Goal:
  
  A : Type
  x : A
  xs : list A
  f : A → bool
  H0 : (λ (l : list A) (H : ∀ x : A, In x l → bool) (x : bool),
          ∀ (H0 := CoreTactics.block) (f : A → bool) 
            (l0 : list A) (g : ∀ x0 : A, In x0 l0 → bool),
            g = (λ (x0 : A) (_ : In x0 l0), f x0)
            → {| pr1 := l; pr2 := H |} = {| pr1 := l0; pr2 := g |}
              → x = forallb_InP l0 g
                → let H1 := CoreTactics.block in
                  forallb_InP l0 g = forallb f l0) xs
         (λ (x0 : A) (inx : In x0 xs),
            (λ (x1 : A) (_ : In x1 (x :: xs)), f x1) x0
              (forallb_InP_obligations_obligation_2 x xs x0 inx))
         (forallb_InP xs
            (λ (x0 : A) (inx : In x0 xs),
               (λ (x1 : A) (_ : In x1 (x :: xs)), f x1) x0
                 (forallb_InP_obligations_obligation_2 x xs x0 inx)))
  ============================
   (let H := CoreTactics.block in
    forallb_InP (x :: xs) (λ (x0 : A) (_ : In x0 (x :: xs)), f x0) =
    forallb f (x :: xs))


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