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
  H : ∀ x : A, P x → f x = x
  ============================
   (f x :: map f l = x :: l)


DEBUG:Going to execute:
fun id0 id1 X2 => assert X2; [ exact (id0 id1) | clear id0 ]