reserve X for set;

theorem Th3:
  for X be non empty set, x,y be Element of InclPoset X holds x <= y iff x c= y
proof
  let X be non empty set;
  let x,y be Element of InclPoset X;
  thus x <= y implies x c= y
  proof
    assume x <= y;
    then [x,y] in the InternalRel of InclPoset X by ORDERS_2:def 5;
    hence thesis by WELLORD2:def 1;
  end;
  thus x c= y implies x <= y
  proof
    assume x c= y;
    then [x,y] in RelIncl X by WELLORD2:def 1;
    hence thesis by ORDERS_2:def 5;
  end;
end;
