src/HOL/Tools/datatype_abs_proofs.ML
author haftmann
Fri Dec 16 09:00:11 2005 +0100 (2005-12-16)
changeset 18418 bf448d999b7e
parent 18377 0e1d025d57b3
child 18728 6790126ab5f6
permissions -rw-r--r--
re-arranged tuples (theory * 'a) to ('a * theory) in Pure
     1 (*  Title:      HOL/Tools/datatype_abs_proofs.ML
     2     ID:         $Id$
     3     Author:     Stefan Berghofer, TU Muenchen
     4 
     5 Proofs and defintions independent of concrete representation
     6 of datatypes  (i.e. requiring only abstract properties such as
     7 injectivity / distinctness of constructors and induction)
     8 
     9  - case distinction (exhaustion) theorems
    10  - characteristic equations for primrec combinators
    11  - characteristic equations for case combinators
    12  - equations for splitting "P (case ...)" expressions
    13  - datatype size function
    14  - "nchotomy" and "case_cong" theorems for TFL
    15 
    16 *)
    17 
    18 signature DATATYPE_ABS_PROOFS =
    19 sig
    20   val prove_casedist_thms : string list ->
    21     DatatypeAux.descr list -> (string * sort) list -> thm ->
    22     theory attribute list -> theory -> thm list * theory
    23   val prove_primrec_thms : bool -> string list ->
    24     DatatypeAux.descr list -> (string * sort) list ->
    25       DatatypeAux.datatype_info Symtab.table -> thm list list -> thm list list ->
    26         simpset -> thm -> theory -> (string list * thm list) * theory
    27   val prove_case_thms : bool -> string list ->
    28     DatatypeAux.descr list -> (string * sort) list ->
    29       string list -> thm list -> theory -> (thm list list * string list) * theory
    30   val prove_split_thms : string list ->
    31     DatatypeAux.descr list -> (string * sort) list ->
    32       thm list list -> thm list list -> thm list -> thm list list -> theory ->
    33         (thm * thm) list * theory
    34   val prove_size_thms : bool -> string list ->
    35     DatatypeAux.descr list -> (string * sort) list ->
    36       string list -> thm list -> theory -> thm list * theory
    37   val prove_nchotomys : string list -> DatatypeAux.descr list ->
    38     (string * sort) list -> thm list -> theory -> thm list * theory
    39   val prove_weak_case_congs : string list -> DatatypeAux.descr list ->
    40     (string * sort) list -> theory -> thm list * theory
    41   val prove_case_congs : string list ->
    42     DatatypeAux.descr list -> (string * sort) list ->
    43       thm list -> thm list list -> theory -> thm list * theory
    44 end;
    45 
    46 structure DatatypeAbsProofs: DATATYPE_ABS_PROOFS =
    47 struct
    48 
    49 open DatatypeAux;
    50 
    51 (************************ case distinction theorems ***************************)
    52 
    53 fun prove_casedist_thms new_type_names descr sorts induct case_names_exhausts thy =
    54   let
    55     val _ = message "Proving case distinction theorems ...";
    56 
    57     val descr' = List.concat descr;
    58     val recTs = get_rec_types descr' sorts;
    59     val newTs = Library.take (length (hd descr), recTs);
    60 
    61     val {maxidx, ...} = rep_thm induct;
    62     val induct_Ps = map head_of (HOLogic.dest_conj (HOLogic.dest_Trueprop (concl_of induct)));
    63 
    64     fun prove_casedist_thm ((i, t), T) =
    65       let
    66         val dummyPs = map (fn (Var (_, Type (_, [T', T'']))) =>
    67           Abs ("z", T', Const ("True", T''))) induct_Ps;
    68         val P = Abs ("z", T, HOLogic.imp $ HOLogic.mk_eq (Var (("a", maxidx+1), T), Bound 0) $
