let f be PartFunc of (REAL 3),REAL; :: thesis: for u0 being Element of REAL 3 st f is_hpartial_differentiable`12_in u0 holds
SVF1 (2,(pdiff1 (f,1)),u0) is_continuous_in (proj (2,3)) . u0
let u0 be Element of REAL 3; :: thesis: ( f is_hpartial_differentiable`12_in u0 implies SVF1 (2,(pdiff1 (f,1)),u0) is_continuous_in (proj (2,3)) . u0 )
assume f is_hpartial_differentiable`12_in u0 ; :: thesis: SVF1 (2,(pdiff1 (f,1)),u0) is_continuous_in (proj (2,3)) . u0
then pdiff1 (f,1) is_partial_differentiable_in u0,2 by Th20;
hence SVF1 (2,(pdiff1 (f,1)),u0) is_continuous_in (proj (2,3)) . u0 by PDIFF_4:32; :: thesis: verum