theorem Th19:
  a <= b implies for P being Subset of R^1 st P = [. a,b .] holds
  Closed-Interval-TSpace(a,b) = R^1|P
proof
  assume
A1: a <= b;
  let P be Subset of R^1;
  assume P = [. a,b .];
  then [#](Closed-Interval-TSpace(a,b)) = P by A1,Th18;
  hence thesis by PRE_TOPC:def 5;
end;
