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