Goal:
  
  A : Type
  P : nat → A → A → Type
  Q : nat → A → A → Type
  i : nat
  hd : A
  tl : list A
  tl' : list A
  H : OnOne2i P (S i) tl tl'
  HPQ : ∀ (i : nat) (x y : A), P i x y → ∑ z : A, Q i x z × Q i y z
  r : list A
  o : OnOne2i Q (S i) tl r
  o0 : OnOne2i Q (S i) tl' r
  ============================
   (OnOne2i Q i (hd :: tl) (hd :: r) × OnOne2i Q i (hd :: tl') (hd :: r))


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