reserve n,m,k,i for Nat,
  h,r,r1,r2,x0,x1,x2,x for Real,
  S for Functional_Sequence of REAL,REAL,
  y for set;
reserve f,f1,f2 for Function of REAL,REAL;

theorem Th5:
  cD(f,h).x = f.(x+h/2) - f.(x-h/2)
proof
 reconsider xx=x as Element of REAL by XREAL_0:def 1;
  dom (Shift(f,h/2) - Shift(f,-h/2)) = REAL by FUNCT_2:def 1;
  hence cD(f,h).x = Shift(f,h/2).xx - Shift(f,-h/2).xx by VALUED_1:13
    .= f.(x+h/2) - Shift(f,-h/2).x by Def2
    .= f.(x+h/2) - f.(x+-h/2) by Def2
    .= f.(x+h/2) - f.(x-h/2);
end;
