src/HOL/BNF/Tools/bnf_gfp_tactics.ML
author blanchet
Wed May 01 19:33:49 2013 +0200 (2013-05-01)
changeset 51850 106afdf5806c
parent 51798 ad3a241def73
child 51893 596baae88a88
permissions -rw-r--r--
renamed a few FP-related files, to make it clear that these are not the sum of LFP + GFP but rather shared basic libraries
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(*  Title:      HOL/BNF/Tools/bnf_gfp_tactics.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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Tactics for the codatatype construction.
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*)
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signature BNF_GFP_TACTICS =
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sig
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  val mk_Lev_sbd_tac: Proof.context -> cterm option list -> thm list -> thm list ->
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    thm list list -> tactic
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  val mk_bd_card_order_tac: thm -> tactic
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  val mk_bd_cinfinite_tac: thm -> tactic
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  val mk_bis_Gr_tac: thm -> thm list -> thm list -> thm list -> thm list ->
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    {prems: 'a, context: Proof.context} -> tactic
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  val mk_bis_O_tac: Proof.context -> int -> thm -> thm list -> thm list -> tactic
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  val mk_bis_Union_tac: thm -> thm list -> {prems: 'a, context: Proof.context} -> tactic
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  val mk_bis_converse_tac: int -> thm -> thm list -> thm list -> tactic
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  val mk_bis_srel_tac: Proof.context -> int -> thm -> thm list -> thm list -> thm list ->
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    thm list list -> tactic
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  val mk_carT_set_tac: int -> int -> thm -> thm -> thm -> thm ->
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    {prems: 'a, context: Proof.context} -> tactic
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  val mk_card_of_carT_tac: Proof.context -> int -> thm list -> thm -> thm -> thm -> thm -> thm ->
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    thm list -> tactic
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  val mk_coalgT_tac: int -> thm list -> thm list -> thm list list ->
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    {prems: 'a, context: Proof.context} -> tactic
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  val mk_coalg_final_tac: int -> thm -> thm list -> thm list -> thm list list -> thm list list ->
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    tactic
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  val mk_coalg_set_tac: thm -> tactic
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  val mk_coalg_thePull_tac: int -> thm -> thm list -> thm list list -> (int -> tactic) list ->
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    {prems: 'a, context: Proof.context} -> tactic
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  val mk_coind_wit_tac: thm -> thm list -> thm list -> thm list ->
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    {prems: 'a, context: Proof.context} -> tactic
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  val mk_col_bd_tac: int -> int -> cterm option list -> thm list -> thm list -> thm -> thm ->
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    thm list list -> tactic
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  val mk_col_natural_tac: cterm option list -> thm list -> thm list -> thm list -> thm list list ->
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    {prems: 'a, context: Proof.context} -> tactic
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  val mk_congruent_str_final_tac: int -> thm -> thm -> thm -> thm list -> tactic
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  val mk_corec_tac: int -> thm list -> thm -> thm -> thm list ->
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    {prems: 'a, context: Proof.context} -> tactic
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  val mk_corec_unique_mor_tac: thm list -> thm list -> thm -> {prems: 'a, context: Proof.context} ->
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    tactic
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  val mk_dtor_map_coinduct_tac: int -> int list -> thm -> thm -> tactic
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  val mk_dtor_map_strong_coinduct_tac: int list -> ctyp option list -> cterm option list -> thm ->
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    thm -> thm -> tactic
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  val mk_dtor_set_tac: int -> thm -> thm -> thm list -> tactic
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  val mk_dtor_srel_coinduct_tac: 'a list -> thm -> thm -> tactic
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  val mk_dtor_srel_strong_coinduct_tac: Proof.context -> int -> ctyp option list ->
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    cterm option list -> thm -> thm list -> thm list -> tactic
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  val mk_dtor_srel_tac: Proof.context -> thm list -> int -> thm -> thm -> thm -> thm -> thm list ->
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    thm -> thm -> thm list -> thm list -> thm list list -> tactic
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  val mk_dtor_o_ctor_tac: thm -> thm -> thm -> thm -> thm list ->
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    {prems: 'a, context: Proof.context} -> tactic
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  val mk_equiv_lsbis_tac: thm -> thm -> thm -> thm -> thm -> thm -> tactic
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  val mk_hset_minimal_tac: int -> thm list -> thm -> {prems: 'a, context: Proof.context} -> tactic
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  val mk_hset_rec_minimal_tac: int -> cterm option list -> thm list -> thm list ->
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    {prems: 'a, context: Proof.context} -> tactic
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  val mk_in_bd_tac: Proof.context -> thm -> thm list -> thm -> thm -> thm -> thm -> thm list ->
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    thm -> thm -> thm -> thm -> thm -> thm -> tactic
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  val mk_incl_lsbis_tac: int -> int -> thm -> tactic
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  val mk_isNode_hset_tac: int -> thm -> thm list -> {prems: 'a, context: Proof.context} -> tactic
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  val mk_length_Lev'_tac: thm -> tactic
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  val mk_length_Lev_tac: Proof.context -> cterm option list -> thm list -> thm list -> tactic
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  val mk_map_comp_tac: int -> int -> thm list -> thm list -> thm list -> thm -> tactic
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  val mk_mcong_tac: Proof.context -> int -> (int -> tactic) -> thm list -> thm list -> thm list ->
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    thm list list -> thm list list -> thm list list list -> tactic
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  val mk_map_id_tac: thm list -> thm -> thm -> tactic
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  val mk_map_tac: int -> int -> ctyp option -> thm -> thm -> thm -> tactic
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  val mk_dtor_map_unique_tac: thm -> thm list -> {prems: 'a, context: Proof.context} -> tactic
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  val mk_mor_Abs_tac: thm list -> thm list -> {prems: 'a, context: Proof.context} -> tactic
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  val mk_mor_Rep_tac: int -> thm list -> thm list -> thm list -> thm list list -> thm list ->
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    thm list -> {prems: 'a, context: Proof.context} -> tactic
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  val mk_mor_T_final_tac: thm -> thm list -> thm list -> tactic
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  val mk_mor_UNIV_tac: thm list -> thm -> tactic
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  val mk_mor_beh_tac: int -> thm -> thm -> thm list -> thm list -> thm list -> thm list ->
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    thm list list -> thm list list -> thm list -> thm list -> thm list -> thm list -> thm list ->
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    thm list -> thm list -> thm list -> thm list list -> thm list list list -> thm list list list ->
