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)
  ============================
   (S n < S #|l| → ∃ x : A, nth n l d = x ∧ P x)


DEBUG:Going to execute:
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.