
theorem
  for G1, G2 being non-Dmulti _Graph holds G2 is G1-Disomorphic iff
    ex f being directed PVertexMapping of G1, G2 st f is Disomorphism
proof
  let G1, G2 be non-Dmulti _Graph;
  hereby
    assume G2 is G1-Disomorphic;
    then consider F being PGraphMapping of G1, G2 such that
      A1: F is Disomorphism by GLIB_010:def 24;
    consider f being directed PVertexMapping of G1, G2 such that
      A2: F_V = f & f is Disomorphism by A1, Th26;
    take f;
    thus f is Disomorphism by A2;
  end;
  given f being directed PVertexMapping of G1, G2 such that
    A3: f is Disomorphism;
  DPVM2PGM f is Disomorphism by A3, Th48;
  hence thesis by GLIB_010:def 24;
end;
