theorem Th15: :: PDIFF_4:15

for f being PartFunc of (REAL 3),REAL
for u being Element of REAL 3 holds
( f is_partial_differentiable_in u,3 iff ex x0, y0, z0 being Real st
( u = <*x0,y0,z0*> & ex N being Neighbourhood of z0 st
( N c= dom (SVF1 (3,f,u)) & ex L being LinearFunc ex R being RestFunc st
for z being Real st z in N holds
((SVF1 (3,f,u)) . z) - ((SVF1 (3,f,u)) . z0) = (L . (z - z0)) + (R . (z - z0)) ) ) )