Theorems · Theorem · dynamical systems
Function.Injective.mem_periodicPts
∀ {α : Type u_1} {f : α → α} [Finite α], Function.Injective f → ∀ (x : α), x ∈ Function.periodicPts f- Defined in
- Mathlib.Dynamics.PeriodicPts.Lemmas
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 64 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Finite
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- Finitestatement and proof · cited by 3,029
- Nat.iterateproof · cited by 740
- lt_or_gt_of_neproof · cited by 41
- Function.periodicPtsstatement · cited by 33
- not_injective_infinite_finiteproof · cited by 7
- Function.mk_mem_periodicPtsproof · cited by 3
- Function.iterate_cancelproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- Function.injective_iff_periodicPts_eq_univproof · cited by 0