ → ℂ} (hf : Summable f) :
   filter_upwards [Filter.mem_atTop (N + 1)]
   intro M hM
   rw [Finset.sum_Ico_eq_sub]
-  linarith
+  linarith only [hM]
 
 lemma _root_.Complex.cpow_tendsto {s : ℂ} (s_re_gt : 1 < s.re) :
     Tendsto (fun (x : ℕ) ↦ (x : ℂ) ^ (1 - s)) atTop (𝓝 0) := by
-  have one_sub_s_re_ne : (1 - s).re ≠ 0 := by simp only [sub_re, one_re]; linarith
+  have one_sub_s_re_ne : (1 - s).re ≠ 0 := by simp only [sub_re, one_re]; linarith only [s_re_gt]
   rw [tendsto_zero_iff_norm_tendsto_zero]
   simp_rw [Complex.norm_natCast_cpow_of_re_ne_zero _ (one_sub_s_re_ne)]
   rw [(by simp only [sub_re, one_re, neg_sub] : (1 - s).re = - (s - 1).re)]
@@ -922,7 +922,7 @@ lemma ZetaSum_aux2 {N : ℕ} (N_pos : 0 < N) {s : ℂ} (s_re_gt : 1 < s.re) :
     ∑' (n : ℕ), 1 / (n + N + 1 : ℂ) ^ s =
     (- N ^ (1 - s)) / (1 - s) - N ^ (-s) / 2
       + s * ∫ x in Ioi (N : ℝ), (⌊x⌋ + 1 / 2 - x) * (x : ℂ) ^ (-(s + 1)) := by
-  have s_ne_zero : s ≠ 0 := fun hs ↦ by linarith [zero_re ▸ hs ▸ s_re_gt]
+  have s_ne_zero : s ≠ 0 := fun hs ↦ by linarith only [zero_re ▸ hs ▸ s_re_gt, s_re_gt, hs]
   have s_ne_one : s ≠ 1 := fun hs ↦ (lt_self_iff_false _).mp <| one_re ▸ hs ▸ s_re_gt
   apply tendsto_nhds_unique (X := ℂ) (Y := ℕ) (l := atTop)
     (f := fun k ↦ ((k : ℂ) ^ (1 - s) - (N : ℂ) ^ (1 - s)) / (1 - s) +
@@ -969,7 +969,7 @@ lemma ZetaBnd_aux1b (N : ℕ) (Npos : 1 ≤ N) {σ t : ℝ} (σpos : 0 < σ) :
       simp only [id_eq, intervalIntegral.integral_of_le hu, norm_div]
       apply setIntegral_congr_fun (by simp)
       intro x hx; beta_reduce
-      iterate 2 (rw [norm_cpow_eq_rpow_re_of_pos (by linarith [hx.1])])
+      iterate 2 (rw [norm_cpow_eq_rpow_re_of_pos (by linarith only [hx.1, hx])])
       simp
     · apply IntegrableOn.integrable ?_ |>.norm
       convert! integrableOn_of_Zeta0_fun (s := σ + t * I) Npos (by simp [σpos]) using 1
@@ -979,7 +979,8 @@ lemma ZetaBnd_aux1b (N : ℕ) (Npos : 1 ≤ N) {σ t : ℝ} (σpos : 0 < σ) :
     have : (N ^ (-σ) - t ^ (-σ)) / σ ≤ N ^ (-σ) / σ :=
       div_le_div_iff_of_pos_right σpos |>.mpr (by simp [Real.rpow_nonneg (by linarith)])
     apply le_trans ?_ this
-    convert! ZetaBnd_aux1a (a := N) (b := t) (by positivity) (by linarith) ?_ <;> simp [σpos]
+    convert! ZetaBnd_aux1a (a := N) (b := t) (by positivity) (by
+      linarith only [ht]) ?_ <;> simp [σpos]
 
 /-
 For any $N\ge1$ and $s = \sigma + tI \in \C$, $\sigma=\in(0,2], 2 < |t|$,
@@ -998,7 +999,7 @@ lemma ZetaBnd_aux1 (N : ℕ) (Npos : 1 ≤ N) {σ t : ℝ} (hσ : σ ∈ Ioc 0 2
   refine le_trans (by apply norm_add_le) ?_
   simp only [Complex.norm_of_nonneg hσ.1.le, Complex.norm_mul, norm_real, Real.norm_eq_abs, norm_I,
     mul_one]
-  linarith [hσ.2]
+  linarith only [hσ.2, hσ, ht]
 
 /-
 Big-Oh version of Lemma \ref{ZetaBnd_aux1}.
@@ -1023,7 +1024,7 @@ lemma ZetaBnd_aux1p (N : ℕ) (Npos : 1 ≤ N) {σ : ℝ} (hσ : σ ∈ Ioc 0 2)
   rw [norm_norm, norm_mul, mul_div_assoc, norm_mul]
   have : 2 * (‖|t|‖ * ‖↑N ^ (-σ) / σ‖) = (2 * |t|) * ((N : ℝ) ^ (-σ) / σ) := by
     simp only [Real.norm_eq_abs, _root_.abs_abs, norm_div]
-    have : σ ≠ 0 := by linarith [hσ.1]
+    have : σ ≠ 0 := by linarith only [hσ.1, hσ]
     field_simp
     rw [abs_of_pos hσ.1]
     have : 0 < (N : ℝ) ^ (-σ) := by
@@ -1035,7 +1036,7 @@ lemma ZetaBnd_aux1p (N : ℕ) (Npos : 1 ≤ N) {σ : ℝ} (hσ : σ ∈ Ioc 0 2)
   apply mul_le_mul ?_ (ZetaBnd_aux1b N Npos hσ.1) (norm_nonneg _) (by positivity)
   refine le_trans (by apply norm_add_le) ?_
   simp only [norm_real, norm_mul, norm_I, mul_one, Complex.norm_of_nonneg hσ.1.le, Real.norm_eq_abs]
-  linarith [hσ.2]
+  linarith only [hσ.2, ht, hσ]
 
