Theorems · Theorem · nonassociative algebras

LieSubmodule.lcs_le_iff

∀ {R : Type u} {L : Type v} {M : Type w} [inst : CommRing R] [inst_1 : LieRing L] [inst_2 : LieAlgebra R L]
  [inst_3 : AddCommGroup M] [inst_4 : Module R M] [inst_5 : LieRingModule L M] {N₁ N₂ : LieSubmodule R L M}
  [inst_6 : LieModule R L M] (k : ℕ), LieSubmodule.lcs k N₁ ≤ N₂ ↔ N₁ ≤ LieSubmodule.ucs k N₂

Defined in

Mathlib.Algebra.Lie.Nilpotent

Cited by

3 results in Mathlib

Foundations

Depth 28 from the axioms · uses propext, Quot.sound

Assumes

CommRingLieRingLieAlgebraAddCommGroupModuleLieRingModuleLieModule