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    thm list list list -> thm list list -> thm list list -> thm list -> thm list -> thm list ->
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    {prems: 'a, context: Proof.context} -> tactic
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  val mk_mor_comp_tac: thm -> thm list -> thm list -> thm list -> tactic
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  val mk_mor_elim_tac: thm -> tactic
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  val mk_mor_hset_rec_tac: int -> int -> cterm option list -> int -> thm list -> thm list ->
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    thm list -> thm list list -> thm list list -> tactic
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  val mk_mor_hset_tac: thm -> thm -> tactic
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  val mk_mor_incl_tac: thm -> thm list -> tactic
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  val mk_mor_str_tac: 'a list -> thm -> tactic
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  val mk_mor_sum_case_tac: 'a list -> thm -> tactic
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  val mk_mor_thePull_fst_tac: int -> thm -> thm list -> thm list -> (int -> tactic) list ->
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    {prems: thm list, context: Proof.context} -> tactic
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  val mk_mor_thePull_snd_tac: int -> thm -> thm list -> thm list -> (int -> tactic) list ->
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    {prems: thm list, context: Proof.context} -> tactic
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  val mk_mor_thePull_pick_tac: thm -> thm list -> thm list ->
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    {prems: 'a, context: Proof.context} -> tactic
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  val mk_mor_unfold_tac: int -> thm -> thm list -> thm list -> thm list -> thm list -> thm list ->
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    thm list -> tactic
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  val mk_prefCl_Lev_tac: Proof.context -> cterm option list -> thm list -> thm list -> tactic
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  val mk_pickWP_assms_tac: thm list -> thm list -> thm -> (int -> tactic)
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  val mk_pick_col_tac: int -> int -> cterm option list -> thm list -> thm list -> thm list ->
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    thm list list -> thm list -> (int -> tactic) list -> {prems: 'a, context: Proof.context} ->
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    tactic
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  val mk_raw_coind_tac: thm -> thm -> thm -> thm -> thm -> thm -> thm -> thm -> thm -> thm list ->
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    thm list -> thm list -> thm -> thm list -> tactic
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  val mk_rv_last_tac: ctyp option list -> cterm option list -> thm list -> thm list -> tactic
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  val mk_sbis_lsbis_tac: Proof.context -> thm list -> thm -> thm -> tactic
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  val mk_set_Lev_tac: Proof.context -> cterm option list -> thm list -> thm list -> thm list ->
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    thm list -> thm list list -> tactic
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  val mk_set_bd_tac: thm -> thm -> thm -> tactic
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  val mk_set_hset_incl_hset_tac: int -> thm list -> thm -> int -> tactic
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  val mk_set_image_Lev_tac: Proof.context -> cterm option list -> thm list -> thm list ->
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    thm list -> thm list -> thm list list -> thm list list -> tactic
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  val mk_set_incl_hin_tac: thm list -> tactic
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  val mk_set_incl_hset_tac: thm -> thm -> tactic
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  val mk_set_le_tac: int -> thm -> thm list -> thm list list -> tactic
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  val mk_set_map_tac: thm -> thm -> tactic
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  val mk_set_rv_Lev_tac: Proof.context -> int -> cterm option list -> thm list -> thm list ->
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    thm list -> thm list -> thm list list -> thm list list -> tactic
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  val mk_strT_hset_tac: Proof.context -> int -> int -> int -> ctyp option list ->
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    ctyp option list -> cterm option list -> thm list -> thm list -> thm list -> thm list ->
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    thm list list -> thm list list -> thm list list -> thm -> thm list list -> tactic
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  val mk_unfold_unique_mor_tac: thm list -> thm -> thm -> thm list -> tactic
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  val mk_unique_mor_tac: thm list -> thm -> tactic
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  val mk_wit_tac: int -> thm list -> thm list -> thm list -> thm list ->
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    {prems: 'a, context: Proof.context} -> tactic
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  val mk_wpull_tac: int -> thm -> thm -> thm -> thm -> thm -> thm list -> thm list -> tactic
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end;
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structure BNF_GFP_Tactics : BNF_GFP_TACTICS =
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struct
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open BNF_Tactics
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open BNF_Util
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open BNF_FP_Util
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open BNF_GFP_Util
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val fst_convol_fun_cong_sym = @{thm fst_convol} RS fun_cong RS sym;
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val list_inject_iffD1 = @{thm list.inject[THEN iffD1]};
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val nat_induct = @{thm nat_induct};
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val o_apply_trans_sym = o_apply RS trans RS sym;
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val ord_eq_le_trans = @{thm ord_eq_le_trans};
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val ord_eq_le_trans_trans_fun_cong_image_id_id_apply =
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  @{thm ord_eq_le_trans[OF trans[OF fun_cong[OF image_id] id_apply]]};
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val ordIso_ordLeq_trans = @{thm ordIso_ordLeq_trans};
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val snd_convol_fun_cong_sym = @{thm snd_convol} RS fun_cong RS sym;
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val sum_case_weak_cong = @{thm sum_case_weak_cong};
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val trans_fun_cong_image_id_id_apply = @{thm trans[OF fun_cong[OF image_id] id_apply]};
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fun mk_coalg_set_tac coalg_def =
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  dtac (coalg_def RS iffD1) 1 THEN
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  REPEAT_DETERM (etac conjE 1) THEN
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  EVERY' [dtac @{thm rev_bspec}, atac] 1 THEN
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  REPEAT_DETERM (eresolve_tac [CollectE, conjE] 1) THEN atac 1;
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fun mk_mor_elim_tac mor_def =
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  (dtac (subst OF [mor_def]) THEN'
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  REPEAT o etac conjE THEN'
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  TRY o rtac @{thm image_subsetI} THEN'
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  etac bspec THEN'
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  atac) 1;
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fun mk_mor_incl_tac mor_def map_id's =
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  (stac mor_def THEN'
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  rtac conjI THEN'
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  CONJ_WRAP' (K (EVERY' [rtac ballI, etac set_mp, stac id_apply, atac])) map_id's THEN'
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  CONJ_WRAP' (fn thm =>
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   (EVERY' [rtac ballI, rtac (thm RS trans), rtac sym, rtac (id_apply RS arg_cong)])) map_id's) 1;
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fun mk_mor_comp_tac mor_def mor_images morEs map_comp_ids =
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  let
