
theorem :: theorem 3.1 (x)
  for R, S being RelStr, a, b being Element of R [*] S st (the carrier
of R) /\ (the carrier of S) is lower Subset of S & a <= b & b in the carrier of
  R holds a in the carrier of R
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 lower Subset of S and
A2: a <= b and
A3: b in the carrier of R;
  [a,b] in the InternalRel of R [*] S by A2,ORDERS_2:def 5;
  hence thesis by A1,A3,Th21;
end;
