Goal:
  
  A : Type
  P : A → Type
  p : A → bool
  x : A
  l : list A
  p0 : P x
  X : All P l
  IHX : ∀ p : A → bool, (∀ x : A, P x → p x) → forallb p l
  H : ∀ x : A, P x → p x
  ============================
   (is_true (forallb p l))


DEBUG:Going to execute:
match goal with
           | |- _ → _ => intro; t_tauto_intuit
           | |- _ => t_reduce; t_solver
           end