Goal:
  
  A : Type
  B : Type
  R : A → B → Type
  a : A
  l1 : list A
  IHl1 : ∀ (l2 : list A) (r : list B),
           All2 R (l1 ++ l2) r
           → ∑ r1 r2 : list B, r = r1 ++ r2 × All2 R l1 r1 × All2 R l2 r2
  l2 : list A
  r : list B
  X1' : list A
  X1 : list B
  X : All2 R X1' X1
  ============================
   ({| pr1 := a :: l1 ++ l2; pr2 := r |} = {| pr1 := X1'; pr2 := X1 |}
    → let H := CoreTactics.block in
      let H0 := CoreTactics.block in
      ∑ r1 r2 : list B, r = r1 ++ r2 × All2 R (a :: l1) r1 × All2 R l2 r2)


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