Theorems · Theorem · dynamical systems
Function.IsPeriodicPt.iterate_mod_apply
∀ {α : Type u_1} {f : α → α} {x : α} {n : ℕ}, Function.IsPeriodicPt f n x → ∀ (m : ℕ), f^[m % n] x = f^[m] x- Defined in
- Mathlib.Dynamics.PeriodicPts.Defs
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 24 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Nat.iteratestatement and proof · cited by 740
- Function.IsPeriodicPtstatement and proof · cited by 68
- Function.iterate_add_applyproof · cited by 24
- Function.IsFixedPt.eqproof · cited by 14
- Function.IsPeriodicPt.mul_constproof · cited by 6
Cited by2
Results whose statement or proof uses this declaration.
- Function.iterate_mod_minimalPeriod_eqproof · cited by 3
- Function.IsPeriodicPt.modproof · cited by 2