Theorems · Theorem · nonassociative algebras

LieIdeal.comap_bracket_incl_of_le

∀ {R : Type u} {L : Type v} [inst : CommRing R] [inst_1 : LieRing L] [inst_2 : LieAlgebra R L] (I : LieIdeal R L)
  {I₁ I₂ : LieIdeal R L},
  I₁ ≤ I → I₂ ≤ I → ⁅LieIdeal.comap I.incl I₁, LieIdeal.comap I.incl I₂⁆ = LieIdeal.comap I.incl ⁅I₁, I₂⁆

This is a very useful result; it allows us to use the fact that inclusion distributes over the Lie bracket operation on ideals, subject to the conditions shown.

Defined in

Mathlib.Algebra.Lie.IdealOperations

Cited by

1 results in Mathlib

Foundations

Depth 81 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingLieRingLieAlgebra