reserve i for Integer,
  a, b, r, s for Real;

theorem Th38:
  a <= b & r <= s implies for A being Subset of
  Closed-Interval-TSpace(a,b), B being Subset of Closed-Interval-TSpace(r,s)
  holds product ((1,2)-->(A,B)) is Subset of Trectangle(a,b,r,s)
proof
  set T = Closed-Interval-TSpace(a,b);
  set S = Closed-Interval-TSpace(r,s);
  assume a <= b & r <= s;
  then
A1: the carrier of T = [.a,b.] & the carrier of S = [.r,s.] by TOPMETR:18;
  let A be Subset of T;
  let B be Subset of S;
  closed_inside_of_rectangle(a,b,r,s) = product ((1,2)-->([.a,b.],[.r,s.])
  ) by Th30;
  then product ((1,2)-->(A,B)) c= closed_inside_of_rectangle(a,b,r,s) by A1,
TOPREAL6:21;
  hence thesis by PRE_TOPC:8;
end;
