typo

[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 91a2335c7998f44e40589b0cbd7751c64db3d680..9e0e4b5fbb8e19c245c707d29f931923e91f2579 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).
@@ -25,10 +25,76 @@ inductive And (A,B:CProp) : CProp ≝
  
 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 35 for @{'and3 $a $b $c}.
+ 
+interpretation "constructive ternary and" 'and3 x y z = (Conj3 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" 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).
+
+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 a, break b\rangle)" left associative with precedence 70 for @{ 'pair $a $b}.
+interpretation "pair" 'pair a b = (pair _ _ a b).
+
 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}.
+
+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).
+
+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].
+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.
 
@@ -46,4 +112,3 @@ 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.
-