Definition eval_tt (env : Env) (tt : Term' * Annot) := eval' env (fst tt).Definition eval_clause (env : Env) (cl : clause) := ~ make_conj  (eval_tt env) cl.Definition eval_cnf (env : Env) (f:cnf) := make_conj  (eval_clause  env) f.

Lemma eval_cnf_and_opt : forall env x y, eval_cnf env (and_cnf_opt x y) <-> eval_cnf env (and_cnf x y).