Definition eval_bf {A : Type} (ea : forall (k: kind), A -> rtyp k) (k: kind) (f: BFormula A k) := eval_f e_rtyp ea f.

Lemma eval_bf_map : forall T U (fct: T-> U) env (k: kind) (f:BFormula T k) , eval_bf env (map_bformula fct f) = eval_bf (fun b x => env b (fct x)) f.