(* similar remark apply here… *)

Lemma map_BC_to_TRS_infos_iff bcl st f:
f ∈ flat_map all_lhs_funcs (snd (lm_to_ml (map BC_to_TRS bcl) st)) ↔
f ∈ map fst (get_infos (snd (lm_to_ml (map BC_to_TRS bcl) st))).