reserve h,r,r1,r2,x0,x1,x2,x3,x4,x5,x,a,b,c,k for Real,
  f,f1,f2 for Function of REAL,REAL;

theorem
  [!(r1(#)f1+r2(#)f2),x0,x1,x2!] = r1*[!f1,x0,x1,x2!]+r2*[!f2,x0,x1,x2!]
proof
  [!(r1(#)f1+r2(#)f2),x0,x1,x2!] = [!(r1(#)f1),x0,x1,x2!]+[!(r2(#)f2),x0,
  x1,x2!] by Th6
    .= r1*[!f1,x0,x1,x2!]+[!(r2(#)f2),x0,x1,x2!] by Th5;
  hence thesis by Th5;
end;
