theorem Th9: :: PDIFF_2:9

for f being PartFunc of (REAL 2),REAL
for z being Element of REAL 2 holds
( f is_partial_differentiable_in z,1 iff ex x0, y0 being Real st
( z = <*x0,y0*> & ex N being Neighbourhood of x0 st
( N c= dom (SVF1 (1,f,z)) & ex L being LinearFunc ex R being RestFunc st
for x being Real st x in N holds
((SVF1 (1,f,z)) . x) - ((SVF1 (1,f,z)) . x0) = (L . (x - x0)) + (R . (x - x0)) ) ) )