Goal:
  
  A : Type
  B : Type
  k : nat
  Q : nat → A → Type
  R : nat → A → B → Type
  l : list A
  l' : list B
  n : nat
  x : A
  y : B
  xs : list A
  ys : list B
  r : R n x y
  rs : All2i R (S n) xs ys
  ih : Alli Q (S n) xs
       → All2i (λ (i : nat) (x : A) (y : B), Q i x × R i x y) (S n) xs ys
  q1' : nat
  q1 : list A
  q : Alli Q (pr1 {| pr1 := q1'; pr2 := q1 |})
        (pr2 {| pr1 := q1'; pr2 := q1 |})
  ============================
   ({| pr1 := n; pr2 := x :: xs |} = {| pr1 := q1'; pr2 := q1 |}
    → let H := CoreTactics.block in
      let H0 := CoreTactics.block in
      All2i (λ (i : nat) (x : A) (y : B), Q i x × R i x y) n 
        (x :: xs) (y :: 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