Theorems · Theorem · nonassociative algebras

LieSubalgebra.mem_lieSpan

∀ {R : Type u} {L : Type v} [inst : CommRing R] [inst_1 : LieRing L] [inst_2 : LieAlgebra R L] {s : Set L} {x : L},
  x ∈ LieSubalgebra.lieSpan R L s ↔ ∀ (K : LieSubalgebra R L), s ⊆ ↑K → x ∈ K

Defined in

Mathlib.Algebra.Lie.Subalgebra

Cited by

2 results in Mathlib

Foundations

Depth 63 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingLieRingLieAlgebra