Ltac hint_msg_aux R1 A :=
  lazymatch A with
  | data_at => idtac
  | field_at => idtac
  | data_at_ => idtac
  | field_at_ => idtac
  | memory_block => idtac
  | @exp _ _ _ _  => idtac "
Or, perhaps you need to do [Intros x] to introduce the EXistential" R1 "in your SEP clause."
  | _ _ => idtac
  | _ => idtac "
Or, perhaps the definition [" A "] needs to be unfolded so that your SEP conjuct" R1 "can be used effectively."
  end.Ltac hint_msg_aux2 R p2 :=
 match R with
  | nil => idtac
  | ?R1 :: ?R' =>
     lazymatch R1 with
              | ?A _ _ _ _ _ _ _ _ _ _ p2 => hint_msg_aux R1 A
              | ?A _ _ _ _ _ _ _ _ _ p2 => hint_msg_aux R1 A
              | ?A _ _ _ _ _ _ _ _ p2 => hint_msg_aux R1 A
              | ?A _ _ _ _ _ _ _ p2 => hint_msg_aux R1 A
              | ?A _ _ _ _ _ _ p2 => hint_msg_aux R1 A
              | ?A _ _ _ _ _ p2 => hint_msg_aux R1 A
              | ?A _ _ _ _ p2 => hint_msg_aux R1 A
              | ?A _ _ _ p2 => hint_msg_aux R1 A
              | ?A _ _ p2 => hint_msg_aux R1 A
              | ?A _ p2 => hint_msg_aux R1 A
              | ?A p2 => hint_msg_aux R1 A
              | context [p2] => hint_msg_aux R1 R1
              | _ => idtac
             end;
      hint_msg_aux2 R' p2
   end.Definition proj_val t_root gfs v :=
   repinject (nested_field_type t_root gfs) (proj_reptype t_root gfs v).Definition upd_val t_root gfs v v0 :=
   upd_reptype t_root gfs v (valinject (nested_field_type t_root gfs) v0).Ltac SEP_field_at_unify' gfs :=
  match goal with
  | |- field_at ?shl ?tl ?gfsl ?vl ?pl = field_at ?shr ?tr ?gfsr ?vr ?pr =>
      unify tl tr;
      unify (skipn (length gfs - length gfsl) gfs) gfsl;
      unify gfsl gfsr;
      unify shl shr;
      unify vl vr;
      generalize vl; intro;
      rewrite <- ?field_at_offset_zero; reflexivity
  end.Ltac SEP_field_at_unify gfs :=
  match goal with
  | |- data_at _ _ _ _ = _ =>
      unfold data_at; SEP_field_at_unify' gfs
  | |- data_at_ _ _ _ = _ =>
      unfold data_at_, field_at_; SEP_field_at_unify' gfs
  | |- field_at _ _ _ _ _ = _ =>
      SEP_field_at_unify' gfs
  | |- field_at_ _ _ _ _ = _ =>
      unfold field_at_; SEP_field_at_unify' gfs
  end.Ltac SEP_field_at_strong_unify' gfs :=
  match goal with
  | |- @field_at ?cs ?shl ?tl ?gfsl ?vl ?pl = ?Rv ?vr /\ (_ = fun v => field_at ?shr ?tr ?gfsr v ?pr) =>
      unify tl tr;
      unify (skipn (length gfs - length gfsl) gfs) gfsl;
      unify gfsl gfsr;
      unify shl shr;
      unify vl vr;
      split;
      [ match type of vl with
        | ?tv1 => unify Rv (fun v: tv1 => @field_at cs shl tl gfsl v pl)
        end; reflexivity
      | extensionality;
        rewrite <- ?field_at_offset_zero; reflexivity]
  | |- @data_at ?cs ?shl ?tl ?vl ?pl = ?Rv ?vr /\ (_ = fun v => field_at ?shr ?tr ?gfsr v ?pr) =>
      unify tl tr;
      unify gfsr (@nil gfield);
      unify shl shr;
      unify vl vr;
      split;
      [ match type of vl with
        | ?tv1 => unify Rv (fun v: tv1 => @data_at cs shl tl v pl)
        end; reflexivity
      | extensionality;
        unfold data_at;
        rewrite <- ?field_at_offset_zero; reflexivity]
  end.Ltac SEP_field_at_strong_unify gfs :=
  match goal with
  | |- data_at_ ?sh ?t ?p = _ /\ _ =>
      change (data_at_ sh t p) with (data_at sh t (default_val t) p);
      SEP_field_at_strong_unify' gfs
  | |- field_at_ _ _ _ _ = _ /\ _ =>
      unfold field_at_; SEP_field_at_strong_unify' gfs
  | _ => SEP_field_at_strong_unify' gfs
  end.(* simplifies a list expression into [e1; e2; ...] form without simplifying its elements *)
Ltac eval_list l :=
  let l' := eval hnf in l in lazymatch l' with
