Theorems · Theorem · real analysis
Function.Periodic.add_antiperiod_eq
∀ {α : Type u_1} {β : Type u_2} {f : α → β} {c₁ c₂ : α} [inst : AddMonoid α] [inst_1 : Neg β],
Function.Periodic f c₁ → Function.Antiperiodic f c₂ → f (c₁ + c₂) = -f 0- Defined in
- Mathlib.Algebra.Ring.Periodic
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 8 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- AddMonoidstatement and proof · cited by 2,864
- Function.Periodicstatement and proof · cited by 154
- Function.Antiperiodicstatement and proof · cited by 66
- Function.Antiperiodic.eqproof · cited by 3
- Function.Periodic.add_antiperiodproof · cited by 2
Cited by4
Results whose statement or proof uses this declaration.
- Real.cos_int_mul_two_pi_add_piproof · cited by 1
- Real.cos_nat_mul_two_pi_add_piproof · cited by 0
- Complex.cos_nat_mul_two_pi_add_piproof · cited by 0
- Complex.cos_int_mul_two_pi_add_piproof · cited by 0