Theorems · Theorem · nonassociative algebras
LieSubalgebra.submodule_span_le_lieSpan
∀ {R : Type u} {L : Type v} [inst : CommRing R] [inst_1 : LieRing L] [inst_2 : LieAlgebra R L] {s : Set L},
Submodule.span R s ≤ (LieSubalgebra.lieSpan R L s).toSubmodule- Defined in
- Mathlib.Algebra.Lie.Subalgebra
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 65 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.
Cites11
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
- LieRingstatement and proof · cited by 1,548
- Submodule.spanstatement · cited by 1,504
- LieAlgebrastatement and proof · cited by 1,246
- Submodule.span_leproof · cited by 164
- LieSubalgebra.toSubmodulestatement · cited by 90
- LieSubalgebra.lieSpanstatement and proof · cited by 33
- LieSubalgebra.subset_lieSpanproof · cited by 19
- LieSubalgebra.coe_toSubmoduleproof · cited by 5
Cited by2
Results whose statement or proof uses this declaration.
- LieSubalgebra.coe_lieSpan_eq_span_of_forall_lie_eq_zeroproof · cited by 1
- RootPairing.GeckConstruction.cartanSubalgebra_eq_lieSpanproof · cited by 0