not_to_not

[helm.git] / helm / software / matita / library / logic / connectives.ma

diff --git a/helm/software/matita/library/logic/connectives.ma b/helm/software/matita/library/logic/connectives.ma
index bb08b8038bf51c37d533a0889c2493fd04fdc810..76d0323166ad947578481e7c06bb4d8d8b3cc41a 100644 (file)
--- a/helm/software/matita/library/logic/connectives.ma
+++ b/helm/software/matita/library/logic/connectives.ma
@@ -12,8 +12,6 @@
 (*                                                                        *)
 (**************************************************************************)
 
-set "baseuri" "cic:/matita/logic/connectives/".
-
 inductive True: Prop \def
 I : True.
 
@@ -26,8 +24,7 @@ default "false" cic:/matita/logic/connectives/False.ind.
 definition Not: Prop \to Prop \def
 \lambda A. (A \to False).
 
-(*CSC: the URI must disappear: there is a bug now *)
-interpretation "logical not" 'not x = (cic:/matita/logic/connectives/Not.con x).
+interpretation "logical not" 'not x = (Not x).
 
 theorem absurd : \forall A,C:Prop. A \to \lnot A \to C.
 intros. elim (H1 H).
@@ -35,11 +32,16 @@ qed.
 
 default "absurd" cic:/matita/logic/connectives/absurd.con.
 
+theorem not_to_not : \forall A,B:Prop. (A → B) \to ¬B →¬A.
+intros.unfold.intro.apply H1.apply (H H2).
+qed.
+
+default "absurd" cic:/matita/logic/connectives/absurd.con.
+
 inductive And (A,B:Prop) : Prop \def
     conj : A \to B \to (And A B).
 
-(*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).
+interpretation "logical and" 'and x y = (And x y).
 
 theorem proj1: \forall A,B:Prop. A \land B \to A.
 intros. elim H. assumption.
@@ -53,9 +55,7 @@ inductive Or (A,B:Prop) : Prop \def
      or_introl : A \to (Or A B)
    | or_intror : B \to (Or A B).
 
-(*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).
+interpretation "logical or" 'or x y = (Or x y).
 
 theorem Or_ind':
  \forall A,B:Prop.
@@ -75,10 +75,10 @@ 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).
+interpretation "exists" 'exists x = (ex ? x).
 
 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.
 
+definition iff :=
+ \lambda A,B. (A -> B) \land (B -> A).