 lemma isOpen_aux : IsOpen {z : ℂ | z ≠ 1 ∧ 0 < z.re} := by
   refine IsOpen.inter isOpen_ne ?_
@@ -1051,30 +1052,15 @@ lemma integrable_log_over_pow {r : ℝ} (rneg : r < 0) {N : ℕ} (Npos : 0 < N)
       intro x hx; left; contrapose! Npos with h; exact_mod_cast h ▸ mem_Ici.mp hx
     · apply continuous_id.continuousOn.log ?_ |>.abs
       intro x hx; simp only [id_eq]; contrapose! Npos with h; exact_mod_cast h ▸ mem_Ici.mp hx
-  · have := isLittleO_log_rpow_atTop (r := -r / 2) (by linarith) |>.isBigO
-    rw [Asymptotics.isBigO_iff_eventually, Filter.eventually_atTop] at this
-    obtain ⟨C, hC⟩ := this
-    have hh := hC C (by simp)
-    rw [Asymptotics.isBigO_atTop_iff_eventually_exists]
-    have := Filter.eventually_atTop.mp hh
-    obtain ⟨x₀, hx₀ ⟩ := this
-    filter_upwards [hh, Filter.mem_atTop x₀, Filter.mem_atTop 1]
-    intro x hx x_gt x_pos
-    use C
-    intro y hy
-    simp only [norm_mul, Real.norm_eq_abs, _root_.abs_abs]
-    simp only [Real.norm_eq_abs] at hx
-    have y_pos : 0 < y := by linarith
-    have : y ^ (r / 2 - 1) = y ^ (r - 1) * y ^ (-r / 2) := by
-      rw [← Real.rpow_add y_pos]; ring_nf
-    rw [this, abs_mul]
-    have y_gt : y ≥ x₀ := by linarith
-    have := hx₀ y y_gt
-    simp only [Real.norm_eq_abs] at this
-    rw [← mul_assoc, mul_comm C, mul_assoc]
-    exact mul_le_mul_of_nonneg_left (hbc := this) (a := |y ^ (r - 1)|) (ha := by simp)
+  · have hlog := (isLittleO_log_rpow_atTop (r := -r / 2) (by linarith only [rneg])).isBigO
+    have h := ((isBigO_refl (fun x : ℝ ↦ x ^ (r - 1)) atTop).mul hlog).norm_left
+    refine h.congr' (Eventually.of_forall fun x ↦ norm_mul _ _) ?_
+    filter_upwards [eventually_gt_atTop (0 : ℝ)] with x hx
+    rw [← Real.rpow_add hx]
+    congr 1
+    ring
   · have := integrableOn_Ioi_rpow_iff (s := r / 2 - 1) (t := N) (by simp [Npos]) |>.mpr
-      (by linarith [rneg])
+      (by linarith only [rneg])
     exact integrableOn_Ioi_iff_integrableAtFilter_atTop_nhdsWithin.mp this |>.1
 
 open MeasureTheory in
@@ -1090,17 +1076,17 @@ lemma integrableOn_of_Zeta0_fun_log {N : ℕ} (Npos : 0 < N) {s : ℂ} (s_re_gt
       · intro x hx
         apply ContinuousWithinAt.cpow ?_ continuous_const.continuousWithinAt ?_
         · exact RCLike.continuous_ofReal.continuousWithinAt
-        · simp only [ofReal_mem_slitPlane]; linarith [mem_Ioi.mp hx]
+        · simp only [ofReal_mem_slitPlane]; linarith only [mem_Ioi.mp hx, hx]
       · apply RCLike.continuous_ofReal.continuousOn.comp ?_ (mapsTo_image _ _)
         refine continuous_id.continuousOn.log ?_
-        intro x hx; simp only [id_eq]; linarith [mem_Ioi.mp hx]
+        intro x hx; simp only [id_eq]; linarith only [mem_Ioi.mp hx, hx]
     · simp only [norm_mul, norm_real]
-      have := integrable_log_over_pow (r := -s.re) (by linarith) Npos
+      have := integrable_log_over_pow (r := -s.re) (by linarith only [s_re_gt]) Npos
       apply IntegrableOn.congr_fun this ?_ (by simp)
       intro x hx
       simp only [mul_eq_mul_right_iff, norm_eq_zero, Real.log_eq_zero]
       left
-      have xpos : 0 < x := by linarith [mem_Ioi.mp hx]
+      have xpos : 0 < x := by linarith only [mem_Ioi.mp hx, hx]
       simp [norm_cpow_eq_rpow_re_of_pos xpos, Real.abs_rpow_of_nonneg xpos.le,
         abs_eq_self.mpr xpos.le]
   · apply Measurable.add ?_ measurable_const |>.sub (by fun_prop) |>.aestronglyMeasurable
@@ -1149,7 +1135,7 @@ lemma hasDerivAt_Zeta0Integral {N : ℕ} (Npos : 0 < N) {s : ℂ} (hs : s ∈ {s
          _ = |x ^ (-z.re - 1)| * |(Real.log x)| * |(⌊x⌋ + 1 / 2 - x)| := by simp
          _ ≤ _ := ?_
     · congr! 2
-      simp only [Real.norm_eq_abs, norm_cpow_eq_rpow_re_of_pos (by linarith),
+      simp only [Real.norm_eq_abs, norm_cpow_eq_rpow_re_of_pos (by linarith only [hx]),
         sub_re, neg_re, one_re]
       apply abs_eq_self.mpr ?_ |>.symm
       positivity
@@ -1158,17 +1144,17 @@ lemma hasDerivAt_Zeta0Integral {N : ℕ} (Npos : 0 < N) {s : ℂ} (hs : s ∈ {s
       simp only [Metric.mem_ball, ε, Complex.dist_eq] at hz
       apply le_trans (b := 1 * |x ^ (-z.re - 1)|)
       · apply mul_le_mul_of_nonneg_right (le_trans (ZetaSum_aux1_3 _) (by norm_num)) <| abs_nonneg _
-      · simp_rw [one_mul, Real.abs_rpow_of_nonneg (by linarith : 0 ≤ x)]
+      · simp_rw [one_mul, Real.abs_rpow_of_nonneg (by linarith only [hx] : 0 ≤ x)]
         apply Real.rpow_le_rpow_of_exponent_le <| le_abs.mpr (by left; exact hx.le)
         have := abs_le.mp <| le_trans (abs_re_le_norm (z-s)) hz.le
         simp only [sub_re, neg_le_sub_iff_le_add, tsub_le_iff_right] at this
-        linarith [this.1]
+        linarith only [this.1, this]
   have h_bound : ∀ᵐ x ∂μ, ∀ z ∈ Metric.ball s ε, ‖F' z x‖ ≤ bound x := by
     apply ae_restrict_of_ae_restrict_of_subset IoiSubIoi1
     exact h_bound1
   have bound_integrable : Integrable bound μ := by
     simp only [bound]
-    convert! integrable_log_over_pow (r := -s.re / 2) (by linarith) Npos using 0
+    convert! integrable_log_over_pow (r := -s.re / 2) (by linarith only [hs]) Npos using 0
   have h_diff : ∀ᵐ x ∂μ, ∀ z ∈ Metric.ball s ε, HasDerivAt (fun w ↦ F w x) (F' z x) z := by
     simp only [F, F', f]
     apply ae_restrict_of_ae_restrict_of_subset IoiSubIoi1
@@ -1184,14 +1170,14 @@ lemma hasDerivAt_Zeta0Integral {N : ℕ} (Npos : 0 < N) {s : ℂ} (hs : s ∈ {s
       · simp only [mul_one, mul_eq_mul_left_iff, cpow_eq_zero_iff, ofReal_eq_zero, ne_eq]
         left
         rw [Complex.ofReal_log]
-        linarith
+        linarith only [one_lt_x]
       · right
         intro h
         simp only [Metric.mem_ball, ε, Complex.dist_eq,
           neg_eq_iff_eq_neg.mp <| sub_eq_zero.mp h] at hz
         have := (abs_le.mp <| le_trans (abs_re_le_norm (-1-s)) hz.le).1
         simp only [sub_re, neg_re, one_re, neg_le_sub_iff_le_add, le_neg_add_iff_add_le] at this
-        linarith
+        linarith only [hs, this]
     · apply hasDerivAt_id _ |>.neg |>.sub_const
   convert! (hasDerivAt_integral_of_dominated_loc_of_deriv_le (F := F) (F' := F') (x₀ := s)
     (s := Metric.ball s ε) (bound := bound) (μ := μ) (Metric.ball_mem_nhds s ε_pos)
@@ -1279,7 +1265,7 @@ lemma isPathConnected_aux : IsPathConnected {z : ℂ | z ≠ 1 ∧ 0 < z.re} :=
         I_re, add_zero, ofReal_re, one_mul, add_im, one_im, I_im, zero_add, ofReal_im, mul_zero,
         sub_zero, re_ofNat, sub_re, im_ofNat, sub_im, sub_self, f]
       intro x hx; simp only [mem_Icc] at hx
-      refine ⟨?_, by linarith⟩
+      refine ⟨?_, by linarith only [hx]⟩
       intro h
       rw [Complex.ext_iff] at h; simp [(by apply And.right; simpa [w_im] using h : x = 0)] at h
     · let f : ℝ → ℂ := fun t ↦ w * t + (1 + I) * (1 - t)
@@ -1297,9 +1283,9 @@ lemma isPathConnected_aux : IsPathConnected {z : ℂ | z ≠ 1 ∧ 0 < z.re} :=
         have : x = 1 := by linarith [(by apply And.right; simpa [w_im] using h : 1 - x = 0)]
         rw [Complex.ext_iff, one_re, one_im]; exact ⟨by simpa [this, w_im] using h, w_im⟩
       · by_cases hxx : x = 0
-        · simp only [hxx]; linarith
+        · simp only [hxx]; linarith only []
         · have : 0 < x := lt_of_le_of_ne hx.1 (Ne.symm hxx)
-          have : 0 ≤ 1 - x := by linarith
+          have : 0 ≤ 1 - x := by linarith only [hx]
           have := hw.2
           positivity
   · let f : ℝ → ℂ := fun t ↦ w * t + 2 * (1 - t)
@@ -1314,9 +1300,9 @@ lemma isPathConnected_aux : IsPathConnected {z : ℂ | z ≠ 1 ∧ 0 < z.re} :=
       rw [Complex.ext_iff] at h;
       simp [(by apply And.right; simpa [w_im] using h : x = 0)] at h
     · by_cases hxx : x = 0
-      · simp only [hxx]; linarith
+      · simp only [hxx]; linarith only []
       · have : 0 < x := lt_of_le_of_ne hx.1 (Ne.symm hxx)
-        have : 0 ≤ 1 - x := by linarith
+        have : 0 ≤ 1 - x := by linarith only [hx]
         have := hw.2
         positivity
 
