 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 Th54:
  cdif(f,h).1.x = cdif(f,h).0.(x+h/2)-cdif(f,h).0.(x-h/2)
proof
  cdif(f,h).1.x = cD(f,h).x by DIFF_3:16
    .= f.(x+h/2)-f.(x-h/2) by DIFF_1:5
    .= cdif(f,h).0.(x+h/2)-f.(x-h/2) by DIFF_1:def 8
    .= cdif(f,h).0.(x+h/2)-cdif(f,h).0.(x-h/2) by DIFF_1:def 8;
  hence thesis;
end;
