Mathlib Map

Theorems · Theorem · real analysis

Function.Antiperiodic.odd_nsmul_antiperiodic

∀ {α : Type u_1} {β : Type u_2} {f : α → β} {c : α} [inst : AddMonoid α] [inst_1 : InvolutiveNeg β],
  Function.Antiperiodic f c → ∀ (n : ℕ), Function.Antiperiodic f ((2 * n + 1) • c)
Defined in
Mathlib.Algebra.Ring.Periodic
Cited by
1 results in Mathlib
Foundations
Depth 22 from the axioms · uses propext, Quot.sound
Assumes
AddMonoidInvolutiveNeg
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

Function.Antiperiodic.add_nsmul_eq · cited by 1Antiperiodic.add_nsmul_eqAddMonoid · cited by 2864AddMonoidadd_assoc · cited by 746add_assocInvolutiveNeg · cited by 151InvolutiveNegFunction.Antiperiodic · cited by 66Function.Antiperiodicone_nsmul · cited by 63one_nsmuladd_nsmul · cited by 44add_nsmulFunction.Antiperiodic.even_nsmul_periodic · cited by 2Antiperiodic.even_nsmul_p…Antiperiodic.odd_nsmul_antipe…CITED BYCITES

Cites7

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by1

Results whose statement or proof uses this declaration.