
theorem Th167:
  for G1 being _Graph, G2 being G1-Disomorphic _Graph
  for G3 being removeLoops of G1, G4 being removeLoops of G2
  holds G4 is G3-Disomorphic
proof
  let G1 be _Graph, G2 be G1-Disomorphic _Graph;
  let G3 be removeLoops of G1, G4 be removeLoops of G2;
  consider F0 being PGraphMapping of G1, G2 such that
    A1: F0 is Disomorphism by Def24;
  reconsider F0 as one-to-one PGraphMapping of G1, G2 by A1;
  consider F being one-to-one PGraphMapping of G3, G4 such that
    F = F0 | G3 and
    F0 is weak_SG-embedding implies F is weak_SG-embedding and
    F0 is isomorphism implies F is isomorphism and
    A2: F0 is Disomorphism implies F is Disomorphism by Th165;
  thus thesis by A1, A2;
end;
