Goal:
  
  X : Type
  Y : Type
  R : nat → X → Y → Type
  n : nat
  a0 : X
  xs : list X
  xs' : list X
  l : list Y
  a2' : nat
  a2 : sigma (λ _ : list X, list Y)
  a : All2i R (pr1 {| pr1 := a2'; pr2 := a2 |})
        (pr1 (pr2 {| pr1 := a2'; pr2 := a2 |}))
        (pr2 (pr2 {| pr1 := a2'; pr2 := a2 |}))
  ============================
   ({| pr1 := n; pr2 := {| pr1 := a0 :: xs ++ xs'; pr2 := l |} |} =
    {| pr1 := a2'; pr2 := a2 |}
    → let H := CoreTactics.block in
      (∀ (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')
      → let H0 := CoreTactics.block in
        ∑ ys ys' : list Y,
          l = ys ++ ys'
          × All2i R n (a0 :: xs) ys × All2i R (n + #|a0 :: xs|) xs' ys')


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