Goal:
  
  X : Type
  Y : Type
  R : nat → X → Y → Type
  n : nat
  a0 : X
  xs : list X
  xs' : list X
  l : list Y
  a : All2i R n ((a0 :: xs) ++ xs') l
  IHxs : ∀ (n : nat) (xs' : list X) (l : list Y),
           All2i R n (xs ++ xs') l
           → ∑ ys ys' : list Y,
               l = ys ++ ys' × All2i R n xs ys × All2i R (n + #|xs|) xs' ys'
  ============================
   (∑ ys ys' : list Y,
      l = ys ++ ys'
      × All2i R n (a0 :: xs) ys × All2i R (n + #|a0 :: xs|) xs' ys')


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)