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


DEBUG:Going to execute:
hnf in (type of id')