Theorems · Theorem · real analysis
Function.Antiperiodic.sub_nsmul_eq
∀ {α : Type u_1} {β : Type u_2} {f : α → β} {c x : α} [inst : AddGroup 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 74 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- AddGroupSubtractionMonoid
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- AddGroupstatement and proof · cited by 4,410
- Units.valproof · cited by 1,966
- SubtractionMonoidstatement and proof · cited by 208
- Int.negOnePowproof · cited by 156
- natCast_zsmulproof · cited by 118
- Function.Antiperiodicstatement and proof · cited by 66
- Function.Antiperiodic.sub_zsmul_eqproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- Function.Antiperiodic.sub_nat_mul_eqproof · cited by 2