Theorems · Theorem · group theory

Finset.sum_bijective

∀ {ι : Type u_1} {κ : Type u_2} {M : Type u_3} [inst : AddCommMonoid M] {s : Finset ι} {t : Finset κ} {f : ι → M}
  {g : κ → M} (e : ι → κ),
  Function.Bijective e → (∀ (i : ι), i ∈ s ↔ e i ∈ t) → (∀ i ∈ s, f i = g (e i)) → ∑ i ∈ s, f i = ∑ i ∈ t, g i

Specialization of Finset.sum_bij that automatically fills in most arguments. See Fintype.sum_bijective for the version where s and t are univ.

Defined in

Mathlib.Algebra.BigOperators.Group.Finset.Defs

Cited by

4 results in Mathlib

Foundations

Depth 58 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

AddCommMonoid