CAT2

[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 167c33317c8d4810e7cd0533e5b3aab7b0bf7b6f..644acc2183a3d813951252fd8921a175f4b5c340 100644 (file)
--- a/helm/software/matita/contribs/formal_topology/overlap/cprop_connectives.ma
+++ b/helm/software/matita/contribs/formal_topology/overlap/cprop_connectives.ma
@@ -14,7 +14,8 @@
 
 include "logic/connectives.ma".
 
-definition Type3 : Type := Type.
+definition Type4 : Type := Type.
+definition Type3 : Type4 := Type.
 definition Type2 : Type3 := Type.
 definition Type1 : Type2 := Type.
 definition Type0 : Type1 := Type.
@@ -23,20 +24,25 @@ 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.
+definition Type_of_Type4: Type4 → Type := λx.x.
 coercion Type_of_Type0.
 coercion Type_of_Type1.
 coercion Type_of_Type2.
 coercion Type_of_Type3.
+coercion Type_of_Type4.
 
 definition CProp0 : Type1 := Type0.
 definition CProp1 : Type2 := Type1.
 definition CProp2 : Type3 := Type2.
+definition CProp3 : Type4 := Type3.
 definition CProp_of_CProp0: CProp0 → CProp ≝ λx.x.
 definition CProp_of_CProp1: CProp1 → CProp ≝ λx.x.
 definition CProp_of_CProp2: CProp2 → CProp ≝ λx.x.
+definition CProp_of_CProp3: CProp3 → CProp ≝ λx.x.
 coercion CProp_of_CProp0.
 coercion CProp_of_CProp1.
 coercion CProp_of_CProp2.
+coercion CProp_of_CProp3.
 
 inductive Or (A,B:CProp0) : CProp0 ≝
  | Left : A → Or A B
@@ -155,3 +161,15 @@ 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.
+
+definition reflexive1: ∀A:Type1.∀R:A→A→CProp1.CProp1 ≝ λA:Type1.λR:A→A→CProp1.∀x:A.R x x.
+definition symmetric1: ∀A:Type1.∀R:A→A→CProp1.CProp1 ≝ λC:Type1.λlt:C→C→CProp1. ∀x,y:C.lt x y → lt y x.
+definition transitive1: ∀A:Type1.∀R:A→A→CProp1.CProp1 ≝ λA:Type1.λR:A→A→CProp1.∀x,y,z:A.R x y → R y z → R x z.
+
+definition reflexive2: ∀A:Type2.∀R:A→A→CProp2.CProp2 ≝ λA:Type2.λR:A→A→CProp2.∀x:A.R x x.
+definition symmetric2: ∀A:Type2.∀R:A→A→CProp2.CProp2 ≝ λC:Type2.λlt:C→C→CProp2. ∀x,y:C.lt x y → lt y x.
+definition transitive2: ∀A:Type2.∀R:A→A→CProp2.CProp2 ≝ λA:Type2.λR:A→A→CProp2.∀x,y,z:A.R x y → R y z → R x z.
+
+definition reflexive3: ∀A:Type3.∀R:A→A→CProp3.CProp3 ≝ λA:Type3.λR:A→A→CProp3.∀x:A.R x x.
+definition symmetric3: ∀A:Type3.∀R:A→A→CProp3.CProp3 ≝ λC:Type3.λlt:C→C→CProp3. ∀x,y:C.lt x y → lt y x.
+definition transitive3: ∀A:Type3.∀R:A→A→CProp3.CProp3 ≝ λA:Type3.λR:A→A→CProp3.∀x,y,z:A.R x y → R y z → R x z.