Theorems · Theorem · real analysis
Function.Antiperiodic.even_zsmul_periodic
∀ {α : Type u_1} {β : Type u_2} {f : α → β} {c : α} [inst : AddGroup α] [inst_1 : InvolutiveNeg β],
Function.Antiperiodic f c → ∀ (n : ℤ), Function.Periodic f ((2 * n) • c)- Defined in
- Mathlib.Algebra.Ring.Periodic
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 37 from the axioms · uses propext, Quot.sound
- Assumes
- AddGroupInvolutiveNeg
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.
- AddGroupstatement and proof · cited by 4,410
- mul_commproof · cited by 2,262
- Function.Periodicstatement and proof · cited by 154
- InvolutiveNegstatement and proof · cited by 151
- two_nsmulproof · cited by 67
- Function.Antiperiodicstatement and proof · cited by 66
- two_zsmulproof · cited by 21
- Function.Periodic.zsmulproof · cited by 9
- mul_zsmulproof · cited by 5
- Function.Antiperiodic.periodicproof · cited by 3
Cited by2
Results whose statement or proof uses this declaration.
- Function.Antiperiodic.add_zsmul_eqproof · cited by 3
- Function.Antiperiodic.odd_zsmul_antiperiodicproof · cited by 1