Goal:
  
  A : Type
  x : A
  xs : list A
  f : A → bool
  H0 : ∀ (H := CoreTactics.block) (f0 : A → bool) 
         (l : list A) (g : ∀ x : A, In x l → bool),
         g = (λ (x : A) (_ : In x l), f0 x)
         → {| pr1 := xs; pr2 := λ (x : A) (_ : In x xs), f x |} =
           {| pr1 := l; pr2 := g |}
           → forallb_InP xs (λ (x : A) (_ : In x xs), f x) = forallb_InP l g
             → let H0 := CoreTactics.block in forallb_InP l g = forallb f0 l
  ============================
   (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:
cbn beta in hyp