Goal:
  
  A : Type
  H : ReflectEq A
  a1 : A
  l1 : list A
  a2 : A
  l2 : list A
  Heq : (a1 == a2) = false
  ============================
   (∀ l3 l4 l : list A,
      {| pr1 := a1 :: l1; pr2 := a2 :: l2 |} = {| pr1 := l3; pr2 := l4 |}
      → ([], a1 :: l1, a2 :: l2) = split_prefix l3 l4
        → let H := CoreTactics.block in
          is_prefix l l3
          → is_prefix l l4 → is_prefix l (fst (fst (split_prefix l3 l4))))


DEBUG:Going to execute:
match goal with
           | |- context [ eq_rect_r _ _ eq_refl ] => progress simpl eq_rect_r
           | |- context [ eq_rect _ _ _ _ eq_refl ] => 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