reserve n,m for Element of NAT;
reserve h,k,r,r1,r2,x,x0,x1,x2,x3 for Real;
reserve f,f1,f2 for Function of REAL,REAL;

theorem Th1:
  cD(f,h).x = fD(f,h/2).x - fD(f,-h/2).x
proof
  cD(f,h).x = f.(x+h/2) - f.x + f.x - f.(x-h/2) by DIFF_1:5
    .= (f.(x+h/2)-f.x) - (f.(x-h/2)-f.x)
    .= fD(f,h/2).x - (f.(x-h/2)-f.x) by DIFF_1:3
    .= fD(f,h/2).x - fD(f,-h/2).x by DIFF_1:3;
  hence thesis;
end;
