Goal:
  
  A : Type
  B : Type
  C : Type
  R : nat → A → C → Type
  g : A → B → C
  x : A
  xs : list A
  ih : ∀ (l' : list B) (k : nat),
         All2i (λ (i : nat) (x : A) (y : B), R i x (g x y)) k xs l'
         → All2i R k xs (map2 g xs l')
  y : B
  ys : list B
  k : nat
  z1' : nat
  z1 : sigma (λ _ : list A, list B)
  z : All2i (λ (i : nat) (x : A) (y : B), R i x (g x y))
        (pr1 {| pr1 := z1'; pr2 := z1 |})
        (pr1 (pr2 {| pr1 := z1'; pr2 := z1 |}))
        (pr2 (pr2 {| pr1 := z1'; pr2 := z1 |}))
  ============================
   ({| pr1 := k; pr2 := {| pr1 := x :: xs; pr2 := y :: ys |} |} =
    {| pr1 := z1'; pr2 := z1 |}
    → let H := CoreTactics.block in
      let H0 := CoreTactics.block in All2i R (S k) xs (map2 g xs ys))


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