
theorem
  for G1 being _Graph, E being set, G2 being reverseEdgeDirections of G1, E
  for W1 being Walk of G1, W2 being Walk of G2
  st W1 = W2 holds W1 is minlength iff W2 is minlength
proof
  let G1 be _Graph, E be set, G2 be reverseEdgeDirections of G1, E;
  let W1 be Walk of G1, W2 be Walk of G2;
  assume A1: W1 = W2;
  hence W1 is minlength implies W2 is minlength by Lm3;
  G1 is reverseEdgeDirections of G2, E by GLIB_007:3;
  hence thesis by A1, Lm3;
end;
