Theorems · Theorem · real analysis

Function.Odd.finsetSum_eq_zero

∀ {α : Type u_3} {β : Type u_4} [inst : AddCommGroup β] [IsAddTorsionFree β] [inst_2 : InvolutiveNeg α] {f : α → β},
  Function.Odd f → ∀ {s : Finset α}, Finset.map (Equiv.toEmbedding (Equiv.neg α)) s = s → s.sum f = 0

The sum of values of an odd function over a symmetric finite set is zero.

Defined in

Mathlib.Algebra.Group.EvenFunction

Cited by

2 results in Mathlib

Foundations

Depth 56 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

AddCommGroupIsAddTorsionFreeInvolutiveNeg