X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=helm%2Fmatita%2Flibrary%2Flogic%2Fconnectives.ma;h=4cbea3529a7ec983b39f814f1243f1a5f92568ab;hb=4167cea65ca58897d1a3dbb81ff95de5074700cc;hp=a5aab65f5d16fb77eda84a18be88e163802a86d2;hpb=9c8bb7e7c2548d2f37e5387cdce45df2b8fc9b43;p=helm.git

diff --git a/helm/matita/library/logic/connectives.ma b/helm/matita/library/logic/connectives.ma
index a5aab65f5..4cbea3529 100644
--- a/helm/matita/library/logic/connectives.ma
+++ b/helm/matita/library/logic/connectives.ma
@@ -26,7 +26,10 @@ default "false" cic:/matita/logic/connectives/False.ind.
 definition Not: Prop \to Prop \def
 \lambda A. (A \to False).
 
-theorem absurd : \forall A,C:Prop. A \to Not A \to C.
+(*CSC: the URI must disappear: there is a bug now *)
+interpretation "logical not" 'not x = (cic:/matita/logic/connectives/Not.con x).
+
+theorem absurd : \forall A,C:Prop. A \to \lnot A \to C.
 intros. elim (H1 H).
 qed.
 
@@ -35,22 +38,53 @@ default "absurd" cic:/matita/logic/connectives/absurd.con.
 inductive And (A,B:Prop) : Prop \def
     conj : A \to B \to (And A B).
 
-theorem proj1: \forall A,B:Prop. (And A B) \to A.
+(*CSC: the URI must disappear: there is a bug now *)
+interpretation "logical and" 'and x y = (cic:/matita/logic/connectives/And.ind#xpointer(1/1) x y).
+
+theorem proj1: \forall A,B:Prop. A \land B \to A.
 intros. elim H. assumption.
 qed.
 
-theorem proj2: \forall A,B:Prop. (And A B) \to B.
+theorem proj2: \forall A,B:Prop. A \land B \to B.
 intros. elim H. assumption.
 qed.
 
 inductive Or (A,B:Prop) : Prop \def
      or_introl : A \to (Or A B)
    | or_intror : B \to (Or A B).
-   
-definition decidable : Prop \to Prop \def \lambda A:Prop. Or A (Not A).
+
+(*CSC: the URI must disappear: there is a bug now *)
+interpretation "logical or" 'or x y =
+  (cic:/matita/logic/connectives/Or.ind#xpointer(1/1) x y).
+
+theorem Or_ind':
+ \forall A,B:Prop.
+  \forall P: A \lor B \to Prop.
+   (\forall p:A. P (or_introl ? ? p)) \to
+   (\forall q:B. P (or_intror ? ? q)) \to
+    \forall p:A \lor B. P p.
+ intros.
+ apply
+  (match p return \lambda p.P p with
+    [(or_introl p) \Rightarrow H p
+    |(or_intror q) \Rightarrow H1 q]).
+qed.
+
+definition decidable : Prop \to Prop \def \lambda A:Prop. A \lor \lnot A.
 
 inductive ex (A:Type) (P:A \to Prop) : Prop \def
     ex_intro: \forall x:A. P x \to ex A P.
 
+(*CSC: the URI must disappear: there is a bug now *)
+interpretation "exists" 'exists \eta.x =
+  (cic:/matita/logic/connectives/ex.ind#xpointer(1/1) _ x).
+
+notation < "hvbox(\exists ident i opt (: ty) break . p)"
+  right associative with precedence 20
+for @{ 'exists ${default
+  @{\lambda ${ident i} : $ty. $p)}
+  @{\lambda ${ident i} . $p}}}.
+
 inductive ex2 (A:Type) (P,Q:A \to Prop) : Prop \def
     ex_intro2: \forall x:A. P x \to Q x \to ex2 A P Q.
+