Goal:
  
  A : Type
  B : Type
  P : A → B → Type
  t : A
  y : B
  l : list A
  l' : list B
  r : P t y
  Hall : All2 P l l'
  IHHall : ∀ n : nat,
             nth_error l n = Some t
             → ∑ t' : B, nth_error l' n = Some t' × P t t'
  ============================
   (Some y = Some y × P t y)


DEBUG:Going to execute:
<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