Theorems · Theorem · real analysis
Function.Periodic.not_injective
∀ {R : Type u_4} {X : Type u_5} [inst : AddZeroClass R] {f : R → X} {c : R},
Function.Periodic f c → c ≠ 0 → ¬Function.Injective fA periodic function f : R → X on a semiring (or, more generally, AddZeroClass)
of non-zero period is not injective.
- Defined in
- Mathlib.Algebra.Ring.Periodic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 7 from the axioms · uses no axioms
- Assumes
- AddZeroClass
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.
- AddZeroClassstatement and proof · cited by 1,237
- Function.Periodicstatement and proof · cited by 154
- Function.Periodic.eqproof · cited by 12
Cited by1
Results whose statement or proof uses this declaration.
- IsMIntegralCurve.periodic_xor_injectiveproof · cited by 0