src/HOL/Codatatype/Tools/bnf_gfp.ML
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construct high-level iterator RHS
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(*  Title:      HOL/Codatatype/Tools/bnf_gfp.ML
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    Author:     Dmitriy Traytel, TU Muenchen
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    Author:     Andrei Popescu, TU Muenchen
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    Author:     Jasmin Blanchette, TU Muenchen
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    Copyright   2012
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Codatatype construction.
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*)
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signature BNF_GFP =
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sig
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  val bnf_gfp: binding list -> mixfix list -> (string * sort) list -> typ list list ->
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    BNF_Def.BNF list -> local_theory ->
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    (term list * term list * term list * term list * thm list * thm list * thm list) * local_theory
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end;
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structure BNF_GFP : BNF_GFP =
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struct
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open BNF_Def
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open BNF_Util
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open BNF_Tactics
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open BNF_FP_Util
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open BNF_GFP_Util
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open BNF_GFP_Tactics
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datatype wit_tree = Leaf of int | Node of (int * int * int list) * wit_tree list;
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fun mk_tree_args (I, T) (I', Ts) = (sort_distinct int_ord (I @ I'), T :: Ts);
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fun finish Iss m seen i (nwit, I) =
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  let
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    val treess = map (fn j =>
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        if j < m orelse member (op =) seen j then [([j], Leaf j)]
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        else
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          map_index (finish Iss m (insert (op =) j seen) j) (nth Iss (j - m))
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          |> flat
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          |> minimize_wits)
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      I;
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  in
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    map (fn (I, t) => (I, Node ((i - m, nwit, filter (fn i => i < m) I), t)))
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      (fold_rev (map_product mk_tree_args) treess [([], [])])
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    |> minimize_wits
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  end;
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fun tree_to_fld_wit vars _ _ (Leaf j) = ([j], nth vars j)
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  | tree_to_fld_wit vars flds witss (Node ((i, nwit, I), subtrees)) =
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     (I, nth flds i $ (Term.list_comb (snd (nth (nth witss i) nwit),
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       map (snd o tree_to_fld_wit vars flds witss) subtrees)));
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fun tree_to_coind_wits _ (Leaf j) = []
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  | tree_to_coind_wits lwitss (Node ((i, nwit, I), subtrees)) =
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     ((i, I), nth (nth lwitss i) nwit) :: maps (tree_to_coind_wits lwitss) subtrees;
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(*all bnfs have the same lives*)
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fun bnf_gfp bs mixfixes resDs Dss_insts bnfs lthy =
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  let
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    val timer = time (Timer.startRealTimer ());
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    val live = live_of_bnf (hd bnfs);
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    val n = length bnfs; (*active*)
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    val ks = 1 upto n;
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    val m = live - n (*passive, if 0 don't generate a new bnf*);
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    val ls = 1 upto m;
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    val b = Binding.name (fold_rev (fn b => fn s => Binding.name_of b ^ s) bs "");
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    (* TODO: check if m, n etc are sane *)
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    val Dss = map (fn Ds => map TFree (fold Term.add_tfreesT Ds [])) Dss_insts;
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    val deads = fold (union (op =)) Dss (map TFree resDs);
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    val names_lthy = fold Variable.declare_typ deads lthy;
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    (* tvars *)
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    val ((((((((passiveAs, activeAs), allAs)), (passiveBs, activeBs)),
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      (passiveCs, activeCs)), passiveXs), passiveYs), idxT) = names_lthy
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      |> mk_TFrees live
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      |> apfst (`(chop m))
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      ||> mk_TFrees live
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      ||>> apfst (chop m)
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      ||> mk_TFrees live
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      ||>> apfst (chop m)
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      ||>> mk_TFrees m
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      ||>> mk_TFrees m
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      ||> fst o mk_TFrees 1
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      ||> the_single;
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    val Ass = replicate n allAs;
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    val allBs = passiveAs @ activeBs;
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    val Bss = replicate n allBs;
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    val allCs = passiveAs @ activeCs;
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    val allCs' = passiveBs @ activeCs;
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    val Css' = replicate n allCs';
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    (* typs *)
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    fun mk_FTs Ts = map2 (fn Ds => mk_T_of_bnf Ds Ts) Dss bnfs;
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    val (params, params') = `(map Term.dest_TFree) (deads @ passiveAs);
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    val FTsAs = mk_FTs allAs;
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    val FTsBs = mk_FTs allBs;
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    val FTsCs = mk_FTs allCs;
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    val ATs = map HOLogic.mk_setT passiveAs;
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    val BTs = map HOLogic.mk_setT activeAs;
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    val B'Ts = map HOLogic.mk_setT activeBs;
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    val B''Ts = map HOLogic.mk_setT activeCs;
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    val sTs = map2 (fn T => fn U => T --> U) activeAs FTsAs;
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    val s'Ts = map2 (fn T => fn U => T --> U) activeBs FTsBs;
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    val s''Ts = map2 (fn T => fn U => T --> U) activeCs FTsCs;
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    val fTs = map2 (fn T => fn U => T --> U) activeAs activeBs;
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    val all_fTs = map2 (fn T => fn U => T --> U) allAs allBs;
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    val self_fTs = map (fn T => T --> T) activeAs;
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    val gTs = map2 (fn T => fn U => T --> U) activeBs activeCs;
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    val all_gTs = map2 (fn T => fn U => T --> U) allBs allCs';
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    val RTs = map2 (fn T => fn U => HOLogic.mk_prodT (T, U)) activeAs activeBs;
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    val sRTs = map2 (fn T => fn U => HOLogic.mk_prodT (T, U)) activeAs activeAs;
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    val R'Ts = map2 (fn T => fn U => HOLogic.mk_prodT (T, U)) activeBs activeCs;
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    val setsRTs = map HOLogic.mk_setT sRTs;
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    val setRTs = map HOLogic.mk_setT RTs;
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    val all_sbisT = HOLogic.mk_tupleT setsRTs;
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    val setR'Ts = map HOLogic.mk_setT R'Ts;
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    val FRTs = mk_FTs (passiveAs @ RTs);
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    val sumBsAs = map2 (curry mk_sumT) activeBs activeAs;
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    val sumFTs = mk_FTs (passiveAs @ sumBsAs);
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    val sum_sTs = map2 (fn T => fn U => T --> U) activeAs sumFTs;
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   123
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   124
    (* terms *)
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   125
    val mapsAsAs = map4 mk_map_of_bnf Dss Ass Ass bnfs;
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   126
    val mapsAsBs = map4 mk_map_of_bnf Dss Ass Bss bnfs;
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   127
    val mapsBsCs' = map4 mk_map_of_bnf Dss Bss Css' bnfs;
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   128
    val mapsAsCs' = map4 mk_map_of_bnf Dss Ass Css' bnfs;
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    val map_Inls = map4 mk_map_of_bnf Dss Bss (replicate n (passiveAs @ sumBsAs)) bnfs;
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   130
    val map_Inls_rev = map4 mk_map_of_bnf Dss (replicate n (passiveAs @ sumBsAs)) Bss bnfs;
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    val map_fsts = map4 mk_map_of_bnf Dss (replicate n (passiveAs @ RTs)) Ass bnfs;
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    val map_snds = map4 mk_map_of_bnf Dss (replicate n (passiveAs @ RTs)) Bss bnfs;
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   133
    fun mk_setss Ts = map3 mk_sets_of_bnf (map (replicate live) Dss)
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      (map (replicate live) (replicate n Ts)) bnfs;
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    val setssAs = mk_setss allAs;
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    val setssAs' = transpose setssAs;
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   137
    val bis_setss = mk_setss (passiveAs @ RTs);
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   138
    val relsAsBs = map4 mk_rel_of_bnf Dss Ass Bss bnfs;
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   139
    val bds = map3 mk_bd_of_bnf Dss Ass bnfs;
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   140
    val sum_bd = Library.foldr1 (uncurry mk_csum) bds;
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   141
    val sum_bdT = fst (dest_relT (fastype_of sum_bd));
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    val witss = map wits_of_bnf bnfs;
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   143
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   144
    val emptys = map (fn T => HOLogic.mk_set T []) passiveAs;
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   145
    val Zeros = map (fn empty =>
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   146
     HOLogic.mk_tuple (map (fn U => absdummy U empty) activeAs)) emptys;
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   147
    val hrecTs = map fastype_of Zeros;
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   148
    val hsetTs = map (fn hrecT => Library.foldr (op -->) (sTs, HOLogic.natT --> hrecT)) hrecTs;
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   149
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   150
    val (((((((((((((((((((((((((((((((((((zs, zs'), zs_copy), zs_copy2),
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   151
      z's), As), As_copy), Bs), Bs_copy), B's), B''s), ss), sum_ss), s's), s''s), fs), fs_copy),
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      self_fs), all_fs), gs), all_gs), xFs), xFs_copy), RFs), (Rtuple, Rtuple')), (hrecs, hrecs')),
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      (nat, nat')), Rs), Rs_copy), R's), sRs), (idx, idx')), Idx), Ris), Kss),
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      names_lthy) = lthy
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      |> mk_Frees' "b" activeAs
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      ||>> mk_Frees "b" activeAs
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   157
      ||>> mk_Frees "b" activeAs
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      ||>> mk_Frees "b" activeBs
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   159
      ||>> mk_Frees "A" ATs
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      ||>> mk_Frees "A" ATs
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      ||>> mk_Frees "B" BTs
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      ||>> mk_Frees "B" BTs
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      ||>> mk_Frees "B'" B'Ts
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      ||>> mk_Frees "B''" B''Ts
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   165
      ||>> mk_Frees "s" sTs
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   166
      ||>> mk_Frees "sums" sum_sTs
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      ||>> mk_Frees "s'" s'Ts
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   168
      ||>> mk_Frees "s''" s''Ts
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   169
      ||>> mk_Frees "f" fTs
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      ||>> mk_Frees "f" fTs
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   171
      ||>> mk_Frees "f" self_fTs
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   172
      ||>> mk_Frees "f" all_fTs
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   173
      ||>> mk_Frees "g" gTs
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   174
      ||>> mk_Frees "g" all_gTs
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   175
      ||>> mk_Frees "x" FTsAs
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   176
      ||>> mk_Frees "x" FTsAs
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   177
      ||>> mk_Frees "x" FRTs
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   178
      ||>> yield_singleton (apfst (op ~~) oo mk_Frees' "Rtuple") all_sbisT
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   179
      ||>> mk_Frees' "rec" hrecTs
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   180
      ||>> yield_singleton (apfst (op ~~) oo mk_Frees' "n") HOLogic.natT
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   181
      ||>> mk_Frees "R" setRTs
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   182
      ||>> mk_Frees "R" setRTs
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   183
      ||>> mk_Frees "R'" setR'Ts
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   184
      ||>> mk_Frees "R" setsRTs
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   185
      ||>> yield_singleton (apfst (op ~~) oo mk_Frees' "i") idxT
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   186
      ||>> yield_singleton (mk_Frees "I") (HOLogic.mk_setT idxT)
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   187
      ||>> mk_Frees "Ri" (map (fn T => idxT --> T) setRTs)
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   188
      ||>> mk_Freess "K" (map (fn AT => map (fn T => T --> AT) activeAs) ATs);
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   189
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   190
    val passive_UNIVs = map HOLogic.mk_UNIV passiveAs;
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   191
    val passive_diags = map mk_diag As;
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   192
    val active_UNIVs = map HOLogic.mk_UNIV activeAs;
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   193
    val sum_UNIVs = map HOLogic.mk_UNIV sumBsAs;
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   194
    val passive_ids = map HOLogic.id_const passiveAs;
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   195
    val active_ids = map HOLogic.id_const activeAs;
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   196
    val Inls = map2 Inl_const activeBs activeAs;
