X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=helm%2Fsoftware%2Fmatita%2Flibrary%2Flogic%2Fcprop_connectives.ma;h=266bb11a46484b921f2aa228257ebd3b21ea5ee2;hb=10dbebadd2931de5b93871a6b4989e07f668e166;hp=facda284891ed948ba1ed1e650e69c405fdd6b84;hpb=d990d5c64d0b9c07baef4257e7931321a42ae695;p=helm.git

diff --git a/helm/software/matita/library/logic/cprop_connectives.ma b/helm/software/matita/library/logic/cprop_connectives.ma
index facda2848..266bb11a4 100644
--- a/helm/software/matita/library/logic/cprop_connectives.ma
+++ b/helm/software/matita/library/logic/cprop_connectives.ma
@@ -100,6 +100,26 @@ interpretation "exT \snd" 'pi2 = (pi2exT _ _).
 interpretation "exT \snd" 'pi2a x = (pi2exT _ _ x).
 interpretation "exT \snd" 'pi2b x y = (pi2exT _ _ x y).
 
+inductive exP (A:Type) (P:A→Prop) : CProp ≝
+  ex_introP: ∀w:A. P w → exP A P.
+  
+interpretation "dependent pair for Prop" 'dependent_pair a b = 
+  (ex_introP _ _ a b).
+
+interpretation "CProp exists for Prop" 'exists \eta.x = (exP _ x).
+
+definition pi1exP ≝ λA,P.λx:exP A P.match x with [ex_introP x _ ⇒ x].
+definition pi2exP ≝ 
+  λA,P.λx:exP A P.match x return λx.P (pi1exP ?? x) with [ex_introP _ p ⇒ p].
+
+interpretation "exT \fst" 'pi1 = (pi1exP _ _).
+interpretation "exT \fst" 'pi1a x = (pi1exP _ _ x).
+interpretation "exT \fst" 'pi1b x y = (pi1exP _ _ x y).
+interpretation "exT \snd" 'pi2 = (pi2exP _ _).
+interpretation "exT \snd" 'pi2a x = (pi2exP _ _ x).
+interpretation "exT \snd" 'pi2b x y = (pi2exP _ _ x y).
+
+
 inductive exT23 (A:Type) (P:A→CProp) (Q:A→CProp) (R:A→A→CProp) : CProp ≝
   ex_introT23: ∀w,p:A. P w → Q p → R w p → exT23 A P Q R.