Goal:
  
  A : Type
  x : A
  xs : list A
  H : ∀ x0 : A, In x0 (x :: xs) → 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),
            H x0 (forallb_InP_obligations_obligation_2 x xs x0 inx))
         (forallb_InP xs
            (λ (x0 : A) (inx : In x0 xs),
               H x0 (forallb_InP_obligations_obligation_2 x xs x0 inx)))
  ============================
   (∀ (H0 := CoreTactics.block) (f : A → bool) (l : list A) 
      (g : ∀ x : A, In x l → bool),
      g = (λ (x : A) (_ : In x l), f x)
      → {| pr1 := x :: xs; pr2 := H |} = {| pr1 := l; pr2 := g |}
        → H x (forallb_InP_obligations_obligation_1 x xs) &&
          forallb_InP xs
            (λ (x0 : A) (inx : In x0 xs),
               H x0 (forallb_InP_obligations_obligation_2 x xs x0 inx)) =
          forallb_InP l g
          → let H := CoreTactics.block in forallb_InP l g = forallb f l)


DEBUG:Going to execute:
intros _

Goals:
    A : Type  H : ∀ x : A, In x [] → bool
  ============================
   (∀ (f : A → bool) (l : list A) (g : ∀ x : A, In x l → bool),
      g = (λ (x : A) (_ : In x l), f x)
      → {| pr1 := []; pr2 := H |} = {| pr1 := l; pr2 := g |}
        → true = forallb_InP l g
          → let H := CoreTactics.block in forallb_InP l g = forallb f l)

  
  A : Type
  x : A
  xs : list A
  H : ∀ x0 : A, In x0 (x :: xs) → 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),
            H x0 (forallb_InP_obligations_obligation_2 x xs x0 inx))
         (forallb_InP xs
            (λ (x0 : A) (inx : In x0 xs),
               H x0 (forallb_InP_obligations_obligation_2 x xs x0 inx)))
  ============================
   (∀ (f : A → bool) (l : list A) (g : ∀ x : A, In x l → bool),
      g = (λ (x : A) (_ : In x l), f x)
      → {| pr1 := x :: xs; pr2 := H |} = {| pr1 := l; pr2 := g |}
        → H x (forallb_InP_obligations_obligation_1 x xs) &&
          forallb_InP xs
            (λ (x0 : A) (inx : In x0 xs),
               H x0 (forallb_InP_obligations_obligation_2 x xs x0 inx)) =
          forallb_InP l g
          → let H := CoreTactics.block in forallb_InP l g = forallb f l)


DEBUG:Going to execute:
DepElim.simplify_dep_elim

Goals:
    A : Type  H : ∀ x : A, In x [] → bool
  ============================
   (∀ (f : A → bool) (l : list A) (g : ∀ x : A, In x l → bool),
      g = (λ (x : A) (_ : In x l), f x)
      → {| pr1 := []; pr2 := H |} = {| pr1 := l; pr2 := g |}
        → true = forallb_InP l g
          → let H := CoreTactics.block in forallb_InP l g = forallb f l)

  
  A : Type
  x : A
  xs : list A
  H : ∀ x0 : A, In x0 (x :: xs) → 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),
            H x0 (forallb_InP_obligations_obligation_2 x xs x0 inx))
         (forallb_InP xs
            (λ (x0 : A) (inx : In x0 xs),
               H x0 (forallb_InP_obligations_obligation_2 x xs x0 inx)))
  ============================
   (∀ (f : A → bool) (l : list A) (g : ∀ x : A, In x l → bool),
      g = (λ (x : A) (_ : In x l), f x)
      → {| pr1 := x :: xs; pr2 := H |} = {| pr1 := l; pr2 := g |}
        → H x (forallb_InP_obligations_obligation_1 x xs) &&
          forallb_InP xs
            (λ (x0 : A) (inx : In x0 xs),
               H x0 (forallb_InP_obligations_obligation_2 x xs x0 inx)) =
          forallb_InP l g
          → let H := CoreTactics.block in forallb_InP l g = forallb f l)


DEBUG:Going to execute:
repeat DepElim.simplify_one_dep_elim