diff --git a/Mathlib/Algebra/Lie/Ideal.lean b/Mathlib/Algebra/Lie/Ideal.lean index c7bdf292d59f00..6fd2210fcd1161 100644 --- a/Mathlib/Algebra/Lie/Ideal.lean +++ b/Mathlib/Algebra/Lie/Ideal.lean @@ -72,6 +72,12 @@ theorem LieIdeal.toLieSubalgebra_toSubmodule (I : LieIdeal R L) : ((I : LieSubalgebra R L) : Submodule R L) = LieSubmodule.toSubmodule I := rfl +instance LieIdeal.bracket {R L : Type*} [CommRing R] [LieRing L] [LieAlgebra R L] + (I : LieIdeal R L) [Bracket L M] : Bracket I M where + bracket x m := ⁅(x : L), m⁆ + +instance (priority := 2000) (I : LieIdeal R L) : Bracket I I := inferInstance + /-- An ideal of `L` is a Lie subalgebra of `L`, so it is a Lie ring. -/ instance LieIdeal.lieRing (I : LieIdeal R L) : LieRing I := inferInstanceAs <| LieRing I.toLieSubalgebra