theorem
  union G.componentSet() = the_Vertices_of G
proof
  now
    let x be object;
    thus x in union G.componentSet() implies x in the_Vertices_of G;
    assume x in the_Vertices_of G;
    then reconsider x9=x as Vertex of G;
    set Y = G.reachableFrom(x9);
    x in Y & Y in G.componentSet() by Def8,Lm1;
    hence x in union G.componentSet() by TARSKI:def 4;
  end;
  hence thesis by TARSKI:2;
end;