    69           Var (("P", 0), HOLogic.boolT))
    70         val insts = Library.take (i, dummyPs) @ (P::(Library.drop (i + 1, dummyPs)));
    71         val cert = cterm_of thy;
    72         val insts' = (map cert induct_Ps) ~~ (map cert insts);
    73         val induct' = refl RS ((List.nth
    74           (split_conj_thm (cterm_instantiate insts' induct), i)) RSN (2, rev_mp))
    75 
    76       in
    77         standard (Goal.prove thy [] (Logic.strip_imp_prems t) (Logic.strip_imp_concl t)
    78           (fn prems => EVERY
    79             [rtac induct' 1,
    80              REPEAT (rtac TrueI 1),
    81              REPEAT ((rtac impI 1) THEN (eresolve_tac prems 1)),
    82              REPEAT (rtac TrueI 1)]))
    83       end;
    84 
    85     val casedist_thms = map prove_casedist_thm ((0 upto (length newTs - 1)) ~~
    86       (DatatypeProp.make_casedists descr sorts) ~~ newTs)
    87   in
    88     thy
    89     |> store_thms_atts "exhaust" new_type_names (map single case_names_exhausts) casedist_thms
    90   end;
    91 
    92 
    93 (*************************** primrec combinators ******************************)
    94 
    95 fun prove_primrec_thms flat_names new_type_names descr sorts
    96     (dt_info : datatype_info Symtab.table) constr_inject dist_rewrites dist_ss induct thy =
    97   let
    98     val _ = message "Constructing primrec combinators ...";
    99 
   100     val big_name = space_implode "_" new_type_names;
   101     val thy0 = add_path flat_names big_name thy;
   102 
   103     val descr' = List.concat descr;
   104     val recTs = get_rec_types descr' sorts;
   105     val used = foldr add_typ_tfree_names [] recTs;
   106     val newTs = Library.take (length (hd descr), recTs);
   107 
   108     val induct_Ps = map head_of (HOLogic.dest_conj (HOLogic.dest_Trueprop (concl_of induct)));
   109 
   110     val big_rec_name' = big_name ^ "_rec_set";
   111     val rec_set_names = map (Sign.full_name (Theory.sign_of thy0))
   112       (if length descr' = 1 then [big_rec_name'] else
   113         (map ((curry (op ^) (big_rec_name' ^ "_")) o string_of_int)
   114           (1 upto (length descr'))));
   115 
   116     val (rec_result_Ts, reccomb_fn_Ts) = DatatypeProp.make_primrec_Ts descr sorts used;
   117 
   118     val rec_set_Ts = map (fn (T1, T2) => reccomb_fn_Ts ---> HOLogic.mk_setT
   119       (HOLogic.mk_prodT (T1, T2))) (recTs ~~ rec_result_Ts);
   120 
   121     val rec_fns = map (uncurry (mk_Free "f"))
   122       (reccomb_fn_Ts ~~ (1 upto (length reccomb_fn_Ts)));
   123     val rec_sets = map (fn c => list_comb (Const c, rec_fns))
   124       (rec_set_names ~~ rec_set_Ts);
   125 
   126     (* introduction rules for graph of primrec function *)
   127 
   128     fun make_rec_intr T set_name ((rec_intr_ts, l), (cname, cargs)) =
   129       let
   130         fun mk_prem ((dt, U), (j, k, prems, t1s, t2s)) =
   131           let val free1 = mk_Free "x" U j
   132           in (case (strip_dtyp dt, strip_type U) of
   133              ((_, DtRec m), (Us, _)) =>
   134                let
   135                  val free2 = mk_Free "y" (Us ---> List.nth (rec_result_Ts, m)) k;
   136                  val i = length Us
   137                in (j + 1, k + 1, HOLogic.mk_Trueprop (HOLogic.list_all
   138                      (map (pair "x") Us, HOLogic.mk_mem (HOLogic.mk_prod
   139                        (app_bnds free1 i, app_bnds free2 i),
   140                          List.nth (rec_sets, m)))) :: prems,
   141                    free1::t1s, free2::t2s)