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    fun fbetw_tac image = EVERY' [rtac ballI, stac o_apply, etac image, etac image, atac];
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    fun mor_tac ((mor_image, morE), map_comp_id) =
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      EVERY' [rtac ballI, stac o_apply, rtac trans, rtac (map_comp_id RS sym), rtac trans,
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        etac (morE RS arg_cong), atac, etac morE, etac mor_image, atac];
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  in
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    (stac mor_def THEN' rtac conjI THEN'
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    CONJ_WRAP' fbetw_tac mor_images THEN'
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    CONJ_WRAP' mor_tac ((mor_images ~~ morEs) ~~ map_comp_ids)) 1
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  end;
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fun mk_mor_UNIV_tac morEs mor_def =
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  let
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    val n = length morEs;
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    fun mor_tac morE = EVERY' [rtac ext, rtac trans, rtac o_apply, rtac trans, etac morE,
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      rtac UNIV_I, rtac sym, rtac o_apply];
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  in
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    EVERY' [rtac iffI, CONJ_WRAP' mor_tac morEs,
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    stac mor_def, rtac conjI, CONJ_WRAP' (K (rtac ballI THEN' rtac UNIV_I)) morEs,
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    CONJ_WRAP' (fn i =>
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      EVERY' [dtac (mk_conjunctN n i), rtac ballI, etac @{thm pointfreeE}]) (1 upto n)] 1
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  end;
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fun mk_mor_str_tac ks mor_UNIV =
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  (stac mor_UNIV THEN' CONJ_WRAP' (K (rtac refl)) ks) 1;
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fun mk_mor_sum_case_tac ks mor_UNIV =
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  (stac mor_UNIV THEN' CONJ_WRAP' (K (rtac @{thm sum_case_comp_Inl[symmetric]})) ks) 1;
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fun mk_set_incl_hset_tac def rec_Suc =
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  EVERY' (stac def ::
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    map rtac [@{thm incl_UNION_I}, UNIV_I, @{thm ord_le_eq_trans}, @{thm Un_upper1},
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      sym, rec_Suc]) 1;
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fun mk_set_hset_incl_hset_tac n defs rec_Suc i =
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  EVERY' (map (TRY oo stac) defs @
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    map rtac [@{thm UN_least}, subsetI, @{thm UN_I}, UNIV_I, set_mp, equalityD2, rec_Suc, UnI2,
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      mk_UnIN n i] @
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    [etac @{thm UN_I}, atac]) 1;
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fun mk_set_incl_hin_tac incls =
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  if null incls then rtac subset_UNIV 1
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  else EVERY' [rtac subsetI, rtac CollectI,
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    CONJ_WRAP' (fn incl => EVERY' [rtac subset_trans, etac incl, atac]) incls] 1;
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fun mk_hset_rec_minimal_tac m cts rec_0s rec_Sucs {context = ctxt, prems = _} =
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  EVERY' [rtac (Drule.instantiate' [] cts nat_induct),
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    REPEAT_DETERM o rtac allI,
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    CONJ_WRAP' (fn thm => EVERY'
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      [rtac ord_eq_le_trans, rtac thm, rtac @{thm empty_subsetI}]) rec_0s,
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    REPEAT_DETERM o rtac allI,
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    CONJ_WRAP' (fn rec_Suc => EVERY'
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      [rtac ord_eq_le_trans, rtac rec_Suc,
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        if m = 0 then K all_tac
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        else (rtac @{thm Un_least} THEN' Goal.assume_rule_tac ctxt),
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        CONJ_WRAP_GEN' (rtac (Thm.permute_prems 0 1 @{thm Un_least}))
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          (K (EVERY' [rtac @{thm UN_least}, REPEAT_DETERM o eresolve_tac [allE, conjE],
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            rtac subset_trans, atac, Goal.assume_rule_tac ctxt])) rec_0s])
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      rec_Sucs] 1;
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fun mk_hset_minimal_tac n hset_defs hset_rec_minimal {context = ctxt, prems = _} =
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  (CONJ_WRAP' (fn def => (EVERY' [rtac ord_eq_le_trans, rtac def,
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    rtac @{thm UN_least}, rtac rev_mp, rtac hset_rec_minimal,
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    EVERY' (replicate ((n + 1) * n) (Goal.assume_rule_tac ctxt)), rtac impI,
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    REPEAT_DETERM o eresolve_tac [allE, conjE], atac])) hset_defs) 1
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fun mk_mor_hset_rec_tac m n cts j rec_0s rec_Sucs morEs set_mapss coalg_setss =
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  EVERY' [rtac (Drule.instantiate' [] cts nat_induct),
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    REPEAT_DETERM o rtac allI,
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   239
    CONJ_WRAP' (fn thm => EVERY' (map rtac [impI, thm RS trans, thm RS sym])) rec_0s,
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   240
    REPEAT_DETERM o rtac allI,
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   241
    CONJ_WRAP'
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   242
      (fn (rec_Suc, (morE, ((passive_set_maps, active_set_maps), coalg_sets))) =>
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   243
        EVERY' [rtac impI, rtac (rec_Suc RS trans), rtac (rec_Suc RS trans RS sym),
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   244
          if m = 0 then K all_tac
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   245
          else EVERY' [rtac @{thm Un_cong}, rtac box_equals,
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   246
            rtac (nth passive_set_maps (j - 1) RS sym),
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   247
            rtac trans_fun_cong_image_id_id_apply, etac (morE RS arg_cong), atac],
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   248
          CONJ_WRAP_GEN' (rtac (Thm.permute_prems 0 1 @{thm Un_cong}))
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   249
            (fn (i, (set_map, coalg_set)) =>
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   250
              EVERY' [rtac sym, rtac trans, rtac (refl RSN (2, @{thm UN_cong})),
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   251
                etac (morE RS sym RS arg_cong RS trans), atac, rtac set_map,
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   252
                rtac (@{thm UN_simps(10)} RS trans), rtac (refl RS @{thm UN_cong}),
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   253
                ftac coalg_set, atac, dtac set_mp, atac, rtac mp, rtac (mk_conjunctN n i),
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   254
                REPEAT_DETERM o etac allE, atac, atac])
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   255
            (rev ((1 upto n) ~~ (active_set_maps ~~ coalg_sets)))])
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   256
      (rec_Sucs ~~ (morEs ~~ (map (chop m) set_mapss ~~ map (drop m) coalg_setss)))] 1;
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   257
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   258
fun mk_mor_hset_tac hset_def mor_hset_rec =
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   259
  EVERY' [rtac (hset_def RS trans), rtac (refl RS @{thm UN_cong} RS trans), etac mor_hset_rec,
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   260
    atac, atac, rtac (hset_def RS sym)] 1
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   261
wenzelm@51798
   262
fun mk_bis_srel_tac ctxt m bis_def srel_O_Grs map_comps map_cong0s set_mapss =
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   263
  let