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   197
    val fsts = map fst_const RTs;
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   198
    val snds = map snd_const RTs;
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   199
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   200
    (* thms *)
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   201
    val bd_card_orders = map bd_card_order_of_bnf bnfs;
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   202
    val bd_card_order = hd bd_card_orders
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   203
    val bd_Card_orders = map bd_Card_order_of_bnf bnfs;
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   204
    val bd_Card_order = hd bd_Card_orders;
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   205
    val bd_Cinfinites = map bd_Cinfinite_of_bnf bnfs;
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   206
    val bd_Cinfinite = hd bd_Cinfinites;
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   207
    val bd_Cnotzeros = map bd_Cnotzero_of_bnf bnfs;
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   208
    val bd_Cnotzero = hd bd_Cnotzeros;
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   209
    val in_bds = map in_bd_of_bnf bnfs;
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   210
    val in_monos = map in_mono_of_bnf bnfs;
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   211
    val map_comps = map map_comp_of_bnf bnfs;
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   212
    val map_comp's = map map_comp'_of_bnf bnfs;
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   213
    val map_congs = map map_cong_of_bnf bnfs;
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   214
    val map_id's = map map_id'_of_bnf bnfs;
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   215
    val pred_defs = map pred_def_of_bnf bnfs;
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   216
    val rel_congs = map rel_cong_of_bnf bnfs;
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   217
    val rel_converses = map rel_converse_of_bnf bnfs;
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   218
    val rel_defs = map rel_def_of_bnf bnfs;
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   219
    val rel_Grs = map rel_Gr_of_bnf bnfs;
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   220
    val rel_Ids = map rel_Id_of_bnf bnfs;
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   221
    val rel_monos = map rel_mono_of_bnf bnfs;
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   222
    val rel_Os = map rel_O_of_bnf bnfs;
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   223
    val map_wpulls = map map_wpull_of_bnf bnfs;
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   224
    val set_bdss = map set_bd_of_bnf bnfs;
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   225
    val set_natural'ss = map set_natural'_of_bnf bnfs;
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   226
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   227
    val timer = time (timer "Extracted terms & thms");
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   228
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    (* derived thms *)
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   230
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    (*map g1 ... gm g(m+1) ... g(m+n) (map id ... id f(m+1) ... f(m+n) x)=
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      map g1 ... gm (g(m+1) o f(m+1)) ... (g(m+n) o f(m+n)) x*)
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    fun mk_map_comp_id x mapAsBs mapBsCs mapAsCs map_comp =
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      let
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        val lhs = Term.list_comb (mapBsCs, all_gs) $
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          (Term.list_comb (mapAsBs, passive_ids @ fs) $ x);
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        val rhs =
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          Term.list_comb (mapAsCs, take m all_gs @ map HOLogic.mk_comp (drop m all_gs ~~ fs)) $ x;
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      in
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        Skip_Proof.prove lthy [] []
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          (fold_rev Logic.all (x :: fs @ all_gs) (mk_Trueprop_eq (lhs, rhs)))
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          (K (mk_map_comp_id_tac map_comp))
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        |> Thm.close_derivation
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      end;
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    val map_comp_id_thms = map5 mk_map_comp_id xFs mapsAsBs mapsBsCs' mapsAsCs' map_comp's;
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    (*forall a : set(m+1) x. f(m+1) a = a; ...; forall a : set(m+n) x. f(m+n) a = a ==>
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      map id ... id f(m+1) ... f(m+n) x = x*)
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    fun mk_map_congL x mapAsAs sets map_cong map_id' =
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      let
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        fun mk_prem set f z z' =
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          HOLogic.mk_Trueprop
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            (mk_Ball (set $ x) (Term.absfree z' (HOLogic.mk_eq (f $ z, z))));
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        val prems = map4 mk_prem (drop m sets) self_fs zs zs';
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        val goal = mk_Trueprop_eq (Term.list_comb (mapAsAs, passive_ids @ self_fs) $ x, x);
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      in
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        Skip_Proof.prove lthy [] []
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          (fold_rev Logic.all (x :: self_fs) (Logic.list_implies (prems, goal)))
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          (K (mk_map_congL_tac m map_cong map_id'))
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        |> Thm.close_derivation
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      end;
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    val map_congL_thms = map5 mk_map_congL xFs mapsAsAs setssAs map_congs map_id's;
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    val in_mono'_thms = map (fn thm =>
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      (thm OF (replicate m subset_refl)) RS @{thm set_mp}) in_monos;
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    val in_cong'_thms = map (fn bnf => in_cong_of_bnf bnf OF (replicate m refl)) bnfs;
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    val map_arg_cong_thms =
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      let
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        val prems = map2 (curry mk_Trueprop_eq) xFs xFs_copy;
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        val maps = map (fn map => Term.list_comb (map, all_fs)) mapsAsBs;
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        val concls =
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          map3 (fn x => fn y => fn map => mk_Trueprop_eq (map $ x, map $ y)) xFs xFs_copy maps;
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        val goals =
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          map4 (fn prem => fn concl => fn x => fn y =>
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            fold_rev Logic.all (x :: y :: all_fs) (Logic.mk_implies (prem, concl)))
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          prems concls xFs xFs_copy;
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      in
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        map (fn goal => Skip_Proof.prove lthy [] [] goal
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          (K ((hyp_subst_tac THEN' rtac refl) 1)) |> Thm.close_derivation) goals
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      end;
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    val timer = time (timer "Derived simple theorems");
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    (* coalgebra *)
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    val coalg_bind = Binding.suffix_name ("_" ^ coN ^ algN) b;
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    val coalg_name = Binding.name_of coalg_bind;
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    val coalg_def_bind = (Thm.def_binding coalg_bind, []);
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    (*forall i = 1 ... n: (\<forall>x \<in> Bi. si \<in> Fi_in A1 .. Am B1 ... Bn)*)
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    val coalg_spec =
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      let
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        val coalgT = Library.foldr (op -->) (ATs @ BTs @ sTs, HOLogic.boolT);
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        val ins = map3 mk_in (replicate n (As @ Bs)) setssAs FTsAs;
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        fun mk_coalg_conjunct B s X z z' =
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          mk_Ball B (Term.absfree z' (HOLogic.mk_mem (s $ z, X)));
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        val lhs = Term.list_comb (Free (coalg_name, coalgT), As @ Bs @ ss);
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        val rhs = Library.foldr1 HOLogic.mk_conj (map5 mk_coalg_conjunct Bs ss ins zs zs')
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      in
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        mk_Trueprop_eq (lhs, rhs)
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      end;
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    val ((coalg_free, (_, coalg_def_free)), (lthy, lthy_old)) =
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        lthy
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        |> Specification.definition (SOME (coalg_bind, NONE, NoSyn), (coalg_def_bind, coalg_spec))
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        ||> `Local_Theory.restore;
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    (*transforms defined frees into consts*)
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    val phi = Proof_Context.export_morphism lthy_old lthy;
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    val coalg = fst (Term.dest_Const (Morphism.term phi coalg_free));
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    val coalg_def = Morphism.thm phi coalg_def_free;
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    fun mk_coalg As Bs ss =
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      let
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        val args = As @ Bs @ ss;
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        val Ts = map fastype_of args;
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        val coalgT = Library.foldr (op -->) (Ts, HOLogic.boolT);
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      in
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        Term.list_comb (Const (coalg, coalgT), args)
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      end;
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    val coalg_prem = HOLogic.mk_Trueprop (mk_coalg As Bs ss);
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    val coalg_in_thms = map (fn i =>
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      coalg_def RS @{thm subst[of _ _ "%x. x"]} RS mk_conjunctN n i RS bspec) ks
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    val coalg_set_thmss =
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      let
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        val coalg_prem = HOLogic.mk_Trueprop (mk_coalg As Bs ss);
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        fun mk_prem x B = HOLogic.mk_Trueprop (HOLogic.mk_mem (x, B));
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        fun mk_concl s x B set = HOLogic.mk_Trueprop (mk_subset (set $ (s $ x)) B);
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        val prems = map2 mk_prem zs Bs;
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        val conclss = map3 (fn s => fn x => fn sets => map2 (mk_concl s x) (As @ Bs) sets)
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          ss zs setssAs;
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        val goalss = map3 (fn x => fn prem => fn concls => map (fn concl =>
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          fold_rev Logic.all (x :: As @ Bs @ ss)
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            (Logic.list_implies (coalg_prem :: [prem], concl))) concls) zs prems conclss;
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      in
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        map (fn goals => map (fn goal => Skip_Proof.prove lthy [] [] goal
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          (K (mk_coalg_set_tac coalg_def)) |> Thm.close_derivation) goals) goalss
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      end;
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parents:
diff changeset
   346
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
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parents:
diff changeset
   347
    val coalg_set_thmss' = transpose coalg_set_thmss;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
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parents:
diff changeset
   348
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
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parents:
diff changeset
   349
    fun mk_tcoalg ATs BTs = mk_coalg (map HOLogic.mk_UNIV ATs) (map HOLogic.mk_UNIV BTs);
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parents:
diff changeset
   350
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
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parents:
diff changeset
   351
    val tcoalg_thm =
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
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parents:
diff changeset
   352
      let
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
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parents:
diff changeset
   353
        val goal = fold_rev Logic.all ss
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
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parents:
diff changeset
   354
          (HOLogic.mk_Trueprop (mk_tcoalg passiveAs activeAs ss))
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
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parents:
diff changeset
   355
      in
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
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parents:
diff changeset
   356
        Skip_Proof.prove lthy [] [] goal
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
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parents:
diff changeset
   357
          (K (stac coalg_def 1 THEN CONJ_WRAP
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
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parents:
diff changeset
   358
            (K (EVERY' [rtac ballI, rtac CollectI,
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
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parents:
diff changeset
   359
              CONJ_WRAP' (K (EVERY' [rtac @{thm subset_UNIV}])) allAs] 1)) ss))
49109
0e5b859e1c91 no more aliases for Local_Theory.note; use Thm.close_derivation in internal theorems;
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parents: 49105
diff changeset
   360
        |> Thm.close_derivation
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
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diff changeset
   361
      end;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
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parents:
diff changeset
   362
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
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parents:
diff changeset
   363
    val timer = time (timer "Coalgebra definition & thms");
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
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parents:
diff changeset
   364
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   365
    (* morphism *)
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
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parents:
diff changeset
   366
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
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parents:
diff changeset
   367
    val mor_bind = Binding.suffix_name ("_" ^ morN) b;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
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parents:
diff changeset
   368
    val mor_name = Binding.name_of mor_bind;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
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parents:
diff changeset
   369
    val mor_def_bind = (Thm.def_binding mor_bind, []);
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
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parents:
diff changeset
   370
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
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parents:
diff changeset
   371
    (*fbetw) forall i = 1 ... n: (\<forall>x \<in> Bi. fi x \<in> B'i)*)
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
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parents:
diff changeset
   372
    (*mor) forall i = 1 ... n: (\<forall>x \<in> Bi.
