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
  ============================
   ({| pr1 := a :: l1 ++ l2; pr2 := r |} = {| pr1 := []; pr2 := [] |}
    → 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:
match goal with
           | |- context [ rew <- [_] eq_refl in _ ] =>
                 progress simpl eq_rect_r
           | |- context [ rew [_] eq_refl in _ ] => progress simpl eq_rect
           | |- context [ Prop.Logic.transport _ eq_refl _ ] =>
                 progress simpl Prop.Logic.transport
           | |- context [ Logic.eq_elim _ _ _ _ _ eq_refl ] =>
                 progress simpl eq_rect
           | |- context [ Logic.eq_elim_r _ _ _ _ eq_refl ] =>
                 progress simpl Logic.eq_elim_r
           | |- context [ noConfusion_inv _ ] =>
                 progress simpl noConfusion_inv
           | |- DepElim.opaque_ind_pack_eq_inv ?G eq_refl =>
                 apply (DepElim.simplify_ind_pack_inv B x p G)
           | |- let _ := CoreTactics.block in _ => fail 1
           | |- _ => simplify * || simplify ?; cbv beta
           | |- _ → ?B =>
                 let ty := type of B in
                 intro || (let H := fresh in
                           intro
                           H)
           | |- ∀ x, _ => let H := fresh x in
                          intro
                          H
           | |- _ => intro
           end