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   264
    val n = length srel_O_Grs;
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   265
    val thms = ((1 upto n) ~~ map_comps ~~ map_cong0s ~~ set_mapss ~~ srel_O_Grs);
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   266
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   267
    fun mk_if_tac ((((i, map_comp), map_cong0), set_maps), srel_O_Gr) =
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   268
      EVERY' [rtac allI, rtac allI, rtac impI, dtac (mk_conjunctN n i),
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   269
        etac allE, etac allE, etac impE, atac, etac bexE, etac conjE,
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   270
        rtac (srel_O_Gr RS equalityD2 RS set_mp),
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   271
        rtac @{thm relcompI}, rtac @{thm converseI},
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   272
        EVERY' (map (fn thm =>
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   273
          EVERY' [rtac @{thm GrI}, REPEAT_DETERM o eresolve_tac [CollectE, conjE],
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   274
            rtac CollectI,
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   275
            CONJ_WRAP' (fn (i, thm) =>
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   276
              if i <= m
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   277
              then EVERY' [rtac ord_eq_le_trans, rtac thm, rtac subset_trans,
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   278
                etac @{thm image_mono}, rtac @{thm image_subsetI}, etac @{thm Id_onI}]
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   279
              else EVERY' [rtac ord_eq_le_trans, rtac trans, rtac thm,
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   280
                rtac trans_fun_cong_image_id_id_apply, atac])
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   281
            (1 upto (m + n) ~~ set_maps),
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   282
            rtac trans, rtac trans, rtac map_comp, rtac map_cong0, REPEAT_DETERM_N m o rtac thm,
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   283
            REPEAT_DETERM_N n o rtac (@{thm o_id} RS fun_cong), atac])
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   284
          @{thms fst_diag_id snd_diag_id})];
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   285
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   286
    fun mk_only_if_tac ((((i, map_comp), map_cong0), set_maps), srel_O_Gr) =
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   287
      EVERY' [dtac (mk_conjunctN n i), rtac allI, rtac allI, rtac impI,
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   288
        etac allE, etac allE, etac impE, atac,
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   289
        dtac (srel_O_Gr RS equalityD1 RS set_mp),
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   290
        REPEAT_DETERM o eresolve_tac [CollectE, @{thm relcompE}, @{thm converseE}],
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   291
        REPEAT_DETERM o eresolve_tac [@{thm GrE}, exE, conjE],
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   292
        REPEAT_DETERM o dtac Pair_eqD,
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   293
        REPEAT_DETERM o etac conjE,
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   294
        hyp_subst_tac ctxt,
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   295
        REPEAT_DETERM o eresolve_tac [CollectE, conjE],
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   296
        rtac bexI, rtac conjI, rtac trans, rtac map_comp, rtac trans, rtac map_cong0,
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   297
        REPEAT_DETERM_N m o rtac (@{thm id_o} RS fun_cong),
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   298
        REPEAT_DETERM_N n o rtac (@{thm o_id} RS fun_cong),
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   299
        etac sym, rtac trans, rtac map_comp, rtac trans, rtac map_cong0,
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   300
        REPEAT_DETERM_N m o rtac (@{thm id_o} RS fun_cong),
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   301
        REPEAT_DETERM_N n o rtac (@{thm o_id} RS fun_cong),
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   302
        rtac trans, rtac map_cong0,
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   303
        REPEAT_DETERM_N m o EVERY' [rtac @{thm Id_onD'}, etac set_mp, atac],
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   304
        REPEAT_DETERM_N n o rtac refl,
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   305
        etac sym, rtac CollectI,
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   306
        CONJ_WRAP' (fn (i, thm) =>
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   307
          if i <= m
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   308
          then EVERY' [rtac ord_eq_le_trans, rtac thm, rtac @{thm image_subsetI},
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   309
            rtac @{thm Id_on_fst}, etac set_mp, atac]
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   310
          else EVERY' [rtac ord_eq_le_trans, rtac trans, rtac thm,
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   311
            rtac trans_fun_cong_image_id_id_apply, atac])
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   312
        (1 upto (m + n) ~~ set_maps)];
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   313
  in
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   314
    EVERY' [rtac (bis_def RS trans),
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   315
      rtac iffI, etac conjE, etac conjI, CONJ_WRAP' mk_if_tac thms,
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   316
      etac conjE, etac conjI, CONJ_WRAP' mk_only_if_tac thms] 1
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   317
  end;
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   318
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   319
fun mk_bis_converse_tac m bis_srel srel_congs srel_converses =
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   320
  EVERY' [stac bis_srel, dtac (bis_srel RS iffD1),
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   321
    REPEAT_DETERM o etac conjE, rtac conjI,
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   322
    CONJ_WRAP' (K (EVERY' [rtac @{thm converse_shift}, etac subset_trans,
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   323
      rtac equalityD2, rtac @{thm converse_Times}])) srel_congs,
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   324
    CONJ_WRAP' (fn (srel_cong, srel_converse) =>
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   325
      EVERY' [rtac allI, rtac allI, rtac impI, rtac @{thm set_mp[OF equalityD2]},
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   326
        rtac (srel_cong RS trans),
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   327
        REPEAT_DETERM_N m o rtac (@{thm converse_Id_on} RS sym),
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   328
        REPEAT_DETERM_N (length srel_congs) o rtac refl,
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   329
        rtac srel_converse,
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   330
        REPEAT_DETERM o etac allE,
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   331
        rtac @{thm converseI}, etac mp, etac @{thm converseD}]) (srel_congs ~~ srel_converses)] 1;
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   332
wenzelm@51798
   333
fun mk_bis_O_tac ctxt m bis_srel srel_congs srel_Os =
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   334
  EVERY' [stac bis_srel, REPEAT_DETERM o dtac (bis_srel RS iffD1),
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   335
    REPEAT_DETERM o etac conjE, rtac conjI,
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   336
    CONJ_WRAP' (K (EVERY' [etac @{thm relcomp_subset_Sigma}, atac])) srel_congs,
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   337
    CONJ_WRAP' (fn (srel_cong, srel_O) =>
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   338
      EVERY' [rtac allI, rtac allI, rtac impI, rtac @{thm set_mp[OF equalityD2]},
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   339
        rtac (srel_cong RS trans),
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   340
        REPEAT_DETERM_N m o rtac @{thm Id_on_Comp},
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   341
        REPEAT_DETERM_N (length srel_congs) o rtac refl,
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   342
        rtac srel_O,
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   343
        etac @{thm relcompE},
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   344
        REPEAT_DETERM o dtac Pair_eqD,
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   345
