Sambin's result holds trivially since most of the fields of the objects of

[helm.git] / helm / software / matita / contribs / formal_topology / overlap / cprop_connectives.ma

diff --git a/helm/software/matita/contribs/formal_topology/overlap/cprop_connectives.ma b/helm/software/matita/contribs/formal_topology/overlap/cprop_connectives.ma
index 4855bf658cb6403081a39c4f04b2f23de5ba7ab9..167c33317c8d4810e7cd0533e5b3aab7b0bf7b6f 100644 (file)
--- a/helm/software/matita/contribs/formal_topology/overlap/cprop_connectives.ma
+++ b/helm/software/matita/contribs/formal_topology/overlap/cprop_connectives.ma
@@ -19,18 +19,24 @@ definition Type2 : Type3 := Type.
 definition Type1 : Type2 := Type.
 definition Type0 : Type1 := Type.
 
-definition Type_OF_Type0: Type0 → Type := λx.x.
-definition Type_OF_Type1: Type1 → Type := λx.x.
-definition Type_OF_Type2: Type2 → Type := λx.x.
-definition Type_OF_Type3: Type3 → Type := λx.x.
-coercion Type_OF_Type0.
-coercion Type_OF_Type1.
-coercion Type_OF_Type2.
-coercion Type_OF_Type3.
+definition Type_of_Type0: Type0 → Type := λx.x.
+definition Type_of_Type1: Type1 → Type := λx.x.
+definition Type_of_Type2: Type2 → Type := λx.x.
+definition Type_of_Type3: Type3 → Type := λx.x.
+coercion Type_of_Type0.
+coercion Type_of_Type1.
+coercion Type_of_Type2.
+coercion Type_of_Type3.
 
 definition CProp0 : Type1 := Type0.
 definition CProp1 : Type2 := Type1.
 definition CProp2 : Type3 := Type2.
+definition CProp_of_CProp0: CProp0 → CProp ≝ λx.x.
+definition CProp_of_CProp1: CProp1 → CProp ≝ λx.x.
+definition CProp_of_CProp2: CProp2 → CProp ≝ λx.x.
+coercion CProp_of_CProp0.
+coercion CProp_of_CProp1.
+coercion CProp_of_CProp2.
 
 inductive Or (A,B:CProp0) : CProp0 ≝
  | Left : A → Or A B
@@ -86,18 +92,12 @@ record Iff1 (A,B:CProp1) : CProp1 ≝
    fi1: B → A
  }.
  
-interpretation "logical iff" 'iff x y = (Iff x y).
-
 notation "hvbox(a break ⇔ b)" right associative with precedence 25 for @{'iff1 $a $b}.
+interpretation "logical iff" 'iff x y = (Iff x y).
 interpretation "logical iff type1" 'iff1 x y = (Iff1 x y).
 
 inductive exT (A:Type0) (P:A→CProp0) : CProp0 ≝
   ex_introT: ∀w:A. P w → exT A P.
-  
-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).
 
 interpretation "CProp exists" 'exists \eta.x = (exT _ x).
 
@@ -154,4 +154,4 @@ definition antisymmetric: ∀A:Type0. ∀R:A→A→CProp0. ∀eq:A→A→Prop.CP
 
 definition reflexive: ∀C:Type0. ∀lt:C→C→CProp0.CProp0 ≝ λA:Type0.λR:A→A→CProp0.∀x:A.R x x.
 
-definition transitive: ∀C:Type0. ∀lt:C→C→CProp0.CProp0 ≝ λA:Type0.λR:A→A→CProp0.∀x,y,z:A.R x y → R y z → R x z.
\ No newline at end of file
+definition transitive: ∀C:Type0. ∀lt:C→C→CProp0.CProp0 ≝ λA:Type0.λR:A→A→CProp0.∀x,y,z:A.R x y → R y z → R x z.