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
  h : forall n : nat, P (max - n)
  n : nat
  n0 : ~ max <= n
  ============================
   (max - (max - n) = n)


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