unary_morphism_N : seoidN -> setoidN -> setoidN (was ... -> setoidN+1)

[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 6accfaeaab9ad7e07ba260eec624551756be3038..873a9df60988a632084b8c6f24e9c2b00b619590 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
@@ -19,8 +19,8 @@ record basic_topology: Type2 ≝
  { carrbt:> OA;
    A: carrbt ⇒ carrbt;
    J: carrbt ⇒ carrbt;
-   A_is_saturation: is_saturation ? A;
-   J_is_reduction: is_reduction ? J;
+   A_is_saturation: is_o_saturation ? A;
+   J_is_reduction: is_o_reduction ? J;
    compatibility: ∀U,V. (A U >< J V) = (U >< J V)
  }.
 
@@ -108,7 +108,6 @@ theorem continuous_relation_eq_inv':
 qed.
 *)
 
-axiom daemon: False.
 definition continuous_relation_comp:
  ∀o1,o2,o3.
   continuous_relation_setoid o1 o2 →
@@ -158,16 +157,16 @@ definition BTop: category2.
        alias symbol "invert" = "setoid1 symmetry".
        lapply (.= †(saturated o1 o2 a' (A o1 x) : ?));
         [3: apply (b⎻* ); | 5: apply Hletin; |1,2: skip;
-        |apply ((saturation_idempotent ?? (A_is_saturation o1) x)^-1); ]
+        |apply ((o_saturation_idempotent ?? (A_is_saturation o1) x)^-1); ]
        change in e1 with (∀x.b⎻* (A o2 x) = b'⎻* (A o2 x));
        apply (.= (e1 (a'⎻* (A o1 x))));
        alias symbol "invert" = "setoid1 symmetry".
        lapply (†((saturated ?? a' (A o1 x) : ?) ^ -1));
         [2: apply (b'⎻* ); |4: apply Hletin; | skip;
-        |apply ((saturation_idempotent ?? (A_is_saturation o1) x)^-1);]]
+        |apply ((o_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 : ?));