Theorems · Theorem · linear algebra

PiTensorProduct.ofDFinsuppEquiv_tprod_single

∀ {R : Type u_1} {ι : Type u_2} {κ : ι → Type u_3} {M : (i : ι) → κ i → Type u_4} [inst : CommSemiring R]
  [inst_1 : (i : ι) → (j : κ i) → AddCommMonoid (M i j)] [inst_2 : (i : ι) → (j : κ i) → Module R (M i j)]
  [inst_3 : Fintype ι] [inst_4 : DecidableEq ι] [inst_5 : (i : ι) → DecidableEq (κ i)] (p : (i : ι) → κ i)
  (x : (i : ι) → M i (p i)),
  PiTensorProduct.ofDFinsuppEquiv ((PiTensorProduct.tprod R) fun i => fun₀ | p i => x i) =
    fun₀ | p => (PiTensorProduct.tprod R) fun i => x i

Defined in

Mathlib.LinearAlgebra.PiTensorProduct.DFinsupp

Cited by

2 results in Mathlib

Foundations

Depth 92 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommSemiringAddCommMonoidModuleFintypeDecidableEqDecidableEq