
theorem
  for A being non empty RelStr, a1,a2 being Element of A st
    A is strongly_connected holds
      a1 = a2 or a1 < a2 or a2 < a1
proof
  let A be non empty RelStr;
  let a1, a2 be Element of A;
  assume A is strongly_connected;
  then A1: a1 <= a2 or a2 <= a1 by Th25;
  assume A2: not a1 = a2;
  assume not a1 < a2;
  then not a1 <= a2 by A2, ORDERS_2:def 6;
  hence a2 < a1 by A1, A2, ORDERS_2:def 6;
end;
