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


DEBUG:Going to execute:
fun H =>
             match goal with
             | H':_ |- _ => match H' with
                            | H => idtac
                            end
             end