Theorems · Theorem · nonassociative algebras
LieSubalgebra.subset_lieSpan
∀ {R : Type u} {L : Type v} [inst : CommRing R] [inst_1 : LieRing L] [inst_2 : LieAlgebra R L] {s : Set L},
s ⊆ ↑(LieSubalgebra.lieSpan R L s)- Defined in
- Mathlib.Algebra.Lie.Subalgebra
- Cited by
- 19 results in Mathlib
- Foundations
- Depth 64 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.
Cites9
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
- SetLike.coestatement and proof · cited by 8,199
- LieRingstatement and proof · cited by 1,548
- LieAlgebrastatement and proof · cited by 1,246
- LieSubalgebrastatement and proof · cited by 418
- SetLike.mem_coeproof · cited by 302
- LieSubalgebra.lieSpanstatement · cited by 33
- LieSubalgebra.mem_lieSpanproof · cited by 2
Cited by19
Results whose statement or proof uses this declaration.
- LieSubalgebra.lieSpan_inductionstatement and proof · cited by 9
- LieSubalgebra.lieSpan_leproof · cited by 7
- LieAlgebra.Basis.iSup_cartan_borelLower_borelUpper_eq_topproof · cited by 4
- LieSubalgebra.submodule_span_le_lieSpanproof · cited by 2
- LieSubalgebra.isLieAbelian_lieSpan_iffproof · cited by 1
- LieSubalgebra.lieSpan_eqproof · cited by 1
- RootPairing.GeckConstruction.h_mem_lieAlgebraproof · cited by 1
- LieAlgebra.Basis.coroot_eq_h'proof · cited by 1
- LieSubalgebra.span_univproof · cited by 0
- LieSubalgebra.coe_lieSpan_submodule_eq_iffproof · cited by 0
- RootPairing.GeckConstruction.ωConj_mem_of_memproof · cited by 0
- LieSubalgebra.lieSpan_lieSpan_coe_preimageproof · cited by 0