reserve G, G1, G2 for _Graph, H for Subgraph of G;

theorem Th192:
  G is connected iff G | _GraphSelectors in G.allComponents()
proof
  hereby
    assume G is connected;
    then G is Component of G by GLIB_002:30;
    hence G | _GraphSelectors in G.allComponents() by Th191;
  end;
  assume G | _GraphSelectors in G.allComponents();
  then G | _GraphSelectors is Component of G by Th189;
  hence G is connected by GLIB_000:128, GLIBPRE1:38;
end;
