
theorem
  for G1, G2 being non-multi _Graph
  for f being directed PVertexMapping of G1, G2
  holds PVM2PGM(f) = DPVM2PGM(f)
proof
  let G1, G2 be non-multi _Graph;
  let f be directed PVertexMapping of G1, G2;
  A1: (PVM2PGM f)_V = f & (DPVM2PGM f)_V = f;
  dom (PVM2PGM f)_E = G1.edgesBetween(dom f) &
    dom (DPVM2PGM f)_E = G1.edgesBetween(dom f) by Def10, Def11;
  hence thesis by A1, GLIB_010:40;
end;
