From: Enrico Tassi <enrico.tassi@inria.fr>
Date: Thu, 21 Sep 2006 15:59:21 +0000 (+0000)
Subject: added notation
X-Git-Tag: 0.4.95@7852~1012
X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=commitdiff_plain;h=0ed7fb39e919a6a4814dc5e9d435edf924cca72f;p=helm.git

added notation
---

diff --git a/matita/library/datatypes/constructors.ma b/matita/library/datatypes/constructors.ma
index 3f74db5ad..3567dd915 100644
--- a/matita/library/datatypes/constructors.ma
+++ b/matita/library/datatypes/constructors.ma
@@ -20,6 +20,18 @@ inductive void : Set \def.
 inductive Prod (A,B:Set) : Set \def
 pair : A \to B \to Prod A B.
 
+interpretation "Pair construction" 'pair x y =
+ (cic:/matita/datatypes/constructors/Prod.ind#xpointer(1/1/1) _ _ x y).
+
+notation "hvbox(\langle x break , y \rangle )" with precedence 89
+for @{ 'pair $x $y}.
+
+interpretation "Product" 'product x y =
+ (cic:/matita/datatypes/constructors/Prod.ind#xpointer(1/1) x y).
+
+notation "hvbox(x break \times y)" with precedence 89
+for @{ 'product $x $y}.
+
 definition fst \def \lambda A,B:Set.\lambda p: Prod A B.
 match p with
 [(pair a b) \Rightarrow a]. 
@@ -28,8 +40,20 @@ definition snd \def \lambda A,B:Set.\lambda p: Prod A B.
 match p with
 [(pair a b) \Rightarrow b].
 
-theorem eq_pair_fst_snd: \forall A,B:Set.\forall p: Prod A B.
-p = pair A B (fst A B p) (snd A B p).
+interpretation "First projection" 'fst x =
+ (cic:/matita/datatypes/constructors/fst.con _ _ x).
+
+notation "\fst x" with precedence 89
+for @{ 'fst $x}.
+
+interpretation "Second projection" 'snd x =
+ (cic:/matita/datatypes/constructors/snd.con _ _ x).
+
+notation "\snd x" with precedence 89
+for @{ 'snd $x}.
+
+theorem eq_pair_fst_snd: \forall A,B:Set.\forall p:Prod A B.
+p = 〈 (\fst p), (\snd p) 〉.
 intros.elim p.simplify.reflexivity.
 qed.