Goal:
  
  A : Type
  B : Type
  t' : A
  P : B → A → A → Type
  b : B
  bs : list B
  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 t' = Some t' × (t' = t') + (∑ i' : B, Some b = Some i' × P i' t' t'))


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