some more work on q

[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 a0a701694ccc9ba1c7bac93758cfb3b0527ef261..09b9a6c67fb189d61070b5adf27f5f131bf5a547 100644 (file)
--- a/helm/software/matita/contribs/dama/dama/cprop_connectives.ma
+++ b/helm/software/matita/contribs/dama/dama/cprop_connectives.ma
@@ -13,6 +13,7 @@
 (**************************************************************************)
 
 include "logic/equality.ma".
+include "datatypes/constructors.ma".
 
 inductive Or (A,B:CProp) : CProp ≝
  | Left : A → Or A B
@@ -20,6 +21,25 @@ inductive Or (A,B:CProp) : CProp ≝
 
 interpretation "constructive or" 'or x y = (Or x y).
 
+inductive Or3 (A,B,C:CProp) : CProp ≝
+ | Left3 : A → Or3 A B C
+ | Middle3 : B → Or3 A B C
+ | Right3 : C → Or3 A B C.
+
+interpretation "constructive ternary or" 'or3 x y z= (Or3 x y z).
+
+notation < "hvbox(a break ∨ b break ∨ c)" with precedence 35 for @{'or3 $a $b $c}.
+
+inductive Or4 (A,B,C,D:CProp) : CProp ≝
+ | Left3 : A → Or4 A B C D
+ | Middle3 : B → Or4 A B C D
+ | Right3 : C → Or4 A B C D
+ | Extra3: D → Or4 A B C D.
+
+interpretation "constructive ternary or" 'or4 x y z t = (Or4 x y z t).
+
+notation < "hvbox(a break ∨ b break ∨ c break ∨ d)" with precedence 35 for @{'or4 $a $b $c $d}.
+
 inductive And (A,B:CProp) : CProp ≝
  | Conj : A → B → And A B.
  
@@ -28,59 +48,38 @@ 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" with precedence 35 for @{'and3 $a $b $c}.
+notation < "hvbox(a break ∧ b break ∧ c)" with precedence 35 for @{'and3 $a $b $c}.
  
-interpretation "constructive ternary and" 'and3 x y z = (Conj3 x y z).
+interpretation "constructive ternary and" 'and3 x y z = (And3 x y z).
 
 inductive And4 (A,B,C,D:CProp) : CProp ≝
  | Conj4 : A → B → C → D → And4 A B C D.
 
-notation < "a ∧ b ∧ c ∧ d" with precedence 35 for @{'and4 $a $b $c $d}.
+notation < "hvbox(a break ∧ b break ∧ c break ∧ d)" with precedence 35 for @{'and4 $a $b $c $d}.
  
-interpretation "constructive quaternary and" 'and4 x y z t = (Conj4 x y z t).
-
-coinductive product (A,B:Type) : Type ≝ pair : ∀a:A.∀b:B.product A B.
-
-notation "a \times b" left associative with precedence 70 for @{'product $a $b}.
-interpretation "prod" 'product a b = (product a b).
- 
-definition first : ∀A.∀P.A × P → A ≝ λA,P,s.match s with [pair x _ ⇒ x].
-definition second : ∀A.∀P.A × P → P ≝ λA,P,s.match s with [pair _ y ⇒ y].
-
-interpretation "pair pi1" 'pi1 = (first _ _).
-interpretation "pair pi2" 'pi2 = (second _ _).
-interpretation "pair pi1" 'pi1a x = (first _ _ x).
-interpretation "pair pi2" 'pi2a x = (second _ _ x).
-interpretation "pair pi1" 'pi1b x y = (first _ _ x y).
-interpretation "pair pi2" 'pi2b x y = (second _ _ x y).
-
-notation "hvbox(\langle term 19 a, break term 19 b\rangle)" 
-with precedence 90 for @{ 'pair $a $b}.
-interpretation "pair" 'pair a b = (pair _ _ a b).
+interpretation "constructive quaternary and" 'and4 x y z t = (And4 x y z t).
 
 inductive exT (A:Type) (P:A→CProp) : CProp ≝
   ex_introT: ∀w:A. P w → exT A P.
 
 interpretation "CProp exists" 'exists \eta.x = (exT _ x).
-interpretation "dependent pair" 'pair a b = (ex_introT _ _ a b).
 
-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}.
+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).
-interpretation "exT snd" 'pi2 = (pi2exT _ _).
-interpretation "exT snd" 'pi2a x = (pi2exT _ _ x).
-interpretation "exT snd" 'pi2b x y = (pi2exT _ _ 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).
 
 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.
@@ -90,12 +89,12 @@ definition pi1exT23 ≝
 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 \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.
 
@@ -113,3 +112,4 @@ definition antisymmetric ≝ λA:Type.λR:A→A→CProp.λeq:A→A→Prop.∀x:A
 definition reflexive ≝ λA:Type.λR:A→A→CProp.∀x:A.R x x.
 
 definition transitive ≝ λA:Type.λR:A→A→CProp.∀x,y,z:A.R x y → R y z → R x z.
+