X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=helm%2Fsoftware%2Fmatita%2Fcontribs%2Fassembly%2Fstring%2Fstring.ma;h=3226eac436c3f01716b938ac75cc30bc2718a768;hb=34e2c8f59dd7924e15a7746644182d12ad09fed3;hp=f60b8a804c46f3a7bb5d42de6de1ffd1db4355ac;hpb=05e6e4771934d95be8b4cffcc87eeb7b27250536;p=helm.git

diff --git a/helm/software/matita/contribs/assembly/string/string.ma b/helm/software/matita/contribs/assembly/string/string.ma
index f60b8a804..3226eac43 100755
--- a/helm/software/matita/contribs/assembly/string/string.ma
+++ b/helm/software/matita/contribs/assembly/string/string.ma
@@ -38,17 +38,77 @@ definition isNull_str ≝
  [ nil ⇒ true | cons _ _ ⇒ false ].
 
 (* strcmp *)
-let rec strCmp_str (str,str':aux_str_type) ≝
+let rec eqStr_str (str,str':aux_str_type) ≝
  match str with
   [ nil ⇒ match str' with
-   [ nil ⇒ true | cons _ _ ⇒ false ]
+   [ nil => true
+   | cons _ _ => false ]
   | cons h t ⇒ match str' with
    [ nil ⇒ false
-   | cons h' t' ⇒ match eqAsciiMin h h' with
-    [ true ⇒ strCmp_str t t' | false ⇒ false ]
-  ]].
+   | cons h' t' ⇒ (eqAsciiMin h h')⊗(eqStr_str t t')
+   ]
+  ].
 
-axiom eqbstrcmpstr_to_eq : ∀s,s'.strCmp_str s s' = true → s = s'.
+lemma eqex_switch : ∀e1,e2.eq_ex e1 e2 = eq_ex e2 e1.
+ intros;
+ elim e1;
+ elim e2;
+ reflexivity.
+qed.
+
+lemma eqb8_switch : ∀b1,b2.eq_b8 b1 b2 = eq_b8 b2 b1.
+ intros;
+ elim b1;
+ elim b2;
+ unfold eq_b8;
+ rewrite > eqex_switch in ⊢ (? ? % ?);
+ rewrite > eqex_switch in ⊢ (? ? (? ? %) ?);
+ reflexivity.
+qed.
+
+lemma eqasciimin_switch : ∀a1,a2.eqAsciiMin a1 a2 = eqAsciiMin a2 a1.
+ intros;
+ unfold eqAsciiMin;
+ rewrite > eqb8_switch in ⊢ (? ? % ?);
+ reflexivity.
+qed.
+
+lemma eq_to_eqstr : ∀s,s'.s = s' → eqStr_str s s' = true.
+ do 2 intro;
+ intro;
+ rewrite < H;
+ elim s;
+ [ 1: reflexivity
+ | 2: simplify;
+      rewrite > (eq_to_eqasciimin a a (refl_eq ??));
+      rewrite > H1;
+      reflexivity
+ ].
+qed.
+
+lemma eqstr_to_eq : ∀s,s'.eqStr_str s s' = true → s = s'.
+ intros 1;
+ elim s 0;
+ intros;
+ [ simplify in H:(%);
+   cases s' in H;
+   simplify;
+   intros;
+   [ reflexivity
+   | destruct H
+   ]
+ | elim s' in H1;
+   [ simplify in H1;
+     destruct H1
+   | simplify in H2;
+     lapply (andb_true_true ?? H2);
+     lapply (andb_true_true_r ?? H2);
+     rewrite > (H ? Hletin1);
+     rewrite > (eqasciimin_to_eq ?? Hletin);
+     reflexivity
+   ]
+ ].
+qed.
 
 (* strcat *)
 definition strCat_str ≝
@@ -70,5 +130,27 @@ definition get_name_strId ≝ λsid:aux_strId_type.match sid with [ STR_ID n _ 
 definition get_id_strId ≝ λsid:aux_strId_type.match sid with [ STR_ID _ d ⇒ d ].
 
 (* confronto *)
-definition strCmp_strId ≝
-λsid,sid':aux_strId_type.(strCmp_str (get_name_strId sid) (get_name_strId sid'))⊗(eqb (get_id_strId sid) (get_id_strId sid')).
+definition eqStrId_str ≝
+λsid,sid':aux_strId_type.(eqStr_str (get_name_strId sid) (get_name_strId sid'))⊗(eqb (get_id_strId sid) (get_id_strId sid')).
+
+lemma eq_to_eqstrid : ∀s,s'.s = s' → eqStrId_str s s' = true.
+ intros 3;
+ rewrite < H;
+ elim s;
+ simplify;
+ rewrite > (eq_to_eqstr a a (refl_eq ??));
+ rewrite > (eq_to_eqb_true n n (refl_eq ??));
+ reflexivity.
+qed.
+
+lemma eqstrid_to_eq : ∀s,s'.eqStrId_str s s' = true → s = s'.
+ intros 2;
+ elim s 0;
+ elim s' 0;
+ intros 4;
+ simplify;
+ intro;
+ rewrite > (eqstr_to_eq a1 a (andb_true_true ?? H));
+ rewrite > (eqb_true_to_eq n1 n (andb_true_true_r ?? H));
+ reflexivity.
+qed.