Goal:
  
  A : Type
  P : A → Type
  a : A
  l : list A
  n : nat
  x : A
  Hnth : nth_error (a :: l) n = Some x
  HPl : All P (a :: l)
  IHl : ∀ n : nat, nth_error l n = Some x → All P l → P x
  ============================
   (P x)


DEBUG:Going to execute:
destruct n

Goals:
  
  A : Type
  P : A → Type
  a : A
  l : list A
  x : A
  Hnth : nth_error (a :: l) 0 = Some x
  HPl : All P (a :: l)
  IHl : ∀ n : nat, nth_error l n = Some x → All P l → P x
  ============================
   (P x)

  
  A : Type
  P : A → Type
  a : A
  l : list A
  n : nat
  x : A
  Hnth : nth_error (a :: l) (S n) = Some x
  HPl : All P (a :: l)
  IHl : ∀ n : nat, nth_error l n = Some x → All P l → P x
  ============================
   (P x)


DEBUG:Going to execute:
cbn in Hnth
DEBUG LTAC Evaluated term: n