X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=helm%2Fsoftware%2Fmatita%2Flibrary%2Fdemo%2Fpropositional_sequent_calculus.ma;h=fb5278d6bdd78d44646652e6111317dc0fe3e370;hb=dcb1f00a9377a496b65d34f77a9c860b506df6c5;hp=4498676a3ef10f8a793464138f94e2638e130730;hpb=af130d273b6be7fbcc2fb2504f3b28ef8fa2344f;p=helm.git

diff --git a/helm/software/matita/library/demo/propositional_sequent_calculus.ma b/helm/software/matita/library/demo/propositional_sequent_calculus.ma
index 4498676a3..fb5278d6b 100644
--- a/helm/software/matita/library/demo/propositional_sequent_calculus.ma
+++ b/helm/software/matita/library/demo/propositional_sequent_calculus.ma
@@ -163,11 +163,10 @@ let rec and_of_list l ≝
   | cons F l' ⇒ FAnd F (and_of_list l')
   ].
 
-alias id "Nil" = "cic:/matita/list/list.ind#xpointer(1/1/1)".
 let rec or_of_list l ≝
  match l with
-  [ Nil ⇒ FFalse
-  | Cons F l' ⇒ FOr F (or_of_list l')
+  [ nil ⇒ FFalse
+  | cons F l' ⇒ FOr F (or_of_list l')
   ].
 
 definition formula_of_sequent ≝
@@ -397,7 +396,7 @@ theorem mem_to_exists_l1_l2:
   [ simplify in H1;
     destruct H1
   | simplify in H2;
-    apply (bool_elim ? (eq n t));
+    apply (bool_elim ? (eq n a));
     intro;
      [ apply (ex_intro ? ? []);
        apply (ex_intro ? ? l1);
@@ -409,8 +408,8 @@ theorem mem_to_exists_l1_l2:
        elim (H H1 H2);
        elim H4;
        rewrite > H5;
-       apply (ex_intro ? ? (t::a));
-       apply (ex_intro ? ? a1);
+       apply (ex_intro ? ? (a::a1));
+       apply (ex_intro ? ? a2);
        simplify;
        reflexivity
      ]
@@ -423,8 +422,7 @@ lemma same_atom_to_eq: ∀f1,f2. same_atom f1 f2 = true → f1=f2.
   [1,2:
     simplify in H;
     destruct H
-  | generalize in match H; clear H;
-    elim f2;
+  | elim f2 in H ⊢ %;
      [1,2:
        simplify in H;
        destruct H
@@ -434,7 +432,7 @@ lemma same_atom_to_eq: ∀f1,f2. same_atom f1 f2 = true → f1=f2.
      |4,5:
        simplify in H2;
        destruct H2
-     | simplify in H2;
+     | simplify in H1;
        destruct H1
      ]
   |4,5:
@@ -468,7 +466,7 @@ lemma mem_same_atom_to_exists:
   [ simplify in H;
     destruct H
   | simplify in H1;
-    apply (bool_elim ? (same_atom f t));
+    apply (bool_elim ? (same_atom f a));
     intros;
      [ elim (same_atom_to_exists ? ? H2);
        autobatch
@@ -492,14 +490,14 @@ lemma look_for_axiom:
     simplify;
     reflexivity
   | intros;
-    generalize in match (refl_eq ? (mem ? same_atom t l2));
-    elim (mem ? same_atom t l2) in ⊢ (? ? ? %→?);
+    generalize in match (refl_eq ? (mem ? same_atom a l2));
+    elim (mem ? same_atom a l2) in ⊢ (? ? ? %→?);
      [ left;
        elim (mem_to_exists_l1_l2 ? ? ? ? same_atom_to_eq H1);
        elim H2; clear H2;
        elim (mem_same_atom_to_exists ? ? H1);
        rewrite > H2 in H3;
-       apply (ex_intro ? ? a2);
+       apply (ex_intro ? ? a3);
        rewrite > H2;
        apply (ex_intro ? ? []);
        simplify;
@@ -507,22 +505,22 @@ lemma look_for_axiom:
      | elim (H l2);
         [ left;
           decompose;
-          apply (ex_intro ? ? a);
-          apply (ex_intro ? ? (t::a1));
+          apply (ex_intro ? ? a1);
+          apply (ex_intro ? ? (a::a2));
           simplify;
-          apply (ex_intro ? ? a2);
           apply (ex_intro ? ? a3);
+          apply (ex_intro ? ? a4);
           autobatch
         | right;
           intro;
-          apply (bool_elim ? (same_atom t (FAtom n1)));
+          apply (bool_elim ? (same_atom a (FAtom n1)));
            [ intro;
              rewrite > (eq_to_eq_mem ? ? transitiveb_same_atom ? ? ? H3) in H1;
              rewrite > H1;
              autobatch
            | intro;
              change in ⊢ (? ? (? % ?) ?) with
-              (match same_atom (FAtom n1) t with
+              (match same_atom (FAtom n1) a with
                 [true ⇒ true
                 |false ⇒ mem ? same_atom (FAtom n1) l
                 ]);
@@ -589,22 +587,16 @@ lemma sizel_0_no_axiom_is_tautology:
  intros;
  lapply (H1 (λn.mem ? same_atom (FAtom n) l1)); clear H1;
  simplify in Hletin;  
- generalize in match Hletin; clear Hletin;
- generalize in match H2; clear H2;
- generalize in match H; clear H;
- elim l1 0;
+ elim l1 in Hletin H2 H ⊢ % 0;
   [ intros;
     simplify in H2;
-    generalize in match H2; clear H2;
-    generalize in match H1; clear H1;
-    generalize in match H; clear H;
-    elim l2 0;
+    elim l2 in H2 H1 H ⊢ % 0;
      [ intros;
        simplify in H2;
        destruct H2
      | simplify;
        intro;
-       elim t;
+       elim a;
         [ right;
           apply (ex_intro ? ? []);
           simplify;
@@ -617,10 +609,10 @@ lemma sizel_0_no_axiom_is_tautology:
              elim (not_eq_nil_append_cons ? ? ? ? H6)
            | elim H4;
              right;
-             apply (ex_intro ? ? (FFalse::a));
+             apply (ex_intro ? ? (FFalse::a1));
              simplify;
              elim H5;
-             apply (ex_intro ? ? a1);
+             apply (ex_intro ? ? a2);
              autobatch
            |3,4: autobatch
            | assumption
@@ -632,7 +624,7 @@ lemma sizel_0_no_axiom_is_tautology:
              elim (not_eq_nil_append_cons ? ? ? ? H5)
            | right;
              elim H4;
-             apply (ex_intro ? ? (FAtom n::a));
+             apply (ex_intro ? ? (FAtom n::a1));
              simplify;
              elim H;
              autobatch
@@ -645,11 +637,11 @@ lemma sizel_0_no_axiom_is_tautology:
         ]
      ]
   | intro;
-    elim t;
+     elim a;
      [ elim H;
         [ left;
           elim H4;
-          apply (ex_intro ? ? (FTrue::a));
+          apply (ex_intro ? ? (FTrue::a1));
           simplify;
           elim H5;
           autobatch
@@ -669,7 +661,7 @@ lemma sizel_0_no_axiom_is_tautology:
      | elim H;
         [ left;
           elim H4;
-          apply (ex_intro ? ? (FAtom n::a));
+          apply (ex_intro ? ? (FAtom n::a1));
           simplify;
           elim H5;
           autobatch
@@ -678,8 +670,7 @@ lemma sizel_0_no_axiom_is_tautology:
         | assumption
         | lapply (H2 n1); clear H2;
           simplify in Hletin;
-          generalize in match Hletin; clear Hletin;
-          elim (eqb n1 n);
+          elim (eqb n1 n) in Hletin ⊢ %;
            [ simplify in H2;
              rewrite > H2;
              autobatch
@@ -694,10 +685,7 @@ lemma sizel_0_no_axiom_is_tautology:
           rewrite > eqb_n_n in H3;
           simplify in H3;
 (*
-          generalize in match H3;
-          generalize in match H1; clear H1;
-          generalize in match H; clear H;
-          elim l 0;
+          elim l in H3 H1 H ⊢ % 0;
            [ elim l2 0;
               [ intros;
                 simplify in H2;
@@ -715,9 +703,7 @@ lemma sizel_0_no_axiom_is_tautology:
                  ]
                     
