for G being RealNormSpace-Sequence
for S being RealNormSpace
for f being PartFunc of (product G),S
for x being Point of (product G)
for i being set st f is_differentiable_in x holds
( f is_partial_differentiable_in x,i & partdiff (f,x,i) = (diff (f,x)) * (reproj ((In (i,(dom G))),(0. (product G)))) )