        etac conjE, hyp_subst_tac ctxt,
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   346
        REPEAT_DETERM o etac allE, rtac @{thm relcompI},
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   347
        etac mp, atac, etac mp, atac]) (srel_congs ~~ srel_Os)] 1;
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   348
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   349
fun mk_bis_Gr_tac bis_srel srel_Grs mor_images morEs coalg_ins
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   350
  {context = ctxt, prems = _} =
traytel@51447
   351
  unfold_thms_tac ctxt (bis_srel :: @{thm Id_on_Gr} :: srel_Grs) THEN
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   352
  EVERY' [rtac conjI,
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   353
    CONJ_WRAP' (fn thm => rtac (@{thm Gr_incl} RS ssubst) THEN' etac thm) mor_images,
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   354
    CONJ_WRAP' (fn (coalg_in, morE) =>
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   355
      EVERY' [rtac allI, rtac allI, rtac impI, rtac @{thm GrI}, etac coalg_in,
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   356
        etac @{thm GrD1}, etac (morE RS trans), etac @{thm GrD1},
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   357
        etac (@{thm GrD2} RS arg_cong)]) (coalg_ins ~~ morEs)] 1;
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   358
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   359
fun mk_bis_Union_tac bis_def in_monos {context = ctxt, prems = _} =
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   360
  let
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   361
    val n = length in_monos;
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   362
    val ks = 1 upto n;
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   363
  in
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   364
    unfold_thms_tac ctxt [bis_def] THEN
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   365
    EVERY' [rtac conjI,
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   366
      CONJ_WRAP' (fn i =>
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   367
        EVERY' [rtac @{thm UN_least}, dtac bspec, atac,
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   368
          dtac conjunct1, etac (mk_conjunctN n i)]) ks,
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   369
      CONJ_WRAP' (fn (i, in_mono) =>
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   370
        EVERY' [rtac allI, rtac allI, rtac impI, etac @{thm UN_E}, dtac bspec, atac,
blanchet@48975
   371
          dtac conjunct2, dtac (mk_conjunctN n i), etac allE, etac allE, dtac mp,
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   372
          atac, etac bexE, rtac bexI, atac, rtac in_mono,
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   373
          REPEAT_DETERM_N n o etac @{thm incl_UNION_I[OF _ subset_refl]},
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   374
          atac]) (ks ~~ in_monos)] 1
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   375
  end;
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   376
wenzelm@51798
   377
fun mk_sbis_lsbis_tac ctxt lsbis_defs bis_Union bis_cong =
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   378
  let
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   379
    val n = length lsbis_defs;
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   380
  in
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   381
    EVERY' [rtac (Thm.permute_prems 0 1 bis_cong), EVERY' (map rtac lsbis_defs),
blanchet@48975
   382
      rtac bis_Union, rtac ballI, REPEAT_DETERM o eresolve_tac [CollectE, conjE, exE],
wenzelm@51798
   383
      hyp_subst_tac ctxt, etac bis_cong, EVERY' (map (rtac o mk_nth_conv n) (1 upto n))] 1
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   384
  end;
blanchet@48975
   385
blanchet@48975
   386
fun mk_incl_lsbis_tac n i lsbis_def =
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   387
  EVERY' [rtac @{thm xt1(3)}, rtac lsbis_def, rtac @{thm incl_UNION_I}, rtac CollectI,
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   388
    REPEAT_DETERM_N n o rtac exI, rtac conjI, rtac refl, atac, rtac equalityD2,
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   389
    rtac (mk_nth_conv n i)] 1;
blanchet@48975
   390
traytel@51447
   391
fun mk_equiv_lsbis_tac sbis_lsbis lsbis_incl incl_lsbis bis_Id_on bis_converse bis_O =
traytel@49488
   392
  EVERY' [rtac (@{thm equiv_def} RS iffD2),
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   393
traytel@49488
   394
    rtac conjI, rtac (@{thm refl_on_def} RS iffD2),
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   395
    rtac conjI, rtac lsbis_incl, rtac ballI, rtac set_mp,
traytel@51447
   396
    rtac incl_lsbis, rtac bis_Id_on, atac, etac @{thm Id_onI},
blanchet@48975
   397
traytel@49488
   398
    rtac conjI, rtac (@{thm sym_def} RS iffD2),
blanchet@49305
   399
    rtac allI, rtac allI, rtac impI, rtac set_mp,
blanchet@48975
   400
    rtac incl_lsbis, rtac bis_converse, rtac sbis_lsbis, etac @{thm converseI},
blanchet@48975
   401
traytel@49488
   402
    rtac (@{thm trans_def} RS iffD2),
blanchet@49305
   403
    rtac allI, rtac allI, rtac allI, rtac impI, rtac impI, rtac set_mp,
blanchet@48975
   404
    rtac incl_lsbis, rtac bis_O, rtac sbis_lsbis, rtac sbis_lsbis,
blanchet@48975
   405
    etac @{thm relcompI}, atac] 1;
blanchet@48975
   406
blanchet@51766
   407
fun mk_coalgT_tac m defs strT_defs set_mapss {context = ctxt, prems = _} =
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   408
  let
blanchet@48975
   409
    val n = length strT_defs;
blanchet@48975
   410
    val ks = 1 upto n;
blanchet@48975
   411
    fun coalg_tac (i, ((passive_sets, active_sets), def)) =
blanchet@48975
   412
      EVERY' [rtac ballI, REPEAT_DETERM o eresolve_tac [CollectE, exE, conjE],
wenzelm@51798
   413
        hyp_subst_tac ctxt, rtac (def RS trans RS @{thm ssubst_mem}), etac (arg_cong RS trans),
blanchet@48975
   414
        rtac (mk_sum_casesN n i), rtac CollectI,
blanchet@49305
   415
        EVERY' (map (fn thm => EVERY' [rtac conjI, rtac (thm RS ord_eq_le_trans),
blanchet@49585
   416
          etac ((trans OF [@{thm image_id} RS fun_cong, id_apply]) RS ord_eq_le_trans)])
blanchet@49305
   417
          passive_sets),
blanchet@49305
   418
        CONJ_WRAP' (fn (i, thm) => EVERY' [rtac (thm RS ord_eq_le_trans),
blanchet@48975
   419
          rtac @{thm image_subsetI}, rtac CollectI, rtac exI, rtac exI, rtac conjI, rtac refl,
blanchet@48975
   420
          rtac conjI,
blanchet@49305
   421
          rtac conjI, etac @{thm empty_Shift}, dtac set_rev_mp,
blanchet@48975
   422
            etac equalityD1, etac CollectD,
blanchet@48975
   423
          rtac conjI, etac @{thm Shift_clists},
blanchet@48975
   424
          rtac conjI, etac @{thm Shift_prefCl},
blanchet@48975
   425
          rtac conjI, rtac ballI,
blanchet@48975
   426
            rtac conjI, dtac @{thm iffD1[OF ball_conj_distrib]}, dtac conjunct1,
blanchet@49504
   427
            SELECT_GOAL (unfold_thms_tac ctxt @{thms Succ_Shift shift_def}),
blanchet@48975
   428
            etac bspec, etac @{thm ShiftD},
blanchet@48975
   429
            CONJ_WRAP' (fn i => EVERY' [rtac ballI, etac CollectE, dtac @{thm ShiftD},
blanchet@48975
   430
              dtac bspec, etac thin_rl, atac, dtac conjunct2, dtac (mk_conjunctN n i),
blanchet@48975
   431
              dtac bspec, rtac CollectI, etac @{thm set_mp[OF equalityD1[OF Succ_Shift]]},
blanchet@48975
   432
              REPEAT_DETERM o eresolve_tac [exE, conjE], rtac exI,
blanchet@48975
   433
              rtac conjI, rtac (@{thm shift_def} RS fun_cong RS trans),
blanchet@48975
   434
              rtac (@{thm append_Cons} RS sym RS arg_cong RS trans), atac,
blanchet@48975
   435
              REPEAT_DETERM_N m o (rtac conjI THEN' atac),
blanchet@48975
   436
              CONJ_WRAP' (K (EVERY' [etac trans, rtac @{thm Collect_cong},
blanchet@48975
   437
                rtac @{thm eqset_imp_iff}, rtac sym, rtac trans, rtac @{thm Succ_Shift},
blanchet@48975
   438
                rtac (@{thm append_Cons} RS sym RS arg_cong)])) ks]) ks,
blanchet@48975
   439
          rtac allI, rtac impI, REPEAT_DETERM o eresolve_tac [allE, impE],
blanchet@48975
   440
          etac @{thm not_in_Shift}, rtac trans, rtac (@{thm shift_def} RS fun_cong), atac,
blanchet@48975
   441
          dtac bspec, atac, dtac conjunct2, dtac (mk_conjunctN n i), dtac bspec,
blanchet@48975
   442
          etac @{thm set_mp[OF equalityD1]}, atac,
blanchet@48975
   443
          REPEAT_DETERM o eresolve_tac [exE, conjE], rtac exI,
blanchet@48975
   444
          rtac conjI, rtac (@{thm shift_def} RS fun_cong RS trans),
blanchet@48975
   445
          etac (@{thm append_Nil} RS sym RS arg_cong RS trans),
blanchet@48975
   446
          REPEAT_DETERM_N m o (rtac conjI THEN' atac),
blanchet@48975
   447
          CONJ_WRAP' (K (EVERY' [etac trans, rtac @{thm Collect_cong},
blanchet@48975
