(***)
intros. apply Trans with(f(couple(zero G)y)). auto with
algebra. apply Trans with(f(couple(zero G)z)). apply Trans with
(f(couple((min x)+'x)y)). auto with algebra. apply Trans with
(f(couple((min x)+' x)z)). apply Trans with(f(couple(min x)
(f(couple x y)))). apply LA2. apply Trans with(f(couple(min x)
(f(couple x z)))). auto with algebra. apply Sym. apply LA2.
auto with algebra. auto with algebra. Qed.

(* Specifications: *)
Lemma StabHx_bij: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)(x:Orb7_s G S f LA1 LA2 p),
exists M:MAP(Stab2_s G S f LA1 LA2 p)(Hx_s G S f LA1 LA2 p x),
injective M /\ surjective M.