Theorems · Theorem · nonassociative algebras
LieSubalgebra.lie_mem
∀ {R : Type u} {L : Type v} [inst : CommRing R] [inst_1 : LieRing L] [inst_2 : LieAlgebra R L] (L' : LieSubalgebra R L)
{x y : L}, x ∈ L' → y ∈ L' → ⁅x, y⁆ ∈ L'- Defined in
- Mathlib.Algebra.Lie.Subalgebra
- Cited by
- 10 results in Mathlib
- Foundations
- Depth 13 from the axioms · uses no axioms
- Assumes
- CommRingLieRingLieAlgebra
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CommRingstatement and proof · cited by 17,173
- LieRingstatement and proof · cited by 1,548
- LieAlgebrastatement and proof · cited by 1,246
- Bracket.bracketstatement · cited by 642
- LieSubalgebrastatement and proof · cited by 418
- LieSubalgebra.lie_mem'proof · cited by 2
Cited by10
Results whose statement or proof uses this declaration.
- LieSubalgebra.lieSpan_inductionstatement and proof · cited by 9
- LieAlgebra.Basis.iSup_cartan_borelLower_borelUpper_eq_topproof · cited by 4
- LieAlgebra.engel_isBot_of_isMinproof · cited by 1
- LieAlgebra.isEngelian_of_isNoetherianproof · cited by 1
- LieSubalgebra.lie_mem_sup_of_mem_normalizerproof · cited by 1
- LieSubalgebra.coe_lieSpan_submodule_eq_iffproof · cited by 0
- RootPairing.GeckConstruction.ωConj_mem_of_memproof · cited by 0
- LieSubalgebra.comap_lieSpan_range_eqproof · cited by 0
- LieSubalgebra.lieSpan_lieSpan_coe_preimageproof · cited by 0
- LieSubalgebra.lieSpan_negproof · cited by 0