Goal:
  
  A : Type
  t : A
  P : nat → A → A → Type
  i : nat
  tl : list A
  tl' : list A
  X : OnOne2i P (S i) tl tl'
  IHX : ∀ n : nat,
          nth_error tl n = Some t
          → ∑ t' : A,
              nth_error tl' n = Some t' × (t = t') + P (S i + n)%nat t t'
  ============================
   (Some t = Some t × (t = t) + P (i + 0) t t)


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