(**)
intros. red. intuition. Qed.

(* Specifications: *)
Lemma simple_P7:
forall(U:Type)(A:Ensemble U),
simple_3 _ 2(fun i:nat=>INR i)(fun i:nat=>if eq_nat_dec i 0 then Complement _ A
else if eq_nat_dec i 1 then A else Empty_set _).
Lemma simple_P8:
forall(U:Type)(F:Ensemble(Ensemble U))(F':sigalg_0 _ F)(F'':sigalg_1 _ F)(F''':
sigalg_2 _ F),
forall A:Ensemble U,F A->
let n:=2 in
let v:=fun i:nat=>INR i in
let w:=fun i:nat=>if eq_nat_dec i 0 then Complement _ A else if
eq_nat_dec i 1 then A else Empty_set _ in
msurable _ _ F' F'' F''' (fun x:U=>v(proj1_sig(simple_P0 _ n v w
(simple_P4 _ _)(simple_P5 _ _)(simple_P6 _ _)(simple_P7 _ _) x))).