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:
let rec t_tauto_intuit :=
            <Coq.Init.Tauto.simplif> flags;
             <Coq.Init.Tauto.axioms> flags ||
               match reverse goal with
               | id:(?X1 → ?X2) → ?X3
                 |- _ =>
                     Ltac.cut X3;
                      [ intro; clear id; t_tauto_intuit
                      | Ltac.cut (X1 → X2);
                         [ exact
                         id
                         | generalize (λ y : X2, id (λ x : X1, y)); intro;
                            clear id; (solve [ t_tauto_intuit ]) ] ]
               | id:¬ ?X1 → ?X3
                 |- _ =>
                     Ltac.cut X3;
                      [ intro; clear id; t_tauto_intuit
                      | Ltac.cut (¬ X1);
                         [ exact
                         id
                         | clear id; intro; (solve [ t_tauto_intuit ]) ] ]
               | |- ?X1 =>
                     <Coq.Init.Tauto.is_disj> flags X1; (solve
                      [ Ltac.left; t_tauto_intuit
                      | Ltac.right; t_tauto_intuit ])
               end ||
                 match goal with
                 | |- _ → _ => intro; t_tauto_intuit
                 | |- _ => t_reduce; t_solver
                 end || t_solver
           in
           t_tauto_intuit