Ltac match_postcondition := 
cbv beta iota zeta; unfold_post;  extensionality rho; 
   repeat rewrite exp_uncurry;
   try rewrite no_post_exists; repeat rewrite exp_unfold;
tryif apply exp_congr
 then (intros ?vret;
          apply equal_f; 
          apply PROP_LOCAL_SEP_ext; [reflexivity | | reflexivity];
          (reflexivity || fail "The funspec of the function has a POSTcondition
that is ill-formed.  The LOCALS part of the postcondition
should be (temp ret_temp ...), but it is not"))
 else fail "The funspec of the function should have a POSTcondition that starts
with an existential, that is,  EX _:_, PROP...LOCAL...SEP".(*
Ltac match_postcondition := 
cbv beta iota zeta; unfold_post; extensionality rho;
   repeat rewrite exp_uncurry;
   try rewrite no_post_exists; repeat rewrite exp_unfold;
   first [apply exp_congr; intros ?vret; reflexivity
           | give_EX_warning
           ].
*)
Ltac  forward_call_id1_wow := 
let H := fresh in intro H;
eapply (semax_call_id1_wow _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ H); 
 clear H; 
 lazymatch goal with Frame := _ : list mpred |- _ => try clear Frame end;
 [check_result_type
 |apply Logic.I
 | match_postcondition
 | prove_delete_temp
 | unify_postcondition_exps
 | unfold fold_right_and; repeat rewrite and_True; auto
 ].Ltac forward_call_id1_x_wow :=
let H := fresh in intro H;
eapply (semax_call_id1_x_wow 
             _ _ _ _ _ _ _ _ _ _
             _ _ _ _ _ _ _ _ _ _ 
             _ _ _ _ _ _ _ _ _ H); 
 clear H;
 lazymatch goal with Frame := _ : list mpred |- _ => try clear Frame end;
 [ check_result_type | check_result_type
 | apply Coq.Init.Logic.I | apply Coq.Init.Logic.I | reflexivity
 | (clear; let H := fresh in intro H; inversion H)
 | match_postcondition
 | prove_delete_temp
 | prove_delete_temp
 | unify_postcondition_exps
 | unfold fold_right_and; repeat rewrite and_True; auto
 ].Ltac forward_call_id1_y_wow :=
let H := fresh in intro H;
eapply (semax_call_id1_y_wow 
             _ _ _ _ _ _ _ _ _ _
             _ _ _ _ _ _ _ _ _ _ 
             _ _ _ _ _ _ _ _ _ H); 
 clear H;
 lazymatch goal with Frame := _ : list mpred |- _ => try clear Frame end;
 [ check_result_type | check_result_type
 | apply Coq.Init.Logic.I | apply Coq.Init.Logic.I | reflexivity
 | (clear; let H := fresh in intro H; inversion H)
 | match_postcondition
 | prove_delete_temp
 | prove_delete_temp
 | unify_postcondition_exps
 | unfold fold_right_and; repeat rewrite and_True; auto
 ].Ltac forward_call_id01_wow :=
let H := fresh in intro H;
eapply (semax_call_id01_wow _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ H); 
 clear H;
 lazymatch goal with Frame := _ : list mpred |- _ => try clear Frame end;
 [ apply Coq.Init.Logic.I 
 | match_postcondition
 | unify_postcondition_exps
 | unfold fold_right_and; repeat rewrite and_True; auto
 ].Ltac forward_call_id00_wow  :=
let H := fresh in intro H;
eapply (semax_call_id00_wow _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ H); 
 clear H;
 lazymatch goal with Frame := _ : list mpred |- _ => try clear Frame end;
 [ check_result_type 
 | cbv beta iota zeta; unfold_post; (* extensionality rho; *)
    repeat rewrite exp_uncurry;
    try rewrite no_post_exists0;
    (* apply equal_f; *)
    apply exp_congr; intros ?vret;
    apply PROP_LOCAL_SEP_ext; [reflexivity | | reflexivity];
    (reflexivity || fail "The funspec of the function has a POSTcondition
that is ill-formed.  The LOCALS part of the postcondition
should be empty, but it is not")
 | unify_postcondition_exps
 | unfold fold_right_and; repeat rewrite and_True; auto
 ].Ltac simpl_strong_cast :=
