Theorems · Theorem · real analysis
Function.Periodic.nat_mul_eq
∀ {α : Type u_1} {β : Type u_2} {f : α → β} {c : α} [inst : NonAssocSemiring α],
Function.Periodic f c → ∀ (n : ℕ), f (↑n * c) = f 0- Defined in
- Mathlib.Algebra.Ring.Periodic
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 22 from the axioms · uses propext, Quot.sound
- Assumes
- NonAssocSemiring
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.
- NonAssocSemiringstatement and proof · cited by 805
- Function.Periodicstatement and proof · cited by 154
- Function.Periodic.nat_mulproof · cited by 15
- Function.Periodic.eqproof · cited by 12
Cited by5
Results whose statement or proof uses this declaration.
- Complex.cos_nat_mul_two_piproof · cited by 0
- Complex.exp_nat_mul_two_pi_mul_Iproof · cited by 0
- Real.tan_nat_mul_piproof · cited by 0
- Complex.tan_nat_mul_piproof · cited by 0
- Real.cos_nat_mul_two_piproof · cited by 0