@@ -1426,7 +1412,7 @@ lemma ZetaBnd_aux2 {n : ℕ} {t A σ : ℝ} (Apos : 0 < A) (σpos : 0 < σ) (n_l
   · have : ‖(n : ℂ) ^ (-s)‖ = n ^ (-s.re) := norm_cpow_eq_rpow_re_of_pos n_gt_0' (-s)
     rw [this, abs_eq_self.mpr <| Real.rpow_nonneg n_gt_0'.le _]; simp [s]
   · apply Real.exp_le_exp_of_le <| mul_le_mul_of_nonneg_left _ <| Real.log_nonneg n_ge_1
-    rw [neg_sub, neg_le_sub_iff_le_add, add_comm, ← Real.log_abs]; linarith
+    rw [neg_sub, neg_le_sub_iff_le_add, add_comm, ← Real.log_abs]; linarith only [σ_ge]
   · simp only [neg_sub, le_neg_add_iff_add_le]
     ring_nf
     conv => rw [mul_comm, ← mul_assoc, ← Real.log_abs]; rhs; rw [← one_mul A]
@@ -1445,13 +1431,13 @@ lemma UpperBnd_aux {A σ t : ℝ} (hA : A ∈ Ioc 0 (1 / 2)) (t_gt : 3 < |t|)
     let N := ⌊|t|⌋₊;
     0 < N ∧ N ≤ |t| ∧ 1 < Real.log |t| ∧ 1 - A < σ ∧ 0 < σ ∧ σ + t * I ≠ 1 := by
   intro N
-  have Npos : 0 < N := Nat.floor_pos.mpr (by linarith)
+  have Npos : 0 < N := Nat.floor_pos.mpr (by linarith only [t_gt])
   have N_le_t : N ≤ |t| := Nat.floor_le <| abs_nonneg _
   have logt_gt := logt_gt_one t_gt.le
   have σ_gt : 1 - A < σ := by
     apply lt_of_lt_of_le ((sub_lt_sub_iff_left (a := 1)).mpr ?_) σ_ge
-    exact (div_lt_iff₀ (by linarith)).mpr <| lt_mul_right hA.1 logt_gt
-  refine ⟨Npos, N_le_t, logt_gt, σ_gt, by linarith [hA.2], ?_⟩
+    exact (div_lt_iff₀ (by linarith only [logt_gt])).mpr <| lt_mul_right hA.1 logt_gt
+  refine ⟨Npos, N_le_t, logt_gt, σ_gt, by linarith only [hA.2, σ_gt, hA], ?_⟩
   contrapose! t_gt
   simp only [Complex.ext_iff, add_re, ofReal_re, mul_re, I_re, mul_zero, ofReal_im, I_im, mul_one,
     sub_self, add_zero, one_re, add_im, mul_im, zero_add, one_im] at t_gt
@@ -1462,10 +1448,10 @@ lemma UpperBnd_aux2 {A σ t : ℝ} (t_ge : 3 < |t|) (σ_ge : 1 - A / Real.log |t
   have : |t| ^ (1 - σ) ≤ |t| ^ (A / Real.log |t|) :=
     Real.rpow_le_rpow_of_exponent_le (by linarith) (by linarith)
   apply le_trans this ?_
-  conv => lhs; lhs; rw [← Real.exp_log (by linarith : 0 < |t|)]
+  conv => lhs; lhs; rw [← Real.exp_log (by linarith only [t_ge] : 0 < |t|)]
   rw [div_eq_mul_inv, Real.rpow_mul (by positivity), ← Real.exp_mul, ← Real.exp_mul, mul_comm,
     ← mul_assoc, inv_mul_cancel₀, one_mul]
-  apply Real.log_ne_zero.mpr; split_ands <;> linarith
+  apply Real.log_ne_zero.mpr; split_ands <;> linarith only [t_ge]
 
