clear.
unfold cnf_tt, eval_cnf,eval_clause.
simpl. tauto.
Qed.

(* Specifications: *)
Lemma eval_cnf_and_opt : forall env x y, eval_cnf env (and_cnf_opt x y) <-> eval_cnf env (and_cnf x y).
Definition eval_opt_clause (env : Env) (cl: option clause) :=
match cl with
| None => True
| Some cl => eval_clause env cl
end.
Lemma add_term_correct : forall env t cl , eval_opt_clause env (add_term t cl) <-> eval_clause env (t::cl).
Lemma no_middle_eval_tt : forall env a,
eval_tt env a \/ ~ eval_tt env a.