Theorems · Theorem · real analysis
Function.Periodic.zsmul
∀ {α : Type u_1} {β : Type u_2} {f : α → β} {c : α} [inst : AddGroup α],
Function.Periodic f c → ∀ (n : ℤ), Function.Periodic f (n • c)- Defined in
- Mathlib.Algebra.Ring.Periodic
- Cited by
- 9 results in Mathlib
- Foundations
- Depth 21 from the axioms · uses propext, Quot.sound
- Assumes
- AddGroup
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.
- AddGroupstatement and proof · cited by 4,410
- Function.Periodicstatement and proof · cited by 154
- natCast_zsmulproof · cited by 118
- negSucc_zsmulproof · cited by 45
- Function.Periodic.nsmulproof · cited by 9
- Function.Periodic.negproof · cited by 8
Cited by9
Results whose statement or proof uses this declaration.
- Function.Periodic.int_mulproof · cited by 18
- Function.Periodic.sub_zsmul_eqproof · cited by 3
- Function.Periodic.intervalIntegral_add_zsmul_eqproof · cited by 2
- Function.Antiperiodic.even_zsmul_periodicproof · cited by 2
- Function.Periodic.map_vadd_zmultiplesproof · cited by 1
- Function.Periodic.exists_mem_Iocproof · cited by 1
- Function.Periodic.exists_mem_Icoproof · cited by 0
- Function.Periodic.zsmul_eqproof · cited by 0
- Function.Periodic.zsmul_sub_eqproof · cited by 0