The singature of the "by" universe is added to the goal signature

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

diff --git a/helm/software/matita/library/logic/cprop_connectives.ma b/helm/software/matita/library/logic/cprop_connectives.ma
index facda284891ed948ba1ed1e650e69c405fdd6b84..d2e91d555a289ee4c5383854ca1d7d762fcadf84 100644 (file)
--- a/helm/software/matita/library/logic/cprop_connectives.ma
+++ b/helm/software/matita/library/logic/cprop_connectives.ma
@@ -75,44 +75,63 @@ interpretation "logical iff type1" 'iff1 x y = (Iff1 x y).
 
 inductive exT (A:Type) (P:A→CProp) : CProp ≝
   ex_introT: ∀w:A. P w → exT A P.
-  
-notation "\ll term 19 a, break term 19 b \gg" 
-with precedence 90 for @{'dependent_pair $a $b}.
-interpretation "dependent pair" 'dependent_pair a b = 
-  (ex_introT _ _ a b).
 
-interpretation "CProp exists" 'exists \eta.x = (exT _ x).
+interpretation "CProp exists" 'exists x = (exT _ x).
 
 notation "\ll term 19 a, break term 19 b \gg" 
 with precedence 90 for @{'dependent_pair $a $b}.
 interpretation "dependent pair" 'dependent_pair a b = 
   (ex_introT _ _ a b).
 
-
 definition pi1exT ≝ λA,P.λx:exT A P.match x with [ex_introT x _ ⇒ x].
-definition pi2exT ≝ 
-  λA,P.λx:exT A P.match x return λx.P (pi1exT ?? x) with [ex_introT _ p ⇒ p].
 
 interpretation "exT \fst" 'pi1 = (pi1exT _ _).
 interpretation "exT \fst" 'pi1a x = (pi1exT _ _ x).
 interpretation "exT \fst" 'pi1b x y = (pi1exT _ _ x y).
+
+definition pi2exT ≝ 
+  λA,P.λx:exT A P.match x return λx.P (pi1exT ? ? x) with [ex_introT _ p ⇒ p].
+
 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 x = (exP _ x).
+
+definition pi1exP ≝ λA,P.λx:exP A P.match x with [ex_introP x _ ⇒ x].
+
+interpretation "exP \fst" 'pi1 = (pi1exP _ _).
+interpretation "exP \fst" 'pi1a x = (pi1exP _ _ x).
+interpretation "exP \fst" 'pi1b x y = (pi1exP _ _ x y).
+
+definition pi2exP ≝ 
+  λA,P.λx:exP A P.match x return λx.P (pi1exP ?? x) with [ex_introP _ p ⇒ p].
+
+interpretation "exP \snd" 'pi2 = (pi2exP _ _).
+interpretation "exP \snd" 'pi2a x = (pi2exP _ _ x).
+interpretation "exP \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.
 
 definition pi1exT23 ≝
   λA,P,Q,R.λx:exT23 A P Q R.match x with [ex_introT23 x _ _ _ _ ⇒ x].
+
+interpretation "exT2 \fst" 'pi1 = (pi1exT23 _ _ _ _).
+interpretation "exT2 \fst" 'pi1a x = (pi1exT23 _ _ _ _ x).
+interpretation "exT2 \fst" 'pi1b x y = (pi1exT23 _ _ _ _ x y).
+
 definition pi2exT23 ≝
   λA,P,Q,R.λx:exT23 A P Q R.match x with [ex_introT23 _ x _ _ _ ⇒ x].
 
-interpretation "exT2 \fst" 'pi1 = (pi1exT23 _ _ _ _).
 interpretation "exT2 \snd" 'pi2 = (pi2exT23 _ _ _ _).   
-interpretation "exT2 \fst" 'pi1a x = (pi1exT23 _ _ _ _ x).
 interpretation "exT2 \snd" 'pi2a x = (pi2exT23 _ _ _ _ x).
-interpretation "exT2 \fst" 'pi1b x y = (pi1exT23 _ _ _ _ x y).
 interpretation "exT2 \snd" 'pi2b x y = (pi2exT23 _ _ _ _ x y).
 
 inductive exT2 (A:Type) (P,Q:A→CProp) : CProp ≝