Theorems · Theorem · linear algebra

TensorProduct.finsuppLeft_apply_tmul_apply

∀ {R : Type u_1} {S : Type u_2} [inst : CommSemiring R] [inst_1 : Semiring S] [inst_2 : Algebra R S] {M : Type u_3}
  [inst_3 : AddCommMonoid M] [inst_4 : Module R M] [inst_5 : Module S M] [inst_6 : IsScalarTower R S M] {N : Type u_4}
  [inst_7 : AddCommMonoid N] [inst_8 : Module R N] {ι : Type u_5} [inst_9 : DecidableEq ι] (p : ι →₀ M) (n : N) (i : ι),
  ((TensorProduct.finsuppLeft R S M N ι) (p ⊗ₜ[R] n)) i = p i ⊗ₜ[R] n

Defined in

Mathlib.LinearAlgebra.DirectSum.Finsupp

Cited by

2 results in Mathlib

Foundations

Depth 95 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommSemiringSemiringAlgebraAddCommMonoidModuleModuleIsScalarTowerAddCommMonoidModuleDecidableEq