Theorems · Theorem · real analysis
Function.Antiperiodic.odd_zsmul_antiperiodic
∀ {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.Antiperiodic f ((2 * n + 1) • c)- Defined in
- Mathlib.Algebra.Ring.Periodic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 38 from the axioms · uses propext, Quot.sound
- Assumes
- AddGroupInvolutiveNeg
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
- add_assocproof · cited by 746
- InvolutiveNegstatement and proof · cited by 151
- Function.Antiperiodicstatement and proof · cited by 66
- one_zsmulproof · cited by 59
- add_zsmulproof · cited by 21
- Function.Antiperiodic.even_zsmul_periodicproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- Function.Antiperiodic.add_zsmul_eqproof · cited by 3