
theorem Th3:
  for R being non empty real RelStr for x,y being Element of R
  holds x <= y iff x <<= y
proof
  let R be non empty real RelStr;
  let x,y be Element of R;
  [x,y] in the InternalRel of R iff x <= y by Def1;
  hence thesis by ORDERS_2:def 5;
end;
