(* similar remark apply here… *)

(* main is the only function with maximum rank *)
Lemma BC_to_TRS_main_has_unique_max_rank bc n s:
arities bc = ok_arities n s → ∀ st f,
let trs := snd (BC_to_TRS bc st) in
f < trs.(main) → get_rank trs f < get_rank trs trs.(main).