X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=helm%2Fsoftware%2Fmatita%2Flibrary%2Fdecidable_kit%2Ffintype.ma;h=e44b641977e2503d15308fcf4b6dd61b95ed2374;hb=5c10d402b5de7233bc83d7f685b274832e383212;hp=ad71a4511dd6d7583a5de136dd5b39dd3ffd1287;hpb=32d8d8d419e0b910435da275361bb55d49bc43a9;p=helm.git

diff --git a/helm/software/matita/library/decidable_kit/fintype.ma b/helm/software/matita/library/decidable_kit/fintype.ma
index ad71a4511..e44b64197 100644
--- a/helm/software/matita/library/decidable_kit/fintype.ma
+++ b/helm/software/matita/library/decidable_kit/fintype.ma
@@ -12,8 +12,6 @@
 (*                                                                        *)
 (**************************************************************************)
 
-set "baseuri" "cic:/matita/decidable_kit/fintype/".
-
 include "decidable_kit/eqtype.ma".
 include "decidable_kit/list_aux.ma".
 
@@ -51,13 +49,13 @@ lemma mem_filter :
   mem d2 x (filter d1 d2 p l) = false.
 intros 5 (d1 d2 x l p); 
 elim l; simplify; [reflexivity]
-generalize in match (refl_eq ? (p t));
-generalize in match (p t) in ⊢ (? ? ? % → %); intros 1 (b); cases b; clear b; intros (Hpt);
+generalize in match (refl_eq ? (p a));
+generalize in match (p a) in ⊢ (? ? ? % → %); intros 1 (b); cases b; clear b; intros (Hpt);
 [1: apply H; intros (y Hyl);
     apply H1; simplify; 
     rewrite > Hyl; rewrite > orbC; reflexivity;
 |2: simplify; apply (cmpP d2 x s); simplify; intros (E);
-    [1: rewrite < (H1 t); simplify; [rewrite > Hpt; rewrite > E]
+    [1: rewrite < (H1 a); simplify; [rewrite > Hpt; rewrite > E]
         simplify; rewrite > cmp_refl; reflexivity
     |2: apply H; intros; apply H1; simplify; rewrite > H2;
         rewrite > orbC; reflexivity]]
@@ -67,12 +65,12 @@ lemma count_O :
   ∀d:eqType.∀p:d→bool.∀l:list d. 
     (∀x:d.mem d x l = true → notb (p x) = true) → count d p l = O.
 intros 3 (d p l); elim l; simplify; [1: reflexivity]
-generalize in match (refl_eq ? (p t));
-generalize in match (p t) in ⊢ (? ? ? % → %); intros 1 (b);
+generalize in match (refl_eq ? (p a));
+generalize in match (p a) in ⊢ (? ? ? % → %); intros 1 (b);
 cases b; simplify; 
 [2:intros (Hpt); apply H; intros; apply H1; simplify;
-   apply (cmpP d x t); [2: rewrite > H2;]; intros; reflexivity;
-|1:intros (H2); lapply (H1 t); [2:simplify; rewrite > cmp_refl; simplify; autobatch]
+   apply (cmpP d x a); [2: rewrite > H2;]; intros; reflexivity;
+|1:intros (H2); lapply (H1 a); [2:simplify; rewrite > cmp_refl; simplify; autobatch]
    rewrite > H2 in Hletin; simplify in Hletin; destruct Hletin]
 qed.    
     
