Goal:
  
  A : Type
  B : Type
  P : B → A → A → Type
  Q : B → A → A → Type
  b : B
  bs : list B
  hd : A
  tl : list A
  tl' : list A
  H : OnOne2All P bs tl tl'
  HPQ : ∀ (i : B) (x y : A), P i x y → ∑ z : A, Q i x z × Q i y z
  r : list A
  o : OnOne2All Q bs tl r
  o0 : OnOne2All Q bs tl' r
  ============================
   (OnOne2All Q (b :: bs) (hd :: tl) (hd :: r)
    × OnOne2All Q (b :: bs) (hd :: tl') (hd :: r))


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