   448
            rtac @{thm eqset_imp_iff}, rtac sym, rtac trans, rtac @{thm Succ_Shift},
blanchet@48975
   449
            rtac (@{thm append_Nil} RS sym RS arg_cong)])) ks]) (ks ~~ active_sets)];
blanchet@48975
   450
  in
blanchet@49504
   451
    unfold_thms_tac ctxt defs THEN
blanchet@51766
   452
    CONJ_WRAP' coalg_tac (ks ~~ (map (chop m) set_mapss ~~ strT_defs)) 1
blanchet@48975
   453
  end;
blanchet@48975
   454
wenzelm@51798
   455
fun mk_card_of_carT_tac ctxt m isNode_defs sbd_sbd
blanchet@48975
   456
  sbd_card_order sbd_Card_order sbd_Cinfinite sbd_Cnotzero in_sbds =
blanchet@48975
   457
  let
blanchet@48975
   458
    val n = length isNode_defs;
blanchet@48975
   459
  in
blanchet@48975
   460
    EVERY' [rtac (Thm.permute_prems 0 1 ctrans),
blanchet@48975
   461
      rtac @{thm card_of_Sigma_ordLeq_Cinfinite}, rtac @{thm Cinfinite_cexp},
blanchet@48975
   462
      if m = 0 then rtac @{thm ordLeq_refl} else rtac @{thm ordLeq_csum2},
blanchet@48975
   463
      rtac @{thm Card_order_ctwo}, rtac @{thm Cinfinite_cexp},
blanchet@48975
   464
      rtac @{thm ctwo_ordLeq_Cinfinite}, rtac sbd_Cinfinite, rtac sbd_Cinfinite,
blanchet@48975
   465
      rtac ctrans, rtac @{thm card_of_diff},
blanchet@49305
   466
      rtac ordIso_ordLeq_trans, rtac @{thm card_of_Field_ordIso},
blanchet@49305
   467
      rtac @{thm Card_order_cpow}, rtac ordIso_ordLeq_trans,
traytel@51782
   468
      rtac @{thm cpow_cexp_ctwo}, rtac ctrans, rtac @{thm cexp_mono1},
blanchet@48975
   469
      if m = 0 then rtac @{thm ordLeq_refl} else rtac @{thm ordLeq_csum2},
traytel@51782
   470
      rtac @{thm Card_order_ctwo}, rtac @{thm Card_order_clists},
blanchet@49305
   471
      rtac @{thm cexp_mono2_Cnotzero}, rtac ordIso_ordLeq_trans,
blanchet@48975
   472
      rtac @{thm clists_Cinfinite},
blanchet@48975
   473
      if n = 1 then rtac sbd_Cinfinite else rtac (sbd_Cinfinite RS @{thm Cinfinite_csum1}),
blanchet@49305
   474
      rtac ordIso_ordLeq_trans, rtac sbd_sbd, rtac @{thm infinite_ordLeq_cexp},
blanchet@48975
   475
      rtac sbd_Cinfinite,
traytel@51782
   476
      if m = 0 then rtac @{thm Card_order_ctwo} else rtac @{thm Card_order_csum},
blanchet@48975
   477
      rtac @{thm Cnotzero_clists},
blanchet@49305
   478
      rtac ballI, rtac ordIso_ordLeq_trans, rtac @{thm card_of_Func_Ffunc},
blanchet@49305
   479
      rtac ordIso_ordLeq_trans, rtac @{thm Func_cexp},
blanchet@48975
   480
      rtac ctrans, rtac @{thm cexp_mono},
blanchet@48975
   481
      rtac @{thm ordLeq_ordIso_trans},
blanchet@48975
   482
      CONJ_WRAP_GEN' (rtac (Thm.permute_prems 0 1
blanchet@48975
   483
          (sbd_Cinfinite RS @{thm Cinfinite_cexp[OF ordLeq_csum2[OF Card_order_ctwo]]}
blanchet@48975
   484
        RSN (3, @{thm Un_Cinfinite_bound}))))
blanchet@48975
   485
        (fn thm => EVERY' [rtac ctrans, rtac @{thm card_of_image}, rtac thm]) (rev in_sbds),
traytel@51782
   486
      rtac @{thm cexp_cong1}, rtac @{thm csum_cong1},
blanchet@48975
   487
      REPEAT_DETERM_N m o rtac @{thm csum_cong2},
blanchet@48975
   488
      CONJ_WRAP_GEN' (rtac @{thm csum_cong})
blanchet@48975
   489
        (K (rtac (sbd_Card_order RS @{thm card_of_Field_ordIso}))) in_sbds,
blanchet@48975
   490
      rtac sbd_Card_order,
blanchet@48975
   491
      rtac @{thm ordLeq_ordIso_trans}, etac @{thm clists_bound},
blanchet@48975
   492
      rtac @{thm clists_Cinfinite}, TRY o rtac @{thm Cinfinite_csum1}, rtac sbd_Cinfinite,
traytel@51782
   493
      rtac FalseE, etac @{thm cpow_clists_czero}, atac,
blanchet@48975
   494
      rtac @{thm card_of_Card_order},
blanchet@49305
   495
      rtac ordIso_ordLeq_trans, rtac @{thm cexp_cprod},
traytel@51782
   496
      rtac @{thm Card_order_csum},
traytel@51782
   497
      rtac ordIso_ordLeq_trans, rtac @{thm cexp_cong2},
blanchet@48975
   498
      rtac @{thm ordIso_transitive}, rtac @{thm cprod_cong2}, rtac sbd_sbd,
blanchet@48975
   499
      rtac @{thm cprod_infinite}, rtac sbd_Cinfinite,
traytel@51782
   500
      rtac @{thm Card_order_csum}, rtac @{thm Card_order_cprod},
traytel@51782
   501
      rtac ctrans, rtac @{thm cexp_mono1},
blanchet@49305
   502
      rtac ordIso_ordLeq_trans, rtac @{thm ordIso_transitive}, rtac @{thm csum_cong1},
blanchet@48975
   503
      rtac @{thm ordIso_transitive},
blanchet@48975
   504
      REPEAT_DETERM_N m o rtac @{thm csum_cong2},
blanchet@48975
   505
      rtac sbd_sbd,
blanchet@48975
   506
      BNF_Tactics.mk_rotate_eq_tac (rtac @{thm ordIso_refl} THEN'
blanchet@48975
   507
        FIRST' [rtac @{thm card_of_Card_order},
blanchet@48975
   508
          rtac @{thm Card_order_csum}, rtac sbd_Card_order])
blanchet@48975
   509
        @{thm ordIso_transitive} @{thm csum_assoc} @{thm csum_com} @{thm csum_cong}
blanchet@48975
   510
        (1 upto m + 1) (m + 1 :: (1 upto m)),
blanchet@48975
   511
      if m = 0 then K all_tac else EVERY' [rtac @{thm ordIso_transitive}, rtac @{thm csum_assoc}],
blanchet@48975
   512
      rtac @{thm csum_com}, rtac @{thm csum_cexp'}, rtac sbd_Cinfinite,
blanchet@48975
   513
      if m = 0 then rtac @{thm Card_order_ctwo} else rtac @{thm Card_order_csum},
blanchet@48975
   514
      if m = 0 then rtac @{thm ordLeq_refl} else rtac @{thm ordLeq_csum2},
traytel@51782
   515
      rtac @{thm Card_order_ctwo}, rtac sbd_Card_order,
blanchet@49305
   516
      rtac ordIso_ordLeq_trans, rtac @{thm cexp_cprod_ordLeq},
traytel@51782
   517
      if m = 0 then rtac @{thm Card_order_ctwo} else rtac @{thm Card_order_csum},
blanchet@48975
   518
      rtac sbd_Cinfinite, rtac sbd_Cnotzero, rtac @{thm ordLeq_refl}, rtac sbd_Card_order,
blanchet@48975
   519
      rtac @{thm cexp_mono2_Cnotzero}, rtac @{thm infinite_ordLeq_cexp},
blanchet@48975
   520
      rtac sbd_Cinfinite,
traytel@51782
   521
      if m = 0 then rtac @{thm Card_order_ctwo} else rtac @{thm Card_order_csum},
blanchet@48975
   522
      rtac sbd_Cnotzero,
blanchet@48975
   523
      rtac @{thm card_of_mono1}, rtac subsetI,
wenzelm@51798
   524
      REPEAT_DETERM o eresolve_tac [CollectE, exE, conjE, @{thm prod_caseE}], hyp_subst_tac ctxt,
blanchet@49305
   525
      rtac @{thm SigmaI}, rtac @{thm DiffI}, rtac set_mp, rtac equalityD2,
blanchet@48975
   526
      rtac (@{thm cpow_def} RS arg_cong RS trans), rtac (@{thm Pow_def} RS arg_cong RS trans),
blanchet@48975
   527
      rtac @{thm Field_card_of}, rtac CollectI, atac, rtac notI, etac @{thm singletonE},
wenzelm@51798
   528
      hyp_subst_tac ctxt, etac @{thm emptyE}, rtac (@{thm Ffunc_def} RS equalityD2 RS set_mp),
blanchet@48975
   529
      rtac CollectI, rtac conjI, rtac ballI, dtac bspec, etac thin_rl, atac, dtac conjunct1,
blanchet@48975
   530
      CONJ_WRAP_GEN' (etac disjE) (fn (i, def) => EVERY'
traytel@49488
   531
        [rtac (mk_UnIN n i), dtac (def RS iffD1),
blanchet@48975
   532
        REPEAT_DETERM o eresolve_tac [exE, conjE], rtac @{thm image_eqI}, atac, rtac CollectI,
blanchet@48975
   533
        REPEAT_DETERM_N m o (rtac conjI THEN' atac),
blanchet@49305
   534
        CONJ_WRAP' (K (EVERY' [etac ord_eq_le_trans, rtac subset_trans,
traytel@49490
   535
          rtac subset_UNIV, rtac equalityD2, rtac @{thm Field_card_order},
blanchet@48975
   536
          rtac sbd_card_order])) isNode_defs]) (1 upto n ~~ isNode_defs),
blanchet@48975
   537
      atac] 1
blanchet@48975
   538
  end;
blanchet@48975
   539
blanchet@51766
   540
fun mk_carT_set_tac n i carT_def strT_def isNode_def set_map {context = ctxt, prems = _}=
blanchet@49305
   541
  EVERY' [dtac (carT_def RS equalityD1 RS set_mp),
blanchet@48975
   542
    REPEAT_DETERM o eresolve_tac [CollectE, exE, conjE],
traytel@49488
   543
    dtac Pair_eqD,
wenzelm@51798
   544
    etac conjE, hyp_subst_tac ctxt,
traytel@49488
   545
    dtac (isNode_def RS iffD1),
blanchet@48975
   546
    REPEAT_DETERM o eresolve_tac [exE, conjE],
blanchet@49305
   547
    rtac (equalityD2 RS set_mp),
blanchet@48975
   548
    rtac (strT_def RS arg_cong RS trans),
blanchet@48975
   549
    etac (arg_cong RS trans),
blanchet@48975
   550
    fo_rtac (mk_sum_casesN n i RS arg_cong RS trans) ctxt,
blanchet@51766
   551
    rtac set_map, rtac imageI, etac (equalityD2 RS set_mp), rtac CollectI,
blanchet@48975
   552
    etac @{thm prefCl_Succ}, atac] 1;
blanchet@48975
   553
wenzelm@51798
   554
fun mk_strT_hset_tac ctxt n m j arg_cong_cTs cTs cts carT_defs strT_defs isNode_defs
blanchet@51766
   555
  set_incl_hsets set_hset_incl_hsetss coalg_setss carT_setss coalgT set_mapss =
blanchet@48975
   556
  let
blanchet@51766
   557
    val set_maps = map (fn xs => nth xs (j - 1)) set_mapss;
blanchet@48975
   558
    val ks = 1 upto n;
blanchet@51766
   559
    fun base_tac (i, (cT, (strT_def, (set_incl_hset, set_map)))) =
blanchet@48975
   560
      CONJ_WRAP' (fn (i', (carT_def, isNode_def)) => rtac impI THEN' etac conjE THEN'
blanchet@48975
   561
        (if i = i'
blanchet@48975
   562
        then EVERY' [rtac @{thm xt1(4)}, rtac set_incl_hset,
blanchet@48975
   563
          rtac (strT_def RS arg_cong RS trans), etac (arg_cong RS trans),
