Goal:
  
  A : Type
  B : Type
  R : A → B → Type
  R' : ∀ (a : A) (b : B), R a b → Type
  x : A
  y : B
  l : list A
  l' : list B
  r : R x y
  rs : All2 R l l'
  r0 : R' x y r
  a0 : All2_dep R' rs
  b0 : All2_dep R' (All2_cons r rs)
  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 := x :: l; pr2 := {| pr1 := y :: l'; pr2 := All2_cons r rs |}
        |};
      pr2 := b0
    |} = b
    → ∀ (H := CoreTactics.block) (e : NoConfusionHom_All2_dep A B R R'
                                        (x :: l) (y :: l') 
                                        (All2_cons r rs)
                                        (All2_dep_cons r0 a0) b0),
        let H0 := CoreTactics.block in
        noConfusionHom_All2_dep_obligation_2 A B R R' 
          (x :: l) (y :: l') (All2_cons r rs) (All2_dep_cons r0 a0) b0
          (noConfusionHom_All2_dep_obligation_1 A B R R' 
             (x :: l) (y :: l') (All2_cons r rs) (All2_dep_cons r0 a0) b0 e) =
        e)


DEBUG:Going to execute:
fun id id' =>
             hnf in id;
              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