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[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 36616b2f8fc74dc10a8f53170abe94b4b1915229..4855bf658cb6403081a39c4f04b2f23de5ba7ab9 100644 (file)
--- a/helm/software/matita/contribs/formal_topology/overlap/cprop_connectives.ma
+++ b/helm/software/matita/contribs/formal_topology/overlap/cprop_connectives.ma
@@ -140,16 +140,18 @@ definition Not : CProp0 → Prop ≝ λx:CProp.x → False.
 
 interpretation "constructive not" 'not x = (Not x).
   
-definition cotransitive ≝
+definition cotransitive: ∀C:Type0. ∀lt:C→C→CProp0.CProp0 ≝
  λC:Type0.λlt:C→C→CProp0.∀x,y,z:C. lt x y → lt x z ∨ lt z y. 
 
-definition coreflexive ≝ λC:Type0.λlt:C→C→CProp0. ∀x:C. ¬ (lt x x).
+definition coreflexive: ∀C:Type0. ∀lt:C→C→CProp0.CProp0 ≝
+ λC:Type0.λlt:C→C→CProp0. ∀x:C. ¬ (lt x x).
 
-definition symmetric ≝ λC:Type0.λlt:C→C→CProp0. ∀x,y:C.lt x y → lt y x.
+definition symmetric: ∀C:Type0. ∀lt:C→C→CProp0.CProp0 ≝
+ λC:Type0.λlt:C→C→CProp0. ∀x,y:C.lt x y → lt y x.
 
-definition antisymmetric ≝ λA:Type0.λR:A→A→CProp0.λeq:A→A→Prop.∀x:A.∀y:A.R x y→R y x→eq x y.
+definition antisymmetric: ∀A:Type0. ∀R:A→A→CProp0. ∀eq:A→A→Prop.CProp0 ≝
+ λA:Type0.λR:A→A→CProp0.λeq:A→A→Prop.∀x:A.∀y:A.R x y→R y x→eq x y.
 
-definition reflexive ≝ λA:Type0.λR:A→A→CProp0.∀x:A.R x x.
+definition reflexive: ∀C:Type0. ∀lt:C→C→CProp0.CProp0 ≝ λA:Type0.λR:A→A→CProp0.∀x:A.R x x.
 
-definition transitive ≝ λA:Type0.λR:A→A→CProp0.∀x,y,z:A.R x y → R y z → R x z.
- 
+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.
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