+ apply (.= (extS_com ??? c c1 ?));
+ apply (.= †(C1 ?????));
+ apply (.= (C1' ?????));
+ apply (.= ((†((extS_singleton ????) \sup -1))‡(†((extS_singleton ????) \sup -1))));
+ apply (.= (extS_com ??????)\sup -1 ‡ (extS_com ??????) \sup -1);
+ apply (.= (extS_singleton ????)‡(extS_singleton ????));
+ apply refl1;
+ | apply (.= (extS_com ??? c c1 ?));
+ apply (.= (†(C2 ???)));
+ apply (.= (C2 ???));
+ apply refl1;]
+ | intros; simplify;
+ change with (comp1 BTop ??? a b = comp1 BTop ??? a' b');
+ apply prop1; assumption]
+qed.
+