 lemma riemannZeta0_zero_aux (N : ℕ) (Npos : 0 < N) :
     ∑ x ∈ Finset.Ico 0 N, ((x : ℝ))⁻¹ = ∑ x ∈ Finset.Ico 1 N, ((x : ℝ))⁻¹ := by
@@ -1522,7 +1508,7 @@ lemma _root_.Nat.self_div_floor_bound {t : ℝ} (t_ge : 1 ≤ |t|) : let N := 
     apply Nat.lt_floor_add_one
 
 lemma UpperBnd_aux5 {σ t : ℝ} (t_ge : 3 < |t|) (σ_le : σ ≤ 2) : (|t| / ⌊|t|⌋₊) ^ σ ≤ 4 := by
-  obtain ⟨h₁, h₂⟩ := Nat.self_div_floor_bound (by linarith)
+  obtain ⟨h₁, h₂⟩ := Nat.self_div_floor_bound (by linarith only [t_ge])
   calc _ ≤ ((|t| / ↑⌊|t|⌋₊) ^ (2 : ℝ)) := by gcongr
        _ ≤ (2 : ℝ) ^ (2 : ℝ) := by gcongr
        _ = 4 := by norm_num
@@ -1532,24 +1518,25 @@ lemma UpperBnd_aux6 {σ t : ℝ} (t_ge : 3 < |t|) (hσ : σ ∈ Ioc (1 / 2) 2)
     ⌊|t|⌋₊ ^ (1 - σ) / ‖1 - (σ + t * I)‖ ≤ |t| ^ (1 - σ) * 2 ∧
     ⌊|t|⌋₊ ^ (-σ) / 2 ≤ |t| ^ (1 - σ) ∧ ⌊|t|⌋₊ ^ (-σ) / σ ≤ 8 * |t| ^ (-σ) := by
   have bnd := UpperBnd_aux5 t_ge hσ.2
-  have bnd' : (|t| / ⌊|t|⌋₊) ^ σ ≤ 2 * |t| := by linarith
+  have bnd' : (|t| / ⌊|t|⌋₊) ^ σ ≤ 2 * |t| := by linarith only [t_ge, bnd]
   split_ands
   · apply (div_le_iff₀ <| norm_pos_iff.mpr <| sub_ne_zero_of_ne neOne.symm).mpr
     conv => rw [mul_assoc]; rhs; rw [mul_comm]
-    apply (div_le_iff₀ <| Real.rpow_pos_of_pos (by linarith) _).mp
+    apply (div_le_iff₀ <| Real.rpow_pos_of_pos (by linarith only [t_ge]) _).mp
     rw [div_rpow_eq_rpow_div_neg (by positivity) (by positivity), neg_sub]
     refine le_trans₄ ?_ bnd' ?_
     · exact Real.rpow_le_rpow_of_exponent_le (one_le_div (by positivity) |>.mpr N_le_t) (by simp)
     · apply (mul_le_mul_iff_right₀ (by norm_num)).mpr; simpa using abs_im_le_norm (1 - (σ + t * I))
   · apply div_le_iff₀ (by norm_num) |>.mpr
-    rw [Real.rpow_sub (by linarith), Real.rpow_one, div_mul_eq_mul_div, mul_comm]
+    rw [Real.rpow_sub (by linarith only [t_ge]), Real.rpow_one, div_mul_eq_mul_div, mul_comm]
     apply div_le_iff₀ (by positivity) |>.mp
     convert! bnd' using 1
-    rw [← Real.rpow_neg (by linarith), div_rpow_neg_eq_rpow_div (by positivity) (by positivity)]
-  · apply div_le_iff₀ (by linarith [hσ.1]) |>.mpr
+    rw [← Real.rpow_neg (by
+      linarith only [t_ge]), div_rpow_neg_eq_rpow_div (by positivity) (by positivity)]
+  · apply div_le_iff₀ (by linarith only [hσ.1, hσ]) |>.mpr
     rw [mul_assoc, mul_comm, mul_assoc]
     apply div_le_iff₀' (by positivity) |>.mp
-    apply le_trans ?_ (by linarith [hσ.1] : 4 ≤ σ * 8)
+    apply le_trans ?_ (by linarith only [hσ.1, hσ] : 4 ≤ σ * 8)
     convert! bnd using 1; exact div_rpow_neg_eq_rpow_div (by positivity) (by positivity)
 
 lemma ZetaUpperBnd' {A σ t : ℝ} (hA : A ∈ Ioc 0 (1 / 2)) (t_gt : 3 < |t|)
@@ -1806,7 +1793,8 @@ lemma DerivUpperBnd_aux7_1 {x σ t : ℝ} (hx : 1 ≤ x) :
 lemma DerivUpperBnd_aux7_2 {x σ : ℝ} (hx : 1 ≤ x) :
     |(↑⌊x⌋ + 1 / 2 - x)| * x ^ (-σ - 1) * x.log ≤ x ^ (-σ - 1) * x.log := by
   rw [← one_mul (x ^ (-σ - 1) * Real.log x), mul_assoc]
-  apply mul_le_mul_of_nonneg_right _ (by bound)
+  apply mul_le_mul_of_nonneg_right _
+    (mul_nonneg (Real.rpow_nonneg (zero_le_one.trans hx) _) (Real.log_nonneg hx))
   exact le_trans (ZetaSum_aux1_3 x) (by norm_num)
 
