A little bit more of notation here and there.

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

diff --git a/helm/matita/library/logic/connectives.ma b/helm/matita/library/logic/connectives.ma
index a5aab65f5d16fb77eda84a18be88e163802a86d2..5a1ad1fdd0f3aa8254dd2a8f1093e0d369486813 100644 (file)
--- 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.
+interpretation "logical not" 'not x = (cic:/matita/logic/connectives/Not.con x).
+alias symbol "not" (instance 0) = "logical not".
+
+theorem absurd : \forall A,C:Prop. A \to \lnot A \to C.
 intros. elim (H1 H).
 qed.
 
@@ -35,19 +38,25 @@ 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.
+interpretation "logical and" 'and x y = (cic:/matita/logic/connectives/And.ind#xpointer(1/1) x y).
+alias symbol "and" (instance 0) = "logical and".
+
+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).
+
+interpretation "logical or" 'or x y = (cic:/matita/logic/connectives/Or.ind#xpointer(1/1) x y).
+alias symbol "or" (instance 0) = "logical or".
    
-definition decidable : Prop \to Prop \def \lambda A:Prop. Or A (Not A).
+definition decidable : Prop \to Prop \def \lambda A:Prop. A \lor \not A.
 
 inductive ex (A:Type) (P:A \to Prop) : Prop \def
     ex_intro: \forall x:A. P x \to ex A P.