Theorems · Theorem · real analysis
Function.Antiperiodic.sub_eq
∀ {α : Type u_1} {β : Type u_2} {f : α → β} {c : α} [inst : AddGroup α] [inst_1 : InvolutiveNeg β],
Function.Antiperiodic f c → ∀ (x : α), f (x - c) = -f x- Defined in
- Mathlib.Algebra.Ring.Periodic
- Cited by
- 12 results in Mathlib
- Foundations
- Depth 9 from the axioms · uses propext
- Assumes
- AddGroupInvolutiveNeg
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
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_add_cancelproof · cited by 344
- InvolutiveNegstatement and proof · cited by 151
- Function.Antiperiodicstatement and proof · cited by 66
Cited by12
Results whose statement or proof uses this declaration.
- Function.Antiperiodic.negproof · cited by 4
- Real.sin_sub_piproof · cited by 1
- Complex.cos_sub_piproof · cited by 1
- Real.cos_sub_piproof · cited by 1
- Real.Angle.cos_sub_piproof · cited by 0
- Complex.cosh_sub_pi_mul_Iproof · cited by 0
- Complex.sinh_sub_pi_mul_Iproof · cited by 0
- Real.Angle.sign_sub_piproof · cited by 0
- Complex.sin_sub_piproof · cited by 0
- Complex.exp_sub_pi_mul_Iproof · cited by 0
- Real.Angle.sin_sub_piproof · cited by 0
- Function.Antiperiodic.const_subproof · cited by 0