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 image_orbit x : {subset image f (orbit x) <= orbit x}.