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 fclosed1 (a : pred T) : fclosed f a -> forall x, (x \in a) = (f x \in a).
Hypothesis eq_f : f =1 f'.