
theorem Th17:
  for L, M being non empty RelStr st L, M are_isomorphic & L is
  antisymmetric holds M is antisymmetric
proof
  let L, M be non empty RelStr such that
A1: L, M are_isomorphic and
A2: L is antisymmetric;
  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 be Element of M such that
A4: x <= y & y <= x;
  reconsider fy = f.y as Element of L;
  reconsider fx = f.x as Element of L;
  fx <= fy & fy <= fx by A3,A4,WAYBEL_0:66;
  then dom f = the carrier of M & fx = fy by A2,FUNCT_2:def 1;
  hence thesis by A3,FUNCT_1:def 4;
end;
