Theorems · Theorem · real analysis
Function.Antiperiodic.periodic_two_mul
∀ {α : Type u_1} {β : Type u_2} {f : α → β} {c : α} [inst : NonAssocSemiring α] [inst_1 : InvolutiveNeg β],
Function.Antiperiodic f c → Function.Periodic f (2 * c)If a function is antiperiodic with antiperiod c, then it is also Periodic with period
2 * c.
- Defined in
- Mathlib.Algebra.Ring.Periodic
- Cited by
- 10 results in Mathlib
- Foundations
- Depth 18 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- NonAssocSemiringstatement and proof · cited by 805
- nsmul_eq_mulproof · cited by 369
- Function.Periodicstatement · cited by 154
- InvolutiveNegstatement and proof · cited by 151
- Function.Antiperiodicstatement and proof · cited by 66
- Function.Antiperiodic.periodicproof · cited by 3
Cited by10
Results whose statement or proof uses this declaration.
- Real.cos_periodicproof · cited by 16
- Complex.cos_periodicproof · cited by 15
- Real.sin_periodicproof · cited by 10
- Complex.sin_periodicproof · cited by 9
- Complex.exp_periodicproof · cited by 8
- Complex.exp_mul_I_periodicproof · cited by 2
- Function.Antiperiodic.int_even_mul_periodicproof · cited by 1
- Function.Antiperiodic.nat_even_mul_periodicproof · cited by 1
- Complex.sinh_periodicproof · cited by 0
- Complex.cosh_periodicproof · cited by 0