
theorem Th94: :: Chordal01
  for G1,G2 being _Graph st G1 == G2 holds G1 is chordal implies G2 is chordal
proof
  let G1,G2 be _Graph such that
A1: G1 == G2;
  assume
A2: G1 is chordal;
  now
    let W be Walk of G2 such that
A3: W.length() > 3 and
A4: W is Cycle-like;
    reconsider W2=W as Walk of G1 by A1,GLIB_001:179;
    2*W2.length() + 1 = len W by GLIB_001:112;
    then
A5: 2*W2.length() + 1 = 2*W.length() + 1 by GLIB_001:112;
    W2 is Cycle-like by A4,Th24;
    then W2 is chordal by A2,A3,A5;
    hence W is chordal by A1,Th85;
  end;
  hence thesis;
end;