blanchet@51766
   564
          rtac (Thm.permute_prems 0 1 (set_map RS box_equals)),
blanchet@49585
   565
          rtac (trans OF [@{thm image_id} RS fun_cong, id_apply]),
blanchet@48975
   566
          rtac (mk_sum_casesN n i RS (Drule.instantiate' [cT] [] arg_cong) RS sym)]
blanchet@49305
   567
        else EVERY' [dtac (carT_def RS equalityD1 RS set_mp),
blanchet@48975
   568
          REPEAT_DETERM o eresolve_tac [CollectE, exE], etac conjE,
traytel@49488
   569
          dtac conjunct2, dtac Pair_eqD, etac conjE,
wenzelm@51798
   570
          hyp_subst_tac ctxt, dtac (isNode_def RS iffD1),
blanchet@48975
   571
          REPEAT_DETERM o eresolve_tac [exE, conjE],
blanchet@48975
   572
          rtac (mk_InN_not_InM i i' RS notE), etac (sym RS trans), atac]))
blanchet@48975
   573
      (ks ~~ (carT_defs ~~ isNode_defs));
blanchet@48975
   574
    fun step_tac (i, (coalg_sets, (carT_sets, set_hset_incl_hsets))) =
blanchet@48975
   575
      dtac (mk_conjunctN n i) THEN'
blanchet@48975
   576
      CONJ_WRAP' (fn (coalg_set, (carT_set, set_hset_incl_hset)) =>
blanchet@48975
   577
        EVERY' [rtac impI, etac conjE, etac impE, rtac conjI,
blanchet@49305
   578
          rtac (coalgT RS coalg_set RS set_mp), atac, etac carT_set, atac, atac,
blanchet@48975
   579
          etac (@{thm shift_def} RS fun_cong RS trans), etac subset_trans,
blanchet@48975
   580
          rtac set_hset_incl_hset, etac carT_set, atac, atac])
blanchet@48975
   581
      (coalg_sets ~~ (carT_sets ~~ set_hset_incl_hsets));
blanchet@48975
   582
  in
blanchet@48975
   583
    EVERY' [rtac (Drule.instantiate' cTs cts @{thm list.induct}),
blanchet@48975
   584
      REPEAT_DETERM o rtac allI, rtac impI,
blanchet@48975
   585
      CONJ_WRAP' base_tac
blanchet@51766
   586
        (ks ~~ (arg_cong_cTs ~~ (strT_defs ~~ (set_incl_hsets ~~ set_maps)))),
blanchet@48975
   587
      REPEAT_DETERM o rtac allI, rtac impI,
blanchet@48975
   588
      REPEAT_DETERM o eresolve_tac [allE, impE], etac @{thm ShiftI},
blanchet@48975
   589
      CONJ_WRAP' (fn i => dtac (mk_conjunctN n i) THEN' rtac (mk_sumEN n) THEN'
blanchet@48975
   590
        CONJ_WRAP_GEN' (K all_tac) step_tac
blanchet@48975
   591
          (ks ~~ (drop m coalg_setss ~~ (carT_setss ~~ set_hset_incl_hsetss)))) ks] 1
blanchet@48975
   592
  end;
blanchet@48975
   593
blanchet@48975
   594
fun mk_isNode_hset_tac n isNode_def strT_hsets {context = ctxt, prems = _} =
blanchet@48975
   595
  let
blanchet@48975
   596
    val m = length strT_hsets;
blanchet@48975
   597
  in
blanchet@48975
   598
    if m = 0 then atac 1
blanchet@49504
   599
    else (unfold_thms_tac ctxt [isNode_def] THEN
blanchet@48975
   600
      EVERY' [REPEAT_DETERM o eresolve_tac [CollectE, exE, conjE],
blanchet@48975
   601
        rtac exI, rtac conjI, atac,
blanchet@48975
   602
        CONJ_WRAP' (fn (thm, i) =>  if i > m then atac
blanchet@48975
   603
          else EVERY' [rtac (thm RS subset_trans), atac, rtac conjI, atac, atac, atac])
blanchet@48975
   604
        (strT_hsets @ (replicate n mp) ~~ (1 upto (m + n)))] 1)
blanchet@48975
   605
  end;
blanchet@48975
   606
wenzelm@51798
   607
fun mk_Lev_sbd_tac ctxt cts Lev_0s Lev_Sucs to_sbdss =
blanchet@48975
   608
  let
blanchet@48975
   609
    val n = length Lev_0s;
blanchet@48975
   610
    val ks = 1 upto n;
blanchet@48975
   611
  in
blanchet@49305
   612
    EVERY' [rtac (Drule.instantiate' [] cts nat_induct),
blanchet@48975
   613
      REPEAT_DETERM o rtac allI,
blanchet@48975
   614
      CONJ_WRAP' (fn Lev_0 =>
blanchet@49305
   615
        EVERY' (map rtac [ord_eq_le_trans, Lev_0, @{thm Nil_clists}])) Lev_0s,
blanchet@48975
   616
      REPEAT_DETERM o rtac allI,
blanchet@48975
   617
      CONJ_WRAP' (fn (Lev_Suc, to_sbds) =>
blanchet@49305
   618
        EVERY' [rtac ord_eq_le_trans, rtac Lev_Suc,
blanchet@48975
   619
          CONJ_WRAP_GEN' (rtac (Thm.permute_prems 0 1 @{thm Un_least}))
blanchet@48975
   620
            (fn (i, to_sbd) => EVERY' [rtac subsetI,
wenzelm@51798
   621
              REPEAT_DETERM o eresolve_tac [CollectE, exE, conjE], hyp_subst_tac ctxt,
blanchet@48975
   622
              rtac @{thm Cons_clists}, rtac (mk_InN_Field n i), etac to_sbd,
blanchet@49305
   623
              etac set_rev_mp, REPEAT_DETERM o etac allE,
blanchet@48975
   624
              etac (mk_conjunctN n i)])
blanchet@48975
   625
          (rev (ks ~~ to_sbds))])
blanchet@48975
   626
      (Lev_Sucs ~~ to_sbdss)] 1
blanchet@48975
   627
  end;
blanchet@48975
   628
wenzelm@51798
   629
fun mk_length_Lev_tac ctxt cts Lev_0s Lev_Sucs =
blanchet@48975
   630
  let
blanchet@48975
   631
    val n = length Lev_0s;
blanchet@48975
   632
    val ks = n downto 1;
blanchet@48975
   633
  in
blanchet@49305
   634
    EVERY' [rtac (Drule.instantiate' [] cts nat_induct),
blanchet@48975
   635
      REPEAT_DETERM o rtac allI,
blanchet@48975
   636
      CONJ_WRAP' (fn Lev_0 =>
blanchet@49305
   637
        EVERY' [rtac impI, dtac (Lev_0 RS equalityD1 RS set_mp),
blanchet@48975
   638
          etac @{thm singletonE}, etac ssubst, rtac @{thm list.size(3)}]) Lev_0s,
blanchet@48975
   639
      REPEAT_DETERM o rtac allI,
blanchet@48975
   640
      CONJ_WRAP' (fn Lev_Suc =>
blanchet@49305
   641
        EVERY' [rtac impI, dtac (Lev_Suc RS equalityD1 RS set_mp),
blanchet@48975
   642
          CONJ_WRAP_GEN' (etac (Thm.permute_prems 1 1 UnE))
wenzelm@51798
   643
            (fn i =>
wenzelm@51798
   644
              EVERY' [REPEAT_DETERM o eresolve_tac [CollectE, exE, conjE], hyp_subst_tac ctxt,
wenzelm@51798
   645
                rtac trans, rtac @{thm length_Cons}, rtac @{thm arg_cong[of _ _ Suc]},
wenzelm@51798
   646
                REPEAT_DETERM o etac allE, dtac (mk_conjunctN n i), etac mp, atac]) ks])
blanchet@48975
   647
      Lev_Sucs] 1
blanchet@48975
   648
  end;
blanchet@48975
   649
blanchet@48975
   650
fun mk_length_Lev'_tac length_Lev =
blanchet@48975
   651
  EVERY' [ftac length_Lev, etac ssubst, atac] 1;
blanchet@48975
   652
wenzelm@51798
   653
fun mk_prefCl_Lev_tac ctxt cts Lev_0s Lev_Sucs =
blanchet@48975
   654
  let
blanchet@48975
   655
    val n = length Lev_0s;
blanchet@48975
   656
    val ks = n downto 1;
blanchet@48975
   657
  in
blanchet@49305
   658
    EVERY' [rtac (Drule.instantiate' [] cts nat_induct),
blanchet@48975
   659
      REPEAT_DETERM o rtac allI,
blanchet@48975
   660
      CONJ_WRAP' (fn Lev_0 =>
blanchet@49305
   661
        EVERY' [rtac impI, etac conjE, dtac (Lev_0 RS equalityD1 RS set_mp),
wenzelm@51798
   662
          etac @{thm singletonE}, hyp_subst_tac ctxt,
wenzelm@51798
   663
          dtac @{thm prefixeq_Nil[THEN subst, of "%x. x"]},
wenzelm@51798
   664
          hyp_subst_tac ctxt,
wenzelm@51798
   665
          rtac @{thm set_mp[OF equalityD2[OF trans[OF arg_cong[OF list.size(3)]]]]},
blanchet@48975
   666
          rtac Lev_0, rtac @{thm singletonI}]) Lev_0s,
blanchet@48975
   667
      REPEAT_DETERM o rtac allI,
blanchet@48975
   668
      CONJ_WRAP' (fn (Lev_0, Lev_Suc) =>
blanchet@49305
   669
        EVERY' [rtac impI, etac conjE, dtac (Lev_Suc RS equalityD1 RS set_mp),
blanchet@48975
   670
          CONJ_WRAP_GEN' (etac (Thm.permute_prems 1 1 UnE))
wenzelm@51798
   671
            (fn i =>
wenzelm@51798
   672
              EVERY' [REPEAT_DETERM o eresolve_tac [CollectE, exE, conjE], hyp_subst_tac ctxt,
wenzelm@51798
   673
              dtac @{thm prefixeq_Cons[THEN subst, of "%x. x"]}, etac disjE, hyp_subst_tac ctxt,
blanchet@48975
   674
              rtac @{thm set_mp[OF equalityD2[OF trans[OF arg_cong[OF list.size(3)]]]]},
blanchet@48975
   675
              rtac Lev_0, rtac @{thm singletonI},
wenzelm@51798
   676
              REPEAT_DETERM o eresolve_tac [exE, conjE], hyp_subst_tac ctxt,
blanchet@48975
   677
              rtac @{thm set_mp[OF equalityD2[OF trans[OF arg_cong[OF length_Cons]]]]},
blanchet@49366
   678
              rtac Lev_Suc, rtac (mk_UnIN n i), rtac CollectI, REPEAT_DETERM o rtac exI, rtac conjI,
blanchet@48975
   679
              rtac refl, etac conjI, REPEAT_DETERM o etac allE, dtac (mk_conjunctN n i),
blanchet@48975
   680
              etac mp, etac conjI, atac]) ks])
blanchet@48975
   681
      (Lev_0s ~~ Lev_Sucs)] 1
blanchet@48975
   682
  end;
blanchet@48975
   683
blanchet@48975
   684
fun mk_rv_last_tac cTs cts rv_Nils rv_Conss =
blanchet@48975
   685
  let
blanchet@48975
   686
    val n = length rv_Nils;
blanchet@48975
   687
    val ks = 1 upto n;
blanchet@48975
   688
  in
blanchet@48975
   689
    EVERY' [rtac (Drule.instantiate' cTs cts @{thm list.induct}),
blanchet@48975
   690
      REPEAT_DETERM o rtac allI,
blanchet@48975
   691
      CONJ_WRAP' (fn rv_Cons =>
blanchet@48975
   692
        CONJ_WRAP' (fn (i, rv_Nil) => (EVERY' [rtac exI,
blanchet@48975
   693
          rtac (@{thm append_Nil} RS arg_cong RS trans),
blanchet@48975
   694
          rtac (rv_Cons RS trans), rtac (mk_sum_casesN n i RS arg_cong RS trans), rtac rv_Nil]))
blanchet@48975
   695
        (ks ~~ rv_Nils))
blanchet@48975
   696
      rv_Conss,
blanchet@48975
   697