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
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parents:
diff changeset
   373
       Fi_map id ... id f1 ... fn (si x) = si' (fi x)*)
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
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parents:
diff changeset
   374
    val mor_spec =
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
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parents:
diff changeset
   375
      let
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
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parents:
diff changeset
   376
        val morT = Library.foldr (op -->) (BTs @ sTs @ B'Ts @ s'Ts @ fTs, HOLogic.boolT);
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
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parents:
diff changeset
   377
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
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parents:
diff changeset
   378
        fun mk_fbetw f B1 B2 z z' =
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
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parents:
diff changeset
   379
          mk_Ball B1 (Term.absfree z' (HOLogic.mk_mem (f $ z, B2)));
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   380
        fun mk_mor B mapAsBs f s s' z z' =
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
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parents:
diff changeset
   381
          mk_Ball B (Term.absfree z' (HOLogic.mk_eq
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
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parents:
diff changeset
   382
            (Term.list_comb (mapAsBs, passive_ids @ fs @ [s $ z]), s' $ (f $ z))));
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   383
        val lhs = Term.list_comb (Free (mor_name, morT), Bs @ ss @ B's @ s's @ fs);
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   384
        val rhs = HOLogic.mk_conj
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   385
          (Library.foldr1 HOLogic.mk_conj (map5 mk_fbetw fs Bs B's zs zs'),
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   386
           Library.foldr1 HOLogic.mk_conj (map7 mk_mor Bs mapsAsBs fs ss s's zs zs'))
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   387
      in
49123
263b0e330d8b more work on sugar + simplify Trueprop + eq idiom everywhere
blanchet
parents: 49121
diff changeset
   388
        mk_Trueprop_eq (lhs, rhs)
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   389
      end;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   390
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   391
    val ((mor_free, (_, mor_def_free)), (lthy, lthy_old)) =
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
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parents:
diff changeset
   392
        lthy
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   393
        |> Specification.definition (SOME (mor_bind, NONE, NoSyn), (mor_def_bind, mor_spec))
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
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parents:
diff changeset
   394
        ||> `Local_Theory.restore;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   395
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   396
    (*transforms defined frees into consts*)
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   397
    val phi = Proof_Context.export_morphism lthy_old lthy;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   398
    val mor = fst (Term.dest_Const (Morphism.term phi mor_free));
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   399
    val mor_def = Morphism.thm phi mor_def_free;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   400
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   401
    fun mk_mor Bs1 ss1 Bs2 ss2 fs =
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   402
      let
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   403
        val args = Bs1 @ ss1 @ Bs2 @ ss2 @ fs;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   404
        val Ts = map fastype_of (Bs1 @ ss1 @ Bs2 @ ss2 @ fs);
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   405
        val morT = Library.foldr (op -->) (Ts, HOLogic.boolT);
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   406
      in
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   407
        Term.list_comb (Const (mor, morT), args)
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   408
      end;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   409
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   410
    val mor_prem = HOLogic.mk_Trueprop (mk_mor Bs ss B's s's fs);
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   411
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   412
    val (mor_image_thms, morE_thms) =
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   413
      let
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   414
        val prem = HOLogic.mk_Trueprop (mk_mor Bs ss B's s's fs);
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   415
        fun mk_image_goal f B1 B2 = fold_rev Logic.all (Bs @ ss @ B's @ s's @ fs)
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   416
          (Logic.mk_implies (prem, HOLogic.mk_Trueprop (mk_subset (mk_image f $ B1) B2)));
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   417
        val image_goals = map3 mk_image_goal fs Bs B's;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   418
        fun mk_elim_goal B mapAsBs f s s' x =
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   419
          fold_rev Logic.all (x :: Bs @ ss @ B's @ s's @ fs)
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   420
            (Logic.list_implies ([prem, HOLogic.mk_Trueprop (HOLogic.mk_mem (x, B))],
49123
263b0e330d8b more work on sugar + simplify Trueprop + eq idiom everywhere
blanchet
parents: 49121
diff changeset
   421
              mk_Trueprop_eq (Term.list_comb (mapAsBs, passive_ids @ fs @ [s $ x]), s' $ (f $ x))));
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   422
        val elim_goals = map6 mk_elim_goal Bs mapsAsBs fs ss s's zs;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   423
        fun prove goal =
49109
0e5b859e1c91 no more aliases for Local_Theory.note; use Thm.close_derivation in internal theorems;
traytel
parents: 49105
diff changeset
   424
          Skip_Proof.prove lthy [] [] goal (K (mk_mor_elim_tac mor_def))
0e5b859e1c91 no more aliases for Local_Theory.note; use Thm.close_derivation in internal theorems;
traytel
parents: 49105
diff changeset
   425
          |> Thm.close_derivation;
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   426
      in
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   427
        (map prove image_goals, map prove elim_goals)
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   428
      end;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   429
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   430
    val mor_image'_thms = map (fn thm => @{thm set_mp} OF [thm, imageI]) mor_image_thms;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   431
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   432
    val mor_incl_thm =
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   433
      let
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   434
        val prems = map2 (HOLogic.mk_Trueprop oo mk_subset) Bs Bs_copy;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   435
        val concl = HOLogic.mk_Trueprop (mk_mor Bs ss Bs_copy ss active_ids);
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   436
      in
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   437
        Skip_Proof.prove lthy [] []
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   438
          (fold_rev Logic.all (Bs @ ss @ Bs_copy) (Logic.list_implies (prems, concl)))
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   439
          (K (mk_mor_incl_tac mor_def map_id's))
49109
0e5b859e1c91 no more aliases for Local_Theory.note; use Thm.close_derivation in internal theorems;
traytel
parents: 49105
diff changeset
   440
        |> Thm.close_derivation
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   441
      end;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   442
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   443
    val mor_id_thm = mor_incl_thm OF (replicate n subset_refl);
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   444
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   445
    val mor_comp_thm =
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   446
      let
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   447
        val prems =
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   448
          [HOLogic.mk_Trueprop (mk_mor Bs ss B's s's fs),
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   449
           HOLogic.mk_Trueprop (mk_mor B's s's B''s s''s gs)];
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   450
        val concl =
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   451
          HOLogic.mk_Trueprop (mk_mor Bs ss B''s s''s (map2 (curry HOLogic.mk_comp) gs fs));
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   452
      in
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   453
        Skip_Proof.prove lthy [] []
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   454
          (fold_rev Logic.all (Bs @ ss @ B's @ s's @ B''s @ s''s @ fs @ gs)
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   455
            (Logic.list_implies (prems, concl)))
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   456
          (K (mk_mor_comp_tac mor_def mor_image'_thms morE_thms map_comp_id_thms))
49109
0e5b859e1c91 no more aliases for Local_Theory.note; use Thm.close_derivation in internal theorems;
traytel
parents: 49105
diff changeset
   457
        |> Thm.close_derivation
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   458
      end;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   459
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   460
    val mor_cong_thm =
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   461
      let
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   462
        val prems = map HOLogic.mk_Trueprop
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   463
         (map2 (curry HOLogic.mk_eq) fs_copy fs @ [mk_mor Bs ss B's s's fs])
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   464
        val concl = HOLogic.mk_Trueprop (mk_mor Bs ss B's s's fs_copy);
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   465
      in
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   466
        Skip_Proof.prove lthy [] []
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   467
          (fold_rev Logic.all (Bs @ ss @ B's @ s's @ fs @ fs_copy)
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   468
            (Logic.list_implies (prems, concl)))
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   469
          (K ((hyp_subst_tac THEN' atac) 1))
49109
0e5b859e1c91 no more aliases for Local_Theory.note; use Thm.close_derivation in internal theorems;
traytel
parents: 49105
diff changeset
   470
        |> Thm.close_derivation
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   471
      end;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   472
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   473
    val mor_UNIV_thm =
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   474
      let
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   475
        fun mk_conjunct mapAsBs f s s' = HOLogic.mk_eq
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   476
            (HOLogic.mk_comp (Term.list_comb (mapAsBs, passive_ids @ fs), s),
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   477
            HOLogic.mk_comp (s', f));
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   478
        val lhs = mk_mor active_UNIVs ss (map HOLogic.mk_UNIV activeBs) s's fs;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   479
        val rhs = Library.foldr1 HOLogic.mk_conj (map4 mk_conjunct mapsAsBs fs ss s's);
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   480
      in
49123
263b0e330d8b more work on sugar + simplify Trueprop + eq idiom everywhere
blanchet
parents: 49121
diff changeset
   481
        Skip_Proof.prove lthy [] [] (fold_rev Logic.all (ss @ s's @ fs) (mk_Trueprop_eq (lhs, rhs)))
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   482
          (K (mk_mor_UNIV_tac morE_thms mor_def))
49109
0e5b859e1c91 no more aliases for Local_Theory.note; use Thm.close_derivation in internal theorems;
traytel
parents: 49105
diff changeset
   483
        |> Thm.close_derivation
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   484
      end;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   485
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   486
    val mor_str_thm =
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   487
      let
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   488
        val maps = map2 (fn Ds => fn bnf => Term.list_comb
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   489
          (mk_map_of_bnf Ds allAs (passiveAs @ FTsAs) bnf, passive_ids @ ss)) Dss bnfs;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   490
      in
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   491
        Skip_Proof.prove lthy [] []
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   492
          (fold_rev Logic.all ss (HOLogic.mk_Trueprop
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   493
            (mk_mor active_UNIVs ss (map HOLogic.mk_UNIV FTsAs) maps ss)))
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   494
          (K (mk_mor_str_tac ks mor_UNIV_thm))
49109
0e5b859e1c91 no more aliases for Local_Theory.note; use Thm.close_derivation in internal theorems;
traytel
parents: 49105
diff changeset
   495
        |> Thm.close_derivation
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   496
      end;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   497
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   498
    val mor_sum_case_thm =
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   499
      let
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   500
        val maps = map3 (fn s => fn sum_s => fn map =>
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   501
          mk_sum_case (HOLogic.mk_comp (Term.list_comb (map, passive_ids @ Inls), s)) sum_s)
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   502
          s's sum_ss map_Inls;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   503
      in
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   504
        Skip_Proof.prove lthy [] []
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   505
          (fold_rev Logic.all (s's @ sum_ss) (HOLogic.mk_Trueprop
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   506
            (mk_mor (map HOLogic.mk_UNIV activeBs) s's sum_UNIVs maps Inls)))
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   507
          (K (mk_mor_sum_case_tac ks mor_UNIV_thm))
49109
0e5b859e1c91 no more aliases for Local_Theory.note; use Thm.close_derivation in internal theorems;
traytel
parents: 49105
diff changeset
   508
        |> Thm.close_derivation
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   509
      end;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   510
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   511
    val timer = time (timer "Morphism definition & thms");
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   512
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   513
    fun hset_rec_bind j = Binding.suffix_name ("_" ^ hset_recN ^ (if m = 1 then "" else
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   514
      string_of_int j)) b;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   515
    val hset_rec_name = Binding.name_of o hset_rec_bind;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   516
    val hset_rec_def_bind = rpair [] o Thm.def_binding o hset_rec_bind;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   517
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   518
    fun hset_rec_spec j Zero hsetT hrec hrec' =
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   519
      let
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   520
        fun mk_Suc s setsAs z z' =
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   521
          let
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   522
            val (set, sets) = apfst (fn xs => nth xs (j - 1)) (chop m setsAs);
