theorem
  bdif(r1(#)f1+r2(#)f2,h).(n+1)/.x
  = r1 * bdif(f1,h).(n+1)/.x + r2 * bdif(f2,h).(n+1)/.x
proof
  set g1 = r1(#)f1;
  set g2 = r2(#)f2;
  bdif(r1(#)f1+r2(#)f2,h).(n+1)/.x
  = bdif(g1,h).(n+1)/.x + bdif(g2,h).(n+1)/.x by Th15
  .= r1 * bdif(f1,h).(n+1)/.x + bdif(g2,h).(n+1)/.x by Th14
  .= r1 * bdif(f1,h).(n+1)/.x + r2 * bdif(f2,h).(n+1)/.x by Th14;
  hence thesis;
end;
