Goal:
  
  A : Type
  B : Type
  C : Type
  R : A → B → C → Type
  x : A
  y : B
  z : C
  l : list A
  l' : list B
  l'' : list C
  r : R x y z
  a : All3 R l l' l''
  b0 : All3 R (x :: l) (y :: l') (z :: l'')
  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 := x :: l; pr2 := {| pr1 := y :: l'; pr2 := z :: l'' |} |};
      pr2 := b0
    |} = b
    → ∀ (H := CoreTactics.block) (e : NoConfusionHom_All3 A B C R 
                                        (x :: l) (y :: l') 
                                        (z :: l'') 
                                        (All3_cons r a) b0),
        let H0 := CoreTactics.block in
        noConfusionHom_All3_obligation_2 A B C R (x :: l) 
          (y :: l') (z :: l'') (All3_cons r a) b0
          (noConfusionHom_All3_obligation_1 A B C R 
             (x :: l) (y :: l') (z :: l'') (All3_cons r a) b0 e) = e)


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