Theorems · Theorem · nonassociative algebras

LieSubmodule.lie_le_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 N' : LieSubmodule R L M) [inst_5 : LieAlgebra R L]
  (I : LieIdeal R L), ⁅I, N⁆ ≤ N' ↔ ∀ x ∈ I, ∀ m ∈ N, ⁅x, m⁆ ∈ N'

Defined in

Mathlib.Algebra.Lie.IdealOperations

Cited by

1 results in Mathlib

Foundations

Depth 25 from the axioms · uses propext, Quot.sound

Assumes

CommRingLieRingAddCommGroupModuleLieRingModuleLieAlgebra