Theorems · Theorem · nonassociative algebras

LieAlgebra.Basis.baseSupp_apply_smul_e

∀ {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) [inst_4 : Fintype ι] (i : ι) (x : ↥H),
  (b.baseSupp i) x • b.e i = ⁅x, b.e i⁆

Defined in: Mathlib.Algebra.Lie.Basis.Basic
Cited by: 3 results in Mathlib
Foundations: Depth 92 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: Finite CommRing LieRing LieAlgebra Fintype

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Cites35

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

DFunLike.coestatement and proof · cited by 62,936
RingHom.idstatement · cited by 18,349
CommRingstatement and proof · cited by 17,173
Fintypestatement and proof · cited by 7,736
Submoduleproof · cited by 7,192
Set.rangeproof · cited by 4,705
Finitestatement and proof · cited by 3,029
map_zeroproof · cited by 1,614
LieRingstatement and proof · cited by 1,548
Submodule.spanproof · cited by 1,504
LieAlgebrastatement and proof · cited by 1,246
map_addproof · cited by 964

Cited by3

Results whose statement or proof uses this declaration.

LieAlgebra.Basis.coroot_eq_h'proof · cited by 1
LieAlgebra.Basis.borelUpper_le_biSupproof · cited by 1
LieAlgebra.Basis.baseSupp_apply_smul_fproof · cited by 1