proposition: Theorem lap_compose_add : ∀ la lb lc, (lap_compose (la + lb) lc = lap_compose la lc + lap_compose lb lc)%lap.
proof: Proof. intros la lb lc. revert lb lc. induction la as [| a]; intros; [ reflexivity | simpl ]. destruct lb as [| b]; simpl. rewrite lap_add_nil_r; reflexivity. rewrite IHla. rewrite lap_mul_add_distr_r. do 2 rewrite <- lap_add_assoc. apply lap_add_compat_l. symmetry. rewrite lap_add_comm. rewrite <- lap_add_assoc. apply lap_add_compat_l. rewrite lap_add_comm; reflexivity. Qed.
imports: Utf8 QArith NPeano Misc Field2 Fsummation