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[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..21c10a4e12b96dee2d4a6c1e09a14a437cd4a297 100644 (file)
--- a/helm/software/matita/contribs/dama/dama/cprop_connectives.ma
+++ b/helm/software/matita/contribs/dama/dama/cprop_connectives.ma
@@ -18,33 +18,61 @@ inductive Or (A,B:CProp) : CProp ≝
    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 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 < "a ∧ b ∧ c" left associative with precedence 60 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.
+
+notation < "a ∧ b ∧ c ∧ d" left associative with precedence 60 for @{'and3 $a $b $c $d}.
+ 
+interpretation "constructive quaternary and" 'and4 x y z t = (Conj4 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).
+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}.
+
+definition pi1exT ≝ λA,P.λx:exT A P.match x with [ex_introT x _ ⇒ x].
+
+interpretation "exT fst" 'pi1 x = (pi1exT _ _ x).
+interpretation "exT fst 2" 'pi12 x y = (pi1exT _ _ 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).
 
-inductive False : CProp ≝ .
 
-definition Not ≝ λx:CProp.x → False.
+definition Not : CProp → Prop ≝ λx:CProp.x → False.
 
-interpretation "constructive not" 'not x = 
-  (cic:/matita/dama/cprop_connectives/Not.con x).
+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. 
@@ -53,7 +81,7 @@ 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.