Section orbit_in.
Variable S : pred_sort (predPredType T).
Hypothesis f_in : {in S, forall x, f x \in S}.
Hypothesis injf : {in S &, injective f}.

Lemma fpath_finv_f_in p : {in S, forall x,
fpath finv x p -> fpath f (last x p) (rev (belast x p))}.