
theorem Th18: :: theorem 3.1 (xi)
  for R, S being RelStr, a, b being Element of R [*] S st (the
  carrier of R) /\ (the carrier of S) is upper Subset of R & a <= b & a in the
  carrier of S holds b in the carrier of S
proof
  let R, S be RelStr, a, b be Element of R [*] S;
  assume that
A1: (the carrier of R) /\ (the carrier of S) is upper Subset of R and
A2: a <= b and
A3: a in the carrier of S;
  [a,b] in the InternalRel of R [*] S by A2,ORDERS_2:def 5;
  hence thesis by A1,A3,Th17;
end;
