Theorems · Theorem · real analysis
Function.Periodic.sub_antiperiod
∀ {α : Type u_1} {β : Type u_2} {f : α → β} {c₁ c₂ : α} [inst : AddGroup α] [inst_1 : InvolutiveNeg β],
Function.Periodic f c₁ → Function.Antiperiodic f c₂ → Function.Antiperiodic f (c₁ - c₂)- Defined in
- Mathlib.Algebra.Ring.Periodic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 13 from the axioms · uses propext, Quot.sound
- Assumes
- AddGroupInvolutiveNeg
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- AddGroupstatement and proof · cited by 4,410
- sub_eq_add_negproof · cited by 1,023
- Function.Periodicstatement and proof · cited by 154
- InvolutiveNegstatement and proof · cited by 151
- Function.Antiperiodicstatement and proof · cited by 66
- Function.Antiperiodic.negproof · cited by 4
- Function.Periodic.add_antiperiodproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- Function.Periodic.sub_antiperiod_eqproof · cited by 4