proposition: Lemma size_step m n p : (size (step m n p) <= (2 ^ (m + n).+1))%N.
proof: Proof. apply: leq_trans (size_sum _ _ _) _. apply/bigmax_leqP_seq => i _ _. apply: leq_trans (size_mul_leq _ _ ) _. rewrite size_polyXn addnS /=. apply: leq_trans (leq_add (size_merge (size_poly _ _) (size_poly _ _)) (leqnn _)) _. by rewrite -mulSn -addnS expnD leq_mul2r ltn_ord orbT. Qed.
imports: mathcomp(all_ssreflect all_algebra ssrnum)