Theorems · Theorem · dynamical systems
Function.minimalPeriod_pos_of_mem_periodicPts
∀ {α : Type u_1} {f : α → α} {x : α}, x ∈ Function.periodicPts f → 0 < Function.minimalPeriod f x- Defined in
- Mathlib.Dynamics.PeriodicPts.Defs
- Cited by
- 9 results in Mathlib
- Foundations
- Depth 19 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- Nat.findproof · cited by 139
- Function.minimalPeriodstatement · cited by 100
- Nat.find_specproof · cited by 74
- Function.periodicPtsstatement and proof · cited by 33
- GT.gt.ltproof · cited by 16
Cited by9
Results whose statement or proof uses this declaration.
- IsOfFinOrder.orderOf_posproof · cited by 17
- IsOfFinAddOrder.addOrderOf_posproof · cited by 16
- Function.IsPeriodicPt.minimalPeriod_posproof · cited by 6
- Function.minimalPeriod_pos_iff_mem_periodicPtsproof · cited by 4
- Function.minimalPeriod_apply_iterateproof · cited by 2
- Function.periodicOrbit_chainproof · cited by 1
- Function.mem_periodicOrbit_iffproof · cited by 1
- Function.isPeriodicPt_factorial_card_of_mem_periodicPtsproof · cited by 1
- Function.periodicOrbit_chain'proof · cited by 0