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 Th25:
  [!(f1-f2),x0,x1!] = [!f1,x0,x1!] - [!f2,x0,x1!]
proof
  reconsider x0,x1 as Element of REAL by XREAL_0:def 1;
  [!(f1-f2),x0,x1!] = (f1.x0-f2.x0-(f1-f2).x1)/(x0-x1) by VALUED_1:15
    .= (f1.x0-f2.x0-(f1.x1-f2.x1))/(x0-x1) by VALUED_1:15
    .= [!f1,x0,x1!] - [!f2,x0,x1!];
  hence thesis;
end;
