reserve i,k,n,m for Element of NAT;
reserve a,b,r,r1,r2,s,x,x1,x2 for Real;
reserve A for non empty closed_interval Subset of REAL;
reserve X for set;

theorem
  for f being PartFunc of REAL,REAL st f|A is bounded_above holds f
  ||A|A is bounded_above;
