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 c84382e85cd1fa1205e64e1ca35f1d2933b42943..09b9a6c67fb189d61070b5adf27f5f131bf5a547 100644 (file)
--- a/helm/software/matita/contribs/dama/dama/cprop_connectives.ma
+++ b/helm/software/matita/contribs/dama/dama/cprop_connectives.ma
@@ -13,38 +13,92 @@
 (**************************************************************************)
 
 include "logic/equality.ma".
+include "datatypes/constructors.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 =
-  (cic:/matita/dama/cprop_connectives/Or.ind#xpointer(1/1) x y).
+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.
  
-interpretation "constructive and" 'and x y =
-  (cic:/matita/dama/cprop_connectives/And.ind#xpointer(1/1) x y).
+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 < "hvbox(a break ∧ b break ∧ c)" with precedence 35 for @{'and3 $a $b $c}.
+ 
+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 < "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 = (And4 x y z t).
 
 inductive exT (A:Type) (P:A→CProp) : CProp ≝
   ex_introT: ∀w:A. P w → exT A P.
 
-inductive ex (A:Type) (P:A→Prop) : Type ≝ (* ??? *)
-  ex_intro: ∀w:A. P w → ex A P.
+interpretation "CProp exists" 'exists \eta.x = (exT _ x).
 
-interpretation "constructive exists" 'exists \eta.x =
-  (cic:/matita/dama/cprop_connectives/ex.ind#xpointer(1/1) _ x).
-  
-interpretation "constructive exists (Type)" 'exists \eta.x =
-  (cic:/matita/dama/cprop_connectives/exT.ind#xpointer(1/1) _ 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].
 
-inductive False : CProp ≝ .
+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 Not ≝ λx:CProp.x → False.
+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.
 
-interpretation "constructive not" 'not x = 
-  (cic:/matita/dama/cprop_connectives/Not.con x).
+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 = (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.
+
+interpretation "constructive not" 'not x = (Not x).
   
 definition cotransitive ≝
  λC:Type.λlt:C→C→CProp.∀x,y,z:C. lt x y → lt x z ∨ lt z y. 
@@ -53,9 +107,9 @@ definition coreflexive ≝ λC:Type.λlt:C→C→CProp. ∀x:C. ¬ (lt x x).
 
 definition symmetric ≝ λC:Type.λlt:C→C→CProp. ∀x,y:C.lt x y → lt y x.
 
-definition antisymmetric ≝ λA:Type.λR:A→A→CProp.λeq:A→A→CProp.∀x:A.∀y:A.R x y→R y x→eq x y.
+definition antisymmetric ≝ λA:Type.λR:A→A→CProp.λeq:A→A→Prop.∀x:A.∀y:A.R x y→R y x→eq x y.
 
 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.
-
+