Theorems · Theorem · group theory

Finset.sum_ninvolution

∀ {ι : Type u_1} {M : Type u_4} {s : Finset ι} [inst : AddCommMonoid M] {f : ι → M} (g : ι → ι),
  (∀ (a : ι), f a + f (g a) = 0) →
    (∀ (a : ι), f a ≠ 0 → g a ≠ a) → (∀ (a : ι), g a ∈ s) → (∀ (a : ι), g (g a) = a) → ∑ x ∈ s, f x = 0

The difference with Finset.sum_involution is that the involution 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.Basic

Cited by

0 results in Mathlib

Foundations

Depth 67 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

AddCommMonoid