Theorems · Theorem · real analysis
Function.Periodic.nat_mul
∀ {α : Type u_1} {β : Type u_2} {f : α → β} {c : α} [inst : NonAssocSemiring α],
Function.Periodic f c → ∀ (n : ℕ), Function.Periodic f (↑n * c)- Defined in
- Mathlib.Algebra.Ring.Periodic
- Cited by
- 15 results in Mathlib
- Foundations
- Depth 21 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
- nsmul_eq_mulproof · cited by 369
- Function.Periodicstatement and proof · cited by 154
- Function.Periodic.nsmulproof · cited by 9
Cited by15
Results whose statement or proof uses this declaration.
- Function.Periodic.nat_mul_sub_eqproof · cited by 6
- Function.Periodic.nat_mul_eqproof · cited by 5
- Function.Antiperiodic.nat_even_mul_periodicproof · cited by 1
- EisensteinSeries.G2_T_transformproof · cited by 1
- Complex.sin_add_nat_mul_two_piproof · cited by 0
- Real.cos_add_nat_mul_two_piproof · cited by 0
- Real.cos_nat_mul_two_pi_add_piproof · cited by 0
- Real.cos_nat_mul_two_pi_sub_piproof · cited by 0
- Real.sin_add_nat_mul_two_piproof · cited by 0
- Real.tan_add_nat_mul_piproof · cited by 0
- Complex.cos_nat_mul_two_pi_add_piproof · cited by 0
- Complex.cos_nat_mul_two_pi_sub_piproof · cited by 0