Goal:
  
  A : Type
  a : A
  l : list A
  n : nat
  P : A → bool
  d : A
  IHl : ∀ n : nat, forallb P l → n < #|l| → ∃ x : A, nth n l d = x ∧ P x
  H : is_true (P a && forallb P l)
  H0 : BinInt.Z.lt
         (BinInt.Z.add (BinInt.Z.of_nat n) (BinNums.Zpos BinNums.xH))
         (BinInt.Z.add (BinInt.Z.of_nat #|l|) (BinNums.Zpos BinNums.xH))
  cstr : BinInt.Z.le BinNums.Z0 (BinInt.Z.of_nat n)
  cstr0 : BinInt.Z.le BinNums.Z0 (BinInt.Z.of_nat #|l|)
  ============================
   (∃ x : A, nth n l d = x ∧ P x)


DEBUG:Going to execute:
Zify.zify_to_euclidean_division_equations