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


DEBUG:Going to execute:
hnf in id;
            match type of id with
            | sigma _ =>
                let xn := fresh id "'" in
                destruct id as [xn id]; DepElim.decompose_exists xn id;
                 cbv beta iota delta [TODO projection TODO projection]
                  in id, id'; DepElim.decompose_exists id id'
            | _ =>
                cbv beta iota delta [TODO projection TODO projection]
                 in id, id'
            end