Theorems · Theorem · nonassociative algebras

LieAlgebra.derivedSeries_of_derivedLength_succ

∀ (R : Type u) (L : Type v) [inst : CommRing R] [inst_1 : LieRing L] [inst_2 : LieAlgebra R L] (I : LieIdeal R L)
  (k : ℕ),
  LieAlgebra.derivedLengthOfIdeal R L I = k + 1 ↔
    IsLieAbelian ↥(LieAlgebra.derivedSeriesOfIdeal R L k I) ∧ LieAlgebra.derivedSeriesOfIdeal R L k I ≠ ⊥

Defined in

Mathlib.Algebra.Lie.Solvable

Cited by

2 results in Mathlib

Foundations

Depth 83 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingLieRingLieAlgebra