minor changes to make the library compile after wilmers new exists.

[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 fe377cbd954d0fd9331935efc7360bdb380b12ba..31cd9c576c236355b73e9335319c88c9b97d1c95 100644 (file)
--- a/helm/software/matita/library/logic/cprop_connectives.ma
+++ b/helm/software/matita/library/logic/cprop_connectives.ma
@@ -12,6 +12,8 @@
 (*                                                                        *)
 (**************************************************************************)
 
+include "logic/connectives.ma".
+
 inductive Or (A,B:CProp) : CProp ≝
  | Left : A → Or A B
  | Right : B → Or A B.
@@ -56,6 +58,21 @@ notation < "hvbox(a break ∧ b break ∧ c break ∧ d)" with precedence 35 for
  
 interpretation "constructive quaternary and" 'and4 x y z t = (And4 x y z t).
 
+record Iff (A,B:CProp) : CProp ≝
+ { if: A → B;
+   fi: B → A
+ }.
+ 
+record Iff1 (A,B:CProp) : CProp ≝
+ { if1: A → B;
+   fi1: B → A
+ }.
+ 
+interpretation "logical iff" 'iff x y = (Iff x y).
+
+notation "hvbox(a break ⇔ b)" right associative with precedence 25 for @{'iff1 $a $b}.
+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.
   
@@ -83,6 +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 "exP \fst" 'pi1 = (pi1exP _ _).
+interpretation "exP \fst" 'pi1a x = (pi1exP _ _ x).
+interpretation "exP \fst" 'pi1b x y = (pi1exP _ _ x y).
+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.
 
@@ -101,7 +138,6 @@ interpretation "exT2 \snd" 'pi2b x y = (pi2exT23 _ _ _ _ x y).
 inductive exT2 (A:Type) (P,Q:A→CProp) : CProp ≝
   ex_introT2: ∀w:A. P w → Q w → exT2 A P Q.
 
-alias id "False" = "cic:/Coq/Init/Logic/False.ind#xpointer(1/1)".
 definition Not : CProp → Prop ≝ λx:CProp.x → False.
 
 interpretation "constructive not" 'not x = (Not x).