 reserve n,m,i,p for Nat,
         h,k,r,r1,r2,x,x0,x1,x2,x3 for Real;
 reserve f,f1,f2,g for Function of REAL,REAL;

theorem Th40:
  fdif(f,h).1.x = fdif(f,h).0.(x+h)-fdif(f,h).0.x
proof
  fdif(f,h).1.x = fD(f,h).x by DIFF_3:7
    .= f.(x+h)-f.x by DIFF_1:3
    .= fdif(f,h).0.(x+h)-f.x by DIFF_1:def 6
    .= fdif(f,h).0.(x+h)-fdif(f,h).0.x by DIFF_1:def 6;
  hence thesis;
end;
