Theorems · Theorem · nonassociative algebras

LieSubmodule.lie_mem

∀ {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] (self : LieSubmodule R L M) {x : L} {m : M},
  m ∈ (↑self).carrier → ⁅x, m⁆ ∈ (↑self).carrier

Defined in

Mathlib.Algebra.Lie.Submodule

Cited by

23 results in Mathlib

Foundations

Depth 8 from the axioms · uses no axioms

Assumes

CommRingLieRingAddCommGroupModuleLieRingModule