X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=helm%2Fsoftware%2Fmatita%2Fcontribs%2Fformal_topology%2Foverlap%2Fcategories.ma;h=75ca005c64b9ce03d24b487c22d103ee97499492;hb=33fbecf99c187fb4fc84a68ee9f479da046e9df9;hp=3ee3915074dd3db68941cbe032c9b4bcb8f3fa40;hpb=2857d1c432f073379552e1572235a86509b665a4;p=helm.git

diff --git a/helm/software/matita/contribs/formal_topology/overlap/categories.ma b/helm/software/matita/contribs/formal_topology/overlap/categories.ma
index 3ee391507..75ca005c6 100644
--- a/helm/software/matita/contribs/formal_topology/overlap/categories.ma
+++ b/helm/software/matita/contribs/formal_topology/overlap/categories.ma
@@ -26,9 +26,9 @@ record setoid : Type1 ≝
    eq: equivalence_relation carr
  }.
 
-definition reflexive1 ≝ λA:Type1.λR:A→A→CProp1.∀x:A.R x x.
-definition symmetric1 ≝ λC:Type1.λlt:C→C→CProp1. ∀x,y:C.lt x y → lt y x.
-definition transitive1 ≝ λA:Type1.λR:A→A→CProp1.∀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.
 
 record equivalence_relation1 (A:Type1) : Type2 ≝
  { eq_rel1:2> A → A → CProp1;
@@ -57,9 +57,9 @@ qed.
 (* questa coercion e' necessaria per problemi di unificazione *)
 coercion setoid1_of_setoid.
 
-definition reflexive2 ≝ λA:Type2.λR:A→A→CProp2.∀x:A.R x x.
-definition symmetric2 ≝ λC:Type2.λlt:C→C→CProp2. ∀x,y:C.lt x y → lt y x.
-definition transitive2 ≝ λA:Type2.λR:A→A→CProp2.∀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.
 
 record equivalence_relation2 (A:Type2) : Type3 ≝
  { eq_rel2:2> A → A → CProp2;