reserve a,a1,b,b1,x,y for Real,
  F,G,H for FinSequence of REAL,
  i,j,k,n,m for Element of NAT,
  I for Subset of REAL,
  X for non empty set,
  x1,R,s for set;
reserve A for non empty closed_interval Subset of REAL;

theorem Th1:
  A is bounded_below bounded_above
proof
  A is real-bounded by RCOMP_1:10;
  hence thesis;
end;
