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.