Theorems · Theorem · group theory

Finset.sum_image_of_pairwise_eq_zero

∀ {ι : Type u_1} {κ : Type u_2} {M : Type u_4} [inst : AddCommMonoid M] [inst_1 : DecidableEq ι] {f : κ → ι} {g : ι → M}
  {I : Finset κ}, ((↑I).Pairwise fun i j => f i = f j → g (f i) = 0) → ∑ s ∈ Finset.image f I, g s = ∑ i ∈ I, g (f i)

A version of Finset.sum_map and Finset.sum_image, but we do not assume that f is injective. Rather, we assume that the image of f on I only overlaps where g (f i) = 0. The conclusion is the same as in sum_image.

Defined in

Mathlib.Algebra.BigOperators.Group.Finset.Basic

Cited by

3 results in Mathlib

Foundations

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

Assumes

AddCommMonoidDecidableEq