Goal:
  
  max : nat
  P : nat -> Prop
  hmax : forall n : nat, n >= max -> P n
  hS : forall n : nat, n < max -> P (S n) -> P n
  n : nat
  IHn : P (S (max - S n))
  n0 : ~ max <= n
  ============================
   (max - S n < max)


DEBUG:Going to execute:
intros; Zify.zify_pre_hook; zify_elim_let; zify_op;
            Zify.zify_iter_specs; Zify.zify_to_euclidean_division_equations;
            Zify.zify_post_hook