try match goal with |- context [strong_cast ?t1 ?t2 ?v] =>
  first [change (strong_cast t1 t2 v) with v
         | change (strong_cast t1 t2 v) with
                (force_val (sem_cast t1 t2 v))
          ]
end.Ltac fwd_skip :=
 match goal with |- semax _ _ Sskip _ =>
   normalize_postcondition;
   first [eapply semax_pre | eapply semax_pre_simple];
      [ | apply semax_skip]
 end.Definition BINDER_NAME := tt.Ltac after_forward_call_binders :=
 repeat match goal with
 | r := BINDER_NAME |- _ =>
    clear r; apply extract_exists_pre; intro r
 | |- _ => apply extract_exists_pre; intros ?vret
 end.Ltac cleanup_no_post_exists :=
 match goal with |-  context[eq_no_post] =>
  let vret := fresh "vret" in let H := fresh in
  apply extract_exists_pre; intro vret;
  apply semax_extract_PROP; intro H;
  change (eq_no_post vret) with (eq vret) in H;
  subst vret
 end
 || unfold eq_no_post.Ltac factor_out_v L :=
 match L with
 | temp _ ?v :: ?L' => factor_out_v' v L'
 | lvar _ _ ?v :: ?L' => factor_out_v' v L'
 | _ => constr:(@nil val)
 end
 with factor_out_v' v L' := let x := fresh "v" in set (x:=v); 
                                let y :=factor_out_v L'
                                 in constr:(x::y).Ltac factor_back L :=
  match L with
  | ?x :: ?y => subst x; factor_back y
  | nil => idtac
 end.Ltac simplify_remove_localdef_temp :=
match goal with |- context [remove_localdef_temp ?i ?L]  =>
let L' := factor_out_v L in
  simpl remove_localdef_temp;
  factor_back L'
end.Ltac after_forward_call :=
    check_POSTCONDITION; 
    try match goal with |- context [remove_localdef_temp] =>
              simplify_remove_localdef_temp
     end;
    unfold_app; 
    try (apply extract_exists_pre; intros _); 
    match goal with
        | |- semax _ _ _ _ => idtac
        | |- unit -> semax _ _ _ _ => intros _
    end;
    match goal with
        | |- @semax ?CS _ _ _ _ _ => try change_compspecs CS
    end;
    repeat (apply semax_extract_PROP; intro); 
    cleanup_no_post_exists; 
    abbreviate_semax; 
    try fwd_skip.Ltac clear_MORE_POST :=
 try match goal with POSTCONDITION := @abbreviate ret_assert _ |- _ =>
        clear POSTCONDITION
      end;
 try match goal with MORE_COMMANDS := @abbreviate statement _ |- _ =>
        clear MORE_COMMANDS
      end.Inductive Ridiculous: Type := .Ltac check_witness_type A witness :=
  (unify A (rmaps.ConstType Ridiculous); (* because [is_evar A] doesn't seem to work *)
             elimtype False)
 ||
 let TA := constr:(functors.MixVariantFunctor._functor
     (rmaps.dependent_type_functor_rec nil A) mpred) in
  let TA' := eval cbv 
     [functors.MixVariantFunctor._functor
      functors.MixVariantFunctorGenerator.fpair
      functors.MixVariantFunctorGenerator.fconst
      functors.MixVariantFunctorGenerator.fidentity
      rmaps.dependent_type_functor_rec
      functors.GeneralFunctorGenerator.CovariantBiFunctor_MixVariantFunctor_compose
      functors.CovariantFunctorGenerator.fconst
      functors.CovariantFunctorGenerator.fidentity
      functors.CovariantBiFunctor._functor
      functors.CovariantBiFunctorGenerator.Fpair
      functors.GeneralFunctorGenerator.CovariantFunctor_MixVariantFunctor
      functors.CovariantFunctor._functor
      functors.MixVariantFunctor.fmap
      ] in TA
 in let TA'' := eval simpl in TA'
  in match type of witness with ?T => 
       unify T TA''
      + (fail "Type of witness does not match type required by funspec WITH clause.
Witness value: " witness "
Witness type: " T "
Funspec type: " TA'')
     end.

Lemma trivial_Forall_inclusion0: forall {A} (G: list A), Forall (fun x => In x G) nil.