fixed notation

diff --git a/helm/software/matita/library/demo/formal_topology.ma b/helm/software/matita/library/demo/formal_topology.ma
index 67f0ffa54deb3050a04b3347e0940eb6be373caa..41c0d5c53cb2253fe4a9ea2e0deca0c275d89529 100644 (file)
--- a/helm/software/matita/library/demo/formal_topology.ma
+++ b/helm/software/matita/library/demo/formal_topology.ma
@@ -12,7 +12,28 @@
 (*                                                                        *)
 (**************************************************************************)
 
-include "datatypes/subsets.ma".
+include "logic/equality.ma".
+include "logic/cprop_connectives.ma".
+
+record powerset (A : Type) : Type ≝ { char : A → CProp }.
+
+interpretation "char" 'subset p = (mk_powerset _ p).  
+
+interpretation "pwset" 'powerset a = (powerset a). 
+
+interpretation "in" 'mem a X = (char _ X a). 
+
+definition subseteq ≝ λA.λu,v:\Omega \sup A.∀x.x ∈ u → x ∈ v.
+
+interpretation "subseteq" 'subseteq u v = (subseteq _ u v).
+
+definition overlaps ≝ λA.λU,V : Ω \sup A. exT2 ? (λx.x ∈ U) (λx.x ∈ V).
+
+interpretation "overlaps" 'overlaps u v = (overlaps _ u v).
+
+definition intersect ≝ λA.λu,v:Ω\sup A.{ y | y ∈ u ∧ y ∈ v }.
+
+interpretation "intersect" 'intersects u v = (intersect _ u v). 
 
 record axiom_set : Type ≝ { 
   A:> Type;
@@ -108,12 +129,12 @@ theorem compatibility: ∀A:axiom_set.∀a:A.∀U,V. a ⋉ V → a ◃ U → U 
  generalize in match H; clear H; 
  apply (covers_elim ?? {a|a ⋉ V → U ⋉ V} ??? H1);
  clear H1; simplify; intros;
-  [ exists [apply a1] assumption
+  [ exists [apply x] assumption
   | cases H2 in j H H1; clear H2 a1; intros; 
     cases (H1 i); clear H1; apply (H3 a1); assumption]
 qed.
 
-definition leq ≝ λA:axiom_set.λa,b:A. a ◃ {b}.
+definition leq ≝ λA:axiom_set.λa,b:A. a ◃ {y|b=y}.
 
 interpretation "covered by one" 'leq a b = (leq _ a b).