
theorem Th33:
  for G1, G2 being non-Dmulti _Graph, f being directed PVertexMapping of G1, G2
  st f is total holds DPVM2PGM(f) is total
proof
  let G1, G2 be non-Dmulti _Graph, f be directed PVertexMapping of G1, G2;
  assume f is total;
  then A1: dom f = the_Vertices_of G1 by PARTFUN1:def 2;
  A2: dom (DPVM2PGM f)_E = G1.edgesBetween(dom f) by Def11
    .= the_Edges_of G1 by A1, GLIB_000:34;
  (DPVM2PGM f)_V = f;
  hence thesis by A1, A2, GLIB_010:def 11;
end;
