Goal:
  
  A : Type
  B : Type
  R : nat → A → B → Type
  n : nat
  b0 : All2i R n [] []
  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 := []; pr2 := [] |} |}; pr2 := b0 |} =
    {| pr1 := {| pr1 := b''; pr2 := b' |}; pr2 := 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:
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