Goal:
  
  A : Type
  a : A
  l : list A
  P : A → bool
  d : A
  IHl : ∀ n : nat, forallb P l → n < #|l| → ∃ x : A, nth n l d = x ∧ P x
  pa : is_true (P a)
  pl : is_true (forallb P l)
  pn : BinInt.Z.lt BinNums.Z0
         (BinInt.Z.add (BinInt.Z.of_nat #|l|) (BinNums.Zpos BinNums.xH))
  cstr : BinInt.Z.le BinNums.Z0 (BinInt.Z.of_nat #|l|)
  ============================
   (a = a ∧ P a)


DEBUG:Going to execute:
Zify.zify_to_euclidean_division_equations