few more files, one diverges

[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 b4c556d83aca9bd2cef911156612ce8f837da713..a18ab47eb4db8cde5207982c7943b4e9fd718dbf 100644 (file)
--- a/helm/software/matita/library/logic/cprop_connectives.ma
+++ b/helm/software/matita/library/logic/cprop_connectives.ma
@@ -12,8 +12,7 @@
 (*                                                                        *)
 (**************************************************************************)
 
-include "logic/equality.ma".
-include "datatypes/constructors.ma".
+include "logic/connectives.ma".
 
 inductive Or (A,B:CProp) : CProp ≝
  | Left : A → Or A B
@@ -59,47 +58,80 @@ 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.
-  
-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).
-
+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].
+
+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].
+  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).
-interpretation "exT \snd" 'pi2 = (pi2exT _ _).
-interpretation "exT \snd" 'pi2a x = (pi2exT _ _ x).
-interpretation "exT \snd" 'pi2b x y = (pi2exT _ _ x y).
+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).
+interpretation "exT2 \snd" 'pi2 = (pi2exT23 ? ? ? ?).   
+interpretation "exT2 \snd" 'pi2a x = (pi2exT23 ? ? ? ? x).
+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.