@@ -84,12 +82,14 @@ cut (∀x:fsort. count fsort (cmp fsort x) enum = (S O));
  [ apply (mk_finType fsort enum Hcut)
  | intros (x); cases x (n Hn); simplify in Hn; clear x;
    generalize in match Hn; generalize in match Hn; clear Hn;
+   unfold enum;
    unfold segment_enum;
    generalize in match bound in ⊢ (% → ? → ? ? (? ? ? (? ? ? ? %)) ?);
-   intros 1 (m); elim m  (Hm Hn p IH Hm Hn); [ destruct Hm ]
+   intros 1 (m); elim m  (Hm Hn p IH Hm Hn); [ simplify in Hm; destruct Hm ]
    simplify; cases (eqP bool_eqType (ltb p bound) true); simplify;
-   [1:unfold segment in ⊢ (? ? match ? % ? ? with [true⇒ ?|false⇒ ?] ?);
-      unfold nat_eqType in ⊢ (? ? match % with [true⇒ ?|false⇒ ?] ?);
+   [1:unfold fsort;
+      unfold segment in ⊢ (? ? match ? % ? ? with [_ ⇒ ?|_ ⇒ ?] ?);
+      unfold nat_eqType in ⊢ (? ? match % with [_ ⇒ ?|_ ⇒ ?] ?);
       simplify; apply (cmpP nat_eqType n p); intros (Enp); simplify;
       [2:rewrite > IH; [1,3: autobatch]
          rewrite <  ltb_n_Sm in Hm; rewrite > Enp in Hm;
@@ -104,8 +104,8 @@ cut (∀x:fsort. count fsort (cmp fsort x) enum = (S O));
          fold simplify (sort nat_eqType); (* CANONICAL?! *)
          cases (in_sub_eq nat_eqType (λx:nat_eqType.ltb x bound) w);
          simplify; [2: reflexivity]
-         generalize in match H1; clear H1; cases s; clear s; intros (H1);
-         unfold segment; simplify; simplify in H1; rewrite > H1;
+         generalize in match H1; clear H1; cases s (r Pr); clear s; intros (H1);
+         unfold fsort; unfold segment; simplify; simplify in H1; rewrite > H1;
          rewrite > iota_ltb in Hw; apply (p2bF ? ? (eqP nat_eqType ? ?));
          unfold Not; intros (Enw); rewrite > Enw in Hw; 
          rewrite > ltb_refl in Hw; destruct Hw]
@@ -135,50 +135,50 @@ intros; cases a; cases b; reflexivity; qed.
 lemma uniq_tail : 
   ∀d:eqType.∀x:d.∀l:list d. uniq d (x::l) = andb (negb (mem d x l)) (uniq d l).
 intros (d x l); elim l; simplify; [reflexivity]
-apply (cmpP d x t); intros (E); simplify ; rewrite > E; [reflexivity]
+apply (cmpP d x a); intros (E); simplify ; try rewrite > E; [reflexivity]
 rewrite > andbA; rewrite > andbC in ⊢ (? ? (? % ?) ?); rewrite < andbA;
 rewrite < H; rewrite > andbC in ⊢ (? ? ? (? % ?)); rewrite < andbA; reflexivity;
 qed.
   
 lemma count_O_mem : ∀d:eqType.∀x:d.∀l:list d.ltb O (count d (cmp d x) l) = mem d x l.
-intros 3 (d x l); elim l [reflexivity] simplify; rewrite < H; cases (cmp d x t);
+intros 3 (d x l); elim l [reflexivity] simplify; rewrite < H; cases (cmp d x a);
 reflexivity; qed.
   
 lemma uniqP : ∀d:eqType.∀l:list d. 
   reflect (∀x:d.mem d x l = true → count d (cmp d x) l = (S O)) (uniq d l).
-intros (d l); apply prove_reflect; elim l; [1: destruct H1 | 3: destruct H]
+intros (d l); apply prove_reflect; elim l; [1: simplify in H1; destruct H1 | 3: simplify in H; destruct H]
 [1: generalize in match H2; simplify in H2; 
     lapply (b2pT ? ? (orbP ? ?) H2) as H3; clear H2; 
     cases H3; clear H3; intros;
-    [2: lapply (uniq_mem ? ? ? H1) as H4; simplify; apply (cmpP d x t);  
+    [2: lapply (uniq_mem ? ? ? H1) as H4; simplify; apply (cmpP d x a);  
         intros (H5); simplify;
         [1: rewrite > count_O; [reflexivity]
-            intros (y Hy); rewrite > H5 in H2 H3 H4 ⊢ %; clear H5; clear x; 
+            intros (y Hy); rewrite > H5 in H2 H3 ⊢ %; clear H5; clear x; 
             rewrite > H2 in H4; destruct H4;
-         |2: simplify; rewrite > H5; simplify; apply H; 
+         |2: simplify; apply H; 
              rewrite > uniq_tail in H1; cases (b2pT ? ? (andbP ? ?) H1); 
              assumption;]
     |1: simplify; rewrite > H2; simplify; rewrite > count_O; [reflexivity]
         intros (y Hy); rewrite > (b2pT ? ? (eqP d ? ?) H2) in H3 ⊢ %;
         clear H2; clear x; lapply (uniq_mem ? ? ? H1) as H4;
-        apply (cmpP d t y); intros (E); [2: reflexivity].
+        apply (cmpP d a y); intros (E); [2: reflexivity].
         rewrite > E in H4; rewrite > H4 in Hy; destruct Hy;]
 |2: rewrite > uniq_tail in H1; 
     generalize in match (refl_eq ? (uniq d l1));
     generalize in match (uniq d l1) in ⊢ (? ? ? % → %); intros 1 (b); cases b; clear b;
     [1: intros (E); rewrite > E in H1; rewrite > andbC in H1; simplify in H1;
-        unfold Not; intros (A); lapply (A t) as A'; 
+        unfold Not; intros (A); lapply (A a) as A'; 
         [1: simplify in A'; rewrite > cmp_refl in A'; simplify in A';
-            destruct A'; clear A'; rewrite < count_O_mem in H1;
-            rewrite > Hcut in H1; destruct H1;  
+            destruct A'; rewrite < count_O_mem in H1;
+            rewrite > Hcut in H1; simplify in H1; destruct H1;  
         |2: simplify; rewrite > cmp_refl; reflexivity;]
     |2: intros (Ul1); lapply (H Ul1); unfold Not; intros (A); apply Hletin;
         intros (r Mrl1); lapply (A r); 
-          [2: simplify; rewrite > Mrl1; cases (cmp d r t); reflexivity]
-        generalize in match Hletin1; simplify; apply (cmpP d r t); 
+          [2: simplify; rewrite > Mrl1; cases (cmp d r a); reflexivity]
+        generalize in match Hletin1; simplify; apply (cmpP d r a); 
         simplify; intros (E Hc); [2: assumption]
         destruct Hc; rewrite < count_O_mem in Mrl1;
-        rewrite > Hcut in Mrl1; destruct Mrl1;]]
+        rewrite > Hcut in Mrl1; simplify in Mrl1; destruct Mrl1;]]
 qed.
     
 lemma mem_finType : ∀d:finType.∀x:d. mem d x (enum d) = true. 
@@ -195,32 +195,32 @@ lemma sub_enumP : ∀d:finType.∀p:d→bool.∀x:sub_eqType d p.
 intros (d p x); cases x (t Ht); clear x;
 generalize in match (mem_finType d t); 
 generalize in match (uniq_fintype_enum d); 
-elim (enum d); [destruct H1] simplify;  
-cases (in_sub_eq d p t1); simplify; 
+elim (enum d); [simplify in H1; destruct H1] simplify;  
+cases (in_sub_eq d p a); simplify; 
 [1:generalize in match H3; clear H3; cases s (r Hr); clear s;
    simplify; intros (Ert1); generalize in match Hr; clear Hr;
    rewrite > Ert1; clear Ert1; clear r; intros (Ht1);
-   unfold  sub_eqType in ⊢ (? ? match ? (% ? ?) ? ? with [true⇒ ?|false⇒ ?] ?); 
-   simplify; apply (cmpP ? t t1); simplify; intros (Ett1);
+   unfold  sub_eqType in ⊢ (? ? match ? (% ? ?) ? ? with [_ ⇒ ?|_ ⇒ ?] ?); 
+   simplify; apply (cmpP ? t a); simplify; intros (Ett1);
    [1: cut (count (sub_eqType d p) (cmp (sub_eqType d p) {t,Ht})
             (filter d (sigma d p) (if_p d p) l) = O); [1:rewrite > Hcut; reflexivity]
        lapply (uniq_mem ? ? ? H1);
        generalize in match Ht; 
        rewrite > Ett1; intros (Ht1'); clear Ht1;
        generalize in match Hletin; elim l; [ reflexivity]
-       simplify; cases (in_sub_eq d p t2); simplify; 
+       simplify; cases (in_sub_eq d p a1); simplify; 
        [1: generalize in match H5; cases s; simplify; intros; clear H5; 
-           unfold sub_eqType in ⊢ (? ? match ? (% ? ?) ? ? with [true⇒ ?|false⇒ ?] ?);
+           unfold sub_eqType in ⊢ (? ? match ? (% ? ?) ? ? with [_ ⇒ ?|_ ⇒ ?] ?);
            simplify; rewrite > H7; simplify in H4;
-           generalize in match H4; clear H4; apply (cmpP ? t1 t2);
+           generalize in match H4; clear H4; apply (cmpP ? a a1);
            simplify; intros; [destruct H5] apply H3; assumption;
        |2: apply H3;
-           generalize in match H4; clear H4; simplify; apply (cmpP ? t1 t2);
+           generalize in match H4; clear H4; simplify; apply (cmpP ? a a1);
            simplify; intros; [destruct H6] assumption;]
    |2: apply H; [ rewrite > uniq_tail in H1; cases (b2pT ? ? (andbP ? ?) H1); assumption]
        simplify in H2; rewrite > Ett1 in H2; simplify in H2; assumption] 
 |2:rewrite > H; [1:reflexivity|2: rewrite > uniq_tail in H1; cases (b2pT ? ? (andbP ? ?) H1); assumption]
-   simplify in H2; generalize in match H2; apply (cmpP ? t t1); 
+   simplify in H2; generalize in match H2; apply (cmpP ? t a); 
    intros (E) [2:assumption] clear H; rewrite > E in Ht; rewrite > H3 in Ht;
    destruct Ht;]
 qed.