Goal:
  
  A : Type
  B : Type
  C : Type
  R : A → B → C → Type
  b0 : All3 R [] [] []
  b : sigma
        (λ index : sigma (λ _ : list A, sigma (λ _ : list B, list C)),
           All3 R (pr1 index) (pr1 (pr2 index)) (pr2 (pr2 index)))
  ============================
   ({|
      pr1 := {| pr1 := []; pr2 := {| pr1 := []; pr2 := [] |} |}; pr2 := b0
    |} = b
    → let H := CoreTactics.block in
      NoConfusionHom_All3 A B C R [] [] [] All3_nil b0
      → let H0 := CoreTactics.block in All3_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