
theorem Th61: :: Complete00
  for G1,G2 being _Graph st G1 == G2 holds G1 is complete implies
  G2 is complete
proof
  let G1,G2 be _Graph such that
A1: G1 == G2;
  assume
A2: G1 is complete;
  now
    let u,v be Vertex of G2 such that
A3: u <> v;
    reconsider v2=v as Vertex of G1 by A1;
    reconsider u2=u as Vertex of G1 by A1;
    u2,v2 are_adjacent by A2,A3;
    hence u,v are_adjacent by A1,Th43;
  end;
  hence thesis;
end;
