general reorganization and first (unconditional) proof of lebesgue over naturals

[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 b42eaf61b8394972857496d3e342e123200f0dac..9e0e4b5fbb8e19c245c707d29f931923e91f2579 100644 (file)
--- a/helm/software/matita/contribs/dama/dama/cprop_connectives.ma
+++ b/helm/software/matita/contribs/dama/dama/cprop_connectives.ma
@@ -39,13 +39,29 @@ notation < "a ∧ b ∧ c ∧ d" left associative with precedence 35 for @{'and4
  
 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).
-
-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 "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}.
@@ -65,6 +81,9 @@ 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 ≝
@@ -93,4 +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.
-