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
  a1 := {|
          pr1 :=
            {| pr1 := n; pr2 := {| pr1 := a0 :: xs ++ xs'; pr2 := l |} |};
          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 := {| pr1 := n; pr2 := {| pr1 := a0 :: xs ++ xs'; pr2 := l |} |}
     : sigma (λ _ : nat, sigma (λ _ : list X, list Y))
  a3 := a
     : (λ index : sigma (λ _ : nat, sigma (λ _ : list X, list Y)),
          All2i R (pr1 index) (pr1 (pr2 index)) (pr2 (pr2 index))) 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:
generalize (eq_refl : t = id'1); clearbody id'2 id'1; clear id' id;
            try unfold signature in id'2; hnf in id'2; 
            simpl in id'2; rename id'2 into id