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[helm.git] / helm / software / matita / contribs / formal_topology / overlap / o-basic_topologies.ma

diff --git a/helm/software/matita/contribs/formal_topology/overlap/o-basic_topologies.ma b/helm/software/matita/contribs/formal_topology/overlap/o-basic_topologies.ma
index be985a43cefd551e01fd6ea942dcc220dea8b622..ae695f624f92907864505483ad0f783db7641420 100644 (file)
--- a/helm/software/matita/contribs/formal_topology/overlap/o-basic_topologies.ma
+++ b/helm/software/matita/contribs/formal_topology/overlap/o-basic_topologies.ma
@@ -15,7 +15,7 @@
 include "o-algebra.ma".
 include "o-saturations.ma".
 
-record basic_topology: Type ≝
+record basic_topology: Type2 ≝
  { carrbt:> OA;
    A: carrbt ⇒ carrbt;
    J: carrbt ⇒ carrbt;
@@ -29,7 +29,7 @@ lemma hint: OA → objs2 OA.
 qed.
 coercion hint.
 
-record continuous_relation (S,T: basic_topology) : Type ≝
+record continuous_relation (S,T: basic_topology) : Type2 ≝
  { cont_rel:> arrows2 OA S T;
    (* reduces uses eq1, saturated uses eq!!! *)
    reduced: ∀U. U = J ? U → cont_rel U = J ? (cont_rel U);
@@ -167,7 +167,7 @@ definition BTop: category2.
         |apply ((saturation_idempotent ?? (A_is_saturation o1) x)^-1);]]
   | intros; simplify;
     change with (((a34⎻* ∘ a23⎻* ) ∘ a12⎻* ) ∘ A o1 = ((a34⎻* ∘ (a23⎻* ∘ a12⎻* )) ∘ A o1));
-    apply rule (#‡ASSOC1\sup -1);
+    apply rule (#‡ASSOC ^ -1);
   | intros; simplify;
     change with ((a⎻* ∘ (id2 ? o1)⎻* ) ∘ A o1 = a⎻* ∘ A o1);
     apply (#‡(id_neutral_right2 : ?));
@@ -176,6 +176,9 @@ definition BTop: category2.
     apply (#‡(id_neutral_left2 : ?));]
 qed.
 
+definition btop_carr: BTop → Type1 ≝ λo:BTop. carr1 (oa_P (carrbt o)).
+coercion btop_carr.
+
 (*
 (*CSC: unused! *)
 (* this proof is more logic-oriented than set/lattice oriented *)
@@ -201,4 +204,4 @@ theorem continuous_relation_eqS:
   [2,4: intros; apply saturation_monotone; try (apply A_is_saturation); apply Hcut;]
  apply Hcut2; assumption.
 qed.
-*)
\ No newline at end of file
+*)