Definition agree_env (fr : positive) (env env' : positive -> Z) : Prop :=
forall x, Pos.le x fr -> env x = env' x.

Lemma agree_env_eval_nformulae :
forall env env' l
(AGREE : agree_env (max_var_nformulae l) env env'),
make_conj (eval_nformula env) l <->
make_conj (eval_nformula env') l.