reserve x for object;
reserve x0,r,r1,r2,g,g1,g2,p,y0 for Real;
reserve n,m,k,l for Element of NAT;
reserve a,b,d for Real_Sequence;
reserve h,h1,h2 for non-zero 0-convergent Real_Sequence;
reserve c,c1 for constant Real_Sequence;
reserve A for open Subset of REAL;
reserve f,f1,f2 for PartFunc of REAL,REAL;
reserve L for LinearFunc;
reserve R for RestFunc;

theorem
  f.x0 <> r & f is_differentiable_in x0 implies ex N be Neighbourhood of
  x0 st N c= dom f & for g st g in N holds f.g <> r
by FCONT_3:7,FDIFF_1:24;
