for m being non zero Element of NAT
for X being Subset of (REAL m)
for f being PartFunc of (REAL m),REAL
for g being PartFunc of (REAL m),(REAL 1)
for i being Nat st <>* f = g & X is open & 1 <= i & i <= m & f is_partial_differentiable_on X,i holds
( f `partial| (X,i) is_continuous_on X iff g `partial| (X,i) is_continuous_on X )