Theorems · Theorem · real analysis
Function.Antiperiodic.neg
∀ {α : Type u_1} {β : Type u_2} {f : α → β} {c : α} [inst : AddGroup α] [inst_1 : InvolutiveNeg β],
Function.Antiperiodic f c → Function.Antiperiodic f (-c)- Defined in
- Mathlib.Algebra.Ring.Periodic
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 12 from the axioms · uses propext, Quot.sound
- Assumes
- AddGroupInvolutiveNeg
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.
- AddGroupstatement and proof · cited by 4,410
- sub_eq_add_negproof · cited by 1,023
- InvolutiveNegstatement and proof · cited by 151
- Function.Antiperiodicstatement and proof · cited by 66
- Function.Antiperiodic.sub_eqproof · cited by 12
Cited by4
Results whose statement or proof uses this declaration.
- Function.Antiperiodic.int_mul_eq_of_eq_zeroproof · cited by 2
- Function.Periodic.sub_antiperiodproof · cited by 1
- Function.Antiperiodic.subproof · cited by 0
- Function.Antiperiodic.neg_eqproof · cited by 0