Theorems · Theorem · dynamical systems
Function.minimalPeriod_pos_iff_mem_periodicPts
∀ {α : Type u_1} {f : α → α} {x : α}, 0 < Function.minimalPeriod f x ↔ x ∈ Function.periodicPts f- Defined in
- Mathlib.Dynamics.PeriodicPts.Defs
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 21 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.
- Setstatement · cited by 53,352
- lt_irreflproof · cited by 190
- Nat.findproof · cited by 139
- Function.minimalPeriodstatement · cited by 100
- not_imp_notproof · cited by 63
- Function.periodicPtsstatement and proof · cited by 33
- Function.minimalPeriod_pos_of_mem_periodicPtsproof · cited by 9
Cited by4
Results whose statement or proof uses this declaration.
- Function.minimalPeriod_iterate_eq_div_gcd'proof · cited by 2
- Function.le_of_lt_minimalPeriod_of_iterate_eqproof · cited by 1
- Function.minimalPeriod_eq_zero_iff_notMem_periodicPtsproof · cited by 1
- Function.mem_periodicPts_iff_isPeriodicPt_factorial_cardproof · cited by 0