
theorem
  for X, Y being non empty RelStr st [:X,Y:] is reflexive holds X is
  reflexive & Y is reflexive
proof
  let X, Y be non empty RelStr such that
A1: [:X,Y:] is reflexive;
  for x being Element of X holds x <= x
  proof
    set y = the Element of Y;
    let x be Element of X;
    [x,y] <= [x,y] by A1,YELLOW_0:def 1;
    hence thesis by Th11;
  end;
  hence X is reflexive by YELLOW_0:def 1;
  for y being Element of Y holds y <= y
  proof
    set x = the Element of X;
    let y be Element of Y;
    [x,y] <= [x,y] by A1,YELLOW_0:def 1;
    hence thesis by Th11;
  end;
  hence thesis by YELLOW_0:def 1;
end;
