Goal:
  
  A : Type
  B : Type
  P : A → B → Type
  L2 : list B
  H : 0 = #|L2|
  X : ∀ (n : nat) (x1 : A) (x2 : B),
        n < 0 → nth_error [] n = Some x1 → nth_error L2 n = Some x2 → P x1 x2
  ============================
   (All2 P [] L2)


DEBUG:Going to execute:
destruct L2

Goals:
  
  A : Type
  B : Type
  P : A → B → Type
  H : 0 = #|[]|
  X : ∀ (n : nat) (x1 : A) (x2 : B),
        n < 0 → nth_error [] n = Some x1 → nth_error [] n = Some x2 → P x1 x2
  ============================
   (All2 P [] [])

  
  A : Type
  B : Type
  P : A → B → Type
  b : B
  L2 : list B
  H : 0 = #|b :: L2|
  X : ∀ (n : nat) (x1 : A) (x2 : B),
        n < 0
        → nth_error [] n = Some x1
          → nth_error (b :: L2) n = Some x2 → P x1 x2
  ============================
   (All2 P [] (b :: L2))


DEBUG:Going to execute:
inv H
DEBUG LTAC Evaluated term: L2

Goals:
  
  A : Type
  B : Type
  P : A → B → Type
  H : 0 = #|[]|
  X : ∀ (n : nat) (x1 : A) (x2 : B),
        n < 0 → nth_error [] n = Some x1 → nth_error [] n = Some x2 → P x1 x2
  ============================
   (All2 P [] [])

  
  A : Type
  B : Type
  P : A → B → Type
  b : B
  L2 : list B
  H : 0 = #|b :: L2|
  X : ∀ (n : nat) (x1 : A) (x2 : B),
        n < 0
        → nth_error [] n = Some x1
          → nth_error (b :: L2) n = Some x2 → P x1 x2
  ============================
   (All2 P [] (b :: L2))


DEBUG:Going to execute:
fun H => inversion_clear H