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[helm.git] / helm / software / matita / library / didactic / exercises / substitution.ma

diff --git a/helm/software/matita/library/didactic/exercises/substitution.ma b/helm/software/matita/library/didactic/exercises/substitution.ma
index 096b5b84c111b74a9a99e20c1c461832b8de7766..8ac8fbc1e96223fc8904d29462aa6842d80bae38 100644 (file)
--- a/helm/software/matita/library/didactic/exercises/substitution.ma
+++ b/helm/software/matita/library/didactic/exercises/substitution.ma
@@ -1,3 +1,17 @@
+(**************************************************************************)
+(*       ___                                                             *)
+(*      ||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 
    ===========
    
@@ -232,7 +246,9 @@ definition v1101 ≝ λx.
 definition esempio1 ≝ 
   (FImpl (FNot (FAtom 3)) (FOr (FAtom 2) (FAnd (FAtom 1) (FAtom 0)))).
 
-eval normalize on [[ esempio1 ]]_v1101.
+(* Decommenta ed esegui. *)
+
+(* eval normalize on [[ esempio1 ]]_v1101. *)
 
 
 (* Esercizio 3
@@ -303,7 +319,9 @@ definition esempio2 ≝ (FAnd (FImpl (FAtom 2) (FAtom 1)) (FAtom 2)).
    
 definition esempio3 ≝ (FOr (FAtom 0) (FAtom 1)).
 
-eval normalize on (esempio2 [ esempio3 / 2]).
+(* Decommenta ed esegui *)
+
+(* eval normalize on (esempio2 [ esempio3 / 2]). *)
 
 (*DOCBEGIN
    
@@ -452,8 +470,8 @@ case FAnd.
   by (*BEGIN*)IH22(*END*) we proved ([[ F2[ G1/x ] ]]_v = [[ F2[ G2/x ] ]]_v) (IH222).
   conclude 
       (min ([[ F1[ G1/x ] ]]_v) ([[ F2[ G1/x ] ]]_v)) 
-    = (min ([[ F1[ G2/x ] ]]_v) ([[ F2[ G1/x ] ]]_v)) by IH222.
-    = (min ([[(F1[ G2/x ])]]_v) ([[(F2[ G2/x ])]]_v)) by (*BEGIN*)IH111(*END*).
+    = (min ([[ F1[ G2/x ] ]]_v) ([[ F2[ G1/x ] ]]_v)) by IH111.
+    = (min ([[(F1[ G2/x ])]]_v) ([[(F2[ G2/x ])]]_v)) by (*BEGIN*)IH222(*END*).
   (*END*)
   done.
 case FOr.
@@ -474,8 +492,8 @@ case FOr.
   by IH22 we proved ([[ F2[ G1/x ] ]]_v = [[ F2[ G2/x ] ]]_v) (IH222).
   conclude 
       (max ([[ F1[ G1/x ] ]]_v) ([[ F2[ G1/x ] ]]_v)) 
-    = (max ([[ F1[ G2/x ] ]]_v) ([[ F2[ G1/x ] ]]_v)) by IH222.
-    = (max ([[(F1[ G2/x ])]]_v) ([[(F2[ G2/x ])]]_v)) by IH111.
+    = (max ([[ F1[ G2/x ] ]]_v) ([[ F2[ G1/x ] ]]_v)) by IH111.
+    = (max ([[(F1[ G2/x ])]]_v) ([[(F2[ G2/x ])]]_v)) by IH222.
   (*END*)
   done.
 case FImpl.