theorem
  [!(f1+r(#)f2),x0,x1!] = [!f1,x0,x1!] + r* [!f2,x0,x1!]
proof
  set g=r(#)f2;
  [!(f1+r(#)f2),x0,x1!] = [!f1,x0,x1!] + [!g,x0,x1!] by DIFF_1:32
    .= [!f1,x0,x1!] + r* [!f2,x0,x1!] by DIFF_1:31;
  hence thesis;
end;
