added notation

diff --git a/matita/library/datatypes/constructors.ma b/matita/library/datatypes/constructors.ma
index 3f74db5ad85cfb8b7e9ce99d414471fe53f88f3b..3567dd915463c8b6c2f809ed8218987a67e78042 100644 (file)
--- 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.