
theorem
  for L being antisymmetric RelStr, R being auxiliary(i) (Relation of L)
  , x, y being Element of L st [x,y] in R & [y,x] in R holds x = y
proof
  let L be antisymmetric RelStr, R be auxiliary(i) (Relation of L), x, y be
  Element of L;
  assume that
A1: [x,y] in R and
A2: [y,x] in R;
A3: y <= x by A2,WAYBEL_4:def 3;
  x <= y by A1,WAYBEL_4:def 3;
  hence thesis by A3,ORDERS_2:2;
end;
