Goal:
  
  X : Type
  Y : Type
  R : nat → X → Y → Type
  n : nat
  a0 : X
  xs : list X
  xs' : list X
  l : list Y
  a2 : sigma (λ _ : nat, sigma (λ _ : list X, list Y))
  a : All2i R (pr1 a2) (pr1 (pr2 a2)) (pr2 (pr2 a2))
  ============================
   ({| pr1 := n; pr2 := {| pr1 := a0 :: xs ++ xs'; pr2 := l |} |} = 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:
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'
DEBUG LTAC Evaluated term: a2
DEBUG LTAC Evaluated term: (sigma (λ _ : nat, sigma (λ _ : list X, list Y)))
Level 3: type of id
 has value 
(sigma (λ _ : nat, sigma (λ _ : list X, list Y)))