
theorem
  for m be non zero Element of NAT, Z be non empty Subset of REAL m,
    f be PartFunc of REAL m,REAL, I,G be non empty FinSequence of NAT
     st f is_partial_differentiable_on Z,G
    holds
      f `partial|(Z,G^I) is_continuous_on Z
        iff  f`partial|(Z,G) `partial|(Z,I) is_continuous_on Z by Th7;
