Theorems · Theorem · nonassociative algebras

LieSubmodule.comap_bracket_eq

∀ {R : Type u} {L : Type v} {M : Type w} {M₂ : Type w₁} [inst : CommRing R] [inst_1 : LieRing L]
  [inst_2 : AddCommGroup M] [inst_3 : Module R M] [inst_4 : LieRingModule L M] [inst_5 : AddCommGroup M₂]
  [inst_6 : Module R M₂] [inst_7 : LieRingModule L M₂] (N₂ : LieSubmodule R L M₂) (f : M →ₗ⁅R,L⁆ M₂)
  [inst_8 : LieAlgebra R L] [LieModule R L M₂] (I : LieIdeal R L) [LieModule R L M],
  f.ker = ⊥ → N₂ ≤ f.range → LieSubmodule.comap f ⁅I, N₂⁆ = ⁅I, LieSubmodule.comap f N₂⁆

Defined in

Mathlib.Algebra.Lie.IdealOperations

Cited by

1 results in Mathlib

Foundations

Depth 71 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingLieRingAddCommGroupModuleLieRingModuleAddCommGroupModuleLieRingModuleLieAlgebraLieModuleLieModule