Theorems · Theorem · dynamical systems
Function.periodicPts_subset_range
∀ {α : Type u_1} {f : α → α}, Function.periodicPts f ⊆ Set.range f- Defined in
- Mathlib.Dynamics.PeriodicPts.Defs
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 51 from the axioms · uses propext, Classical.choice, Quot.sound
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
- Set.rangestatement · cited by 4,705
- Nat.iterateproof · cited by 740
- Function.IsPeriodicPtproof · cited by 68
- Function.iterate_oneproof · cited by 34
- Function.periodicPtsstatement and proof · cited by 33
- Function.iterate_add_applyproof · cited by 24
- Function.mem_periodicPtsproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- Function.injective_iff_periodicPts_eq_univproof · cited by 0