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
  X : All2 R (a :: l1 ++ l2) r
  X0 := {| pr1 := {| pr1 := a :: l1 ++ l2; pr2 := r |}; pr2 := X |}
     : sigma
         (λ index : sigma (λ _ : list A, list B),
            All2 R (pr1 index) (pr2 index))
  X1 := {| pr1 := a :: l1 ++ l2; pr2 := r |} : sigma (λ _ : list A, list B)
  X2 := X
     : (λ index : sigma (λ _ : list A, list B),
          All2 R (pr1 index) (pr2 index)) 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:
try red in (type of id'2)