:: deftheorem defines is_hpartial_differentiable`11_in PDIFF_5:def 1 :
for f being PartFunc of (REAL 3),REAL
for u being Element of REAL 3 holds
( f is_hpartial_differentiable`11_in u iff ex x0, y0, z0 being Real st
( u = <*x0,y0,z0*> & ex N being Neighbourhood of x0 st
( N c= dom (SVF1 (1,(pdiff1 (f,1)),u)) & ex L being LinearFunc ex R being RestFunc st
for x being Real st x in N holds
((SVF1 (1,(pdiff1 (f,1)),u)) . x) - ((SVF1 (1,(pdiff1 (f,1)),u)) . x0) = (L . (x - x0)) + (R . (x - x0)) ) ) );