Goal:
  
  A : Type
  P : A → Type
  f : A → A
  x : A
  l : list A
  p : P x
  X : All P l
  IHX : (∀ x : A, P x → f x = x) → map f l = l
  ============================
   ((∀ x : A, P x → f x = x) → f x :: map f l = x :: l)


DEBUG:Going to execute:
intro