Theorems · Theorem · nonassociative algebras

LieSubmodule.mem_lieSpan

∀ {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] {s : Set M} {x : M},
  x ∈ LieSubmodule.lieSpan R L s ↔ ∀ (N : LieSubmodule R L M), s ⊆ ↑N → x ∈ N

Defined in

Mathlib.Algebra.Lie.Submodule

Cited by

3 results in Mathlib

Foundations

Depth 21 from the axioms · uses propext, Quot.sound

Assumes

CommRingLieRingAddCommGroupModuleLieRingModule