
theorem Th6:
  for a,b being Real, S being sequence of
  Closed-Interval-MSpace(a,b) st a<=b holds S is sequence of RealSpace
proof
  let a,b be Real, S be sequence of Closed-Interval-MSpace(a,b);
  assume a<=b;
  then the carrier of Closed-Interval-MSpace(a,b)=[.a,b.] by TOPMETR:10;
  then dom S=NAT & rng S c= the carrier of RealSpace by FUNCT_2:def 1
,METRIC_1:def 13,XBOOLE_1:1;
  hence thesis by FUNCT_2:2;
end;
