Goal:
  
  X : Type
  Y : Type
  R : nat → X → Y → Type
  n : nat
  l : list X
  a0 : Y
  ys : list Y
  ys' : list Y
  a : All2i R n l (a0 :: ys ++ ys')
  a1 := {|
          pr1 :=
            {| pr1 := n; pr2 := {| pr1 := l; pr2 := a0 :: ys ++ ys' |} |};
          pr2 := a
        |}
     : sigma
         (λ index : sigma (λ _ : nat, sigma (λ _ : list X, list Y)),
            All2i R (pr1 index) (pr1 (pr2 index)) (pr2 (pr2 index)))
  a2 : sigma (λ _ : nat, sigma (λ _ : list X, list Y))
  a3 : (λ index : sigma (λ _ : nat, sigma (λ _ : list X, list Y)),
          All2i R (pr1 index) (pr1 (pr2 index)) (pr2 (pr2 index))) 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:
<coq-core.plugins.ltac::clear@0> $1