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
  pa : is_true (P a)
  pl : is_true (forallb P l)
  pn : 0 < S #|l|
  ============================
   (a = a ∧ P a)


DEBUG:Going to execute:
try arith_congr
Level 0: Backtrace:

No product even after head-reduction.
Level 0: Backtrace:

No product even after head-reduction.
Level 3: Backtrace:

No product even after head-reduction.
Level 2: Backtrace:

No product even after head-reduction.
Level 1: Backtrace:

No product even after head-reduction.
Level 0: Backtrace:

No product even after head-reduction.
Level 0: Backtrace:

No product even after head-reduction.