Goal:
  
  A : Type
  B : Type
  R : nat → A → B → Type
  n : nat
  x : A
  y : B
  l : list A
  r : list B
  r0 : R n x y
  a : All2i R (S n) l r
  b0 : All2i R n (x :: l) (y :: r)
  b'' : nat
  b' : sigma (λ _ : list A, list B)
  b : All2i R (pr1 {| pr1 := b''; pr2 := b' |})
        (pr1 (pr2 {| pr1 := b''; pr2 := b' |}))
        (pr2 (pr2 {| pr1 := b''; pr2 := b' |}))
  ============================
   ({|
      pr1 := {| pr1 := n; pr2 := {| pr1 := x :: l; pr2 := y :: r |} |};
      pr2 := b0
    |} = {| pr1 := {| pr1 := b''; pr2 := b' |}; pr2 := b |}
    → ∀ (H := CoreTactics.block) (e : NoConfusionHom_All2i A B R n 
                                        (x :: l) (y :: r) 
                                        (All2i_cons r0 a) b0),
        let H0 := CoreTactics.block in
        noConfusionHom_All2i_obligation_2 A B R n 
          (x :: l) (y :: r) (All2i_cons r0 a) b0
          (noConfusionHom_All2i_obligation_1 A B R n 
             (x :: l) (y :: r) (All2i_cons r0 a) b0 e) = e)


DEBUG:Going to execute:
fun id id' =>
             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