  | ?h :: ?tl => let tl' := eval_list tl in constr:(h :: tl')
  | (@nil ?T) => constr:(@nil T)
  end.Ltac prove_gfs_suffix gfs :=
  match goal with
  | |- _ = ?gfs1 ++ ?gfs0 =>
       let len := fresh "len" in
       let gfs1' := eval_list (firstn ((length gfs - length gfs0)%nat) gfs) in
       unify gfs1 gfs1';
       reflexivity
  end.Ltac test_field_at_in_SEP :=
cbv beta;
match goal with
| |- ?A /\ ?gfs = _ ++ _ =>
  split; [ match A with
           | _ /\ _ => SEP_field_at_strong_unify gfs
           | _ => SEP_field_at_unify gfs
           end
         | prove_gfs_suffix gfs]
end.Ltac search_field_at_in_SEP := find_nth test_field_at_in_SEP.Ltac quick_typecheck3 :=
 clear;
 repeat match goal with
 | H := _ |- _ => clear H
 | H : _ |- _ => clear H
 end;
 apply quick_derives_right; clear; go_lowerx; intros;
 clear; repeat apply andp_right; auto; fail.Ltac entailer_for_load_tac := default_entailer_for_load_store.Ltac entailer_for_store_tac := default_entailer_for_load_store.Ltac check_hint_type :=
 reflexivity ||
 match goal with
 | |- typeof ?A = ?B =>
     let t0 := constr:(typeof A)
     in let t1 := eval hnf in t0 in let t := eval simpl in t1
      in let t' := eval hnf in B in let t'' := eval simpl in t'
      in fail 1000 "unexpected failure in load/store_tac_with_hint."
             "The expression" A "has type" t "but is expected to have type" t''
  end.Ltac load_tac_with_hint LOCAL2PTREE :=
  eapply semax_PTree_field_load_with_hint;
  [ exact LOCAL2PTREE
  | reflexivity
  | reflexivity
  | reflexivity
  | (solve_msubst_eval_lvalue               || fail 1 "Cannot evaluate right-hand-side expression (sometimes this is caused by missing LOCALs in your precondition)")
  | eassumption (* This line can fail. If it does not, the following should not fail. *)
  | check_hint_type
  | (search_field_at_in_SEP                 || fail 1000 "unexpected failure in load_tac_with_hint."
                                                         "Required field_at does not exists in SEP")
  | (auto                                   || fail 1000 "unexpected failure in load_tac_with_hint."
                                                         "Cannot prove readable_share")
  | first [solve_load_rule_evaluation        | fail 1000 "unexpected failure in load_tac_with_hint."
                                                         "unexpected failure in generating loaded value"]
  | first [entailer_for_load_tac             | fail 1000 "unexpected failure in load_tac_with_hint."
                                                         "unexpected failure in entailer_for_load_tac"]
  | first [entailer_for_load_tac             | fail 1000 "unexpected failure in load_tac_with_hint."
                                                         "unexpected failure in entailer_for_load_tac"]
  ].Ltac load_tac_no_hint LOCAL2PTREE :=
  eapply semax_PTree_field_load_no_hint;
  [ exact LOCAL2PTREE
  | reflexivity (* compute_nested_efield *)
  | reflexivity
  | reflexivity
  | reflexivity
  | (solve_msubst_eval_LR                   || fail 1 "Cannot evaluate right-hand-side expression (sometimes this is caused by missing LOCALs in your precondition)")
  | (solve_msubst_efield_denote             || fail 1 "Cannot evaluate right-hand-side expression (sometimes this is caused by missing LOCALs in your precondition)")
  | econstructor
  | solve_field_address_gen
  | search_field_at_in_SEP (* This line can fail. If it does not, the following should not fail. *)
  | (auto                                   || fail 1000 "unexpected failure in load_tac_no_hint."