   142                end
   143            | _ => (j + 1, k, prems, free1::t1s, t2s))
   144           end;
   145 
   146         val Ts = map (typ_of_dtyp descr' sorts) cargs;
   147         val (_, _, prems, t1s, t2s) = foldr mk_prem (1, 1, [], [], []) (cargs ~~ Ts)
   148 
   149       in (rec_intr_ts @ [Logic.list_implies (prems, HOLogic.mk_Trueprop (HOLogic.mk_mem
   150         (HOLogic.mk_prod (list_comb (Const (cname, Ts ---> T), t1s),
   151           list_comb (List.nth (rec_fns, l), t1s @ t2s)), set_name)))], l + 1)
   152       end;
   153 
   154     val (rec_intr_ts, _) = Library.foldl (fn (x, ((d, T), set_name)) =>
   155       Library.foldl (make_rec_intr T set_name) (x, #3 (snd d)))
   156         (([], 0), descr' ~~ recTs ~~ rec_sets);
   157 
   158     val (thy1, {intrs = rec_intrs, elims = rec_elims, ...}) =
   159       setmp InductivePackage.quiet_mode (!quiet_mode)
   160         (InductivePackage.add_inductive_i false true big_rec_name' false false true
   161            rec_sets (map (fn x => (("", x), [])) rec_intr_ts) []) thy0;
   162 
   163     (* prove uniqueness and termination of primrec combinators *)
   164 
   165     val _ = message "Proving termination and uniqueness of primrec functions ...";
   166 
   167     fun mk_unique_tac ((tac, intrs), ((((i, (tname, _, constrs)), elim), T), T')) =
   168       let
   169         val distinct_tac = (etac Pair_inject 1) THEN
   170           (if i < length newTs then
   171              full_simp_tac (HOL_ss addsimps (List.nth (dist_rewrites, i))) 1
   172            else full_simp_tac dist_ss 1);
   173 
   174         val inject = map (fn r => r RS iffD1)
   175           (if i < length newTs then List.nth (constr_inject, i)
   176             else #inject (the (Symtab.lookup dt_info tname)));
   177 
   178         fun mk_unique_constr_tac n ((tac, intr::intrs, j), (cname, cargs)) =
   179           let
   180             val k = length (List.filter is_rec_type cargs)
   181 
   182           in (EVERY [DETERM tac,
   183                 REPEAT (etac ex1E 1), rtac ex1I 1,
   184                 DEPTH_SOLVE_1 (ares_tac [intr] 1),
   185                 REPEAT_DETERM_N k (etac thin_rl 1 THEN rotate_tac 1 1),
   186                 etac elim 1,
   187                 REPEAT_DETERM_N j distinct_tac,
   188                 etac Pair_inject 1, TRY (dresolve_tac inject 1),
   189                 REPEAT (etac conjE 1), hyp_subst_tac 1,
   190                 REPEAT (EVERY [etac allE 1, dtac mp 1, atac 1]),
   191                 TRY (hyp_subst_tac 1),
   192                 rtac refl 1,
   193                 REPEAT_DETERM_N (n - j - 1) distinct_tac],
   194               intrs, j + 1)
   195           end;
   196 
   197         val (tac', intrs', _) = Library.foldl (mk_unique_constr_tac (length constrs))
   198           ((tac, intrs, 0), constrs);
   199 
   200       in (tac', intrs') end;
   201 
   202     val rec_unique_thms =
   203       let
   204         val rec_unique_ts = map (fn (((set_t, T1), T2), i) =>
   205           Const ("Ex1", (T2 --> HOLogic.boolT) --> HOLogic.boolT) $
   206             absfree ("y", T2, HOLogic.mk_mem (HOLogic.mk_prod
   207               (mk_Free "x" T1 i, Free ("y", T2)), set_t)))
   208                 (rec_sets ~~ recTs ~~ rec_result_Ts ~~ (1 upto length recTs));
   209         val cert = cterm_of thy1
   210         val insts = map (fn ((i, T), t) => absfree ("x" ^ (string_of_int i), T, t))
   211           ((1 upto length recTs) ~~ recTs ~~ rec_unique_ts);
