
theorem
  for G3 being _Graph, G4 being G3-Disomorphic _Graph
  for G1 being addLoops of G3 for G2 being addLoops of G4
  holds G2 is G1-Disomorphic
proof
  let G3 be _Graph, G4 be G3-Disomorphic _Graph;
  let G1 be addLoops of G3;
  let G2 be addLoops of G4;
  consider F0 being PGraphMapping of G3, G4 such that
    A1: F0 is Disomorphism by GLIB_010:def 24;
  A2: dom(F0_V | the_Vertices_of G3) = the_Vertices_of G3
    by A1, GLIB_010:def 11;
  rng(F0_V | the_Vertices_of G3) = the_Vertices_of G4
    by A1, GLIB_010:def 12;
  then consider F being PGraphMapping of G1, G2 such that
    F_V = F0_V & F_E | dom F0_E = F0_E and
    F0 is non empty  implies F is non empty and
    F0 is total implies F is total and
    F0 is onto implies F is onto and
    F0 is one-to-one implies F is one-to-one and
    F0 is directed implies F is directed and
    F0 is weak_SG-embedding implies F is weak_SG-embedding and
    F0 is isomorphism implies F is isomorphism and
    A3: F0 is Disomorphism implies F is Disomorphism by A1, A2, Th29;
  thus thesis by A1, A3, GLIB_010:def 24;
end;
