Theorems · Theorem · nonassociative algebras

LieSubmodule.lcs_add_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] (l k : ℕ), LieSubmodule.lcs (l + k) N₁ ≤ N₂ ↔ LieSubmodule.lcs l N₁ ≤ LieSubmodule.ucs k N₂

Defined in

Mathlib.Algebra.Lie.Nilpotent

Cited by

1 results in Mathlib

Foundations

Depth 27 from the axioms · uses propext, Quot.sound

Assumes

CommRingLieRingLieAlgebraAddCommGroupModuleLieRingModuleLieModule