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'
  o1 : sigma (λ _ : list A, list A)
  o : OnOne2 P (pr1 o1) (pr2 o1)
  ============================
   ({| pr1 := []; pr2 := l' |} = o1
    → let H := CoreTactics.block in
      let H0 := CoreTactics.block in
      ∑ l'' : list A, OnOne2 (λ x y : A, P (f x) (f y)) [] l'')


DEBUG:Going to execute:
destruct id as [xn id]; DepElim.decompose_exists xn id;
            cbv beta iota delta [TODO projection TODO projection] in id, id'