theorem Th10: :: PDIFF_2:10

for f being PartFunc of (REAL 2),REAL
for z being Element of REAL 2 holds
( f is_partial_differentiable_in z,2 iff ex x0, y0 being Real st
( z = <*x0,y0*> & ex N being Neighbourhood of y0 st
( N c= dom (SVF1 (2,f,z)) & ex L being LinearFunc ex R being RestFunc st
for y being Real st y in N holds
((SVF1 (2,f,z)) . y) - ((SVF1 (2,f,z)) . y0) = (L . (y - y0)) + (R . (y - y0)) ) ) )