Goal:
  
  A : Type
  a : A
  l : list A
  n : nat
  P : A → bool
  d : A
  IHl : ∀ n : nat, forallb P l → n < #|l| → ∃ x : A, nth n l d = x ∧ P x
  H : is_true (P a && forallb P l)
  H0 : S n < S #|l|
  ============================
   (∃ x : A, nth n l d = x ∧ P x)


DEBUG:Going to execute:
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