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   523
            fun mk_UN set k = mk_UNION (set $ (s $ z)) (mk_nthN n hrec k);
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   524
          in
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   525
            Term.absfree z'
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   526
              (mk_union (set $ (s $ z), Library.foldl1 mk_union (map2 mk_UN sets ks)))
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   527
          end;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   528
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   529
        val Suc = Term.absdummy HOLogic.natT (Term.absfree hrec'
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   530
          (HOLogic.mk_tuple (map4 mk_Suc ss setssAs zs zs')));
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   531
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   532
        val lhs = Term.list_comb (Free (hset_rec_name j, hsetT), ss);
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   533
        val rhs = mk_nat_rec Zero Suc;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   534
      in
49123
263b0e330d8b more work on sugar + simplify Trueprop + eq idiom everywhere
blanchet
parents: 49121
diff changeset
   535
        mk_Trueprop_eq (lhs, rhs)
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   536
      end;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   537
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   538
    val ((hset_rec_frees, (_, hset_rec_def_frees)), (lthy, lthy_old)) =
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   539
      lthy
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   540
      |> fold_map5 (fn j => fn Zero => fn hsetT => fn hrec => fn hrec' => Specification.definition
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   541
        (SOME (hset_rec_bind j, NONE, NoSyn),
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   542
          (hset_rec_def_bind j, hset_rec_spec j Zero hsetT hrec hrec')))
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   543
        ls Zeros hsetTs hrecs hrecs'
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   544
      |>> apsnd split_list o split_list
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   545
      ||> `Local_Theory.restore;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   546
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   547
    (*transforms defined frees into consts*)
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   548
    val phi = Proof_Context.export_morphism lthy_old lthy;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   549
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   550
    val hset_rec_defs = map (Morphism.thm phi) hset_rec_def_frees;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   551
    val hset_recs = map (fst o Term.dest_Const o Morphism.term phi) hset_rec_frees;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   552
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   553
    fun mk_hset_rec ss nat i j T =
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   554
      let
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   555
        val args = ss @ [nat];
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   556
        val Ts = map fastype_of ss;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   557
        val bTs = map domain_type Ts;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   558
        val hrecT = HOLogic.mk_tupleT (map (fn U => U --> HOLogic.mk_setT T) bTs)
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   559
        val hset_recT = Library.foldr (op -->) (Ts, HOLogic.natT --> hrecT);
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   560
      in
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   561
        mk_nthN n (Term.list_comb (Const (nth hset_recs (j - 1), hset_recT), args)) i
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   562
      end;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   563
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   564
    val hset_rec_0ss = mk_rec_simps n @{thm nat_rec_0} hset_rec_defs;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   565
    val hset_rec_Sucss = mk_rec_simps n @{thm nat_rec_Suc} hset_rec_defs;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   566
    val hset_rec_0ss' = transpose hset_rec_0ss;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   567
    val hset_rec_Sucss' = transpose hset_rec_Sucss;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   568
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   569
    fun hset_bind i j = Binding.suffix_name ("_" ^ hsetN ^
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   570
      (if m = 1 then "" else string_of_int j)) (nth bs (i - 1));
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   571
    val hset_name = Binding.name_of oo hset_bind;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   572
    val hset_def_bind = rpair [] o Thm.def_binding oo hset_bind;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   573
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   574
    fun hset_spec i j =
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   575
      let
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   576
        val U = nth activeAs (i - 1);
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   577
        val z = nth zs (i - 1);
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   578
        val T = nth passiveAs (j - 1);
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   579
        val setT = HOLogic.mk_setT T;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   580
        val hsetT = Library.foldr (op -->) (sTs, U --> setT);
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   581
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   582
        val lhs = Term.list_comb (Free (hset_name i j, hsetT), ss @ [z]);
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   583
        val rhs = mk_UNION (HOLogic.mk_UNIV HOLogic.natT)
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   584
          (Term.absfree nat' (mk_hset_rec ss nat i j T $ z));
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   585
      in
49123
263b0e330d8b more work on sugar + simplify Trueprop + eq idiom everywhere
blanchet
parents: 49121
diff changeset
   586
        mk_Trueprop_eq (lhs, rhs)
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   587
      end;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   588
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   589
    val ((hset_frees, (_, hset_def_frees)), (lthy, lthy_old)) =
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   590
      lthy
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   591
      |> fold_map (fn i => fold_map (fn j => Specification.definition
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   592
        (SOME (hset_bind i j, NONE, NoSyn), (hset_def_bind i j, hset_spec i j))) ls) ks
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   593
      |>> map (apsnd split_list o split_list)
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   594
      |>> apsnd split_list o split_list
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   595
      ||> `Local_Theory.restore;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   596
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   597
    (*transforms defined frees into consts*)
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   598
    val phi = Proof_Context.export_morphism lthy_old lthy;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   599
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   600
    val hset_defss = map (map (Morphism.thm phi)) hset_def_frees;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   601
    val hset_defss' = transpose hset_defss;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   602
    val hset_namess = map (map (fst o Term.dest_Const o Morphism.term phi)) hset_frees;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   603
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   604
    fun mk_hset ss i j T =
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   605
      let
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   606
        val Ts = map fastype_of ss;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   607
        val bTs = map domain_type Ts;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   608
        val hsetT = Library.foldr (op -->) (Ts, nth bTs (i - 1) --> HOLogic.mk_setT T);
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   609
      in
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   610
        Term.list_comb (Const (nth (nth hset_namess (i - 1)) (j - 1), hsetT), ss)
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   611
      end;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   612
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   613
    val hsetssAs = map (fn i => map2 (mk_hset ss i) ls passiveAs) ks;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   614
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   615
    val (set_incl_hset_thmss, set_hset_incl_hset_thmsss) =
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   616
      let
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   617
        fun mk_set_incl_hset s x set hset = fold_rev Logic.all (x :: ss)
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   618
          (HOLogic.mk_Trueprop (mk_subset (set $ (s $ x)) (hset $ x)));
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   619
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   620
        fun mk_set_hset_incl_hset s x y set hset1 hset2 =
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   621
          fold_rev Logic.all (x :: y :: ss)
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   622
            (Logic.mk_implies (HOLogic.mk_Trueprop (HOLogic.mk_mem (x, set $ (s $ y))),
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   623
            HOLogic.mk_Trueprop (mk_subset (hset1 $ x) (hset2 $ y))));
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   624
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   625
        val set_incl_hset_goalss =
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   626
          map4 (fn s => fn x => fn sets => fn hsets =>
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   627
            map2 (mk_set_incl_hset s x) (take m sets) hsets)
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   628
          ss zs setssAs hsetssAs;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   629
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   630
        (*xk : F(i)set(m+k) (si yi) ==> F(k)_hset(j) s1 ... sn xk <= F(i)_hset(j) s1 ... sn yi*)
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   631
        val set_hset_incl_hset_goalsss =
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   632
          map4 (fn si => fn yi => fn sets => fn hsetsi =>
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   633
            map3 (fn xk => fn set => fn hsetsk =>
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   634
              map2 (mk_set_hset_incl_hset si xk yi set) hsetsk hsetsi)
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   635
            zs_copy (drop m sets) hsetssAs)
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   636
          ss zs setssAs hsetssAs;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   637
      in
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   638
        (map3 (fn goals => fn defs => fn rec_Sucs =>
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   639
          map3 (fn goal => fn def => fn rec_Suc =>
49109
0e5b859e1c91 no more aliases for Local_Theory.note; use Thm.close_derivation in internal theorems;
traytel
parents: 49105
diff changeset
   640
            Skip_Proof.prove lthy [] [] goal (K (mk_set_incl_hset_tac def rec_Suc))
0e5b859e1c91 no more aliases for Local_Theory.note; use Thm.close_derivation in internal theorems;
traytel
parents: 49105
diff changeset
   641
            |> Thm.close_derivation)
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   642
          goals defs rec_Sucs)
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   643
        set_incl_hset_goalss hset_defss hset_rec_Sucss,
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   644
        map3 (fn goalss => fn defsi => fn rec_Sucs =>
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   645
          map3 (fn k => fn goals => fn defsk =>
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   646
            map4 (fn goal => fn defk => fn defi => fn rec_Suc =>
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   647
              Skip_Proof.prove lthy [] [] goal
49109
0e5b859e1c91 no more aliases for Local_Theory.note; use Thm.close_derivation in internal theorems;
traytel
parents: 49105
diff changeset
   648
                (K (mk_set_hset_incl_hset_tac n [defk, defi] rec_Suc k))
0e5b859e1c91 no more aliases for Local_Theory.note; use Thm.close_derivation in internal theorems;
traytel
parents: 49105
diff changeset
   649
              |> Thm.close_derivation)
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   650
            goals defsk defsi rec_Sucs)
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   651
          ks goalss hset_defss)
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   652
        set_hset_incl_hset_goalsss hset_defss hset_rec_Sucss)
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   653
      end;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   654
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   655
    val set_incl_hset_thmss' = transpose set_incl_hset_thmss;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   656
    val set_hset_incl_hset_thmsss' = transpose (map transpose set_hset_incl_hset_thmsss);
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   657
    val set_hset_incl_hset_thmsss'' = map transpose set_hset_incl_hset_thmsss';
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   658
    val set_hset_thmss = map (map (fn thm => thm RS @{thm set_mp})) set_incl_hset_thmss;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   659
    val set_hset_hset_thmsss = map (map (map (fn thm => thm RS @{thm set_mp})))
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   660
      set_hset_incl_hset_thmsss;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   661
    val set_hset_thmss' = transpose set_hset_thmss;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   662
    val set_hset_hset_thmsss' = transpose (map transpose set_hset_hset_thmsss);
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   663
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   664
    val set_incl_hin_thmss =
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   665
      let
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   666
        fun mk_set_incl_hin s x hsets1 set hsets2 T =
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   667
          fold_rev Logic.all (x :: ss @ As)
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   668
            (Logic.list_implies
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   669
              (map2 (fn hset => fn A => HOLogic.mk_Trueprop (mk_subset (hset $ x) A)) hsets1 As,
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   670
              HOLogic.mk_Trueprop (mk_subset (set $ (s $ x)) (mk_in As hsets2 T))));
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   671
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   672
        val set_incl_hin_goalss =
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   673
          map4 (fn s => fn x => fn sets => fn hsets =>
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   674
            map3 (mk_set_incl_hin s x hsets) (drop m sets) hsetssAs activeAs)
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   675
          ss zs setssAs hsetssAs;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   676
      in
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   677
        map2 (map2 (fn goal => fn thms =>
49109
0e5b859e1c91 no more aliases for Local_Theory.note; use Thm.close_derivation in internal theorems;
traytel
parents: 49105
diff changeset
   678
          Skip_Proof.prove lthy [] [] goal (K (mk_set_incl_hin_tac thms))
0e5b859e1c91 no more aliases for Local_Theory.note; use Thm.close_derivation in internal theorems;
traytel
parents: 49105
diff changeset
   679
          |> Thm.close_derivation))
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   680
