induction b...
rewrite plus_Sn_m.
rewrite <- plus_Snm_nSm.
rewrite plus_Sn_m.
simpl...
Qed.

(* Specifications: *)
Lemma div2_x_plus_2y a b: div2 (a + 2 * b) = div2 a + b.
Lemma div2_sqrdSn n: div2 (sqrd n) + n <= div2 (sqrd (S n)).
Proof with auto with arith.