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

theorem Th189:
  G2 in G1.allComponents() iff G2 is plain Component of G1
proof
  hereby
    assume G2 in G1.allComponents();
    then consider H being Element of [#]G1.allSG() such that
      A1: G2 = H & H is Component-like;
    thus G2 is plain Component of G1 by A1;
  end;
  assume A2: G2 is plain Component of G1;
  then G2 in [#]G1.allSG() by Th1;
  hence thesis by A2;
end;
