more notation

[helm.git] / helm / software / matita / contribs / dama / dama / cprop_connectives.ma

diff --git a/helm/software/matita/contribs/dama/dama/cprop_connectives.ma b/helm/software/matita/contribs/dama/dama/cprop_connectives.ma
index 21c10a4e12b96dee2d4a6c1e09a14a437cd4a297..b42eaf61b8394972857496d3e342e123200f0dac 100644 (file)
--- a/helm/software/matita/contribs/dama/dama/cprop_connectives.ma
+++ b/helm/software/matita/contribs/dama/dama/cprop_connectives.ma
@@ -15,7 +15,7 @@
 include "logic/equality.ma".
 
 inductive Or (A,B:CProp) : CProp ≝
-   Left : A → Or A B
+ | Left : A → Or A B
  | Right : B → Or A B.
 
 interpretation "constructive or" 'or x y = (Or x y).
@@ -28,14 +28,14 @@ interpretation "constructive and" 'and x y = (And x y).
 inductive And3 (A,B,C:CProp) : CProp ≝
  | Conj3 : A → B → C → And3 A B C.
 
-notation < "a ∧ b ∧ c" left associative with precedence 60 for @{'and3 $a $b $c}.
+notation < "a ∧ b ∧ c" left associative with precedence 35 for @{'and3 $a $b $c}.
  
 interpretation "constructive ternary and" 'and3 x y z = (Conj3 x y z).
 
-inductive And4 (A,B,C:CProp) : CProp ≝
- | Conj4 : A → B → C → And4 A B C.
+inductive And4 (A,B,C,D:CProp) : CProp ≝
+ | Conj4 : A → B → C → D → And4 A B C D.
 
-notation < "a ∧ b ∧ c ∧ d" left associative with precedence 60 for @{'and3 $a $b $c $d}.
+notation < "a ∧ b ∧ c ∧ d" left associative with precedence 35 for @{'and4 $a $b $c $d}.
  
 interpretation "constructive quaternary and" 'and4 x y z t = (Conj4 x y z t).
 
@@ -47,28 +47,35 @@ interpretation "CProp exists" 'exists \eta.x = (exT _ x).
 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.
 
-notation < "'fst' \nbsp x" non associative with precedence 50 for @{'pi1 $x}.
-notation < "'snd' \nbsp x" non associative with precedence 50 for @{'pi2 $x}.
-notation > "'fst' x" non associative with precedence 50 for @{'pi1 $x}.
-notation > "'snd' x" non associative with precedence 50 for @{'pi2 $x}.
-notation < "'fst' \nbsp x \nbsp y" non associative with precedence 50 for @{'pi12 $x $y}.
-notation < "'snd' \nbsp x \nbsp y" non associative with precedence 50 for @{'pi22 $x $y}.
+notation < "'fst' \nbsp x" non associative with precedence 90 for @{'pi1a $x}.
+notation < "'snd' \nbsp x" non associative with precedence 90 for @{'pi2a $x}.
+notation < "'fst' \nbsp x \nbsp y" non associative with precedence 90 for @{'pi1b $x $y}.
+notation < "'snd' \nbsp x \nbsp y" non associative with precedence 90 for @{'pi2b $x $y}.
+notation > "'fst'" non associative with precedence 90 for @{'pi1}.
+notation > "'snd'" non associative with precedence 90 for @{'pi2}.
 
 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 x = (pi1exT _ _ x).
-interpretation "exT fst 2" 'pi12 x y = (pi1exT _ _ x y).
+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).
 
 definition pi1exT23 ≝
   λA,P,Q,R.λx:exT23 A P Q R.match x with [ex_introT23 x _ _ _ _ ⇒ x].
 definition pi2exT23 ≝
   λA,P,Q,R.λx:exT23 A P Q R.match x with [ex_introT23 _ x _ _ _ ⇒ x].
-   
-interpretation "exT2 fst" 'pi1 x = (pi1exT23 _ _ _ _ x).
-interpretation "exT2 snd" 'pi2 x = (pi2exT23 _ _ _ _ x).
-interpretation "exT2 fst 2" 'pi12 x y = (pi1exT23 _ _ _ _ x y).
-interpretation "exT2 snd 2" 'pi22 x y = (pi2exT23 _ _ _ _ x y).
 
+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).
 
 definition Not : CProp → Prop ≝ λx:CProp.x → False.