Theorems · Theorem · dynamical systems
Function.IsPeriodicPt.minimalPeriod_dvd
∀ {α : Type u_1} {f : α → α} {x : α} {n : ℕ}, Function.IsPeriodicPt f n x → Function.minimalPeriod f x ∣ n- Defined in
- Mathlib.Dynamics.PeriodicPts.Defs
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 30 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Function.minimalPeriodstatement and proof · cited by 100
- eq_or_lt_of_leproof · cited by 92
- Function.IsPeriodicPtstatement and proof · cited by 68
- Function.isPeriodicPt_minimalPeriodproof · cited by 11
- Function.IsPeriodicPt.minimalPeriod_posproof · cited by 6
- Function.IsPeriodicPt.eq_zero_of_lt_minimalPeriodproof · cited by 2
- Function.IsPeriodicPt.modproof · cited by 2
Cited by4
Results whose statement or proof uses this declaration.
- orderOf_dvd_of_pow_eq_oneproof · cited by 24
- Function.isPeriodicPt_iff_minimalPeriod_dvdproof · cited by 6
- addOrderOf_dvd_of_nsmul_eq_zeroproof · cited by 6
- Function.Commute.minimalPeriod_of_comp_eq_mul_of_coprimeproof · cited by 2