Goal:
  
  A : Type
  B : Type
  R : A → B → Type
  R' : ∀ (a : A) (b : B), R a b → Type
  b0 : All2_dep R' All2_nil
  b : sigma
        (λ index : sigma (λ xs : list A, sigma (λ ys : list B, All2 R xs ys)),
           All2_dep R' (pr2 (pr2 index)))
  ============================
   ({|
      pr1 := {| pr1 := []; pr2 := {| pr1 := []; pr2 := All2_nil |} |};
      pr2 := b0
    |} = b
    → ∀ (H := CoreTactics.block) (e : NoConfusionHom_All2_dep A B R R' [] []
                                        All2_nil All2_dep_nil b0),
        let H0 := CoreTactics.block in
        noConfusionHom_All2_dep_obligation_2 A B R R' [] [] All2_nil
          All2_dep_nil b0
          (noConfusionHom_All2_dep_obligation_1 A B R R' [] [] All2_nil
             All2_dep_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 index : sigma
                                           (λ xs : list A,
                                              sigma
                                                (λ ys : list B, All2 R xs ys)),
                                 All2_dep R' (pr2 (pr2 index))))
Level 4: type of id
 has value 
(sigma
   (λ index : sigma (λ xs : list A, sigma (λ ys : list B, All2 R xs ys)),
      All2_dep R' (pr2 (pr2 index))))