Theorems · Theorem · linear algebra

finsuppTensorFinsupp_apply

∀ (R : Type u_1) (S : Type u_2) (M : Type u_3) (N : Type u_4) (ι : Type u_5) (κ : Type u_6) [inst : CommSemiring R]
  [inst_1 : AddCommMonoid M] [inst_2 : Module R M] [inst_3 : AddCommMonoid N] [inst_4 : Module R N]
  [inst_5 : Semiring S] [inst_6 : Algebra R S] [inst_7 : Module S M] [inst_8 : IsScalarTower R S M] (f : ι →₀ M)
  (g : κ →₀ N) (i : ι) (k : κ), ((finsuppTensorFinsupp R S M N ι κ) (f ⊗ₜ[R] g)) (i, k) = f i ⊗ₜ[R] g k

Defined in

Mathlib.LinearAlgebra.DirectSum.Finsupp

Cited by

5 results in Mathlib

Foundations

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

Assumes

CommSemiringAddCommMonoidModuleAddCommMonoidModuleSemiringAlgebraModuleIsScalarTower