reserve m,n for non zero Element of NAT;
reserve i,j,k for Element of NAT;
reserve Z for set;

theorem Th14:
for X be Subset of REAL m, f be PartFunc of REAL m,REAL n st X is open holds
  ( f is_differentiable_on X
 iff
    X c=dom f &
    for x be Element of REAL m st x in X holds f is_differentiable_in x )
by PDIFF_6:32;