                                                         "Cannot prove readable_share")
  | first [solve_load_rule_evaluation        | fail 1000 "unexpected failure in load_tac_no_hint."
                                                         "unexpected failure in generating loaded value"]
  | first [solve_legal_nested_field_in_entailment
                                             | fail 1000 "unexpected failure in load_tac_no_hint."
                                                         "unexpected failure in solve_legal_nested_field_in_entailment"]
  | first [entailer_for_load_tac             | fail 1000 "unexpected failure in load_tac_no_hint."
                                                         "unexpected failure in entailer_for_load_tac"]
  | first [entailer_for_load_tac             | fail 1000 "unexpected failure in load_tac_no_hint."
                                                         "unexpected failure in entailer_for_load_tac"]
  ].Ltac cast_load_tac_with_hint LOCAL2PTREE :=
  eapply semax_PTree_field_cast_load_with_hint;
  [ exact LOCAL2PTREE
  | reflexivity
  | reflexivity
  | reflexivity
  | reflexivity
  | (solve_msubst_eval_lvalue               || fail 1 "Cannot evaluate right-hand-side expression (sometimes this is caused by missing LOCALs in your precondition)")
  | eassumption (* This line can fail. If it does not, the following should not fail. *)
  | check_hint_type
  | (search_field_at_in_SEP                 || fail 1000 "unexpected failure in cast_load_tac_with_hint."
                                                         "Required field_at does not exists in SEP")
  | (auto                                   || fail 1000 "unexpected failure in cast_load_tac_with_hint."
                                                         "Cannot prove readable_share")
  | first [solve_load_rule_evaluation        | fail 1000 "unexpected failure in cast_load_tac_with_hint."
                                                         "unexpected failure in generating loaded value"]
  | first [entailer_for_load_tac             | fail 1000 "unexpected failure in cast_load_tac_with_hint."
                                                         "unexpected failure in entailer_for_load_tac"]
  | first [entailer_for_load_tac             | fail 1000 "unexpected failure in cast_load_tac_with_hint."
                                                         "unexpected failure in entailer_for_load_tac"]
  ].Ltac cast_load_tac_no_hint LOCAL2PTREE :=
  eapply semax_PTree_field_cast_load_no_hint;
  [ exact LOCAL2PTREE
  | reflexivity (* compute_nested_efield *)
  | reflexivity
  | reflexivity
  | reflexivity
  | reflexivity
  | (solve_msubst_eval_LR                   || fail 1 "Cannot evaluate right-hand-side expression (sometimes this is caused by missing LOCALs in your precondition)")
  | (solve_msubst_efield_denote             || fail 1 "Cannot evaluate right-hand-side expression (sometimes this is caused by missing LOCALs in your precondition)")
  | econstructor
  | solve_field_address_gen
  | search_field_at_in_SEP (* This line can fail. If it does not, the following should not fail. *)
  | (auto                                   || fail 1000 "unexpected failure in cast_load_tac_no_hint."
                                                         "Cannot prove readable_share")
  | first [solve_load_rule_evaluation        | fail 1000 "unexpected failure in cast_load_tac_no_hint."
                                                         "unexpected failure in generating loaded value"]
  | first [solve_legal_nested_field_in_entailment
                                             | fail 1000 "unexpected failure in cast_load_tac_no_hint."
                                                         "unexpected failure in solve_legal_nested_field_in_entailment"]
  | first [entailer_for_load_tac             | fail 1000 "unexpected failure in cast_load_tac_no_hint."
                                                         "unexpected failure in entailer_for_load_tac"]
  | first [entailer_for_load_tac             | fail 1000 "unexpected failure in cast_load_tac_no_hint."
                                                         "unexpected failure in entailer_for_load_tac"]
  ].

(* Specifications: *)
Lemma data_equal_congr {cs: compspecs}: forall T (v1 v2: reptype T), v1 = v2 -> data_equal v1 v2.