Theorems · Theorem · real analysis
Function.Antiperiodic.int_mul_eq_of_eq_zero
∀ {α : Type u_1} {β : Type u_2} {f : α → β} {c : α} [inst : NonAssocRing α] [inst_1 : SubtractionMonoid β],
Function.Antiperiodic f c → f 0 = 0 → ∀ (n : ℤ), f (↑n * c) = 0- Defined in
- Mathlib.Algebra.Ring.Periodic
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 16 from the axioms · uses propext, Quot.sound
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.
- neg_mulproof · cited by 654
- mul_negproof · cited by 590
- NonAssocRingstatement and proof · cited by 483
- Int.cast_natCastproof · cited by 393
- SubtractionMonoidstatement and proof · cited by 208
- Function.Antiperiodicstatement and proof · cited by 66
- Int.cast_negSuccproof · cited by 32
- Function.Antiperiodic.negproof · cited by 4
- Function.Antiperiodic.nat_mul_eq_of_eq_zeroproof · cited by 3
Cited by2
Results whose statement or proof uses this declaration.
- Real.sin_int_mul_piproof · cited by 5
- Complex.sin_int_mul_piproof · cited by 0