X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=helm%2Fsoftware%2Fmatita%2Fnlibrary%2Ftopology%2Fcantor.ma;h=d3dccb8ee07e66248e17e69f21536cc6fb3013fe;hb=e7264f953fcf2cd2bef9057d83add08996d2ce75;hp=3e9214f37ce61fc5b9f18086aff74da37a8c91b1;hpb=aaa04b3cfa6fc3410c953f21c53796f82bb22411;p=helm.git

diff --git a/helm/software/matita/nlibrary/topology/cantor.ma b/helm/software/matita/nlibrary/topology/cantor.ma
index 3e9214f37..d3dccb8ee 100644
--- a/helm/software/matita/nlibrary/topology/cantor.ma
+++ b/helm/software/matita/nlibrary/topology/cantor.ma
@@ -41,7 +41,7 @@ ntheorem th2_3 :
   ∀A:Ax.∀a:A. a ◃ ∅ → ∃i. ¬ a ∈ 𝐂 a i.
 #A; #a; #H; nelim H;
 ##[ #n; *;
-##| #b; #i_star; #IH1; #IH2; ncases (EM … b i_star); /2/;
+##| #b; #i_star; #IH1; #IH2; ncases (EM … b i_star); /3/;
 ##] 
 nqed.
 
@@ -80,19 +80,18 @@ unification hint 0 ≔ ;
   (* -------------- *) ⊢
          S x ≡ A. 
 
-
 ntheorem col2_4 :
-  ∀A:uAx.∀a:A. a ◃ ∅ → ¬ a ∈ 𝐂 a one. 
+  ∀A:uAx.∀a:uax A. a ◃ ∅ → ¬ a ∈ 𝐂 a one.
 #A; #a; #H; nelim H;
 ##[ #n; *;
-##| #b; #i_star; #IH1; #IH2; #H3; nlapply (IH2 … H3); //;
-##] 
+##| #b; #i_star; #IH1; #IH2; #H3; nlapply (IH2 … H3); /2/;
+##]
 nqed.
 
 ndefinition Z : Ω^axs ≝ { x | x ◃ ∅ }.
 
 ntheorem cover_monotone: ∀A:Ax.∀a:A.∀U,V.U ⊆ V → a ◃ U → a ◃ V.
-#A; #a; #U; #V; #HUV; #H; nelim H; //; 
+#A; #a; #U; #V; #HUV; #H; nelim H; /3/; 
 nqed.
 
 ntheorem th3_1: ¬∃a:axs.Z ⊆ S a ∧ S a ⊆ Z.
@@ -103,7 +102,7 @@ ncut (a ◃ Z); ##[
 ncut (a ◃ ∅); ##[ napply (transitivity … H); nwhd in match Z; //; ##] #H1;
 ncut (¬ a ∈ S a); ##[ napply (col2_4 … H1); ##] #H2;
 ncut (a ∈ S a); ##[ napply ZSa; napply H1; ##] #H3;
-//;
+/2/;
 nqed.
 
 include "nat/nat.ma".
@@ -139,20 +138,18 @@ naxiom Ph :  ∀x.h x = O \liff  x ◃ ∅.
 
 nlemma replace_char:
   ∀A:Ax.∀U,V.U ⊆ V → V ⊆ U → ∀a:A.a ◃ U → a ◃ V.
-#A; #U; #V;  #UV; #VU; #a; #aU; nelim aU; //;
+#A; #U; #V;  #UV; #VU; #a; #aU; nelim aU; /3/;
 nqed.
 
 ntheorem th_ch3: ¬∃a:caxs.∀x.ϕ a x = h x.
 *; #a; #H;
 ncut (a ◃ { x | x ◃ ∅}); ##[
-  napply (replace_char … { x | h x = O }); ##[ ##1,2: #x; ncases (Ph x); //; ##]
+  napply (replace_char … { x | h x = O }); ##[ ##1,2: #x; ncases (Ph x); /2/; ##]
   napply (replace_char … { x | ϕ a x = O }); ##[##1,2: #x; nrewrite > (H x); //; ##]
   napply (axiom_cond … a one); ##] #H1;
 ncut (a ◃ ∅); ##[ napply (transitivity … H1); //; ##] #H2;
 nlapply (col2_4 …H2); #H3;
 ncut (a ∈ 𝐂 a one); ##[
-  nnormalize; ncases (Ph a); nrewrite > (H a); //; ##] #H4;
-//;
-nqed.
-
-
+  nnormalize; ncases (Ph a); nrewrite > (H a); /2/; ##] #H4;
+/2/;
+nqed.
\ No newline at end of file