Theorems · Theorem · real analysis
Function.Odd.sum_eq_zero
∀ {α : Type u_3} {β : Type u_4} [inst : AddCommGroup β] [IsAddTorsionFree β] [inst_2 : Fintype α]
[inst_3 : InvolutiveNeg α] {f : α → β}, Function.Odd f → ∑ a, f a = 0The sum of the values of an odd function is 0.
- Defined in
- Mathlib.Algebra.Group.EvenFunction
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 61 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- AddCommGroupstatement and proof · cited by 12,871
- Fintypestatement and proof · cited by 7,736
- Finset.sumstatement · cited by 5,195
- Finset.univstatement · cited by 3,473
- IsAddTorsionFreestatement and proof · cited by 155
- InvolutiveNegstatement and proof · cited by 151
- Equiv.negproof · cited by 53
- Function.Oddstatement and proof · cited by 38
- Finset.map_univ_equivproof · cited by 12
- Function.Odd.finsetSum_eq_zeroproof · cited by 2
Cited by3
Results whose statement or proof uses this declaration.
- ZMod.completedLFunction_def_evenproof · cited by 2
- ZMod.completedLFunction_def_oddproof · cited by 1
- ZMod.completedLFunction_one_sub_oddproof · cited by 1