Goal:
  
  A : Type
  B : Type
  C : Type
  D : Type
  R : C → D → Type
  f : A → C
  g : B → D
  H1' : list C
  H1 : list D
  H : All2 R (pr1 {| pr1 := H1'; pr2 := H1 |})
        (pr2 {| pr1 := H1'; pr2 := H1 |})
  ============================
   ({| pr1 := []; pr2 := [] |} = {| pr1 := H1'; 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:
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