Theorems · Theorem · dynamical systems
Function.Commute.iterate_eq_of_map_eq
∀ {α : Type u} {f g : α → α}, Function.Commute f g → ∀ (n : ℕ) {x : α}, f x = g x → f^[n] x = g^[n] x- Defined in
- Mathlib.Logic.Function.Iterate
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 10 from the axioms · uses propext
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.
- Nat.iteratestatement and proof · cited by 740
- Function.Commutestatement and proof · cited by 54
- Function.Semiconj.eqproof · cited by 12
- Function.Commute.iterate_leftproof · cited by 9
- Function.Commute.iterate_rightproof · cited by 8
- Function.Commute.reflproof · cited by 5
Cited by2
Results whose statement or proof uses this declaration.
- Function.Commute.iterate_pos_lt_iff_map_ltproof · cited by 3
- CircleDeg1Lift.iterate_eq_of_map_eq_add_intproof · cited by 0