(* similar remark apply here… *)

Lemma BC_to_TRS_lm_to_ml_rank_aux f inf st bcl n s:
let trsl := snd (lm_to_ml (map BC_to_TRS bcl) st) in
(∀ bc : BC, bc ∈ bcl → arities bc = ok_arities n s) →
assoc Nat.eqb f (get_infos trsl) = Some inf →
rank inf ≤ maxl (map rank_main trsl).