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:
repeat (do_intro; try do_atom)
Level 0: Backtrace:

Tactic failure: congruence failed.
Level 0: Backtrace:

Tactic failure: congruence failed.
Level 0: Backtrace:

No applicable tactic.