   212         val induct' = cterm_instantiate ((map cert induct_Ps) ~~
   213           (map cert insts)) induct;
   214         val (tac, _) = Library.foldl mk_unique_tac
   215           (((rtac induct' THEN_ALL_NEW ObjectLogic.atomize_tac) 1
   216               THEN rewtac (mk_meta_eq choice_eq), rec_intrs),
   217             descr' ~~ rec_elims ~~ recTs ~~ rec_result_Ts);
   218 
   219       in split_conj_thm (standard (Goal.prove thy1 [] []
   220         (HOLogic.mk_Trueprop (mk_conj rec_unique_ts)) (K tac)))
   221       end;
   222 
   223     val rec_total_thms = map (fn r => r RS theI') rec_unique_thms;
   224 
   225     (* define primrec combinators *)
   226 
   227     val big_reccomb_name = (space_implode "_" new_type_names) ^ "_rec";
   228     val reccomb_names = map (Sign.full_name (Theory.sign_of thy1))
   229       (if length descr' = 1 then [big_reccomb_name] else
   230         (map ((curry (op ^) (big_reccomb_name ^ "_")) o string_of_int)
   231           (1 upto (length descr'))));
   232     val reccombs = map (fn ((name, T), T') => list_comb
   233       (Const (name, reccomb_fn_Ts @ [T] ---> T'), rec_fns))
   234         (reccomb_names ~~ recTs ~~ rec_result_Ts);
   235 
   236     val (reccomb_defs, thy2) =
   237       thy1
   238       |> Theory.add_consts_i (map (fn ((name, T), T') =>
   239           (Sign.base_name name, reccomb_fn_Ts @ [T] ---> T', NoSyn))
   240           (reccomb_names ~~ recTs ~~ rec_result_Ts))
   241       |> (PureThy.add_defs_i false o map Thm.no_attributes) (map (fn ((((name, comb), set), T), T') =>
   242           ((Sign.base_name name) ^ "_def", Logic.mk_equals (comb, absfree ("x", T,
   243            Const ("The", (T' --> HOLogic.boolT) --> T') $ absfree ("y", T',
   244              HOLogic.mk_mem (HOLogic.mk_prod (Free ("x", T), Free ("y", T')), set))))))
   245                (reccomb_names ~~ reccombs ~~ rec_sets ~~ recTs ~~ rec_result_Ts))
   246       ||> parent_path flat_names;
   247 
   248 
   249     (* prove characteristic equations for primrec combinators *)
   250 
   251     val _ = message "Proving characteristic theorems for primrec combinators ..."
   252 
   253     val rec_thms = map (fn t => standard (Goal.prove thy2 [] [] t
   254       (fn _ => EVERY
   255         [rewrite_goals_tac reccomb_defs,
   256          rtac the1_equality 1,
   257          resolve_tac rec_unique_thms 1,
   258          resolve_tac rec_intrs 1,
   259          REPEAT (rtac allI 1 ORELSE resolve_tac rec_total_thms 1)])))
   260            (DatatypeProp.make_primrecs new_type_names descr sorts thy2)
   261 
   262   in
   263     thy2
   264     |> Theory.add_path (space_implode "_" new_type_names)
   265     |> PureThy.add_thmss [(("recs", rec_thms), [])]
   266     ||> Theory.parent_path
   267     |-> (fn thms => pair (reccomb_names, Library.flat thms))
   268   end;
   269 
   270 
   271 (***************************** case combinators *******************************)
   272 
   273 fun prove_case_thms flat_names new_type_names descr sorts reccomb_names primrec_thms thy =
   274   let
   275     val _ = message "Proving characteristic theorems for case combinators ...";
   276 
   277     val thy1 = add_path flat_names (space_implode "_" new_type_names) thy;
   278 
   279     val descr' = List.concat descr;
   280     val recTs = get_rec_types descr' sorts;
   281     val used = foldr add_typ_tfree_names [] recTs;
   282     val newTs = Library.take (length (hd descr), recTs);
   283     val T' = TFree (variant used "'t", HOLogic.typeS);
   284 
