theorem Th4:
  bD(f,h)/.x = f/.x - f/.(x-h)
proof
P1:dom f = the carrier of V by FUNCT_2:def 1;
  dom Shift(f,-h) = the carrier of V by FUNCT_2:def 1;
  then x in (dom f) /\ (dom Shift(f,-h)) by P1; then
P2: x in dom (f - Shift(f,-h)) by VFUNCT_1:def 2;
  thus bD(f,h)/.x = f/.x - (Shift(f,-h))/.x by P2, VFUNCT_1:def 2
  .= f/.x - f/.(x-h) by Def2;
end;
