Theorems · Theorem · nonassociative algebras
LieSubalgebra.coe_lieSpan_eq_span_of_forall_lie_eq_zero
∀ {R : Type u} {L : Type v} [inst : CommRing R] [inst_1 : LieRing L] [inst_2 : LieAlgebra R L] {s : Set L},
(∀ x ∈ s, ∀ y ∈ s, ⁅x, y⁆ = 0) → (LieSubalgebra.lieSpan R L s).toSubmodule = Submodule.span R s- Defined in
- Mathlib.Algebra.Lie.Subalgebra
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 66 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommRingLieRingLieAlgebra
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites22
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- CommRingstatement and proof · cited by 17,173
- Submodulestatement · cited by 7,192
- le_antisymmproof · cited by 2,068
- LieRingstatement and proof · cited by 1,548
- Submodule.spanstatement and proof · cited by 1,504
- LieAlgebrastatement and proof · cited by 1,246
- Bracket.bracketstatement and proof · cited by 642
- Submodule.subset_spanproof · cited by 234
- AddMemClass.add_memproof · cited by 229
- Submodule.smul_memproof · cited by 204
- LieSubalgebra.toSubmodulestatement · cited by 90
Cited by1
Results whose statement or proof uses this declaration.
- LieAlgebra.Basis.coe_cartan_eq_spanproof · cited by 4