        set_incl_hin_goalss set_hset_incl_hset_thmsss
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   681
      end;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   682
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   683
    val hset_minimal_thms =
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   684
      let
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   685
        fun mk_passive_prem set s x K =
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   686
          Logic.all x (HOLogic.mk_Trueprop (mk_subset (set $ (s $ x)) (K $ x)));
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   687
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   688
        fun mk_active_prem s x1 K1 set x2 K2 =
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   689
          fold_rev Logic.all [x1, x2]
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   690
            (Logic.mk_implies (HOLogic.mk_Trueprop (HOLogic.mk_mem (x2, set $ (s $ x1))),
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   691
              HOLogic.mk_Trueprop (mk_subset (K2 $ x2) (K1 $ x1))));
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   692
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   693
        val premss = map2 (fn j => fn Ks =>
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   694
          map4 mk_passive_prem (map (fn xs => nth xs (j - 1)) setssAs) ss zs Ks @
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   695
            flat (map4 (fn sets => fn s => fn x1 => fn K1 =>
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   696
              map3 (mk_active_prem s x1 K1) (drop m sets) zs_copy Ks) setssAs ss zs Ks))
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   697
          ls Kss;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   698
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   699
        val hset_rec_minimal_thms =
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   700
          let
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   701
            fun mk_conjunct j T i K x = mk_subset (mk_hset_rec ss nat i j T $ x) (K $ x);
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   702
            fun mk_concl j T Ks = list_all_free zs
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   703
              (Library.foldr1 HOLogic.mk_conj (map3 (mk_conjunct j T) ks Ks zs));
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   704
            val concls = map3 mk_concl ls passiveAs Kss;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   705
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   706
            val goals = map2 (fn prems => fn concl =>
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   707
              Logic.list_implies (prems, HOLogic.mk_Trueprop concl)) premss concls
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   708
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   709
            val ctss =
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   710
              map (fn phi => map (SOME o certify lthy) [Term.absfree nat' phi, nat]) concls;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   711
          in
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   712
            map4 (fn goal => fn cts => fn hset_rec_0s => fn hset_rec_Sucs =>
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   713
              singleton (Proof_Context.export names_lthy lthy)
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   714
                (Skip_Proof.prove lthy [] [] goal
49109
0e5b859e1c91 no more aliases for Local_Theory.note; use Thm.close_derivation in internal theorems;
traytel
parents: 49105
diff changeset
   715
                  (mk_hset_rec_minimal_tac m cts hset_rec_0s hset_rec_Sucs))
0e5b859e1c91 no more aliases for Local_Theory.note; use Thm.close_derivation in internal theorems;
traytel
parents: 49105
diff changeset
   716
              |> Thm.close_derivation)
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   717
            goals ctss hset_rec_0ss' hset_rec_Sucss'
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   718
          end;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   719
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   720
        fun mk_conjunct j T i K x = mk_subset (mk_hset ss i j T $ x) (K $ x);
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   721
        fun mk_concl j T Ks = Library.foldr1 HOLogic.mk_conj (map3 (mk_conjunct j T) ks Ks zs);
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   722
        val concls = map3 mk_concl ls passiveAs Kss;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   723
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   724
        val goals = map3 (fn Ks => fn prems => fn concl =>
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   725
          fold_rev Logic.all (Ks @ ss @ zs)
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   726
            (Logic.list_implies (prems, HOLogic.mk_Trueprop concl))) Kss premss concls;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   727
      in
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   728
        map3 (fn goal => fn hset_defs => fn hset_rec_minimal =>
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   729
          Skip_Proof.prove lthy [] [] goal
49109
0e5b859e1c91 no more aliases for Local_Theory.note; use Thm.close_derivation in internal theorems;
traytel
parents: 49105
diff changeset
   730
            (mk_hset_minimal_tac n hset_defs hset_rec_minimal)
0e5b859e1c91 no more aliases for Local_Theory.note; use Thm.close_derivation in internal theorems;
traytel
parents: 49105
diff changeset
   731
          |> Thm.close_derivation)
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   732
        goals hset_defss' hset_rec_minimal_thms
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   733
      end;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   734
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   735
    val mor_hset_thmss =
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   736
      let
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   737
        val mor_hset_rec_thms =
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   738
          let
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   739
            fun mk_conjunct j T i f x B =
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   740
              HOLogic.mk_imp (HOLogic.mk_mem (x, B), HOLogic.mk_eq
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   741
               (mk_hset_rec s's nat i j T $ (f $ x), mk_hset_rec ss nat i j T $ x));
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   742
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   743
            fun mk_concl j T = list_all_free zs
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   744
              (Library.foldr1 HOLogic.mk_conj (map4 (mk_conjunct j T) ks fs zs Bs));
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   745
            val concls = map2 mk_concl ls passiveAs;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   746
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   747
            val ctss =
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   748
              map (fn phi => map (SOME o certify lthy) [Term.absfree nat' phi, nat]) concls;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   749
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   750
            val goals = map (fn concl =>
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   751
              Logic.list_implies ([coalg_prem, mor_prem], HOLogic.mk_Trueprop concl)) concls;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   752
          in
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   753
            map5 (fn j => fn goal => fn cts => fn hset_rec_0s => fn hset_rec_Sucs =>
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   754
              singleton (Proof_Context.export names_lthy lthy)
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   755
                (Skip_Proof.prove lthy [] [] goal
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   756
                  (K (mk_mor_hset_rec_tac m n cts j hset_rec_0s hset_rec_Sucs
49109
0e5b859e1c91 no more aliases for Local_Theory.note; use Thm.close_derivation in internal theorems;
traytel
parents: 49105
diff changeset
   757
                    morE_thms set_natural'ss coalg_set_thmss)))
0e5b859e1c91 no more aliases for Local_Theory.note; use Thm.close_derivation in internal theorems;
traytel
parents: 49105
diff changeset
   758
              |> Thm.close_derivation)
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   759
            ls goals ctss hset_rec_0ss' hset_rec_Sucss'
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   760
          end;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   761
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   762
        val mor_hset_rec_thmss = map (fn thm => map (fn i =>
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   763
          mk_specN n thm RS mk_conjunctN n i RS mp) ks) mor_hset_rec_thms;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   764
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   765
        fun mk_prem x B = HOLogic.mk_Trueprop (HOLogic.mk_mem (x, B));
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   766
49123
263b0e330d8b more work on sugar + simplify Trueprop + eq idiom everywhere
blanchet
parents: 49121
diff changeset
   767
        fun mk_concl j T i f x =
263b0e330d8b more work on sugar + simplify Trueprop + eq idiom everywhere
blanchet
parents: 49121
diff changeset
   768
          mk_Trueprop_eq (mk_hset s's i j T $ (f $ x), mk_hset ss i j T $ x);
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   769
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   770
        val goalss = map2 (fn j => fn T => map4 (fn i => fn f => fn x => fn B =>
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   771
          fold_rev Logic.all (x :: As @ Bs @ ss @ B's @ s's @ fs)
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   772
            (Logic.list_implies ([coalg_prem, mor_prem,
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   773
              mk_prem x B], mk_concl j T i f x))) ks fs zs Bs) ls passiveAs;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   774
      in
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   775
        map3 (map3 (fn goal => fn hset_def => fn mor_hset_rec =>
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   776
          Skip_Proof.prove lthy [] [] goal
49109
0e5b859e1c91 no more aliases for Local_Theory.note; use Thm.close_derivation in internal theorems;
traytel
parents: 49105
diff changeset
   777
            (K (mk_mor_hset_tac hset_def mor_hset_rec))
0e5b859e1c91 no more aliases for Local_Theory.note; use Thm.close_derivation in internal theorems;
traytel
parents: 49105
diff changeset
   778
          |> Thm.close_derivation))
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   779
        goalss hset_defss' mor_hset_rec_thmss
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   780
      end;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   781
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   782
    val timer = time (timer "Hereditary sets");
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   783
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   784
    (* bisimulation *)
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   785
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   786
    val bis_bind = Binding.suffix_name ("_" ^ bisN) b;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   787
    val bis_name = Binding.name_of bis_bind;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   788
    val bis_def_bind = (Thm.def_binding bis_bind, []);
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   789
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   790
    fun mk_bis_le_conjunct R B1 B2 = mk_subset R (mk_Times (B1, B2));
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   791
    val bis_le = Library.foldr1 HOLogic.mk_conj (map3 mk_bis_le_conjunct Rs Bs B's)
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   792
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   793
    val bis_spec =
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   794
      let
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   795
        val bisT = Library.foldr (op -->) (ATs @ BTs @ sTs @ B'Ts @ s'Ts @ setRTs, HOLogic.boolT);
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   796
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   797
        val fst_args = passive_ids @ fsts;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   798
        val snd_args = passive_ids @ snds;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   799
        fun mk_bis R s s' b1 b2 RF map1 map2 sets =
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   800
          list_all_free [b1, b2] (HOLogic.mk_imp
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   801
            (HOLogic.mk_mem (HOLogic.mk_prod (b1, b2), R),
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   802
            mk_Bex (mk_in (As @ Rs) sets (snd (dest_Free RF))) (Term.absfree (dest_Free RF)
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   803
              (HOLogic.mk_conj
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   804
                (HOLogic.mk_eq (Term.list_comb (map1, fst_args) $ RF, s $ b1),
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   805
                HOLogic.mk_eq (Term.list_comb (map2, snd_args) $ RF, s' $ b2))))));
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   806
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   807
        val lhs = Term.list_comb (Free (bis_name, bisT), As @ Bs @ ss @ B's @ s's @ Rs);
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   808
        val rhs = HOLogic.mk_conj
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   809
          (bis_le, Library.foldr1 HOLogic.mk_conj
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   810
            (map9 mk_bis Rs ss s's zs z's RFs map_fsts map_snds bis_setss))
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   811
      in
49123
263b0e330d8b more work on sugar + simplify Trueprop + eq idiom everywhere
blanchet
parents: 49121
diff changeset
   812
        mk_Trueprop_eq (lhs, rhs)
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   813
      end;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   814
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   815
    val ((bis_free, (_, bis_def_free)), (lthy, lthy_old)) =
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   816
        lthy
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   817
        |> Specification.definition (SOME (bis_bind, NONE, NoSyn), (bis_def_bind, bis_spec))
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   818
        ||> `Local_Theory.restore;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   819
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   820
    (*transforms defined frees into consts*)
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   821
    val phi = Proof_Context.export_morphism lthy_old lthy;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   822
    val bis = fst (Term.dest_Const (Morphism.term phi bis_free));
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   823
    val bis_def = Morphism.thm phi bis_def_free;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   824
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   825
    fun mk_bis As Bs1 ss1 Bs2 ss2 Rs =
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   826
      let
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   827
        val args = As @ Bs1 @ ss1 @ Bs2 @ ss2 @ Rs;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   828
        val Ts = map fastype_of args;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   829
        val bisT = Library.foldr (op -->) (Ts, HOLogic.boolT);
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   830
      in
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   831
        Term.list_comb (Const (bis, bisT), args)
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   832
      end;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   833
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   834
    val bis_cong_thm =
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   835
      let
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   836
        val prems = map HOLogic.mk_Trueprop
