(***)
intros. elim(excluded_middle_informative(f(couple g p)='p)).
intro a. exists g;simpl;auto. intro b. exists(zero G);simpl;
auto. Defined.

(* Specifications: *)
Lemma G2Stab_compat:forall(G:group)(S:Setoid)(f:Map(cart G S)S)
(LA1:forall(s:S),f(couple(zero G)s)='s)
(LA2:forall(g1 g2:G)(s:S),
f(couple(g1+'g2)s)='f(couple g1(f(couple g2 s))))
(p:S),fun_compatible(G2Stab G S f LA1 LA2 p).