Theorems · Theorem · real analysis
Function.Antiperiodic.even_nsmul_periodic
∀ {α : Type u_1} {β : Type u_2} {f : α → β} {c : α} [inst : AddMonoid α] [inst_1 : InvolutiveNeg β],
Function.Antiperiodic f c → ∀ (n : ℕ), Function.Periodic f ((2 * n) • c)- Defined in
- Mathlib.Algebra.Ring.Periodic
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 21 from the axioms · uses propext, Quot.sound
- Assumes
- AddMonoidInvolutiveNeg
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.
- AddMonoidstatement and proof · cited by 2,864
- Function.Periodicstatement · cited by 154
- InvolutiveNegstatement and proof · cited by 151
- Function.Antiperiodicstatement and proof · cited by 66
- mul_nsmulproof · cited by 24
- Function.Periodic.nsmulproof · cited by 9
- Function.Antiperiodic.periodicproof · cited by 3
Cited by2
Results whose statement or proof uses this declaration.
- Function.Antiperiodic.add_nsmul_eqproof · cited by 1
- Function.Antiperiodic.odd_nsmul_antiperiodicproof · cited by 1