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   837
         (mk_bis As Bs ss B's s's Rs :: map2 (curry HOLogic.mk_eq) Rs_copy Rs)
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   838
        val concl = HOLogic.mk_Trueprop (mk_bis As Bs ss B's s's Rs_copy);
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   839
      in
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   840
        Skip_Proof.prove lthy [] []
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   841
          (fold_rev Logic.all (As @ Bs @ ss @ B's @ s's @ Rs @ Rs_copy)
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   842
            (Logic.list_implies (prems, concl)))
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   843
          (K ((hyp_subst_tac THEN' atac) 1))
49109
0e5b859e1c91 no more aliases for Local_Theory.note; use Thm.close_derivation in internal theorems;
traytel
parents: 49105
diff changeset
   844
        |> Thm.close_derivation
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   845
      end;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   846
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   847
    val bis_rel_thm =
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   848
      let
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   849
        fun mk_conjunct R s s' b1 b2 rel =
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   850
          list_all_free [b1, b2] (HOLogic.mk_imp
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   851
            (HOLogic.mk_mem (HOLogic.mk_prod (b1, b2), R),
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   852
            HOLogic.mk_mem (HOLogic.mk_prod (s $ b1, s' $ b2),
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   853
              Term.list_comb (rel, passive_diags @ Rs))));
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   854
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   855
        val rhs = HOLogic.mk_conj
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   856
          (bis_le, Library.foldr1 HOLogic.mk_conj
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   857
            (map6 mk_conjunct Rs ss s's zs z's relsAsBs))
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   858
      in
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   859
        Skip_Proof.prove lthy [] []
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   860
          (fold_rev Logic.all (As @ Bs @ ss @ B's @ s's @ Rs)
49123
263b0e330d8b more work on sugar + simplify Trueprop + eq idiom everywhere
blanchet
parents: 49121
diff changeset
   861
            (mk_Trueprop_eq (mk_bis As Bs ss B's s's Rs, rhs)))
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   862
          (K (mk_bis_rel_tac m bis_def rel_defs map_comp's map_congs set_natural'ss))
49109
0e5b859e1c91 no more aliases for Local_Theory.note; use Thm.close_derivation in internal theorems;
traytel
parents: 49105
diff changeset
   863
        |> Thm.close_derivation
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   864
      end;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   865
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   866
    val bis_converse_thm =
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   867
      Skip_Proof.prove lthy [] []
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   868
        (fold_rev Logic.all (As @ Bs @ ss @ B's @ s's @ Rs)
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   869
          (Logic.mk_implies
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   870
            (HOLogic.mk_Trueprop (mk_bis As Bs ss B's s's Rs),
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   871
            HOLogic.mk_Trueprop (mk_bis As B's s's Bs ss (map mk_converse Rs)))))
49109
0e5b859e1c91 no more aliases for Local_Theory.note; use Thm.close_derivation in internal theorems;
traytel
parents: 49105
diff changeset
   872
        (K (mk_bis_converse_tac m bis_rel_thm rel_congs rel_converses))
0e5b859e1c91 no more aliases for Local_Theory.note; use Thm.close_derivation in internal theorems;
traytel
parents: 49105
diff changeset
   873
      |> Thm.close_derivation;
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   874
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   875
    val bis_O_thm =
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   876
      let
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   877
        val prems =
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   878
          [HOLogic.mk_Trueprop (mk_bis As Bs ss B's s's Rs),
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   879
           HOLogic.mk_Trueprop (mk_bis As B's s's B''s s''s R's)];
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   880
        val concl =
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   881
          HOLogic.mk_Trueprop (mk_bis As Bs ss B''s s''s (map2 (curry mk_rel_comp) Rs R's));
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   882
      in
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   883
        Skip_Proof.prove lthy [] []
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   884
          (fold_rev Logic.all (As @ Bs @ ss @ B's @ s's @ B''s @ s''s @ Rs @ R's)
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   885
            (Logic.list_implies (prems, concl)))
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   886
          (K (mk_bis_O_tac m bis_rel_thm rel_congs rel_Os))
49109
0e5b859e1c91 no more aliases for Local_Theory.note; use Thm.close_derivation in internal theorems;
traytel
parents: 49105
diff changeset
   887
        |> Thm.close_derivation
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   888
      end;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   889
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   890
    val bis_Gr_thm =
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   891
      let
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   892
        val concl =
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   893
          HOLogic.mk_Trueprop (mk_bis As Bs ss B's s's (map2 mk_Gr Bs fs));
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   894
      in
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   895
        Skip_Proof.prove lthy [] []
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   896
          (fold_rev Logic.all (As @ Bs @ ss @ B's @ s's @ fs)
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   897
            (Logic.list_implies ([coalg_prem, mor_prem], concl)))
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   898
          (mk_bis_Gr_tac bis_rel_thm rel_Grs mor_image_thms morE_thms coalg_in_thms)
49109
0e5b859e1c91 no more aliases for Local_Theory.note; use Thm.close_derivation in internal theorems;
traytel
parents: 49105
diff changeset
   899
        |> Thm.close_derivation
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   900
      end;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   901
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   902
    val bis_image2_thm = bis_cong_thm OF
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   903
      ((bis_O_thm OF [bis_Gr_thm RS bis_converse_thm, bis_Gr_thm]) ::
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   904
      replicate n @{thm image2_Gr});
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   905
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   906
    val bis_diag_thm = bis_cong_thm OF ((mor_id_thm RSN (2, bis_Gr_thm)) ::
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   907
      replicate n @{thm diag_Gr});
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   908
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   909
    val bis_Union_thm =
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   910
      let
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   911
        val prem =
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   912
          HOLogic.mk_Trueprop (mk_Ball Idx
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   913
            (Term.absfree idx' (mk_bis As Bs ss B's s's (map (fn R => R $ idx) Ris))));
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   914
        val concl =
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   915
          HOLogic.mk_Trueprop (mk_bis As Bs ss B's s's (map (mk_UNION Idx) Ris));
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   916
      in
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   917
        Skip_Proof.prove lthy [] []
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   918
          (fold_rev Logic.all (Idx :: As @ Bs @ ss @ B's @ s's @ Ris)
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   919
            (Logic.mk_implies (prem, concl)))
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   920
          (mk_bis_Union_tac bis_def in_mono'_thms)
49109
0e5b859e1c91 no more aliases for Local_Theory.note; use Thm.close_derivation in internal theorems;
traytel
parents: 49105
diff changeset
   921
        |> Thm.close_derivation
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   922
      end;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   923
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   924
    (* self-bisimulation *)
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   925
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   926
    fun mk_sbis As Bs ss Rs = mk_bis As Bs ss Bs ss Rs;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   927
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   928
    val sbis_prem = HOLogic.mk_Trueprop (mk_sbis As Bs ss sRs);
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   929
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   930
    (* largest self-bisimulation *)
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   931
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   932
    fun lsbis_bind i = Binding.suffix_name ("_" ^ lsbisN ^ (if n = 1 then "" else
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   933
      string_of_int i)) b;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   934
    val lsbis_name = Binding.name_of o lsbis_bind;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   935
    val lsbis_def_bind = rpair [] o Thm.def_binding o lsbis_bind;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   936
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   937
    val all_sbis = HOLogic.mk_Collect (fst Rtuple', snd Rtuple', list_exists_free sRs
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   938
      (HOLogic.mk_conj (HOLogic.mk_eq (Rtuple, HOLogic.mk_tuple sRs), mk_sbis As Bs ss sRs)));
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   939
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   940
    fun lsbis_spec i RT =
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   941
      let
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   942
        fun mk_lsbisT RT =
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   943
          Library.foldr (op -->) (map fastype_of (As @ Bs @ ss), RT);
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   944
        val lhs = Term.list_comb (Free (lsbis_name i, mk_lsbisT RT), As @ Bs @ ss);
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   945
        val rhs = mk_UNION all_sbis (Term.absfree Rtuple' (mk_nthN n Rtuple i));
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   946
      in
49123
263b0e330d8b more work on sugar + simplify Trueprop + eq idiom everywhere
blanchet
parents: 49121
diff changeset
   947
        mk_Trueprop_eq (lhs, rhs)
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   948
      end;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   949
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   950
    val ((lsbis_frees, (_, lsbis_def_frees)), (lthy, lthy_old)) =
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   951
      lthy
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   952
      |> fold_map2 (fn i => fn RT => Specification.definition
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   953
        (SOME (lsbis_bind i, NONE, NoSyn), (lsbis_def_bind i, lsbis_spec i RT))) ks setsRTs
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   954
      |>> apsnd split_list o split_list
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   955
      ||> `Local_Theory.restore;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   956
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   957
    (*transforms defined frees into consts*)
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   958
    val phi = Proof_Context.export_morphism lthy_old lthy;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   959
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   960
    val lsbis_defs = map (Morphism.thm phi) lsbis_def_frees;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   961
    val lsbiss = map (fst o Term.dest_Const o Morphism.term phi) lsbis_frees;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   962
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   963
    fun mk_lsbis As Bs ss i =
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   964
      let
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   965
        val args = As @ Bs @ ss;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   966
        val Ts = map fastype_of args;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   967
        val RT = mk_relT (`I (HOLogic.dest_setT (fastype_of (nth Bs (i - 1)))));
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   968
        val lsbisT = Library.foldr (op -->) (Ts, RT);
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   969
      in
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   970
        Term.list_comb (Const (nth lsbiss (i - 1), lsbisT), args)
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   971
      end;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   972
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   973
    val sbis_lsbis_thm =
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   974
      Skip_Proof.prove lthy [] []
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   975
        (fold_rev Logic.all (As @ Bs @ ss)
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   976
          (HOLogic.mk_Trueprop (mk_sbis As Bs ss (map (mk_lsbis As Bs ss) ks))))
49109
0e5b859e1c91 no more aliases for Local_Theory.note; use Thm.close_derivation in internal theorems;
traytel
parents: 49105
diff changeset
   977
        (K (mk_sbis_lsbis_tac lsbis_defs bis_Union_thm bis_cong_thm))
0e5b859e1c91 no more aliases for Local_Theory.note; use Thm.close_derivation in internal theorems;
traytel
parents: 49105
diff changeset
   978
      |> Thm.close_derivation;
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   979
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   980
    val lsbis_incl_thms = map (fn i => sbis_lsbis_thm RS
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   981
      (bis_def RS @{thm subst[of _ _ "%x. x"]} RS conjunct1 RS mk_conjunctN n i)) ks;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   982
    val lsbisE_thms = map (fn i => (mk_specN 2 (sbis_lsbis_thm RS
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   983
      (bis_def RS @{thm subst[of _ _ "%x. x"]} RS conjunct2 RS mk_conjunctN n i))) RS mp) ks;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   984
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   985
    val incl_lsbis_thms =
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   986
      let
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   987
        fun mk_concl i R = HOLogic.mk_Trueprop (mk_subset R (mk_lsbis As Bs ss i));
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   988
        val goals = map2 (fn i => fn R => fold_rev Logic.all (As @ Bs @ ss @ sRs)
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   989
          (Logic.mk_implies (sbis_prem, mk_concl i R))) ks sRs;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   990
      in
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   991
        map3 (fn goal => fn i => fn def => Skip_Proof.prove lthy [] [] goal
49109
0e5b859e1c91 no more aliases for Local_Theory.note; use Thm.close_derivation in internal theorems;
traytel
parents: 49105
diff changeset
   992
          (K (mk_incl_lsbis_tac n i def)) |> Thm.close_derivation) goals ks lsbis_defs
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   993
      end;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   994
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   995
    val equiv_lsbis_thms =
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   996
      let