 lemma DerivUpperBnd_aux7_3 {x σ : ℝ} (xpos : 0 < x) (σnz : σ ≠ 0) :
@@ -1828,14 +1816,15 @@ lemma DerivUpperBnd_aux7_3' {a σ : ℝ} (apos : 0 < a) (σnz : σ ≠ 0) :
     ∀ x ∈ Ici a, HasDerivAt (fun t ↦ -(1 / σ ^ 2 * t ^ (-σ) + 1 / σ * t ^ (-σ) * Real.log t))
       (x ^ (-σ - 1) * Real.log x) x := by
   intro x hx
-  simp at hx
-  exact DerivUpperBnd_aux7_3 (by linarith) σnz
+  change a ≤ x at hx
+  exact DerivUpperBnd_aux7_3 (by linarith only [apos, hx]) σnz
 
 lemma DerivUpperBnd_aux7_nonneg {a σ : ℝ} (ha : 1 ≤ a) :
     ∀ x ∈ Ioi a, 0 ≤ x ^ (-σ - 1) * Real.log x := by
   intro x hx
   simp at hx
-  bound
+  exact mul_nonneg (Real.rpow_nonneg (zero_le_one.trans (ha.trans hx.le)) _)
+    (Real.log_nonneg (ha.trans hx.le))
 
 lemma DerivUpperBnd_aux7_tendsto {σ : ℝ} (σpos : 0 < σ) :
     Tendsto (fun t ↦ -(1 / σ ^ 2 * t ^ (-σ) + 1 / σ * t ^ (-σ) * Real.log t)) atTop (nhds 0) := by
@@ -1924,7 +1913,7 @@ theorem DerivUpperBnd_aux7 {A σ t : ℝ} (t_gt : 3 < |t|) (hσ : σ ∈ Icc (1
   apply mul_le_mul _ _ (by positivity) (by positivity)
   · apply le_trans (by apply norm_add_le)
     simp [abs_of_pos σpos]
-    linarith [hσ.2]
+    linarith only [hσ.2, t_gt, hσ]
   apply le_trans (by apply norm_integral_le_integral_norm)
   calc ∫ (x : ℝ) in Ioi (N : ℝ), ‖(↑⌊x⌋ + 1 / 2 - ↑x) * (x : ℂ) ^ (-s - 1) * -↑x.log‖
     _ = ∫ (x : ℝ) in Ioi (N : ℝ), |(↑⌊x⌋ + 1 / 2 - x)| * x ^ (-σ - 1) * x.log := by
@@ -1976,7 +1965,7 @@ lemma ZetaDerivUpperBnd' {A σ t : ℝ} (hA : A ∈ Ioc 0 (1 / 2)) (t_gt : 3 < |
         ≤ C * Real.log |t| ^ 2 := by
   intros C N s
   obtain ⟨Npos, N_le_t, logt_gt, σ_gt, _, neOne⟩ := UpperBnd_aux hA t_gt hσ.1
-  replace σ_gt : 1 / 2 < σ := by linarith [hA.2]
+  replace σ_gt : 1 / 2 < σ := by linarith only [hA.2, σ_gt, hA]
   calc _ ≤ Real.exp A * 2 * (Real.log |t|) ^ 2 +
       ‖-(N : ℂ) ^ (1 - s) / (1 - s) ^ 2‖ +
       ‖(Real.log N) * (N : ℂ) ^ (1 - s) / (1 - s)‖ +
@@ -2050,7 +2039,7 @@ lemma ZetaDerivUpperBnd' {A σ t : ℝ} (hA : A ∈ Ioc 0 (1 / 2)) (t_gt : 3 < |
       swap
       · nth_rewrite 1 [← mul_one |t|.log, (by ring : |t|.log ^ 2 = |t|.log * |t|.log)]
         gcongr
-      nlinarith
+      nlinarith only [logt_gt]
 
 /-
 For any $s = \sigma + tI \in \C$, $1/2 \le \sigma\le 2, 3 < |t|$,
@@ -2200,15 +2189,16 @@ lemma ZetaNear1BndExact :
   · simp only [← h, mem_ofPred_eq] at hσ
     apply le_trans hσ ?_
     norm_cast
-    have : 0 ≤ 1 / (σ - 1) := by apply one_div_nonneg.mpr; linarith
+    have : 0 ≤ 1 / (σ - 1) := by apply one_div_nonneg.mpr; linarith only [σ_ge]
     simp only [Real.norm_eq_abs, abs_eq_self.mpr this, mul_div, mul_one]
-    exact div_le_div₀ (by simp [Cpos.le]) (by simp) (by linarith) (by rfl)
+    exact div_le_div₀ (by simp [Cpos.le]) (by simp) (by linarith only [σ_ge]) (by rfl)
   · replace hσ : σ ∈ W := by
       simp only [mem_inter_iff, hV σ_ge, and_true] at hσ
       simp only [mem_Icc, σ_le, and_true, W]
       contrapose! hσ; exact hε ⟨σ_ge.le, hσ⟩
-    apply le_trans (hC σ hσ).le ((le_div_iff₀ (by linarith)).mpr ?_)
-    rw [le_max_iff, mul_comm 2]; exact Or.inl <| mul_le_mul_of_nonneg_left (by linarith) Cpos.le
+    apply le_trans (hC σ hσ).le ((le_div_iff₀ (by linarith only [σ_ge])).mpr ?_)
+    rw [le_max_iff, mul_comm 2]; exact Or.inl <| mul_le_mul_of_nonneg_left (by
+      linarith only [σ_le]) Cpos.le
 
