Theorems · Theorem · nonassociative algebras

LieSubmodule.lie_eq_bot_iff

∀ {R : Type u} {L : Type v} {M : Type w} [inst : CommRing R] [inst_1 : LieRing L] [inst_2 : AddCommGroup M]
  [inst_3 : Module R M] [inst_4 : LieRingModule L M] (N : LieSubmodule R L M) [inst_5 : LieAlgebra R L]
  (I : LieIdeal R L), ⁅I, N⁆ = ⊥ ↔ ∀ x ∈ I, ∀ m ∈ N, ⁅x, m⁆ = 0

Defined in

Mathlib.Algebra.Lie.IdealOperations

Cited by

2 results in Mathlib

Foundations

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

Assumes

CommRingLieRingAddCommGroupModuleLieRingModuleLieAlgebra