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 : A
  y : B
  l : list A
  l' : list B
  r0 : R x y
  X : All2 R l l'
  ============================
   ({| pr1 := a :: l1 ++ l2; pr2 := r |} =
    {| pr1 := x :: l; pr2 := y :: l' |}
    → 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:
simplify *