Theorems · Theorem · real analysis
Function.Periodic.sub_nat_mul_eq
∀ {α : Type u_1} {β : Type u_2} {f : α → β} {c x : α} [inst : NonAssocRing α],
Function.Periodic f c → ∀ (n : ℕ), f (x - ↑n * c) = f x- Defined in
- Mathlib.Algebra.Ring.Periodic
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 23 from the axioms · uses propext, Quot.sound
- Assumes
- NonAssocRing
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- NonAssocRingstatement and proof · cited by 483
- nsmul_eq_mulproof · cited by 369
- Function.Periodicstatement and proof · cited by 154
- Function.Periodic.sub_nsmul_eqproof · cited by 1
Cited by6
Results whose statement or proof uses this declaration.
- Real.cos_sub_nat_mul_two_piproof · cited by 0
- Complex.cos_sub_nat_mul_two_piproof · cited by 0
- Complex.tan_sub_nat_mul_piproof · cited by 0
- Real.tan_sub_nat_mul_piproof · cited by 0
- Complex.sin_sub_nat_mul_two_piproof · cited by 0
- Real.sin_sub_nat_mul_two_piproof · cited by 0