Theorems · Theorem · linear algebra

Finsupp.lsum_single

∀ {α : Type u_1} {M : Type u_2} {N : Type u_3} {R : Type u_5} {R₂ : Type u_6} (S : Type u_8) [inst : Semiring R]
  [inst_1 : Semiring R₂] [inst_2 : Semiring S] [inst_3 : AddCommMonoid M] [inst_4 : Module R M]
  [inst_5 : AddCommMonoid N] [inst_6 : Module R₂ N] {σ : R →+* R₂} [inst_7 : Module S N] [inst_8 : SMulCommClass R₂ S N]
  (f : α → M →ₛₗ[σ] N) (i : α) (m : M), (((Finsupp.lsum S) f) fun₀ | i => m) = (f i) m

Defined in

Mathlib.LinearAlgebra.Finsupp.LSum

Cited by

2 results in Mathlib

Foundations

Depth 77 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

SemiringSemiringSemiringAddCommMonoidModuleAddCommMonoidModuleModuleSMulCommClass