Goal:
  
  A : Type
  t : A
  P : A → A → Type
  tl : list A
  tl' : list A
  X : OnOne2 P tl tl'
  IHX : ∀ n : nat,
          nth_error tl n = Some t
          → ∑ t' : A, nth_error tl' n = Some t' × (t = t') + P t t'
  ============================
   (Some t = Some t × (t = t) + P t t)


DEBUG:Going to execute:
fun => <coq-core.plugins.ltac::split@0>

Goals:
  
  A : Type
  t : A
  P : A → A → Type
  tl : list A
  tl' : list A
  X : OnOne2 P tl tl'
  IHX : ∀ n : nat,
          nth_error tl n = Some t
          → ∑ t' : A, nth_error tl' n = Some t' × (t = t') + P t t'
  ============================
   (Some t = Some t)

  
  A : Type
  t : A
  P : A → A → Type
  tl : list A
  tl' : list A
  X : OnOne2 P tl tl'
  IHX : ∀ n : nat,
          nth_error tl n = Some t
          → ∑ t' : A, nth_error tl' n = Some t' × (t = t') + P t t'
  ============================
   ((t = t) + P t t)%type


DEBUG:Going to execute:
<Coq.Init.Tauto.not_dep_intros>

Goals:
  
  A : Type
  t : A
  P : A → A → Type
  tl : list A
  tl' : list A
  X : OnOne2 P tl tl'
  IHX : ∀ n : nat,
          nth_error tl n = Some t
          → ∑ t' : A, nth_error tl' n = Some t' × (t = t') + P t t'
  ============================
   (Some t = Some t)

  
  A : Type
  t : A
  P : A → A → Type
  tl : list A
  tl' : list A
  X : OnOne2 P tl tl'
  IHX : ∀ n : nat,
          nth_error tl n = Some t
          → ∑ t' : A, nth_error tl' n = Some t' × (t = t') + P t t'
  ============================
   ((t = t) + P t t)%type


DEBUG:Going to execute:
repeat
            match goal with
            | |- ?X1 → ?X2 => intro
            | |- ¬ _ => unfold not at 1; intro
            end