Goal:
  
  A : Type
  B : Type
  C : Type
  D : Type
  R : C → D → Type
  f : A → C
  g : B → D
  H1 : sigma (λ _ : list C, list D)
  H : All2 R (pr1 H1) (pr2 H1)
  ============================
   ({| pr1 := []; pr2 := [] |} = H1
    → let H := CoreTactics.block in
      let H0 := CoreTactics.block in
      All2 (λ (x : A) (y : B), R (f x) (g y)) [] [])


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