Theorems · Theorem · real analysis
Function.Periodic.nat_mul_sub_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 (↑n * c - x) = f (-x)- Defined in
- Mathlib.Algebra.Ring.Periodic
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 22 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
- Function.Periodicstatement and proof · cited by 154
- sub_eq_neg_addproof · cited by 51
- Function.Periodic.nat_mulproof · cited by 15
Cited by6
Results whose statement or proof uses this declaration.
- Complex.cos_nat_mul_two_pi_subproof · cited by 0
- Real.tan_nat_mul_pi_subproof · cited by 0
- Complex.tan_nat_mul_pi_subproof · cited by 0
- Real.sin_nat_mul_two_pi_subproof · cited by 0
- Complex.sin_nat_mul_two_pi_subproof · cited by 0
- Real.cos_nat_mul_two_pi_subproof · cited by 0