Goal:
  
  A : Type
  B : Type
  C : Type
  R : A → B → C → Type
  b0 : All3 R [] [] []
  b' : sigma (λ _ : list A, sigma (λ _ : list B, list C))
  b : All3 R (pr1 b') (pr1 (pr2 b')) (pr2 (pr2 b'))
  ============================
   ({|
      pr1 := {| pr1 := []; pr2 := {| pr1 := []; pr2 := [] |} |}; pr2 := b0
    |} = {| pr1 := b'; pr2 := b |}
    → ∀ (H := CoreTactics.block) (e : NoConfusionHom_All3 A B C R [] [] []
                                        All3_nil b0),
        let H0 := CoreTactics.block in
        noConfusionHom_All3_obligation_2 A B C R [] [] [] All3_nil b0
          (noConfusionHom_All3_obligation_1 A B C R [] [] [] All3_nil b0 e) =
        e)


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 _ : list A, sigma (λ _ : list B, list C)))
Level 5: type of id
 has value 
(sigma (λ _ : list A, sigma (λ _ : list B, list C)))