
theorem Th16:
  for L, M being non empty RelStr st L, M are_isomorphic & L is
  transitive holds M is transitive
proof
  let L, M be non empty RelStr such that
A1: L, M are_isomorphic and
A2: L is transitive;
  M, L are_isomorphic by A1,WAYBEL_1:6;
  then consider f being Function of M, L such that
A3: f is isomorphic;
  let x, y, z be Element of M such that
A4: x <= y & y <= z;
  reconsider fz = f.z as Element of L;
  reconsider fy = f.y as Element of L;
  reconsider fx = f.x as Element of L;
  fx <= fy & fy <= fz by A3,A4,WAYBEL_0:66;
  then fx <= fz by A2;
  hence thesis by A3,WAYBEL_0:66;
end;
