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:
fun c tac =>
             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))