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:
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'
DEBUG LTAC Evaluated term: b
DEBUG LTAC Evaluated term: (sigma
                              (λ index : sigma
                                           (λ _ : list A,
                                              sigma (λ _ : list B, list C)),
                                 All3 R (pr1 index) 
                                   (pr1 (pr2 index)) 
                                   (pr2 (pr2 index))))
Level 4: type of id
 has value 
(sigma
   (λ index : sigma (λ _ : list A, sigma (λ _ : list B, list C)),
      All3 R (pr1 index) (pr1 (pr2 index)) (pr2 (pr2 index))))