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Theorems · Theorem · real analysis

Function.Periodic.neg_nsmul

∀ {α : Type u_1} {β : Type u_2} {f : α → β} {c : α} [inst : AddGroup α],
  Function.Periodic f c → ∀ (n : ℕ), Function.Periodic f (-(n • c))
Defined in
Mathlib.Algebra.Ring.Periodic
Cited by
1 results in Mathlib
Foundations
Depth 21 from the axioms · uses propext, Quot.sound
Assumes
AddGroup
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Function.Periodic.sub_nsmul_eq · cited by 1Periodic.sub_nsmul_eqAddGroup · cited by 4410AddGroupFunction.Periodic · cited by 154Function.PeriodicFunction.Periodic.nsmul · cited by 9Periodic.nsmulFunction.Periodic.neg · cited by 8Periodic.negPeriodic.neg_nsmulCITED BYCITES

Cites4

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Cited by1

Results whose statement or proof uses this declaration.