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'' : list A
  b' : sigma (λ ys : list B, All2 R b'' ys)
  b : All2_dep R' (pr2 (pr2 {| pr1 := b''; pr2 := b' |}))
  ============================
   ({|
      pr1 := {| pr1 := []; pr2 := {| pr1 := []; pr2 := All2_nil |} |};
      pr2 := b0
    |} = {| pr1 := {| pr1 := b''; pr2 := b' |}; pr2 := b |}
    → let H := CoreTactics.block in
      NoConfusionHom_All2_dep A B R R' [] [] All2_nil All2_dep_nil b0
      → let H0 := CoreTactics.block in All2_dep_nil = b0)


DEBUG:Going to execute:
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