Goal:
  
  A : Type
  B : Type
  n : nat
  t' : A
  P : B → A → A → Type
  b : B
  bs : list B
  hd : A
  tl : list A
  tl' : list A
  X : OnOne2All P bs tl tl'
  IHX : ∀ n : nat,
          nth_error tl' n = Some t'
          → ∑ t : A,
              nth_error tl n = Some t
              × (t = t') + (∑ i' : B, nth_error bs n = Some i' × P i' t t')
  ============================
   (nth_error (hd :: tl') n = Some t'
    → ∑ t : A,
        nth_error (hd :: tl) n = Some t
        × (t = t') + (∑ i' : B, nth_error (b :: bs) n = Some i' × P i' t t'))


DEBUG:Going to execute:
destruct n

Goals:
  
  A : Type
  B : Type
  t' : A
  P : B → A → A → Type
  b : B
  bs : list B
  hd : A
  tl : list A
  tl' : list A
  X : OnOne2All P bs tl tl'
  IHX : ∀ n : nat,
          nth_error tl' n = Some t'
          → ∑ t : A,
              nth_error tl n = Some t
              × (t = t') + (∑ i' : B, nth_error bs n = Some i' × P i' t t')
  ============================
   (nth_error (hd :: tl') 0 = Some t'
    → ∑ t : A,
        nth_error (hd :: tl) 0 = Some t
        × (t = t') + (∑ i' : B, nth_error (b :: bs) 0 = Some i' × P i' t t'))

  
  A : Type
  B : Type
  n : nat
  t' : A
  P : B → A → A → Type
  b : B
  bs : list B
  hd : A
  tl : list A
  tl' : list A
  X : OnOne2All P bs tl tl'
  IHX : ∀ n : nat,
          nth_error tl' n = Some t'
          → ∑ t : A,
              nth_error tl n = Some t
              × (t = t') + (∑ i' : B, nth_error bs n = Some i' × P i' t t')
  ============================
   (nth_error (hd :: tl') (S n) = Some t'
    → ∑ t : A,
        nth_error (hd :: tl) (S n) = Some t
        × (t = t') +
          (∑ i' : B, nth_error (b :: bs) (S n) = Some i' × P i' t t'))


DEBUG:Going to execute:
simpl
DEBUG LTAC Evaluated term: n

Goals:
  
  A : Type
  B : Type
  t' : A
  P : B → A → A → Type
  b : B
  bs : list B
  hd : A
  tl : list A
  tl' : list A
  X : OnOne2All P bs tl tl'
  IHX : ∀ n : nat,
          nth_error tl' n = Some t'
          → ∑ t : A,
              nth_error tl n = Some t
              × (t = t') + (∑ i' : B, nth_error bs n = Some i' × P i' t t')
  ============================
   (Some hd = Some t'
    → ∑ t : A,
        Some hd = Some t
        × (t = t') + (∑ i' : B, Some b = Some i' × P i' t t'))

  
  A : Type
  B : Type
  n : nat
  t' : A
  P : B → A → A → Type
  b : B
  bs : list B
  hd : A
  tl : list A
  tl' : list A
  X : OnOne2All P bs tl tl'
  IHX : ∀ n : nat,
          nth_error tl' n = Some t'
          → ∑ t : A,
              nth_error tl n = Some t
              × (t = t') + (∑ i' : B, nth_error bs n = Some i' × P i' t t')
  ============================
   (nth_error tl' n = Some t'
    → ∑ t : A,
        nth_error tl n = Some t
        × (t = t') + (∑ i' : B, nth_error bs n = Some i' × P i' t t'))


DEBUG:Going to execute:
auto

Goals:
  
  A : Type
  B : Type
  t' : A
  P : B → A → A → Type
  b : B
  bs : list B
  hd : A
  tl : list A
  tl' : list A
  X : OnOne2All P bs tl tl'
  IHX : ∀ n : nat,
          nth_error tl' n = Some t'
          → ∑ t : A,
              nth_error tl n = Some t
              × (t = t') + (∑ i' : B, nth_error bs n = Some i' × P i' t t')
  ============================
   (Some hd = Some t'
    → ∑ t : A,
        Some hd = Some t
        × (t = t') + (∑ i' : B, Some b = Some i' × P i' t t'))

  
  A : Type
  B : Type
  n : nat
  t' : A
  P : B → A → A → Type
  b : B
  bs : list B
  hd : A
  tl : list A
  tl' : list A
  X : OnOne2All P bs tl tl'
  IHX : ∀ n : nat,
          nth_error tl' n = Some t'
          → ∑ t : A,
              nth_error tl n = Some t
              × (t = t') + (∑ i' : B, nth_error bs n = Some i' × P i' t t')
  ============================
   (nth_error tl' n = Some t'
    → ∑ t : A,
        nth_error tl n = Some t
        × (t = t') + (∑ i' : B, nth_error bs n = Some i' × P i' t t'))


DEBUG:Going to execute:
<coq-core.plugins.ltac::auto@0> $1 $2 $3