Theorems · Theorem · nonassociative algebras

LieIdeal.comap_bracket_eq

∀ {R : Type u} {L : Type v} {L' : Type w₂} [inst : CommRing R] [inst_1 : LieRing L] [inst_2 : LieAlgebra R L]
  [inst_3 : LieRing L'] [inst_4 : LieAlgebra R L'] {f : L →ₗ⁅R⁆ L'} {J₁ J₂ : LieIdeal R L'},
  f.IsIdealMorphism →
    LieIdeal.comap f ⁅f.idealRange ⊓ J₁, f.idealRange ⊓ J₂⁆ = ⁅LieIdeal.comap f J₁, LieIdeal.comap f J₂⁆ ⊔ f.ker

Defined in

Mathlib.Algebra.Lie.IdealOperations

Cited by

2 results in Mathlib

Foundations

Depth 69 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingLieRingLieAlgebraLieRingLieAlgebra