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


DEBUG:Going to execute:
intro