reserve n,m for Element of NAT;
reserve x, X,X1,Z,Z1 for set;
reserve s,g,r,t,p,x0,x1,x2 for Real;
reserve s1,s2,q1 for Real_Sequence;
reserve Y for Subset of REAL;
reserve f,f1,f2 for PartFunc of REAL,REAL;

theorem
  for f,Y st Y <> {} & Y c= dom f & Y is compact & f|Y is
uniformly_continuous ex x1,x2 st x1 in Y & x2 in Y & f.x1 = upper_bound (f.:Y)
  & f.x2 = lower_bound (f.:Y)
by Th9,FCONT_1:31;
