for n, m being non zero Nat
for i being Nat
for f being PartFunc of (REAL-NS m),(REAL-NS n)
for x being Point of (REAL-NS m) st f is_differentiable_in x & 1 <= i & i <= m holds
( f is_partial_differentiable_in x,i & partdiff (f,x,i) = (diff (f,x)) * (reproj (i,(0. (REAL-NS m)))) )