Theorems · Theorem · nonassociative algebras

LieSubmodule.mk_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 : Submodule R M}
  {h : ∀ {x : L} {m : M}, m ∈ N.carrier → ⁅x, m⁆ ∈ N.carrier}, { toSubmodule := N, lie_mem := h } = ⊥ ↔ N = ⊥

Defined in

Mathlib.Algebra.Lie.Submodule

Cited by

0 results in Mathlib

Foundations

Depth 20 from the axioms · uses propext, Quot.sound

Assumes

CommRingLieRingAddCommGroupModuleLieRingModule