   285     fun mk_dummyT dt = binder_types (typ_of_dtyp descr' sorts dt) ---> T';
   286 
   287     val case_dummy_fns = map (fn (_, (_, _, constrs)) => map (fn (_, cargs) =>
   288       let
   289         val Ts = map (typ_of_dtyp descr' sorts) cargs;
   290         val Ts' = map mk_dummyT (List.filter is_rec_type cargs)
   291       in Const ("arbitrary", Ts @ Ts' ---> T')
   292       end) constrs) descr';
   293 
   294     val case_names = map (fn s =>
   295       Sign.full_name (Theory.sign_of thy1) (s ^ "_case")) new_type_names;
   296 
   297     (* define case combinators via primrec combinators *)
   298 
   299     val (case_defs, thy2) = Library.foldl (fn ((defs, thy),
   300       ((((i, (_, _, constrs)), T), name), recname)) =>
   301         let
   302           val (fns1, fns2) = ListPair.unzip (map (fn ((_, cargs), j) =>
   303             let
   304               val Ts = map (typ_of_dtyp descr' sorts) cargs;
   305               val Ts' = Ts @ map mk_dummyT (List.filter is_rec_type cargs);
   306               val frees' = map (uncurry (mk_Free "x")) (Ts' ~~ (1 upto length Ts'));
   307               val frees = Library.take (length cargs, frees');
   308               val free = mk_Free "f" (Ts ---> T') j
   309             in
   310              (free, list_abs_free (map dest_Free frees',
   311                list_comb (free, frees)))
   312             end) (constrs ~~ (1 upto length constrs)));
   313 
   314           val caseT = (map (snd o dest_Free) fns1) @ [T] ---> T';
   315           val fns = (List.concat (Library.take (i, case_dummy_fns))) @
   316             fns2 @ (List.concat (Library.drop (i + 1, case_dummy_fns)));
   317           val reccomb = Const (recname, (map fastype_of fns) @ [T] ---> T');
   318           val decl = (Sign.base_name name, caseT, NoSyn);
   319           val def = ((Sign.base_name name) ^ "_def",
   320             Logic.mk_equals (list_comb (Const (name, caseT), fns1),
   321               list_comb (reccomb, (List.concat (Library.take (i, case_dummy_fns))) @
   322                 fns2 @ (List.concat (Library.drop (i + 1, case_dummy_fns))) )));
   323           val ([def_thm], thy') =
   324             thy
   325             |> Theory.add_consts_i [decl]
   326             |> (PureThy.add_defs_i false o map Thm.no_attributes) [def];
   327 
   328         in (defs @ [def_thm], thy')
   329         end) (([], thy1), (hd descr) ~~ newTs ~~ case_names ~~
   330           (Library.take (length newTs, reccomb_names)));
   331 
   332     val case_thms = map (map (fn t => standard (Goal.prove thy2 [] [] t
   333       (fn _ => EVERY [rewrite_goals_tac (case_defs @ map mk_meta_eq primrec_thms), rtac refl 1]))))
   334           (DatatypeProp.make_cases new_type_names descr sorts thy2)
   335 
   336   in
   337     thy2
   338     |> parent_path flat_names
   339     |> store_thmss "cases" new_type_names case_thms
   340     |-> (fn thmss => pair (thmss, case_names))
   341   end;
   342 
   343 
   344 (******************************* case splitting *******************************)
   345 
   346 fun prove_split_thms new_type_names descr sorts constr_inject dist_rewrites
   347     casedist_thms case_thms thy =
   348   let
   349     val _ = message "Proving equations for case splitting ...";
   350 
   351     val descr' = List.concat descr;
   352     val recTs = get_rec_types descr' sorts;
   353     val newTs = Library.take (length (hd descr), recTs);
   354 
   355     fun prove_split_thms ((((((t1, t2), inject), dist_rewrites'),
   356         exhaustion), case_thms'), T) =
