proposition: Lemma size_step m n w p : (size (step m n w p) <= (2 ^ (m + n).+1))%N.
proof: Proof. apply: leq_trans (size_sum _ _ _) _. apply/bigmax_leqP_seq => i _ _. apply: leq_trans (size_sum _ _ _) _. apply/bigmax_leqP_seq => j _ _. apply: leq_trans (size_add _ _) _. rewrite geq_max; apply/andP; split; apply: leq_trans (size_scale_leq _ _) _; rewrite size_polyXn. apply: leq_trans (bound_step (ltn_ord i) (ltn_ord j)). by rewrite ltnS leq_addr. by apply: bound_step. Qed.
imports: mathcomp(all_ssreflect all_algebra ssrnum) digitn