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   997
        fun mk_concl i B = HOLogic.mk_Trueprop (mk_equiv B (mk_lsbis As Bs ss i));
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   998
        val goals = map2 (fn i => fn B => fold_rev Logic.all (As @ Bs @ ss)
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   999
          (Logic.mk_implies (coalg_prem, mk_concl i B))) ks Bs;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1000
      in
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1001
        map3 (fn goal => fn l_incl => fn incl_l =>
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1002
          Skip_Proof.prove lthy [] [] goal
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1003
            (K (mk_equiv_lsbis_tac sbis_lsbis_thm l_incl incl_l
49109
0e5b859e1c91 no more aliases for Local_Theory.note; use Thm.close_derivation in internal theorems;
traytel
parents: 49105
diff changeset
  1004
              bis_diag_thm bis_converse_thm bis_O_thm))
0e5b859e1c91 no more aliases for Local_Theory.note; use Thm.close_derivation in internal theorems;
traytel
parents: 49105
diff changeset
  1005
          |> Thm.close_derivation)
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1006
        goals lsbis_incl_thms incl_lsbis_thms
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1007
      end;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1008
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1009
    val timer = time (timer "Bisimulations");
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1010
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1011
    (* bounds *)
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1012
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1013
    val (lthy, sbd, sbdT,
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1014
      sbd_card_order, sbd_Cinfinite, sbd_Cnotzero, sbd_Card_order, set_sbdss, in_sbds) =
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1015
      if n = 1
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1016
      then (lthy, sum_bd, sum_bdT,
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1017
        bd_card_order, bd_Cinfinite, bd_Cnotzero, bd_Card_order, set_bdss, in_bds)
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1018
      else
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1019
        let
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1020
          val sbdT_bind = Binding.suffix_name ("_" ^ sum_bdTN) b;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1021
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1022
          val ((sbdT_name, (sbdT_glob_info, sbdT_loc_info)), lthy) =
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1023
            typedef true NONE (sbdT_bind, params, NoSyn)
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1024
              (HOLogic.mk_UNIV sum_bdT) NONE (EVERY' [rtac exI, rtac UNIV_I] 1) lthy;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1025
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1026
          val sbdT = Type (sbdT_name, params');
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1027
          val Abs_sbdT = Const (#Abs_name sbdT_glob_info, sum_bdT --> sbdT);
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1028
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1029
          val sbd_bind = Binding.suffix_name ("_" ^ sum_bdN) b;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1030
          val sbd_name = Binding.name_of sbd_bind;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1031
          val sbd_def_bind = (Thm.def_binding sbd_bind, []);
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1032
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1033
          val sbd_spec = HOLogic.mk_Trueprop
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1034
            (HOLogic.mk_eq (Free (sbd_name, mk_relT (`I sbdT)), mk_dir_image sum_bd Abs_sbdT));
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1035
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1036
          val ((sbd_free, (_, sbd_def_free)), (lthy, lthy_old)) =
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1037
            lthy
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1038
            |> Specification.definition (SOME (sbd_bind, NONE, NoSyn), (sbd_def_bind, sbd_spec))
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1039
            ||> `Local_Theory.restore;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1040
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1041
          (*transforms defined frees into consts*)
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1042
          val phi = Proof_Context.export_morphism lthy_old lthy;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1043
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1044
          val sbd_def = Morphism.thm phi sbd_def_free;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1045
          val sbd = Const (fst (Term.dest_Const (Morphism.term phi sbd_free)), mk_relT (`I sbdT));
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1046
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1047
          val sbdT_set_def = the (#set_def sbdT_loc_info);
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1048
          val sbdT_Abs_inject = #Abs_inject sbdT_loc_info;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1049
          val sbdT_Abs_cases = #Abs_cases sbdT_loc_info;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1050
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1051
          val Abs_sbdT_inj = mk_Abs_inj_thm sbdT_set_def sbdT_Abs_inject;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1052
          val Abs_sbdT_bij = mk_Abs_bij_thm lthy sbdT_set_def sbdT_Abs_inject sbdT_Abs_cases;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1053
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1054
          fun mk_sum_Cinfinite [thm] = thm
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1055
            | mk_sum_Cinfinite (thm :: thms) =
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1056
              @{thm Cinfinite_csum_strong} OF [thm, mk_sum_Cinfinite thms];
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1057
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1058
          val sum_Cinfinite = mk_sum_Cinfinite bd_Cinfinites;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1059
          val sum_Card_order = sum_Cinfinite RS conjunct2;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1060
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1061
          fun mk_sum_card_order [thm] = thm
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1062
            | mk_sum_card_order (thm :: thms) =
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1063
              @{thm card_order_csum} OF [thm, mk_sum_card_order thms];
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1064
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1065
          val sum_card_order = mk_sum_card_order bd_card_orders;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1066
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1067
          val sbd_ordIso = Local_Defs.fold lthy [sbd_def]
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1068
            (@{thm dir_image} OF [Abs_sbdT_inj, sum_Card_order]);
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1069
          val sbd_card_order =  Local_Defs.fold lthy [sbd_def]
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1070
            (@{thm card_order_dir_image} OF [Abs_sbdT_bij, sum_card_order]);
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1071
          val sbd_Cinfinite = @{thm Cinfinite_cong} OF [sbd_ordIso, sum_Cinfinite];
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1072
          val sbd_Cnotzero = sbd_Cinfinite RS @{thm Cinfinite_Cnotzero};
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1073
          val sbd_Card_order = sbd_Cinfinite RS conjunct2;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1074
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1075
          fun mk_set_sbd i bd_Card_order bds =
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1076
            map (fn thm => @{thm ordLeq_ordIso_trans} OF
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1077
              [bd_Card_order RS mk_ordLeq_csum n i thm, sbd_ordIso]) bds;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1078
          val set_sbdss = map3 mk_set_sbd ks bd_Card_orders set_bdss;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1079
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1080
          fun mk_in_sbd i Co Cnz bd =
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1081
            Cnz RS ((@{thm ordLeq_ordIso_trans} OF
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1082
              [(Co RS mk_ordLeq_csum n i (Co RS @{thm ordLeq_refl})), sbd_ordIso]) RS
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1083
              (bd RS @{thm ordLeq_transitive[OF _
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1084
                cexp_mono2_Cnotzero[OF _ csum_Cnotzero2[OF ctwo_Cnotzero]]]}));
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1085
          val in_sbds = map4 mk_in_sbd ks bd_Card_orders bd_Cnotzeros in_bds;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1086
       in
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1087
         (lthy, sbd, sbdT,
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1088
           sbd_card_order, sbd_Cinfinite, sbd_Cnotzero, sbd_Card_order, set_sbdss, in_sbds)
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1089
       end;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1090
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1091
    fun mk_sbd_sbd 1 = sbd_Card_order RS @{thm ordIso_refl}
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1092
      | mk_sbd_sbd n = @{thm csum_absorb1} OF
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1093
          [sbd_Cinfinite, mk_sbd_sbd (n - 1) RS @{thm ordIso_imp_ordLeq}];
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1094
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1095
    val sbd_sbd_thm = mk_sbd_sbd n;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1096
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1097
    val sbdTs = replicate n sbdT;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1098
    val sum_sbd = Library.foldr1 (uncurry mk_csum) (replicate n sbd);
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1099
    val sum_sbdT = mk_sumTN sbdTs;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1100
    val sum_sbd_listT = HOLogic.listT sum_sbdT;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1101
    val sum_sbd_list_setT = HOLogic.mk_setT sum_sbd_listT;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1102
    val bdTs = passiveAs @ replicate n sbdT;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1103
    val to_sbd_maps = map4 mk_map_of_bnf Dss Ass (replicate n bdTs) bnfs;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1104
    val bdFTs = mk_FTs bdTs;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1105
    val sbdFT = mk_sumTN bdFTs;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1106
    val treeT = HOLogic.mk_prodT (sum_sbd_list_setT, sum_sbd_listT --> sbdFT);
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1107
    val treeQT = HOLogic.mk_setT treeT;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1108
    val treeTs = passiveAs @ replicate n treeT;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1109
    val treeQTs = passiveAs @ replicate n treeQT;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1110
    val treeFTs = mk_FTs treeTs;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1111
    val tree_maps = map4 mk_map_of_bnf Dss (replicate n bdTs) (replicate n treeTs) bnfs;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1112
    val final_maps = map4 mk_map_of_bnf Dss (replicate n treeTs) (replicate n treeQTs) bnfs;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1113
    val tree_setss = mk_setss treeTs;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1114
    val isNode_setss = mk_setss (passiveAs @ replicate n sbdT);
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1115
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1116
    val root = HOLogic.mk_set sum_sbd_listT [HOLogic.mk_list sum_sbdT []];
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1117
    val Zero = HOLogic.mk_tuple (map (fn U => absdummy U root) activeAs);
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1118
    val Lev_recT = fastype_of Zero;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1119
    val LevT = Library.foldr (op -->) (sTs, HOLogic.natT --> Lev_recT);
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1120
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1121
    val Nil = HOLogic.mk_tuple (map3 (fn i => fn z => fn z'=>
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1122
      Term.absfree z' (mk_InN activeAs z i)) ks zs zs');
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1123
    val rv_recT = fastype_of Nil;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1124
    val rvT = Library.foldr (op -->) (sTs, sum_sbd_listT --> rv_recT);
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1125
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1126
    val (((((((((((sumx, sumx'), (kks, kks')), (kl, kl')), (kl_copy, kl'_copy)), (Kl, Kl')),
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1127
      (lab, lab')), (Kl_lab, Kl_lab')), xs), (Lev_rec, Lev_rec')), (rv_rec, rv_rec')),
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1128
      names_lthy) = names_lthy
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1129
      |> yield_singleton (apfst (op ~~) oo mk_Frees' "sumx") sum_sbdT
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1130
      ||>> mk_Frees' "k" sbdTs
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1131
      ||>> yield_singleton (apfst (op ~~) oo mk_Frees' "kl") sum_sbd_listT
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1132
      ||>> yield_singleton (apfst (op ~~) oo mk_Frees' "kl") sum_sbd_listT
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1133
      ||>> yield_singleton (apfst (op ~~) oo mk_Frees' "Kl") sum_sbd_list_setT
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1134
      ||>> yield_singleton (apfst (op ~~) oo mk_Frees' "lab") (sum_sbd_listT --> sbdFT)
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1135
      ||>> yield_singleton (apfst (op ~~) oo mk_Frees' "Kl_lab") treeT
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1136
      ||>> mk_Frees "x" bdFTs
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1137
      ||>> yield_singleton (apfst (op ~~) oo mk_Frees' "rec") Lev_recT
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1138
      ||>> yield_singleton (apfst (op ~~) oo mk_Frees' "rec") rv_recT;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1139
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1140
    val (k, k') = (hd kks, hd kks')
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1141
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1142
    val timer = time (timer "Bounds");
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1143
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1144
    (* tree coalgebra *)
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1145
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1146
    fun isNode_bind i = Binding.suffix_name ("_" ^ isNodeN ^ (if n = 1 then "" else
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1147
      string_of_int i)) b;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1148
    val isNode_name = Binding.name_of o isNode_bind;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1149
    val isNode_def_bind = rpair [] o Thm.def_binding o isNode_bind;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1150
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1151
    val isNodeT =
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1152
      Library.foldr (op -->) (map fastype_of (As @ [Kl, lab, kl]), HOLogic.boolT);
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1153
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1154
    val Succs = map3 (fn i => fn k => fn k' =>
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1155
      HOLogic.mk_Collect (fst k', snd k', HOLogic.mk_mem (mk_InN sbdTs k i, mk_Succ Kl kl)))
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1156
      ks kks kks';
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1157
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1158