 /-- For positive `x` and nonzero `y` we have that
 $|\zeta(x)^3 \cdot \zeta(x+iy)^4 \cdot \zeta(x+2iy)| \ge 1$. -/
@@ -2232,7 +2222,7 @@ theorem ZetaLowerBound1_aux1 {σ t : ℝ} (this : 1 ≤ ‖ζ σ‖ ^ (3 : ℝ)
 lemma ZetaLowerBound1 {σ t : ℝ} (σ_gt : 1 < σ) :
     ‖ζ σ‖ ^ ((3 : ℝ) / 4) * ‖ζ (σ + 2 * t * I)‖ ^ ((1 : ℝ) / 4) * ‖ζ (σ + t * I)‖ ≥ 1 := by
   -- Start with the fundamental identity
-  have := norm_zeta_product_ge_one (x := σ - 1) (by linarith) t
+  have := norm_zeta_product_ge_one (x := σ - 1) (by linarith only [σ_gt]) t
   simp_rw [ge_iff_le, norm_mul, norm_pow, ofReal_sub, ofReal_one, add_sub_cancel, ←
     Real.rpow_natCast]
     at this
@@ -2245,7 +2235,7 @@ lemma ZetaLowerBound2 {σ t : ℝ} (σ_gt : 1 < σ) :
 
 theorem ZetaLowerBound3_aux1 (A : ℝ) (ha : A ∈ Ioc 0 (1 / 2)) (t : ℝ)
   (ht_2 : 3 < |2 * t|) : 0 < A / Real.log |2 * t| := by
-  exact div_pos ha.1 <| Real.log_pos (by linarith)
+  exact div_pos ha.1 <| Real.log_pos (by linarith only [ht_2])
 
 theorem ZetaLowerBound3_aux2 {C : ℝ}
   {σ t : ℝ}
@@ -2258,7 +2248,7 @@ theorem ZetaLowerBound3_aux3 (C : ℝ) (c_near : ℝ) {σ : ℝ} (t : ℝ) (σ_g
     ((1 : ℝ) / 4) =
     c_near ^ ((3 : ℝ) / 4) * C ^ ((1 : ℝ) / 4) * Real.log |t * 2| ^ ((1 : ℝ) / 4) * (-1 + σ) ^
       (-(3 : ℝ) / 4) := by
-  exact (symm) (.trans (by rw [neg_div, Real.rpow_neg (by linarith)]) (by ring))
+  exact (symm) (.trans (by rw [neg_div, Real.rpow_neg (by linarith only [σ_gt])]) (by ring))
 
 theorem ZetaLowerBound3_aux4 (C : ℝ) (hC : 0 < C)
   (c_near : ℝ) (hc_near : 0 < c_near) {σ : ℝ} (t : ℝ) (ht : 3 < |t|)
@@ -2266,9 +2256,14 @@ theorem ZetaLowerBound3_aux4 (C : ℝ) (hC : 0 < C)
    :
   0 < c_near ^ ((3 : ℝ) / 4) * (σ - 1) ^ (-(3 : ℝ) / 4) * C ^ ((1 : ℝ) / 4) * Real.log |2 * t| ^
     ((1 : ℝ) / 4) := by
-  match sub_pos.mpr σ_gt with | S => match Real.log_pos (by simp; linarith : abs (2 *t) > 1) with
+  match sub_pos.mpr σ_gt with
+  | S =>
+    match Real.log_pos (show |2 * t| > 1 from by
+      simp
+      linarith only [ht]) with
     | S => positivity
 
+
 theorem ZetaLowerBound3_aux5
   {σ : ℝ} (t : ℝ)
   (this : ‖ζ σ‖ ^ ((3 : ℝ) / 4) * ‖ζ (σ + 2 * t * I)‖ ^ ((1 : ℝ) / 4) * ‖ζ (σ + t * I)‖ ≥ 1) :
@@ -2300,14 +2295,14 @@ lemma ZetaLowerBound3 :
   -- Upper bound on ‖ζ σ‖ from ZetaNear1BndExact
   have ζ_σ_bound : ‖ζ σ‖ ≤ c_near / (σ - 1) := by
     exact h_near σ ⟨σ_gt, σ_le⟩
-  have ht_2 : 3 < |2 * t| := by simp only [abs_mul, Nat.abs_ofNat]; linarith
+  have ht_2 : 3 < |2 * t| := by simp only [abs_mul, Nat.abs_ofNat]; linarith only [ht]
   -- Upper bound on ‖ζ (σ + 2*t * I)‖ from ZetaUpperBnd
   have σ_in_range : σ ∈ Icc (1 - A / Real.log |2 * t|) 2 := by
     constructor
     · -- σ ≥ 1 - A / Real.log |2*t|
       have : 0 < A / Real.log |2 * t| := by
         exact ZetaLowerBound3_aux1 A ha t ht_2
-      nlinarith
+      exact (sub_lt_self 1 this).le.trans σ_gt.le
     · exact σ_le
   have ζ_2t_bound := h_upper σ (2 * t) ht_2 σ_in_range
   -- Combine the bounds
@@ -2325,7 +2320,7 @@ lemma ZetaLowerBound3 :
          c_near ^ ((3 : ℝ) / 4) * (σ - 1) ^ (-(3 : ℝ) / 4) * C ^ ((1 : ℝ) / 4) * (Real.log |2 *
            t|) ^ ((1 : ℝ) / 4) := by
     rw [Real.div_rpow (by linarith) (by linarith), Real.mul_rpow (by linarith) (Real.log_nonneg
-      (by linarith))]
+      (by linarith only [ht_2]))]
     ring_nf
     exact ZetaLowerBound3_aux3 _ _ _ σ_gt
   rw [this] at denom_bound
@@ -2382,7 +2377,7 @@ lemma Ioi_union_Iio_mem_cocompact {a : ℝ} (ha : 0 ≤ a) : Ioi (a : ℝ) ∪ I
   constructor
   · exact isCompact_Icc
   · rw [@compl_subset_iff_union, ← union_assoc, Icc_union_Ioi_eq_Ici, union_comm, Iio_union_Ici]
-    linarith
+    linarith only [ha]
 
 lemma lt_abs_mem_cocompact {a : ℝ} (ha : 0 ≤ a) : {t | a < |t|} ∈ cocompact ℝ := by
   convert Ioi_union_Iio_mem_cocompact ha using 1; ext t
@@ -2404,7 +2399,7 @@ lemma ZetaInvBound2 :
   refine ⟨c⁻¹, inv_pos.mpr hc, ?_⟩
   intro σ hσ t ht
   have positive_sigma : 0 < σ - 1 := sub_pos.mpr hσ.1
-  have positive_log : 0 < Real.log |t| := Real.log_pos (by linarith)
+  have positive_log : 0 < Real.log |t| := Real.log_pos (by linarith only [ht])
   calc
     _ ≤ (c * (σ - 1) ^ ((3 : ℝ) / 4) / Real.log |t| ^ ((1 : ℝ) / 4))⁻¹ := by
       simpa only [one_div] using one_div_le_one_div_of_le (by positivity) (lower hσ t ht)
@@ -2474,7 +2469,7 @@ lemma Zeta_diff_Bnd :
   have t_ne_zero : t ≠ 0 := by contrapose! t_gt; simp only [t_gt, abs_zero, Nat.ofNat_nonneg]
   rw [← Zeta_eq_int_derivZeta t_ne_zero]
   convert intervalIntegral.norm_integral_le_of_norm_le_const ?_ using 1
-  · congr; rw [_root_.abs_of_nonneg (by linarith)]
+  · congr; rw [_root_.abs_of_nonneg (by linarith only [σ₁_lt_σ₂])]
   · intro σ hσ; rw [uIoc_of_le σ₁_lt_σ₂.le, mem_Ioc] at hσ
     exact hC σ t t_gt ⟨le_trans σ₁_ge hσ.1.le, le_trans hσ.2 σ₂_le⟩
 
