+(**************************************************************************)
+(* ___ *)
+(* ||M|| *)
+(* ||A|| A project by Andrea Asperti *)
+(* ||T|| *)
+(* ||I|| Developers: *)
+(* ||T|| A.Asperti, C.Sacerdoti Coen, *)
+(* ||A|| E.Tassi, S.Zacchiroli *)
+(* \ / *)
+(* \ / This file is distributed under the terms of the *)
+(* v GNU Lesser General Public License Version 2.1 *)
+(* *)
+(**************************************************************************)
+
(* Esercizio 0
===========
= ([[ FOr (FAnd (FAtom x) (F[FTop/x])) (FAnd (FNot (FAtom x)) (F[FBot/x]))]]_v).
= (max [[ (FAnd (FAtom x) (F[FTop/x])) ]]_v [[ (FAnd (FNot (FAtom x)) (F[FBot/x]))]]_v).
= (max (min [[ FAtom x ]]_v [[ F[FTop/x] ]]_v) (min (1 - [[ FAtom x ]]_v) [[ F[FBot/x] ]]_v)).
- = (max (min 0 [[ F[FTop/x] ]]_v) (min (1 - 0) [[ F[FBot/x] ]]_v)) by H.
+ = (max (min 0 [[ F[FTop/x] ]]_v) (min (1 - 0) [[ F[FBot/x] ]]_v)) by H1.
= (max 0 (min 1 [[ F[FBot/x] ]]_v)).
= (max 0 [[ F[FBot/x] ]]_v) by min_1_sem.
= ([[ F[FBot/x] ]]_v).
= ([[ FOr (FAnd (FAtom x) (F[FTop/x])) (FAnd (FNot (FAtom x)) (F[FBot/x]))]]_v).
= (max [[ (FAnd (FAtom x) (F[FTop/x])) ]]_v [[ (FAnd (FNot (FAtom x)) (F[FBot/x]))]]_v).
= (max (min [[ FAtom x ]]_v [[ F[FTop/x] ]]_v) (min (1 - [[ FAtom x ]]_v) [[ F[FBot/x] ]]_v)).
- = (max (min 1 [[ F[FTop/x] ]]_v) (min (1 - 1) [[ F[FBot/x] ]]_v)) by H.
+ = (max (min 1 [[ F[FTop/x] ]]_v) (min (1 - 1) [[ F[FBot/x] ]]_v)) by H1.
= (max (min 1 [[ F[FTop/x] ]]_v) (min 0 [[ F[FBot/x] ]]_v)).
= (max [[ F[FTop/x] ]]_v (min 0 [[ F[FBot/x] ]]_v)) by min_1_sem.
= (max [[ F[FTop/x] ]]_v 0).