let f be PartFunc of (REAL 3),REAL; :: thesis: for u0 being Element of REAL 3 st f is_hpartial_differentiable`31_in u0 holds
SVF1 (1,(pdiff1 (f,3)),u0) is_continuous_in (proj (1,3)) . u0
let u0 be Element of REAL 3; :: thesis: ( f is_hpartial_differentiable`31_in u0 implies SVF1 (1,(pdiff1 (f,3)),u0) is_continuous_in (proj (1,3)) . u0 )
assume f is_hpartial_differentiable`31_in u0 ; :: thesis: SVF1 (1,(pdiff1 (f,3)),u0) is_continuous_in (proj (1,3)) . u0
then pdiff1 (f,3) is_partial_differentiable_in u0,1 by Th25;
hence SVF1 (1,(pdiff1 (f,3)),u0) is_continuous_in (proj (1,3)) . u0 by PDIFF_4:31; :: thesis: verum