Section EqTrajectory.
Variables (T : eqType) (f : T -> T).

(* Specifications: *)
Lemma eq_fpath f' : f =1 f' -> fpath f =2 fpath f'.
Lemma fpath_traject x n : fpath f x (traject f (f x) n).
Lemma trajectP x n y :
reflect (exists2 i, i < n & y = iter i f x) (y \in traject f x n).
Lemma looping_uniq x n : uniq (traject f x n.+1) = ~~ looping x n.
End EqTrajectory.