Goal:
  
  A : Type
  B : Type
  R : nat → A → B → Type
  n : nat
  b0 : All2i R n [] []
  b : sigma
        (λ index : sigma (λ _ : nat, sigma (λ _ : list A, list B)),
           All2i R (pr1 index) (pr1 (pr2 index)) (pr2 (pr2 index)))
  ============================
   ({| pr1 := {| pr1 := n; pr2 := {| pr1 := []; pr2 := [] |} |}; pr2 := b0 |} =
    b
    → let H := CoreTactics.block in
      NoConfusionHom_All2i A B R n [] [] All2i_nil b0
      → let H0 := CoreTactics.block in All2i_nil = b0)


DEBUG:Going to execute:
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