Section Orbit.
Variables (T : finType) (f : T -> T).
Definition order x := #|fconnect f x|.
Definition orbit x := traject f x (order x).
Definition findex x y := index y (orbit x).
Definition finv x := iter (order x).-1 f x.
Hint Resolve in_orbit : core.
Hint Resolve order_gt0 : core.

Lemma findex_max x y : fconnect f x y -> findex x y < order x.