Goal:
  
  A : Type
  B : Type
  P : A → Type
  p : A → bool
  l : list A
  f : A → B
  g : A → B
  ============================
   (All P l
    → forallb p l → (∀ x : A, P x → p x → f x = g x) → map f l = map g l)


DEBUG:Going to execute:
induction 1; simpl