Theorems · Theorem · real analysis
Function.Periodic.sub_eq
∀ {α : Type u_1} {β : Type u_2} {f : α → β} {c : α} [inst : AddGroup α],
Function.Periodic f c → ∀ (x : α), f (x - c) = f x- Defined in
- Mathlib.Algebra.Ring.Periodic
- Cited by
- 13 results in Mathlib
- Foundations
- Depth 9 from the axioms · uses no axioms
- Assumes
- AddGroup
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites3
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
- Function.Periodicstatement and proof · cited by 154
Cited by13
Results whose statement or proof uses this declaration.
- Function.Periodic.negproof · cited by 8
- Function.Periodic.sub_int_mul_eqproof · cited by 7
- Function.Periodic.sub_zsmul_eqproof · cited by 3
- Complex.cos_sub_two_piproof · cited by 1
- Complex.sin_sub_two_piproof · cited by 1
- Complex.tanh_sub_pi_mul_Iproof · cited by 0
- Real.sin_sub_two_piproof · cited by 0
- Circle.exp_sub_two_piproof · cited by 0
- Real.Angle.tan_sub_piproof · cited by 0
- Real.cos_sub_two_piproof · cited by 0
- Complex.tan_sub_piproof · cited by 0
- Real.tan_sub_piproof · cited by 0