@@ -2552,9 +2547,9 @@ lemma ZetaLowerBndStrip :
   have σ'_gt : 1 < σ' := by simp only [σ', lt_add_iff_pos_right]; positivity
   have σ'_le : σ' ≤ 2 := by
     simp only [σ']
-    suffices A / Real.log |t| ^ (9 : ℝ) < 1 by linarith
+    suffices A / Real.log |t| ^ (9 : ℝ) < 1 by linarith only [this]
     apply div_lt_one (by positivity) |>.mpr
-    exact lt_trans₄ (by linarith) logt_gt_one <| ZetaInvBnd_aux' logt_gt_one
+    exact lt_trans₄ (by linarith only [Apos, Ale]) logt_gt_one <| ZetaInvBnd_aux' logt_gt_one
   set s := σ + t * I
   set s' := σ' + t * I
   change ‖ζ s‖ ≥ C / Real.log |t| ^ (7 : ℝ)
@@ -2582,7 +2577,7 @@ lemma ZetaLowerBndStrip :
       exact div_le_div₀ hA'.1.le (by simp [A]) (by positivity) <| ZetaInvBnd_aux logt_gt_one
   · apply sub_le_sub (by simp only [add_sub_cancel_left, σ']; exact_mod_cast le_rfl) ?_
     rw [mul_div_assoc, mul_assoc _ 2 _]
-    apply mul_le_mul (by exact_mod_cast le_rfl) ?_ (by linarith [hσ.2]) (by positivity)
+    apply mul_le_mul (by exact_mod_cast le_rfl) ?_ (by linarith only [hσ.2, hσ]) (by positivity)
     suffices h : σ' + (1 - A / Real.log |t| ^ (9 : ℝ)) ≤ (1 + A / Real.log |t| ^ (9 : ℝ)) + σ by
       simp only [tsub_le_iff_right]
       convert! le_sub_right_of_add_le h using 1; ring_nf
@@ -2605,7 +2600,7 @@ lemma ZetaInvBnd :
   obtain ⟨A, hA, c, hc, lower⟩ := ZetaLowerBndStrip
   refine ⟨A, hA, c⁻¹, inv_pos.mpr hc, ?_⟩
   intro σ t ht hσ
-  have positive_log : 0 < Real.log |t| := Real.log_pos (by linarith)
+  have positive_log : 0 < Real.log |t| := Real.log_pos (by linarith only [ht])
   calc
     _ ≤ (c / Real.log |t| ^ (7 : ℝ))⁻¹ := by
       simpa only [one_div] using one_div_le_one_div_of_le (by positivity) (lower σ t ht hσ)
@@ -2624,7 +2619,7 @@ lemma ZetaLowerBnd :
   intro σ t ht hσ
   apply lower σ t ht
   refine ⟨hσ.1, hσ.2.trans ?_⟩
-  have positive_log : 0 < Real.log |t| := Real.log_pos (by linarith)
+  have positive_log : 0 < Real.log |t| := Real.log_pos (by linarith only [ht])
   exact lt_add_of_pos_right _ (div_pos hA.1 (Real.rpow_pos_of_pos positive_log _))
 
 -- **End collaboration 6/20/25**
@@ -2656,8 +2651,8 @@ lemma ZetaZeroFree9 : ZetaZeroFreeGenProp 9 := by
     apply div_pos hc
     apply Real.rpow_pos_of_pos
     apply Real.log_pos
-    linarith
-  linarith
+    linarith only [ht]
+  linarith only [this, pos_bound]
 
