
theorem Th32:
  for G1, G2 being non-multi _Graph, f being PVertexMapping of G1, G2
  st f is total holds PVM2PGM(f) is total
proof
  let G1, G2 be non-multi _Graph, f be PVertexMapping of G1, G2;
  assume f is total;
  then A1: dom f = the_Vertices_of G1 by PARTFUN1:def 2;
  A2: dom (PVM2PGM f)_E = G1.edgesBetween(dom f) by Def10
    .= the_Edges_of G1 by A1, GLIB_000:34;
  (PVM2PGM f)_V = f;
  hence thesis by A1, A2, GLIB_010:def 11;
end;
