Goal:
  
  A : Type
  P : A → A → Type
  a : A
  l : list A
  l' : list A
  f : A → A
  hp : ∀ x y : A, P (f x) y → ∑ y' : A, y = f y'
  IHl : ∀ l' : list A,
          OnOne2 P (map f l) l'
          → ∑ l'' : list A, OnOne2 (λ x y : A, P (f x) (f y)) l l''
  o : OnOne2 P (map f (a :: l)) l'
  ============================
   (∑ l'' : list A, OnOne2 (λ x y : A, P (f x) (f y)) (a :: l) l'')


DEBUG:Going to execute:
fun H =>
             try intros until H; intro_block_id H || intro_block H;
              (try simpl in H; DepElim.simplify_equations_in H)