Theorems · Theorem · nonassociative algebras

LieAlgebra.Basis.span_ef

∀ {ι : Type u_1} {R : Type u_2} {L : Type u_3} [inst : Finite ι] [inst_1 : CommRing R] [inst_2 : LieRing L]
  [inst_3 : LieAlgebra R L] {H : LieSubalgebra R L} (self : LieAlgebra.Basis ι H),
  LieSubalgebra.lieSpan R L (Set.range self.e ∪ Set.range self.f) = ⊤

Defined in: Mathlib.Algebra.Lie.Basis.Basic
Cited by: 1 results in Mathlib
Foundations: Depth 20 from the axioms · uses propext, Quot.sound
Assumes: Finite CommRing LieRing LieAlgebra

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Cites12

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Setstatement · cited by 53,352
CommRingstatement and proof · cited by 17,173
Top.topstatement · cited by 9,680
Set.rangestatement · cited by 4,705
Finitestatement and proof · cited by 3,029
LieRingstatement and proof · cited by 1,548
LieAlgebrastatement and proof · cited by 1,246
LieSubalgebrastatement and proof · cited by 418
LieAlgebra.Basisstatement and proof · cited by 44
LieSubalgebra.lieSpanstatement · cited by 33
LieAlgebra.Basis.estatement · cited by 15
LieAlgebra.Basis.fstatement · cited by 12

Cited by1

Results whose statement or proof uses this declaration.

LieAlgebra.Basis.iSup_cartan_borelLower_borelUpper_eq_topproof · cited by 4