theorem
  [!(r1(#)f1+r2(#)f2),x0,x1!] = r1*[!f1,x0,x1!] + r2*[!f2,x0,x1!]
proof
  [!(r1(#)f1+r2(#)f2),x0,x1!] = [!(r1(#)f1),x0,x1!]+[!(r2(#)f2),x0,x1!] by Th32
    .= r1*[!f1,x0,x1!]+[!(r2(#)f2),x0,x1!] by Th31
    .= r1*[!f1,x0,x1!]+r2*[!f2,x0,x1!] by Th31;
  hence thesis;
end;
