Theorems · Theorem · real analysis
Function.Antiperiodic.add_nsmul_eq
∀ {α : Type u_1} {β : Type u_2} {f : α → β} {c x : α} [inst : AddMonoid α] [inst_1 : SubtractionMonoid β],
Function.Antiperiodic f c → ∀ (n : ℕ), f (x + n • c) = (-1) ^ n • f x- Defined in
- Mathlib.Algebra.Ring.Periodic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 71 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- AddMonoidSubtractionMonoid
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites14
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- mul_oneproof · cited by 3,885
- AddMonoidstatement and proof · cited by 2,864
- one_smulproof · cited by 1,374
- pow_oneproof · cited by 894
- mul_negproof · cited by 590
- one_powproof · cited by 521
- pow_addproof · cited by 315
- SubtractionMonoidstatement and proof · cited by 208
- Even.neg_powproof · cited by 99
- Function.Antiperiodicstatement and proof · cited by 66
- neg_zsmulproof · cited by 41
- Nat.even_or_odd'proof · cited by 7
Cited by1
Results whose statement or proof uses this declaration.
- Function.Antiperiodic.add_nat_mul_eqproof · cited by 2