Goal:
    A : Type  B : Type  L1 : list A  P : A → B → Type
  ============================
   (∀ L2 : list B,
      #|L1| = #|L2|
      → (∀ (n : nat) (x1 : A) (x2 : B),
           n < #|L1|
           → nth_error L1 n = Some x1 → nth_error L2 n = Some x2 → P x1 x2)
        → All2 P L1 L2)


DEBUG:Going to execute:
induction L1

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

  
  A : Type
  B : Type
  a : A
  L1 : list A
  P : A → B → Type
  IHL1 : ∀ L2 : list B,
           #|L1| = #|L2|
           → (∀ (n : nat) (x1 : A) (x2 : B),
                n < #|L1|
                → nth_error L1 n = Some x1
                  → nth_error L2 n = Some x2 → P x1 x2) → 
             All2 P L1 L2
  ============================
   (∀ L2 : list B,
      #|a :: L1| = #|L2|
      → (∀ (n : nat) (x1 : A) (x2 : B),
           n < #|a :: L1|
           → nth_error (a :: L1) n = Some x1
             → nth_error L2 n = Some x2 → P x1 x2) → 
        All2 P (a :: L1) L2)


DEBUG:Going to execute:
cbn
DEBUG LTAC Evaluated term: L1

Goals:
    A : Type  B : Type  P : A → B → Type
  ============================
   (∀ L2 : list B,
      0 = #|L2|
      → (∀ (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)

  
  A : Type
  B : Type
  a : A
  L1 : list A
  P : A → B → Type
  IHL1 : ∀ L2 : list B,
           #|L1| = #|L2|
           → (∀ (n : nat) (x1 : A) (x2 : B),
                n < #|L1|
                → nth_error L1 n = Some x1
                  → nth_error L2 n = Some x2 → P x1 x2) → 
             All2 P L1 L2
  ============================
   (∀ L2 : list B,
      S #|L1| = #|L2|
      → (∀ (n : nat) (x1 : A) (x2 : B),
           n < S #|L1|
           → nth_error (a :: L1) n = Some x1
             → nth_error L2 n = Some x2 → P x1 x2) → 
        All2 P (a :: L1) L2)


DEBUG:Going to execute:
intros