Theorems · Theorem · general algebraic systems

DFinsupp.sum_of_support_subset

∀ {ι : Type u} {γ : Type w} {β : ι → Type v} [inst : DecidableEq ι] [inst_1 : (i : ι) → Zero (β i)]
  [inst_2 : (i : ι) → (x : β i) → Decidable (x ≠ 0)] [inst_3 : AddCommMonoid γ] {f : Π₀ (i : ι), β i}
  {g : (i : ι) → β i → γ} {s : Finset ι}, f.support ⊆ s → (∀ i ∈ s, g i 0 = 0) → f.sum g = ∑ i ∈ s, g i (f i)

Defined in

Mathlib.Data.DFinsupp.BigOperators

Cited by

1 results in Mathlib

Foundations

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

Assumes

DecidableEqZeroDecidableAddCommMonoid