
theorem Th12:
  for G being _Graph, C being Component of G
  holds Endvertices C c= Endvertices G
proof
  let G be _Graph, C be Component of G;
  now
    let x be object;
    assume x in Endvertices C;
    then consider v being Vertex of C such that
      A1: x = v & v is endvertex by GLIB_006:def 8;
    the_Vertices_of C c= the_Vertices_of G;
    then reconsider w = v as Vertex of G by TARSKI:def 3;
    1 = v.degree() by A1, GLIB_000:174
     .= w.degree() by GLIBPRE0:44;
    hence x in Endvertices G by A1, GLIB_000:174, GLIB_006:56;
  end;
  hence thesis by TARSKI:def 3;
end;
