X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=helm%2Fsoftware%2Fmatita%2Fnlibrary%2Ftopology%2Figft2.ma;h=dc78b768079ef614c53908f3b3639d815c5fbcfd;hb=e7264f953fcf2cd2bef9057d83add08996d2ce75;hp=4529b40d540134b02c97ee7afce247cdf9882022;hpb=9eca05b38858f9d5b36b9a102c6c8c01632b5057;p=helm.git

diff --git a/helm/software/matita/nlibrary/topology/igft2.ma b/helm/software/matita/nlibrary/topology/igft2.ma
index 4529b40d5..dc78b7680 100644
--- a/helm/software/matita/nlibrary/topology/igft2.ma
+++ b/helm/software/matita/nlibrary/topology/igft2.ma
@@ -23,7 +23,7 @@ ndefinition natS ≝ S.
 include "topology/igft.ma".
 
 nlemma hint_auto2 : ∀T.∀U,V:Ω^T.(∀x.x ∈ U → x ∈ V) → U ⊆ V.
-nnormalize; nauto;
+nnormalize; /2/;
 nqed.
 
 alias symbol "covers" = "covers set".
@@ -33,9 +33,7 @@ nlemma cover_ind':
  ∀A:Ax.∀U,P:Ω^A.
    (U ⊆ P) → (∀a:A.∀j:𝐈 a. 𝐂 a j ◃ U → 𝐂 a j ⊆ P → a ∈ P) →
     ◃ U ⊆ P.
- #A; #U; #P; #refl; #infty; #a; #H; nelim H
-  [ nauto | (*nauto depth=4;*) #b; #j; #K1; #K2; 
-            napply infty; nauto; ##] 
+ #A; #U; #P; #refl; #infty; #a; #H; nelim H; /3/. 
 nqed.
 
 alias symbol "covers" (instance 1) = "covers".
@@ -78,7 +76,7 @@ ncoercion uuax : ∀u:uuAx. Ax ≝ uuax on _u : uuAx to Ax.
 
 nlemma eq_rect_Type0_r':
  ∀A.∀a,x.∀p:eq ? x a.∀P: ∀x:A. eq ? x a → Type[0]. P a (refl A a) → P x p.
- #A; #a; #x; #p; ncases p; nauto;
+ #A; #a; #x; #p; ncases p; //;
 nqed.
 
 nlemma eq_rect_Type0_r:
@@ -108,24 +106,24 @@ nlet rec cover_rect
 ≝ ?.
  nlapply (decide_mem_ok … memdec b); nlapply (decide_mem_ko … memdec b);
  ncases (decide_mem … memdec b)
-  [ #_; #H; napply refl; nauto
-  | #H; #_; ncut (uuC … b=uuC … b) [nauto] ncases (uuC … b) in ⊢ (???% → ?)
-    [ #E; napply False_rect_Type0; ncut (b=b) [nauto] ncases p in ⊢ (???% → ?)
-      [ #a; #K; #E2; napply H [ nauto | nrewrite > E2; nauto ]
+  [ #_; #H; napply refl; /2/
+  | #H; #_; ncut (uuC … b=uuC … b) [//] ncases (uuC … b) in ⊢ (???% → ?)
+    [ #E; napply False_rect_Type0; ncut (b=b) [//] ncases p in ⊢ (???% → ?)
+      [ #a; #K; #E2; napply H [ // | nrewrite > E2; // ]
     ##| #a; #i; #K; #E2; nrewrite < E2 in i; nnormalize; nrewrite > E; nnormalize;
-        nauto]
+        //]
   ##| #a; #E;
       ncut (a ◃ U)
-       [ nlapply E; nlapply (H ?) [nauto] ncases p
+       [ nlapply E; nlapply (H ?) [//] ncases p
           [ #x; #Hx; #K1; #_; ncases (K1 Hx)
         ##| #x; #i; #Hx; #K1; #E2; napply Hx; ngeneralize in match i; nnormalize;
-            nrewrite > E2; nnormalize; #_; nauto]##]
+            nrewrite > E2; nnormalize; #_; //]##]
       #Hcut; 
       nlapply (infty b); nnormalize; nrewrite > E; nnormalize; #H2;
       napply (H2 one); #y; #E2; nrewrite > E2 
-      (* [##2: napply cover_rect] nauto depth=1; *)
+      (* [##2: napply cover_rect] //; *)
        [ napply Hcut
-     ##| napply (cover_rect A U memdec P refl infty a); nauto ]##]
+     ##| napply (cover_rect A U memdec P refl infty a); // ]##]
 nqed.
 
 (********* Esempio:
@@ -135,24 +133,10 @@ nqed.
       | S m ⇒ S m * skipfact (pred m) ]
 **)
 
-ntheorem psym_plus: ∀n,m. n + m = m + n.
- #n; nelim n
-  [ #m; nelim m; //; #n0; #H;
-    nchange with (natS n0 = natS (n0 + O));
-    nrewrite < H; //
-  | #n0; #H; #m; nchange with (S (n0 + m) = m + S n0);
-    nrewrite > (H …);
-    nelim m; //;
-    #n1; #E; nrewrite > E; //]
+ntheorem psym_plus: ∀n,m. n + m = m + n.//.
 nqed.
 
-nlemma easy1: ∀n:nat. two * (S n) = two + two * n.
- #n; nelim n;//;
- #n0; #H; nnormalize;
- nrewrite > (psym_plus ??);
- nrewrite > H; nnormalize;
- nrewrite > (psym_plus ??);
- //.
+nlemma easy1: ∀n:nat. two * (S n) = two + two * n.//.
 nqed.
 
 ndefinition skipfact_dom: uuAx.
@@ -172,8 +156,8 @@ ntheorem skipfact_partial:
   | #m; #H; @2
      [ nnormalize; @1
      | nnormalize; #y; nchange in ⊢ (% → ?) with (y = pred (pred (two * (natone + m))));
-       nrewrite > (easy1 …); nchange in ⊢ (% → ?) with (y = two * m);
-       #E; nrewrite > E; nassumption ]##]
+       nnormalize; nrewrite < (plus_n_Sm …); nnormalize;
+       #E; nrewrite > E; napply H ]##]
 nqed.
 
 ndefinition skipfact: ∀n:nat. n ◃ mk_powerclass ? (λx: uuax skipfact_dom.x=O) → nat.
@@ -185,6 +169,5 @@ ndefinition skipfact: ∀n:nat. n ◃ mk_powerclass ? (λx: uuax skipfact_dom.x=
       napply (S m * H (pred m) …); //]
 nqed.
 
-nlemma test: skipfact four ? = eight. ##[##2: napply (skipfact_partial two)]
- nnormalize; //.
+nlemma test: skipfact four ? = eight. ##[##2: napply (skipfact_partial two)] //.
 nqed.
\ No newline at end of file