Theorems · Theorem · general algebraic systems

DFinsupp.sum_add_index

∀ {ι : Type u} {γ : Type w} {β : ι → Type v} [inst : DecidableEq ι] [inst_1 : (i : ι) → AddCommMonoid (β i)]
  [inst_2 : (i : ι) → (x : β i) → Decidable (x ≠ 0)] [inst_3 : AddCommMonoid γ] {f g : Π₀ (i : ι), β i}
  {h : (i : ι) → β i → γ},
  (∀ (i : ι), h i 0 = 0) →
    (∀ (i : ι) (b₁ b₂ : β i), h i (b₁ + b₂) = h i b₁ + h i b₂) → (f + g).sum h = f.sum h + g.sum h

Defined in

Mathlib.Data.DFinsupp.BigOperators

Cited by

1 results in Mathlib

Foundations

Depth 80 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

DecidableEqAddCommMonoidDecidableAddCommMonoid