(* similar remark apply here… *)

Lemma map_BC_to_TRS_lhs_in bcl st r:
r ∈ get_rules (snd ((lm_to_ml (map BC_to_TRS bcl)) st)) →
(lhs_func r) ∈ flat_map all_lhs_funcs (snd (lm_to_ml (map BC_to_TRS bcl) st)).