Theorems · Theorem · group theory

Finset.sum_nbij

∀ {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} (i : ι → κ),
  (∀ a ∈ s, i a ∈ t) → Set.InjOn i ↑s → Set.SurjOn i ↑s ↑t → (∀ a ∈ s, f a = g (i a)) → ∑ x ∈ s, f x = ∑ x ∈ t, g x

Reorder a sum. The difference with Finset.sum_nbij' is that the bijection is specified as a surjective injection, rather than by an inverse function. The difference with Finset.sum_bij is that the bijection is a non-dependent function, rather than being allowed to use membership of the domain of the sum.

Defined in

Mathlib.Algebra.BigOperators.Group.Finset.Defs

Cited by

10 results in Mathlib

Foundations

Depth 55 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

AddCommMonoid