Theorems · Theorem · real analysis
Function.Periodic.int_mul
∀ {α : Type u_1} {β : Type u_2} {f : α → β} {c : α} [inst : NonAssocRing α],
Function.Periodic f c → ∀ (n : ℤ), Function.Periodic f (↑n * c)- Defined in
- Mathlib.Algebra.Ring.Periodic
- Cited by
- 18 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
- zsmul_eq_mulproof · cited by 120
- Function.Periodic.zsmulproof · cited by 9
Cited by18
Results whose statement or proof uses this declaration.
- Function.Periodic.sub_int_mul_eqproof · cited by 7
- Function.Periodic.int_mul_sub_eqproof · cited by 6
- Function.Periodic.int_mul_eqproof · cited by 5
- Function.Periodic.eq_cuspFunctionproof · cited by 4
- Complex.exp_eq_one_iffproof · cited by 3
- Complex.sin_add_int_mul_two_piproof · cited by 1
- Real.Angle.tan_eq_inv_of_two_nsmul_add_two_nsmul_eq_piproof · cited by 1
- Function.Antiperiodic.int_even_mul_periodicproof · cited by 1
- Complex.cos_add_int_mul_two_piproof · cited by 1
- Real.fourierCoeff_tsum_comp_addproof · cited by 1
- Real.cos_int_mul_two_pi_add_piproof · cited by 1
- Real.cos_int_mul_two_pi_sub_piproof · cited by 0