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


DEBUG:Going to execute:
solve [ intuition eauto  3 with core terms ]
Level 0: Backtrace:

Tactic failure: Cannot solve this goal.
Level 5: Backtrace:

Tactic failure: Cannot solve this goal.
Level 4: Backtrace:

Tactic failure: Cannot solve this goal.
Level 4: Backtrace:

Tactic failure: Cannot solve this goal.
Level 3: Backtrace:

Tactic failure: Cannot solve this goal.
Level 2: Backtrace:

Tactic failure: Cannot solve this goal.
Level 1: Backtrace:

Tactic failure: Cannot solve this goal.
Level 0: Backtrace:

Tactic failure: Cannot solve this goal.