reserve i,j,k,n,n1,n2,m for Nat;
reserve a,r,x,y for Real;
reserve A for non empty closed_interval Subset of REAL;
reserve C for non empty set;
reserve X for set;

theorem Th17:
  for f being PartFunc of C,REAL holds (max-f)|X is bounded_below
proof
  let f be PartFunc of C,REAL;
  for c being object st c in X /\ dom max-(f) holds max-(f).c >= 0
by RFUNCT_3:40;
  hence thesis by RFUNCT_1:71;
end;
