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.