
theorem div5:
for F being Field,
    p,q being Polynomial of F holds p = (p div q) *' q + (p mod q)
proof
let F be Field, p,q be Polynomial of F;
thus p = p + 0_.(F) by POLYNOM3:28
      .= p + ((p div q) *' q - (p div q) *' q) by POLYNOM3:29
      .= (p + -((p div q) *' q)) + (p div q) *' q by POLYNOM3:26
      .= (p div q) *' q + (p mod q);
end;
