Theorems · Theorem · linear algebra

LinearMap.finsupp_sum_apply

∀ {R : Type u_4} {R₂ : Type u_5} {M : Type u_6} {M₂ : Type u_7} {ι : Type u_8} [inst : Semiring R]
  [inst_1 : Semiring R₂] [inst_2 : AddCommMonoid M] [inst_3 : AddCommMonoid M₂] {σ₁₂ : R →+* R₂} [inst_4 : Module R M]
  [inst_5 : Module R₂ M₂] {γ : Type u_9} [inst_6 : Zero γ] (t : ι →₀ γ) (g : ι → γ → M →ₛₗ[σ₁₂] M₂) (b : M),
  (t.sum g) b = t.sum fun i d => (g i d) b

Defined in

Mathlib.LinearAlgebra.Finsupp.LSum

Cited by

3 results in Mathlib

Foundations

Depth 60 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

SemiringSemiringAddCommMonoidAddCommMonoidModuleModuleZero