Theorems · Theorem · group theory

Finset.sum_image_of_disjoint

∀ {ι : Type u_1} {κ : Type u_2} {M : Type u_4} [inst : AddCommMonoid M] [inst_1 : DecidableEq ι]
  [inst_2 : PartialOrder ι] [inst_3 : OrderBot ι] {f : κ → ι} {g : ι → M},
  g ⊥ = 0 → ∀ {I : Finset κ}, (↑I).PairwiseDisjoint f → ∑ 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 images of f are disjoint on I, and g ⊥ = 0. The conclusion is the same as in sum_image.

Defined in

Mathlib.Algebra.BigOperators.Group.Finset.Basic

Cited by

1 results in Mathlib

Foundations

Depth 78 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

AddCommMonoidDecidableEqPartialOrderOrderBot