    fun isNode_spec sets x i =
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1159
      let
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1160
        val (passive_sets, active_sets) = chop m (map (fn set => set $ x) sets);
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1161
        val lhs = Term.list_comb (Free (isNode_name i, isNodeT), As @ [Kl, lab, kl]);
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1162
        val rhs = list_exists_free [x]
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1163
          (Library.foldr1 HOLogic.mk_conj (HOLogic.mk_eq (lab $ kl, mk_InN bdFTs x i) ::
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1164
          map2 mk_subset passive_sets As @ map2 (curry HOLogic.mk_eq) active_sets Succs));
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1165
      in
49123
263b0e330d8b more work on sugar + simplify Trueprop + eq idiom everywhere
blanchet
parents: 49121
diff changeset
  1166
        mk_Trueprop_eq (lhs, rhs)
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1167
      end;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1168
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1169
    val ((isNode_frees, (_, isNode_def_frees)), (lthy, lthy_old)) =
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1170
      lthy
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1171
      |> fold_map3 (fn i => fn x => fn sets => Specification.definition
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1172
        (SOME (isNode_bind i, NONE, NoSyn), (isNode_def_bind i, isNode_spec sets x i)))
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1173
        ks xs isNode_setss
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1174
      |>> apsnd split_list o split_list
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1175
      ||> `Local_Theory.restore;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1176
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1177
    (*transforms defined frees into consts*)
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1178
    val phi = Proof_Context.export_morphism lthy_old lthy;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1179
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1180
    val isNode_defs = map (Morphism.thm phi) isNode_def_frees;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1181
    val isNodes = map (fst o Term.dest_Const o Morphism.term phi) isNode_frees;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1182
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1183
    fun mk_isNode As kl i =
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1184
      Term.list_comb (Const (nth isNodes (i - 1), isNodeT), As @ [Kl, lab, kl]);
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1185
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1186
    val isTree =
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1187
      let
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1188
        val empty = HOLogic.mk_mem (HOLogic.mk_list sum_sbdT [], Kl);
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1189
        val Field = mk_subset Kl (mk_Field (mk_clists sum_sbd));
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1190
        val prefCl = mk_prefCl Kl;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1191
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1192
        val tree = mk_Ball Kl (Term.absfree kl'
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1193
          (HOLogic.mk_conj
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1194
            (Library.foldr1 HOLogic.mk_disj (map (mk_isNode As kl) ks),
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1195
            Library.foldr1 HOLogic.mk_conj (map4 (fn Succ => fn i => fn k => fn k' =>
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1196
              mk_Ball Succ (Term.absfree k' (mk_isNode As
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1197
                (mk_append (kl, HOLogic.mk_list sum_sbdT [mk_InN sbdTs k i])) i)))
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1198
            Succs ks kks kks'))));
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1199
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1200
        val undef = list_all_free [kl] (HOLogic.mk_imp
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1201
          (HOLogic.mk_not (HOLogic.mk_mem (kl, Kl)),
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1202
          HOLogic.mk_eq (lab $ kl, mk_undefined sbdFT)));
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1203
      in
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1204
        Library.foldr1 HOLogic.mk_conj [empty, Field, prefCl, tree, undef]
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1205
      end;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1206
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1207
    fun carT_bind i = Binding.suffix_name ("_" ^ carTN ^ (if n = 1 then "" else
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1208
      string_of_int i)) b;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1209
    val carT_name = Binding.name_of o carT_bind;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1210
    val carT_def_bind = rpair [] o Thm.def_binding o carT_bind;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1211
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1212
    fun carT_spec i =
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1213
      let
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1214
        val carTT = Library.foldr (op -->) (ATs, HOLogic.mk_setT treeT);
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1215
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1216
        val lhs = Term.list_comb (Free (carT_name i, carTT), As);
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1217
        val rhs = HOLogic.mk_Collect (fst Kl_lab', snd Kl_lab', list_exists_free [Kl, lab]
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1218
          (HOLogic.mk_conj (HOLogic.mk_eq (Kl_lab, HOLogic.mk_prod (Kl, lab)),
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1219
            HOLogic.mk_conj (isTree, mk_isNode As (HOLogic.mk_list sum_sbdT []) i))));
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1220
      in
49123
263b0e330d8b more work on sugar + simplify Trueprop + eq idiom everywhere
blanchet
parents: 49121
diff changeset
  1221
        mk_Trueprop_eq (lhs, rhs)
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1222
      end;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1223
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1224
    val ((carT_frees, (_, carT_def_frees)), (lthy, lthy_old)) =
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1225
      lthy
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1226
      |> fold_map (fn i => Specification.definition
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1227
        (SOME (carT_bind i, NONE, NoSyn), (carT_def_bind i, carT_spec i))) ks
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1228
      |>> apsnd split_list o split_list
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1229
      ||> `Local_Theory.restore;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1230
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1231
    (*transforms defined frees into consts*)
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1232
    val phi = Proof_Context.export_morphism lthy_old lthy;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1233
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1234
    val carT_defs = map (Morphism.thm phi) carT_def_frees;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1235
    val carTs = map (fst o Term.dest_Const o Morphism.term phi) carT_frees;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1236
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1237
    fun mk_carT As i = Term.list_comb
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1238
      (Const (nth carTs (i - 1),
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1239
         Library.foldr (op -->) (map fastype_of As, HOLogic.mk_setT treeT)), As);
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1240
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1241
    fun strT_bind i = Binding.suffix_name ("_" ^ strTN ^ (if n = 1 then "" else
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1242
      string_of_int i)) b;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1243
    val strT_name = Binding.name_of o strT_bind;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1244
    val strT_def_bind = rpair [] o Thm.def_binding o strT_bind;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1245
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1246
    fun strT_spec mapFT FT i =
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1247
      let
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1248
        val strTT = treeT --> FT;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1249
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1250
        fun mk_f i k k' =
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1251
          let val in_k = mk_InN sbdTs k i;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1252
          in Term.absfree k' (HOLogic.mk_prod (mk_Shift Kl in_k, mk_shift lab in_k)) end;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1253
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1254
        val f = Term.list_comb (mapFT, passive_ids @ map3 mk_f ks kks kks');
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1255
        val (fTs1, fTs2) = apsnd tl (chop (i - 1) (map (fn T => T --> FT) bdFTs));
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1256
        val fs = map mk_undefined fTs1 @ (f :: map mk_undefined fTs2);
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1257
        val lhs = Free (strT_name i, strTT);
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1258
        val rhs = HOLogic.mk_split (Term.absfree Kl' (Term.absfree lab'
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1259
          (mk_sum_caseN fs $ (lab $ HOLogic.mk_list sum_sbdT []))));
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1260
      in
49123
263b0e330d8b more work on sugar + simplify Trueprop + eq idiom everywhere
blanchet
parents: 49121
diff changeset
  1261
        mk_Trueprop_eq (lhs, rhs)
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1262
      end;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1263
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1264
    val ((strT_frees, (_, strT_def_frees)), (lthy, lthy_old)) =
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1265
      lthy
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1266
      |> fold_map3 (fn i => fn mapFT => fn FT => Specification.definition
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1267
        (SOME (strT_bind i, NONE, NoSyn), (strT_def_bind i, strT_spec mapFT FT i)))
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1268
        ks tree_maps treeFTs
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1269
      |>> apsnd split_list o split_list
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1270
      ||> `Local_Theory.restore;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1271
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1272
    (*transforms defined frees into consts*)
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1273
    val phi = Proof_Context.export_morphism lthy_old lthy;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1274
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1275
    val strT_defs = map ((fn def => trans OF [def RS fun_cong, @{thm prod.cases}]) o
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1276
      Morphism.thm phi) strT_def_frees;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1277
    val strTs = map (fst o Term.dest_Const o Morphism.term phi) strT_frees;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1278
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1279
    fun mk_strT FT i = Const (nth strTs (i - 1), treeT --> FT);
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1280
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1281
    val carTAs = map (mk_carT As) ks;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1282
    val carTAs_copy = map (mk_carT As_copy) ks;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1283
    val strTAs = map2 mk_strT treeFTs ks;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1284
    val hset_strTss = map (fn i => map2 (mk_hset strTAs i) ls passiveAs) ks;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1285
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1286
    val coalgT_thm =
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1287
      Skip_Proof.prove lthy [] []
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1288
        (fold_rev Logic.all As (HOLogic.mk_Trueprop (mk_coalg As carTAs strTAs)))
49109
0e5b859e1c91 no more aliases for Local_Theory.note; use Thm.close_derivation in internal theorems;
traytel
parents: 49105
diff changeset
  1289
        (mk_coalgT_tac m (coalg_def :: isNode_defs @ carT_defs) strT_defs set_natural'ss)
0e5b859e1c91 no more aliases for Local_Theory.note; use Thm.close_derivation in internal theorems;
traytel
parents: 49105
diff changeset
  1290
      |> Thm.close_derivation;
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1291
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1292
    val card_of_carT_thms =
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1293
      let
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1294
        val lhs = mk_card_of
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1295
          (HOLogic.mk_Collect (fst Kl_lab', snd Kl_lab', list_exists_free [Kl, lab]
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1296
            (HOLogic.mk_conj (HOLogic.mk_eq (Kl_lab, HOLogic.mk_prod (Kl, lab)), isTree))));
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1297
        val rhs = mk_cexp
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1298
          (if m = 0 then ctwo else
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1299
            (mk_csum (Library.foldr1 (uncurry mk_csum) (map mk_card_of As)) ctwo))
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1300
            (mk_cexp sbd sbd);
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1301
        val card_of_carT =
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1302
          Skip_Proof.prove lthy [] []
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1303
            (fold_rev Logic.all As (HOLogic.mk_Trueprop (mk_ordLeq lhs rhs)))
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1304
            (K (mk_card_of_carT_tac m isNode_defs sbd_sbd_thm
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1305
              sbd_card_order sbd_Card_order sbd_Cinfinite sbd_Cnotzero in_sbds))
49109
0e5b859e1c91 no more aliases for Local_Theory.note; use Thm.close_derivation in internal theorems;
traytel
parents: 49105
diff changeset
  1306
          |> Thm.close_derivation
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1307
      in
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1308
        map (fn def => @{thm ordLeq_transitive[OF
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1309
          card_of_mono1[OF ord_eq_le_trans[OF _ Collect_restrict']]]} OF [def, card_of_carT])
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1310
        carT_defs
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1311
      end;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1312
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1313
    val carT_set_thmss =
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1314
      let
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1315
        val Kl_lab = HOLogic.mk_prod (Kl, lab);
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1316
        fun mk_goal carT strT set k i =
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1317
          fold_rev Logic.all (sumx :: Kl :: lab :: k :: kl :: As)
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1318
            (Logic.list_implies (map HOLogic.mk_Trueprop
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1319
              [HOLogic.mk_mem (Kl_lab, carT), HOLogic.mk_mem (mk_Cons sumx kl, Kl),
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1320
              HOLogic.mk_eq (sumx, mk_InN sbdTs k i)],
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1321
            HOLogic.mk_Trueprop (HOLogic.mk_mem
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents: