Goal:
  
  A : Type
  f : A → bool
  l : list A
  g : ∀ x : A, In x l → bool
  Heqg : g = λ (x : A) (_ : In x l), f x
  ============================
   (forallb_InP l g = forallb f l)


DEBUG:Going to execute:
let elimc := get_elim c in
           let packcall := fresh "packcall" in
           let packcall_fn := fresh "packcall_fn" in
           let elimfn := match elimc with
                         | fun_elim => constr:(f)
                         end in
           let elimn := match elimc with
                        | fun_elim => constr:(n)
                        end in
           CoreTactics.block_goal; uncurry_call elimfn c packcall packcall_fn;
            remember_let packcall_fn; unfold_packcall packcall;
            refine (DepElim.eq_simplification_sigma1 _ _ _ _ _) ||
              refine (DepElim.eq_simplification_sigma1_nondep_dep _ _ _ _ _)
               || refine (DepElim.eq_simplification_sigma1_dep _ _ _ _ _);
            (let H := fresh "eqargs" in
             let Heq := fresh "Heqcall" in
             intros H Heq; try (rewrite <- Heq; clear Heq);
              CoreTactics.revert_until H; revert H; subst packcall_fn;
              clearbody packcall; make_packcall packcall elimfn;
              with_last_secvar ltac:(fun eos => move packcall before eos)
               ltac:(move packcall at top); CoreTactics.revert_until packcall;
              CoreTactics.block_goal; cbv zeta in packcall; revert packcall;
              curry;
              (let elimt := make_refine elimn elimc in
               unshelve refine_ho elimt; intros; cbv beta;
                DepElim.simplify_dep_elim; CoreTactics.intros_until_block;
                DepElim.simplify_dep_elim;
                cbn beta iota
                 delta [Prop.Logic.transport Logic.eq_elim Logic.eq_elim_r
                       eq_rect DepElim.pack_sigma_eq
                       DepElim.pack_sigma_eq_nondep] 
                 in *; DepElim.simplify_IH_hyps; CoreTactics.unblock_goal;
                DepElim.simplify_IH_hyps; tac c))