Theorems · Theorem · nonassociative algebras

LieAlgebra.Basis.coe_cartan_eq_span

∀ {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} (b : LieAlgebra.Basis ι H),
  H.toSubmodule = Submodule.span R (Set.range b.h)

Defined in: Mathlib.Algebra.Lie.Basis.Basic
Cited by: 4 results in Mathlib
Foundations: Depth 67 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: Finite CommRing LieRing LieAlgebra

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Cites15

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
Submodulestatement and proof · cited by 7,192
Set.rangestatement and proof · cited by 4,705
Finitestatement and proof · cited by 3,029
LieRingstatement and proof · cited by 1,548
Submodule.spanstatement and proof · cited by 1,504
LieAlgebrastatement and proof · cited by 1,246
LieSubalgebrastatement and proof · cited by 418
LieSubalgebra.toSubmodulestatement and proof · cited by 90
LieAlgebra.Basisstatement and proof · cited by 44
LieSubalgebra.lieSpanproof · cited by 33
LieAlgebra.Basis.hstatement and proof · cited by 17

Cited by5

Results whose statement or proof uses this declaration.

LieAlgebra.Basis.baseSuppproof · cited by 15
LieAlgebra.Basis.baseSupp_apply_h'proof · cited by 3
LieAlgebra.Basis.baseSupp_apply_smul_eproof · cited by 3
LieAlgebra.Basis.linearIndependent_baseSuppproof · cited by 3
LieAlgebra.Basis.symm_baseSuppproof · cited by 2