   357       let
   358         val cert = cterm_of thy;
   359         val _ $ (_ $ lhs $ _) = hd (Logic.strip_assums_hyp (hd (prems_of exhaustion)));
   360         val exhaustion' = cterm_instantiate
   361           [(cert lhs, cert (Free ("x", T)))] exhaustion;
   362         val tacf = K (EVERY [rtac exhaustion' 1, ALLGOALS (asm_simp_tac
   363           (HOL_ss addsimps (dist_rewrites' @ inject @ case_thms')))])
   364       in
   365         (standard (Goal.prove thy [] [] t1 tacf),
   366          standard (Goal.prove thy [] [] t2 tacf))
   367       end;
   368 
   369     val split_thm_pairs = map prove_split_thms
   370       ((DatatypeProp.make_splits new_type_names descr sorts thy) ~~ constr_inject ~~
   371         dist_rewrites ~~ casedist_thms ~~ case_thms ~~ newTs);
   372 
   373     val (split_thms, split_asm_thms) = ListPair.unzip split_thm_pairs
   374 
   375   in
   376     thy
   377     |> store_thms "split" new_type_names split_thms
   378     ||>> store_thms "split_asm" new_type_names split_asm_thms
   379     |-> (fn (thms1, thms2) => pair (thms1 ~~ thms2))
   380   end;
   381 
   382 (******************************* size functions *******************************)
   383 
   384 fun prove_size_thms flat_names new_type_names descr sorts reccomb_names primrec_thms thy =
   385   if exists (fn (_, (_, _, constrs)) => exists (fn (_, cargs) => exists (fn dt =>
   386     is_rec_type dt andalso not (null (fst (strip_dtyp dt)))) cargs) constrs)
   387       (List.concat descr)
   388   then
   389     ([], thy)
   390   else
   391   let
   392     val _ = message "Proving equations for size function ...";
   393 
   394     val big_name = space_implode "_" new_type_names;
   395     val thy1 = add_path flat_names big_name thy;
   396 
   397     val descr' = List.concat descr;
   398     val recTs = get_rec_types descr' sorts;
   399 
   400     val size_name = "Nat.size";
   401     val size_names = replicate (length (hd descr)) size_name @
   402       map (Sign.full_name (Theory.sign_of thy1)) (DatatypeProp.indexify_names
   403         (map (fn T => name_of_typ T ^ "_size") (Library.drop (length (hd descr), recTs))));
   404     val def_names = map (fn s => s ^ "_def") (DatatypeProp.indexify_names
   405       (map (fn T => name_of_typ T ^ "_size") recTs));
   406 
   407     fun plus (t1, t2) = Const ("op +", [HOLogic.natT, HOLogic.natT] ---> HOLogic.natT) $ t1 $ t2;
   408 
   409     fun make_sizefun (_, cargs) =
   410       let
   411         val Ts = map (typ_of_dtyp descr' sorts) cargs;
   412         val k = length (List.filter is_rec_type cargs);
   413         val t = if k = 0 then HOLogic.zero else
   414           foldl1 plus (map Bound (k - 1 downto 0) @ [HOLogic.mk_nat 1])
   415       in
   416         foldr (fn (T, t') => Abs ("x", T, t')) t (Ts @ replicate k HOLogic.natT)
   417       end;
   418 
   419     val fs = List.concat (map (fn (_, (_, _, constrs)) => map make_sizefun constrs) descr');
   420     val fTs = map fastype_of fs;
   421 
   422     val (size_def_thms, thy') =
   423       thy1
   424       |> Theory.add_consts_i (map (fn (s, T) =>
   425            (Sign.base_name s, T --> HOLogic.natT, NoSyn))
   426            (Library.drop (length (hd descr), size_names ~~ recTs)))
   427       |> (PureThy.add_defs_i true o map Thm.no_attributes) (map (fn (((s, T), def_name), rec_name) =>
   428            (def_name, Logic.mk_equals (Const (s, T --> HOLogic.natT),
   429             list_comb (Const (rec_name, fTs @ [T] ---> HOLogic.natT), fs))))
