(**)
intros U F F' F'' F''' u u' u'' u''' u'''' n v w S0 S1 S2 S3 M g g' g'' E E' H
L H1. elim H1. intros H2 H3. apply H2. split. apply Rge_le. apply S3. apply H.
Qed.

(* Specifications: *)
Lemma u_cmp:
forall(U:Type)(F:Ensemble(Ensemble U))(F':sigalg_0 _ F)(F'':sigalg_1 _ F)(F''':
sigalg_2 _ F)(u:forall A,F A->R)(u'''':msur_3 _ _ F' F'' F''' u)A B A' B',
A=B->u A A'=u B B'.