proposition: Lemma ltn_code s : all (fun j => j < code s) s.
proof: Proof. elim: s => //= i s IHs; rewrite -[_.+1]muln1 leq_mul 1?ltn_expl //=. apply: sub_all IHs => j /leqW lejs; rewrite -[j.+1]mul1n leq_mul ?expn_gt0 //. by rewrite ltnS -[j]mul1n -mul2n leq_mul. Qed.
imports: HB(structures) mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat seq)