
theorem Th27:
  for A being non empty RelStr, a1,a2 being Element of A st
    A is connected & a1 <> a2 holds
      a1 <= a2 or a2 <= a1
proof
  let A be non empty RelStr;
  let a1, a2 be Element of A;
  assume that
    A1: A is connected and
    A2: a1 <> a2;
  [a1,a2] in the InternalRel of A or [a2,a1] in the InternalRel of A
    by A1, A2, RELAT_2:def 6;
  hence a1 <= a2 or a2 <= a1 by ORDERS_2:def 5;
end;
