Much, much nicer now.

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 20923337ef6bdea87b4ecd23c8bc49497f9e0478..640a936ee21a194e1cd35a291ebce95dd2870d15 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
@@ -157,19 +157,16 @@ definition BTop: category2.
        change in e1 with (b⎻* ∘ A o2 = b'⎻* ∘ A o2);
        apply (.= e‡#);
        intro x;
-       change with (eq1 o3 (b⎻* (a'⎻* (A o1 x))) (b'⎻*(a'⎻* (A o1 x))));
-       lapply (saturated o1 o2 a' (A o1 x):?) as X;
-         [ apply ((saturation_idempotent ?? (A_is_saturation o1) x)^-1) ]
-       change in X with (eq1 ? (a'⎻* (A o1 x)) (A o2 (a'⎻* (A o1 x)))); 
+       change with (b⎻* (a'⎻* (A o1 x)) = b'⎻*(a'⎻* (A o1 x)));
        alias symbol "trans" = "trans1".
        alias symbol "prop1" = "prop11".
-       apply (.= †X);
-       whd in e1;
-       lapply (e1 (a'⎻* (A o1 x))) as X1;
-       change in X1 with (eq1 (oa_P (carrbt o3)) (b⎻* (A o2 (a'⎻* (A o1 x)))) (b'⎻* (A o2 (a' \sup ⎻* (A o1 x)))));
-       apply (.= X1);
+       apply (.= †(saturated o1 o2 a' (A o1 x) : ?));
+        [ apply ((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".
-       apply (†(X\sup -1));]
+       apply (†((saturated ?? a' (A o1 x) : ?) ^ -1));
+       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);