theorem Th32:
  f is_hpartial_differentiable`22_in u implies
  hpartdiff22(f,u) = partdiff(pdiff1(f,2),u,2)
proof
    assume
A1: f is_hpartial_differentiable`22_in u;
    consider x0,y0,z0 being Element of REAL such that
A2: u = <*x0,y0,z0*> by FINSEQ_2:103;
    hpartdiff22(f,u) = diff(SVF1(2,pdiff1(f,2),u),y0) by A1,A2,Th14
    .= partdiff(pdiff1(f,2),u,2) by A2,PDIFF_4:20;
    hence thesis;
end;
