
theorem Th26:
  for A being non empty RelStr, B being Subset of A,
    a1,a2 being Element of A st
      the InternalRel of A is_connected_in B & a1 in B & a2 in B & a1 <> a2
      holds
        a1 <= a2 or a2 <= a1
proof
  let A be non empty RelStr, B be Subset of A;
  let a1, a2 be Element of A;
  assume that
    A1: the InternalRel of A is_connected_in B and
    A2: a1 in B and
    A3: a2 in B and
    A4: a1 <> a2;
  [a1,a2] in the InternalRel of A or [a2,a1] in the InternalRel of A
    by A1, A2, A3, A4, RELAT_2:def 6;
  hence a1 <= a2 or a2 <= a1 by ORDERS_2:def 5;
end;