 
 /-
@@ -2681,26 +2676,26 @@ lemma LogDerivZetaBnd :
     apply le_trans (tsub_le_tsub_left ?_ 1) σ_ge
     apply div_le_div_of_nonneg_right (min_le_left A A')
     apply Real.rpow_nonneg
-    linarith
+    linarith only [logt_gt]
   have σ_ge'' : 1 - A' / Real.log |t| ≤ σ := by
     apply le_trans (tsub_le_tsub_left ?_ 1) σ_ge
     apply div_le_div₀ hA'.1.le (min_le_right A A') (lt_trans (by norm_num) logt_gt) ?_
-    rw [← Real.rpow_one (Real.log |t|), ← Real.rpow_mul (by linarith), one_mul]
+    rw [← Real.rpow_one (Real.log |t|), ← Real.rpow_mul (by linarith only [logt_gt]), one_mul]
     exact Real.rpow_le_rpow_of_exponent_le logt_gt.le Nat.one_le_ofNat
   replace h := h σ t t_gt ⟨σ_ge', by calc
     σ < 1 + min A A' / Real.log |t| ^ (9 : ℝ) := σ_lt
     _ ≤ 1 + A / Real.log |t| ^ (9 : ℝ) := by gcongr; simp⟩
   replace h' := h' σ t t_gt ⟨σ_ge'', by
    calc
-    σ ≤ 1 + min A A' / Real.log |t| ^ (9 : ℝ) := by linarith [σ_lt]
+    σ ≤ 1 + min A A' / Real.log |t| ^ (9 : ℝ) := by linarith only [σ_lt]
     _ ≤ 1 + (1/2) / Real.log |t| ^ (9 : ℝ) := by gcongr; simp [Set.mem_Ioc] at hA' hA ⊢ ; simp
       [hA.2]
     _ ≤ 1 + (1/2) / 1 := by
           gcongr
           calc
-            1 ≤ Real.log |t| := by linarith
+            1 ≤ Real.log |t| := by linarith only [logt_gt]
             _ ≤ (Real.log |t|) ^ (9 : ℝ) := Real.self_le_rpow_of_one_le (by linarith) (by linarith)
-    _ ≤ 2 := by linarith
+    _ ≤ 2 := by linarith only []
     ⟩
   simp only [norm_div]
   convert! mul_le_mul h h' (by simp) ?_ using 1 <;> (norm_cast; ring_nf); positivity
@@ -2843,7 +2838,7 @@ lemma ZetaNoZerosInBox (T : ℝ) :
       intro s hs hfalse
       rw [hfalse] at hs
       simp only [norm_zero, ge_iff_le] at hs
-      linarith
+      linarith only [hs]
     rw [ht₀] at ToOneT0
     simp only [ofReal_zero, mul_zero, add_zero] at ToOneT0
     rcases (ToOneT0.eventually ZetaNonZ).exists with ⟨n, hn⟩
@@ -2910,7 +2905,7 @@ theorem LogDerivZetaHolcSmallT :
     obtain ⟨hre_lower, hre_upper⟩ := hre
     have : min σ₂ 2 = σ₂ := by
       apply min_eq_left
-      linarith [hσ₂_lt_one]
+      linarith only [hσ₂_lt_one]
     rwa [← this]
   apply LogDerivZetaHoloOn
   · exact Set.notMem_sdiff_of_mem rfl
@@ -3115,11 +3110,11 @@ theorem triv_bound_zeta :  ∃C ≥ 0, ∀(σ₀ t : ℝ), 1 < σ₀ →
       simp only [mem_ofPred_eq]
       rw [edist_dist, dist_eq_norm]
       norm_cast
-      have U : 0 ≤ σ₀ - 1 := by linarith
+      have U : 0 ≤ σ₀ - 1 := by linarith only [σ₀_gt]
       simp only [Real.norm_of_nonneg U, gt_iff_lt]
       simp only [ENNReal.ofReal_lt_iff_lt_toReal U O1]
       calc
-        _ ≤ boundary - 1 := by linarith
+        _ ≤ boundary - 1 := by linarith only [h]
         _ = ENNReal.toReal (1 + ε_div_two) - 1 := rfl
         _ = ENNReal.toReal (1 + ε_div_two) - ENNReal.toReal (ENNReal.ofReal 1) := by simp
         _ ≤ ENNReal.toReal (1 + ε_div_two - ENNReal.ofReal 1) := ENNReal.le_toReal_sub U4
@@ -3133,7 +3128,7 @@ theorem triv_bound_zeta :  ∃C ≥ 0, ∀(σ₀ t : ℝ), 1 < σ₀ →
       · by_contra a
         have U : σ₀ = 1 := by exact ofReal_eq_one.mp a
         rw [U] at σ₀_gt
-        linarith
+        linarith only [σ₀_gt]
     have bdd := Set.forall_mem_image.mp bound_prop (σ₀_in_U)
     simp only [Function.comp_apply, Pi.sub_apply, Pi.neg_apply, Pi.div_apply] at bdd
     calc
@@ -3153,8 +3148,7 @@ theorem triv_bound_zeta :  ∃C ≥ 0, ∀(σ₀ t : ℝ), 1 < σ₀ →
         norm_cast
       _ ≤ const + (σ₀ - 1)⁻¹ := by
         simp [norm_inv]
-        have pos : 0 ≤ σ₀ - 1 := by
-          linarith
+        have pos : 0 ≤ σ₀ - 1 := by linarith only [σ₀_gt]
         simp [abs_of_nonneg pos]
       _ = (σ₀ - 1)⁻¹ + const := by
         rw [add_comm]
@@ -3166,7 +3160,7 @@ theorem triv_bound_zeta :  ∃C ≥ 0, ∀(σ₀ t : ℝ), 1 < σ₀ →
       simp only [mem_ofPred_eq]
       rw [edist_dist, dist_eq_norm]
       norm_cast
-      have U : 0 ≤ boundary - 1 := by linarith
+      have U : 0 ≤ boundary - 1 := by linarith only [boundary_geq_one]
       simp only [Real.norm_of_nonneg U, gt_iff_lt]
       simp only [ENNReal.ofReal_lt_iff_lt_toReal U O1]
       calc
@@ -3188,7 +3182,7 @@ theorem triv_bound_zeta :  ∃C ≥ 0, ∀(σ₀ t : ℝ), 1 < σ₀ →
     calc
       _ ≤ ‖ζ' boundary / ζ boundary‖ := by
         exact dlog_riemannZeta_bdd_on_vertical_lines_generalized boundary σ₀ t
-          (boundary_geq_one) (by linarith)
+          (boundary_geq_one) (by linarith only [h])
       _ = ‖- ζ' boundary / ζ boundary‖ := by simp only [Complex.norm_div, norm_neg]
       _ = ‖(- ζ' boundary / ζ boundary - (boundary - 1)⁻¹) + (boundary - 1)⁻¹‖ := by
         simp only [Complex.norm_div, norm_neg, ofReal_inv, ofReal_sub, ofReal_one, sub_add_cancel]
@@ -3204,8 +3198,7 @@ theorem triv_bound_zeta :  ∃C ≥ 0, ∀(σ₀ t : ℝ), 1 < σ₀ →
         simpa [*] using! U9
       _ ≤ const + (boundary - 1)⁻¹ := by
         simp [norm_inv]
-        have pos : 0 ≤ boundary - 1 := by
-          linarith
+        have pos : 0 ≤ boundary - 1 := by linarith only [boundary_geq_one]
         simp [abs_of_nonneg pos]
       _ = (boundary - 1)⁻¹ + const := by
         rw [add_comm]
@@ -3232,7 +3225,7 @@ lemma LogDerivZetaBndUnif99 : LogDerivZetaBndUnifGenProp 9 9 := by
     simp only [one_div, mem_Ioc, true_and, T0] at pf_A
     have U := (inv_le_inv₀ (by positivity) (by positivity)).mpr pf_A
     simp only [inv_inv] at U
-    linarith
+    linarith only [T0, pf_A, U]
   refine ⟨A, pf_A, ((1 + C + C_triv) * A⁻¹), (by positivity), fun σ t hyp_t hyp_σ ↦ ?_⟩
   have logt_gt' : (1 : ℝ) < Real.log |t| ^ (9 : ℝ) := by
     calc
@@ -3277,9 +3270,9 @@ lemma LogDerivZetaBndUnif99 : LogDerivZetaBndUnifGenProp 9 9 := by
           ring_nf
           gcongr
           · simp only [inv_pos, le_mul_iff_one_le_left, T0]
-            linarith
+            linarith only [logt_gt']
       _ ≤ (1 + C + C_triv) * A⁻¹ * Real.log |t| ^ (9 : ℝ) := by
           gcongr
-          linarith
+          linarith only [C_pos]
 
 end IwaniecLinearSievePNT