Theorems · Theorem · nonassociative algebras

LieSubmodule.mem_sup

∀ {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) (x : M),
  x ∈ N ⊔ N' ↔ ∃ y ∈ N, ∃ z ∈ N', y + z = x

Defined in

Mathlib.Algebra.Lie.Submodule

Cited by

5 results in Mathlib

Foundations

Depth 69 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingLieRingAddCommGroupModuleLieRingModule