Theorems · Theorem · linear algebra

Finsupp.coe_basis

∀ {R : Type u_1} {M : Type u_2} {ι : Type u_3} [inst : Semiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M]
  {φ : ι → Type u_4} (b : (i : ι) → Module.Basis (φ i) R M),
  ⇑(Finsupp.basis b) = fun ix => fun₀ | ix.fst => (b ix.fst) ix.snd

Defined in: Mathlib.LinearAlgebra.Finsupp.VectorSpace
Cited by: 0 results in Mathlib
Foundations: Depth 86 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: Semiring AddCommMonoid Module

Mathlib docs Source Loogle LeanSearch

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Cites17

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
Modulestatement and proof · cited by 20,661
Semiringstatement and proof · cited by 13,802
AddCommMonoidstatement and proof · cited by 12,281
Finsuppstatement · cited by 5,255
map_zeroproof · cited by 1,614
Module.Basisstatement and proof · cited by 1,477
Finsupp.singlestatement and proof · cited by 943
Module.Basis.reprproof · cited by 498
Finsupp.extproof · cited by 399
Finsupp.single_eq_sameproof · cited by 171
Module.Basis.repr_selfproof · cited by 82

Cited by0

Results whose statement or proof uses this declaration.

Nothing cites this yet.