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

Lemma agree_env_eval_nformula : forall env env' e (AGREE : agree_env (max_var xH (fst e)) env env'), eval_nformula env e <-> eval_nformula env' e.