                  [ autobatch
-                 | generalize in match H4; clear H4;
-                   generalize in match H2; clear H2;
-                   elim t1;
+                 | elim t1 in H4 H2 ⊢ %;
                     [
                     |
                     |
@@ -748,22 +734,22 @@ lemma completeness_base:
  elim S 1; clear S;
  simplify in ⊢ (?→%→?);
  intros;
- elim (look_for_axiom t t1);
+ elim (look_for_axiom a b);
   [ decompose;
     rewrite > H2; clear H2;
     rewrite > H4; clear H4;
-    apply (exchangeL ? a1 a2 (FAtom a));
-    apply (exchangeR ? a3 a4 (FAtom a));
-    apply axiom 
-  | elim (sizel_0_no_axiom_is_tautology t t1 H H1 H2);
+    apply (ExchangeL ? a2 a3 (FAtom a1));
+    apply (ExchangeR ? a4 a5 (FAtom a1));
+    apply Axiom 
+  | elim (sizel_0_no_axiom_is_tautology a b H H1 H2);
      [ decompose;
        rewrite > H3;
-       apply (exchangeL ? a a1 FFalse);
-       apply falseL
+       apply (ExchangeL ? a1 a2 FFalse);
+       apply FalseL
      | decompose;
        rewrite > H3;
-       apply (exchangeR ? a a1 FTrue);
-       apply trueR
+       apply (ExchangeR ? a1 a2 FTrue);
+       apply TrueR
      ]
   ]
 qed.