X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=helm%2Fsoftware%2Fmatita%2Flibrary%2Fdecidable_kit%2Ffintype.ma;h=6bfa6969f1d38e223c1542b744990e82607e5bf6;hb=1ff3965d308be074f3ed5181b3c38921f289b6a9;hp=9002bab6ae0f7f0b29e5cfc579cc6b8127b365f8;hpb=1292d243af469c5cb3dcb3677d84012420de015e;p=helm.git

diff --git a/helm/software/matita/library/decidable_kit/fintype.ma b/helm/software/matita/library/decidable_kit/fintype.ma
index 9002bab6a..6bfa6969f 100644
--- a/helm/software/matita/library/decidable_kit/fintype.ma
+++ b/helm/software/matita/library/decidable_kit/fintype.ma
@@ -84,11 +84,13 @@ 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 [_ ⇒ ?|_ ⇒ ?] ?);
+   [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]
@@ -104,8 +106,8 @@ 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]
@@ -146,7 +148,7 @@ 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;
@@ -170,7 +172,7 @@ intros (d l); apply prove_reflect; elim l; [1: destruct H1 | 3: destruct H]
         unfold Not; intros (A); lapply (A t) as A'; 
         [1: simplify in A'; rewrite > cmp_refl in A'; simplify in A';
             destruct A'; rewrite < count_O_mem in H1;
-            rewrite > Hcut in H1; destruct 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); 
@@ -178,7 +180,7 @@ intros (d l); apply prove_reflect; elim l; [1: destruct H1 | 3: destruct H]
         generalize in match Hletin1; simplify; apply (cmpP d r t); 
         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. 
@@ -195,7 +197,7 @@ 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;  
+elim (enum d); [simplify in H1; destruct H1] simplify;  
 cases (in_sub_eq d p t1); simplify; 
 [1:generalize in match H3; clear H3; cases s (r Hr); clear s;
    simplify; intros (Ert1); generalize in match Hr; clear Hr;