   430             (size_names ~~ recTs ~~ def_names ~~ reccomb_names))
   431       ||> parent_path flat_names;
   432 
   433     val rewrites = size_def_thms @ map mk_meta_eq primrec_thms;
   434 
   435     val size_thms = map (fn t => standard (Goal.prove thy' [] [] t
   436       (fn _ => EVERY [rewrite_goals_tac rewrites, rtac refl 1])))
   437         (DatatypeProp.make_size descr sorts thy')
   438 
   439   in
   440     thy'
   441     |> Theory.add_path big_name
   442     |> PureThy.add_thmss [(("size", size_thms), [])]
   443     ||> Theory.parent_path
   444     |-> (fn thmss => pair (Library.flat thmss))
   445   end;
   446 
   447 fun prove_weak_case_congs new_type_names descr sorts thy =
   448   let
   449     fun prove_weak_case_cong t =
   450        standard (Goal.prove thy [] (Logic.strip_imp_prems t) (Logic.strip_imp_concl t)
   451          (fn prems => EVERY [rtac ((hd prems) RS arg_cong) 1]))
   452 
   453     val weak_case_congs = map prove_weak_case_cong (DatatypeProp.make_weak_case_congs
   454       new_type_names descr sorts thy)
   455 
   456   in thy |> store_thms "weak_case_cong" new_type_names weak_case_congs end;
   457 
   458 (************************* additional theorems for TFL ************************)
   459 
   460 fun prove_nchotomys new_type_names descr sorts casedist_thms thy =
   461   let
   462     val _ = message "Proving additional theorems for TFL ...";
   463 
   464     fun prove_nchotomy (t, exhaustion) =
   465       let
   466         (* For goal i, select the correct disjunct to attack, then prove it *)
   467         fun tac i 0 = EVERY [TRY (rtac disjI1 i),
   468               hyp_subst_tac i, REPEAT (rtac exI i), rtac refl i]
   469           | tac i n = rtac disjI2 i THEN tac i (n - 1)
   470       in 
   471         standard (Goal.prove thy [] [] t (fn _ =>
   472           EVERY [rtac allI 1,
   473            exh_tac (K exhaustion) 1,
   474            ALLGOALS (fn i => tac i (i-1))]))
   475       end;
   476 
   477     val nchotomys =
   478       map prove_nchotomy (DatatypeProp.make_nchotomys descr sorts ~~ casedist_thms)
   479 
   480   in thy |> store_thms "nchotomy" new_type_names nchotomys end;
   481 
   482 fun prove_case_congs new_type_names descr sorts nchotomys case_thms thy =
   483   let
   484     fun prove_case_cong ((t, nchotomy), case_rewrites) =
   485       let
   486         val (Const ("==>", _) $ tm $ _) = t;
   487         val (Const ("Trueprop", _) $ (Const ("op =", _) $ _ $ Ma)) = tm;
   488         val cert = cterm_of (Theory.sign_of thy);
   489         val nchotomy' = nchotomy RS spec;
   490         val nchotomy'' = cterm_instantiate
   491           [(cert (hd (add_term_vars (concl_of nchotomy', []))), cert Ma)] nchotomy'
   492       in
   493         standard (Goal.prove thy [] (Logic.strip_imp_prems t) (Logic.strip_imp_concl t)
   494           (fn prems => 
   495             let val simplify = asm_simp_tac (HOL_ss addsimps (prems @ case_rewrites))
   496             in EVERY [simp_tac (HOL_ss addsimps [hd prems]) 1,
   497                 cut_facts_tac [nchotomy''] 1,
   498                 REPEAT (etac disjE 1 THEN REPEAT (etac exE 1) THEN simplify 1),
   499                 REPEAT (etac exE 1) THEN simplify 1 (* Get last disjunct *)]
   500             end))
   501       end;
   502 
   503     val case_congs = map prove_case_cong (DatatypeProp.make_case_congs
   504       new_type_names descr sorts thy ~~ nchotomys ~~ case_thms)
   505 
   506   in thy |> store_thms "case_cong" new_type_names case_congs end;
   507 
   508 end;