intros. unfold fun_compatible. intros. apply Map_compatible_prf.
apply couple_comp. assumption. apply Refl. Qed.

(* Specifications: *)
Lemma finGOrb:forall(G:group)(S:Setoid)(f:Map(cart G S)S)
(LA1:forall(s:S),f(couple(monoid_unit G)s)=' s)
(LA2:forall(g1 g2:G)(s:S),
f(couple(g1+' g2)s)=' f(couple g1(f(couple g2 s))))
(p:S)(n:Nat)(H:has_n_elements n G),
exists c:Nat,exists v:seq c S,
Orb7_s G S f LA1 LA2 p=' seq_set v /\ distinct v.