Theorems · Theorem · field theory
Function.Antiperiodic.nat_mul_sub_eq
∀ {α : Type u_1} {β : Type u_2} {f : α → β} {c x : α} [inst : NonAssocRing α] [inst_1 : Ring β],
Function.Antiperiodic f c → ∀ (n : ℕ), f (↑n * c - x) = (-1) ^ n * f (-x)- Defined in
- Mathlib.Algebra.Field.Periodic
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 75 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- NonAssocRingRing
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Ringstatement and proof · cited by 7,463
- NonAssocRingstatement and proof · cited by 483
- Int.cast_oneproof · cited by 371
- nsmul_eq_mulproof · cited by 369
- Int.cast_negproof · cited by 224
- zsmul_eq_mulproof · cited by 120
- Function.Antiperiodicstatement and proof · cited by 66
- Int.cast_powproof · cited by 59
- Function.Antiperiodic.nsmul_sub_eqproof · cited by 1
Cited by2
Results whose statement or proof uses this declaration.
- Real.cos_nat_mul_pi_subproof · cited by 2
- Real.sin_nat_mul_pi_subproof · cited by 0