CProp hierarchy is there!

[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..a53961733a72d11f0870538a3f87858555b89772 100644 (file)
--- a/helm/software/matita/contribs/dama/dama/cprop_connectives.ma
+++ b/helm/software/matita/contribs/dama/dama/cprop_connectives.ma
@@ -30,18 +30,10 @@ interpretation "constructive and" 'and x y =
 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 "constructive exists" 'exists \eta.x =
-  (cic:/matita/dama/cprop_connectives/ex.ind#xpointer(1/1) _ x).
-  
-interpretation "constructive exists (Type)" 'exists \eta.x =
+interpretation "CProp exists" 'exists \eta.x =
   (cic:/matita/dama/cprop_connectives/exT.ind#xpointer(1/1) _ x).
 
-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).
@@ -53,7 +45,7 @@ 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.