equivalence_relations made uniform w.r.t. universe level

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

diff --git a/helm/software/matita/contribs/formal_topology/overlap/categories.ma b/helm/software/matita/contribs/formal_topology/overlap/categories.ma
index 3e03cb0935d9be923b32d7ede096e44860147446..ea246ef6c8e501c58a50b571763ccb50ee693812 100644 (file)
--- a/helm/software/matita/contribs/formal_topology/overlap/categories.ma
+++ b/helm/software/matita/contribs/formal_topology/overlap/categories.ma
@@ -57,7 +57,7 @@ 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.
 
-record equivalence_relation1 (A:Type1) : Type1 ≝
+record equivalence_relation1 (A:Type1) : Type2 ≝
  { eq_rel1:2> A → A → CProp1;
    refl1: reflexive1 ? eq_rel1;
    sym1: symmetric1 ? eq_rel1;
@@ -88,7 +88,7 @@ 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.
 
-record equivalence_relation2 (A:Type2) : Type2 ≝
+record equivalence_relation2 (A:Type2) : Type3 ≝
  { eq_rel2:2> A → A → CProp2;
    refl2: reflexive2 ? eq_rel2;
    sym2: symmetric2 ? eq_rel2;
@@ -297,7 +297,7 @@ interpretation "category assoc" 'assoc = (comp_assoc ________).
 
 (* bug grande come una casa?
    Ma come fa a passare la quantificazione larga??? *)
-definition unary_morphism_setoid: setoid → setoid → setoid.
+definition unary_morphism_setoid: setoid → setoid → setoid1.
  intros;
  constructor 1;
   [ apply (unary_morphism s s1);
@@ -393,6 +393,5 @@ qed.
 coercion hint.
 
 interpretation "SET dagger" 'prop1 h = (prop11_SET1 _ _ _ _ _ h).
-notation "hbox(a break ⇒ b)" right associative with precedence 20 for @{ 'Imply $a $b }.
 interpretation "unary morphism1" 'Imply a b = (arrows2 SET1 a b).
 interpretation "SET1 eq" 'eq x y = (eq_rel1 _ (eq'' _) x y).