Goal:
  
  A : Type
  a : A
  l : list A
  P : A → bool
  d : A
  IHl : ∀ n : nat, forallb P l → n < #|l| → ∃ x : A, nth n l d = x ∧ P x
  ============================
   (P a && forallb P l → 0 < S #|l| → ∃ x : A, a = x ∧ P x)


DEBUG:Going to execute:
match goal with
           | H:_ ∧ _ |- _ => exact H || (destruct_hyp H; use_hyps)
           | H:_ * _ |- _ => exact H || (destruct_hyp H; use_hyps)
           | H:_ |- _ => solve [ inversion H ]
           | _ => idtac
           end