      REPEAT_DETERM o rtac allI, rtac (mk_sumEN n),
blanchet@48975
   698
      EVERY' (map (fn i =>
blanchet@48975
   699
        CONJ_WRAP' (fn rv_Cons => EVERY' [REPEAT_DETERM o etac allE, dtac (mk_conjunctN n i),
blanchet@48975
   700
          CONJ_WRAP' (fn i' => EVERY' [dtac (mk_conjunctN n i'), etac exE, rtac exI,
blanchet@48975
   701
            rtac (@{thm append_Cons} RS arg_cong RS trans),
blanchet@49328
   702
            rtac (rv_Cons RS trans), etac (sum_case_weak_cong RS arg_cong RS trans),
blanchet@48975
   703
            rtac (mk_sum_casesN n i RS arg_cong RS trans), atac])
blanchet@48975
   704
          ks])
blanchet@48975
   705
        rv_Conss)
blanchet@48975
   706
      ks)] 1
blanchet@48975
   707
  end;
blanchet@48975
   708
wenzelm@51798
   709
fun mk_set_rv_Lev_tac ctxt m cts Lev_0s Lev_Sucs rv_Nils rv_Conss coalg_setss from_to_sbdss =
blanchet@48975
   710
  let
blanchet@48975
   711
    val n = length Lev_0s;
blanchet@48975
   712
    val ks = 1 upto n;
blanchet@48975
   713
  in
blanchet@49305
   714
    EVERY' [rtac (Drule.instantiate' [] cts nat_induct),
blanchet@48975
   715
      REPEAT_DETERM o rtac allI,
blanchet@48975
   716
      CONJ_WRAP' (fn (i, ((Lev_0, rv_Nil), coalg_sets)) =>
blanchet@48975
   717
        EVERY' [rtac impI, REPEAT_DETERM o etac conjE,
blanchet@49305
   718
          dtac (Lev_0 RS equalityD1 RS set_mp), etac @{thm singletonE}, etac ssubst,
traytel@49488
   719
          rtac (rv_Nil RS arg_cong RS iffD2),
traytel@49488
   720
          rtac (mk_sum_casesN n i RS iffD2),
blanchet@48975
   721
          CONJ_WRAP' (fn thm => etac thm THEN' atac) (take m coalg_sets)])
blanchet@48975
   722
      (ks ~~ ((Lev_0s ~~ rv_Nils) ~~ coalg_setss)),
blanchet@48975
   723
      REPEAT_DETERM o rtac allI,
blanchet@48975
   724
      CONJ_WRAP' (fn ((Lev_Suc, rv_Cons), (from_to_sbds, coalg_sets)) =>
blanchet@49305
   725
        EVERY' [rtac impI, etac conjE, dtac (Lev_Suc RS equalityD1 RS set_mp),
blanchet@48975
   726
          CONJ_WRAP_GEN' (etac (Thm.permute_prems 1 1 UnE))
blanchet@48975
   727
            (fn (i, (from_to_sbd, coalg_set)) =>
wenzelm@51798
   728
              EVERY' [REPEAT_DETERM o eresolve_tac [CollectE, exE, conjE], hyp_subst_tac ctxt,
traytel@49488
   729
              rtac (rv_Cons RS arg_cong RS iffD2),
traytel@49488
   730
              rtac (mk_sum_casesN n i RS arg_cong RS trans RS iffD2),
blanchet@48975
   731
              etac (from_to_sbd RS arg_cong), REPEAT_DETERM o etac allE,
blanchet@49305
   732
              dtac (mk_conjunctN n i), etac mp, etac conjI, etac set_rev_mp,
blanchet@48975
   733
              etac coalg_set, atac])
blanchet@48975
   734
          (rev (ks ~~ (from_to_sbds ~~ drop m coalg_sets)))])
blanchet@48975
   735
      ((Lev_Sucs ~~ rv_Conss) ~~ (from_to_sbdss ~~ coalg_setss))] 1
blanchet@48975
   736
  end;
blanchet@48975
   737
wenzelm@51798
   738
fun mk_set_Lev_tac ctxt cts Lev_0s Lev_Sucs rv_Nils rv_Conss from_to_sbdss =
blanchet@48975
   739
  let
blanchet@48975
   740
    val n = length Lev_0s;
blanchet@48975
   741
    val ks = 1 upto n;
blanchet@48975
   742
  in
blanchet@49305
   743
    EVERY' [rtac (Drule.instantiate' [] cts nat_induct),
blanchet@48975
   744
      REPEAT_DETERM o rtac allI,
blanchet@48975
   745
      CONJ_WRAP' (fn ((i, (Lev_0, Lev_Suc)), rv_Nil) =>
blanchet@49305
   746
        EVERY' [rtac impI, dtac (Lev_0 RS equalityD1 RS set_mp),
wenzelm@51798
   747
          etac @{thm singletonE}, hyp_subst_tac ctxt,
blanchet@48975
   748
          CONJ_WRAP' (fn i' => rtac impI THEN' dtac (sym RS trans) THEN' rtac rv_Nil THEN'
blanchet@48975
   749
            (if i = i'
wenzelm@51798
   750
            then EVERY' [dtac (mk_InN_inject n i), hyp_subst_tac ctxt,
blanchet@48975
   751
              CONJ_WRAP' (fn (i'', Lev_0'') =>
blanchet@48975
   752
                EVERY' [rtac impI, rtac @{thm ssubst_mem[OF append_Nil]},
blanchet@49366
   753
                  rtac (Lev_Suc RS equalityD2 RS set_mp), rtac (mk_UnIN n i''),
blanchet@48975
   754
                  rtac CollectI, REPEAT_DETERM o rtac exI, rtac conjI, rtac refl,
blanchet@49305
   755
                  etac conjI, rtac (Lev_0'' RS equalityD2 RS set_mp),
blanchet@48975
   756
                  rtac @{thm singletonI}])
blanchet@48975
   757
              (ks ~~ Lev_0s)]
blanchet@48975
   758
            else etac (mk_InN_not_InM i' i RS notE)))
blanchet@48975
   759
          ks])
blanchet@48975
   760
      ((ks ~~ (Lev_0s ~~ Lev_Sucs)) ~~ rv_Nils),
blanchet@48975
   761
      REPEAT_DETERM o rtac allI,
blanchet@48975
   762
      CONJ_WRAP' (fn ((Lev_Suc, rv_Cons), from_to_sbds) =>
blanchet@49305
   763
        EVERY' [rtac impI, dtac (Lev_Suc RS equalityD1 RS set_mp),
blanchet@48975
   764
          CONJ_WRAP_GEN' (etac (Thm.permute_prems 1 1 UnE))
blanchet@48975
   765
            (fn (i, from_to_sbd) =>
wenzelm@51798
   766
              EVERY' [REPEAT_DETERM o eresolve_tac [CollectE, exE, conjE], hyp_subst_tac ctxt,
blanchet@48975
   767
                CONJ_WRAP' (fn i' => rtac impI THEN'
blanchet@48975
   768
                  CONJ_WRAP' (fn i'' =>
blanchet@49305
   769
                    EVERY' [rtac impI, rtac (Lev_Suc RS equalityD2 RS set_mp),
blanchet@49366
   770
                      rtac @{thm ssubst_mem[OF append_Cons]}, rtac (mk_UnIN n i),
blanchet@48975
   771
                      rtac CollectI, REPEAT_DETERM o rtac exI, rtac conjI, rtac refl,
blanchet@48975
   772
                      rtac conjI, atac, dtac (sym RS trans RS sym),
blanchet@48975
   773
                      rtac (rv_Cons RS trans), rtac (mk_sum_casesN n i RS trans),
blanchet@48975
   774
                      etac (from_to_sbd RS arg_cong), REPEAT_DETERM o etac allE,
blanchet@48975
   775
                      dtac (mk_conjunctN n i), dtac mp, atac,
blanchet@48975
   776
                      dtac (mk_conjunctN n i'), dtac mp, atac,
blanchet@48975
   777
                      dtac (mk_conjunctN n i''), etac mp, atac])
blanchet@48975
   778
                  ks)
blanchet@48975
   779
                ks])
blanchet@48975
   780
          (rev (ks ~~ from_to_sbds))])
blanchet@48975
   781
      ((Lev_Sucs ~~ rv_Conss) ~~ from_to_sbdss)] 1
blanchet@48975
   782
  end;
blanchet@48975
   783
wenzelm@51798
   784
fun mk_set_image_Lev_tac ctxt cts Lev_0s Lev_Sucs rv_Nils rv_Conss from_to_sbdss to_sbd_injss =
blanchet@48975
   785
  let
blanchet@48975
   786
    val n = length Lev_0s;
blanchet@48975
   787
    val ks = 1 upto n;
blanchet@48975
   788
  in
blanchet@49305
   789
    EVERY' [rtac (Drule.instantiate' [] cts nat_induct),
blanchet@48975
   790
      REPEAT_DETERM o rtac allI,
blanchet@48975
   791
      CONJ_WRAP' (fn ((i, (Lev_0, Lev_Suc)), rv_Nil) =>
blanchet@49305
   792
        EVERY' [rtac impI, dtac (Lev_0 RS equalityD1 RS set_mp),
wenzelm@51798
   793
          etac @{thm singletonE}, hyp_subst_tac ctxt,
blanchet@48975
   794
          CONJ_WRAP' (fn i' => rtac impI THEN'
blanchet@48975
   795
            CONJ_WRAP' (fn i'' => rtac impI  THEN' dtac (sym RS trans) THEN' rtac rv_Nil THEN'
blanchet@48975
   796
              (if i = i''
blanchet@48975
   797
              then EVERY' [dtac @{thm ssubst_mem[OF sym[OF append_Nil]]},
blanchet@49305
   798
                dtac (Lev_Suc RS equalityD1 RS set_mp), dtac (mk_InN_inject n i),
wenzelm@51798
   799
                hyp_subst_tac ctxt,
blanchet@48975
   800
                CONJ_WRAP_GEN' (etac (Thm.permute_prems 1 1 UnE))
blanchet@48975
   801
                  (fn k => REPEAT_DETERM o eresolve_tac [CollectE, exE, conjE] THEN'
traytel@49488
   802
                    dtac list_inject_iffD1 THEN' etac conjE THEN'
blanchet@48975
   803
                    (if k = i'
wenzelm@51798
   804
                    then EVERY' [dtac (mk_InN_inject n k), hyp_subst_tac ctxt, etac imageI]
blanchet@48975
   805
                    else etac (mk_InN_not_InM i' k RS notE)))
blanchet@48975
   806
                (rev ks)]
blanchet@48975
   807
              else etac (mk_InN_not_InM i'' i RS notE)))
blanchet@48975
   808
            ks)
blanchet@48975
   809
          ks])
blanchet@48975
   810
      ((ks ~~ (Lev_0s ~~ Lev_Sucs)) ~~ rv_Nils),
blanchet@48975
   811
      REPEAT_DETERM o rtac allI,
blanchet@48975
   812
      CONJ_WRAP' (fn ((Lev_Suc, rv_Cons), (from_to_sbds, to_sbd_injs)) =>
blanchet@49305
   813
        EVERY' [rtac impI, dtac (Lev_Suc RS equalityD1 RS set_mp),
blanchet@48975
   814
          CONJ_WRAP_GEN' (etac (Thm.permute_prems 1 1 UnE))
blanchet@48975
   815
            (fn (i, (from_to_sbd, to_sbd_inj)) =>
wenzelm@51798
   816
              REPEAT_DETERM o eresolve_tac [CollectE, exE, conjE] THEN' hyp_subst_tac ctxt THEN'
blanchet@48975
   817
              CONJ_WRAP' (fn i' => rtac impI THEN'
blanchet@48975
   818
                dtac @{thm ssubst_mem[OF sym[OF append_Cons]]} THEN'
blanchet@49305
   819
                dtac (Lev_Suc RS equalityD1 RS set_mp) THEN'
blanchet@48975
   820
                CONJ_WRAP_GEN' (etac (Thm.permute_prems 1 1 UnE)) (fn k =>
blanchet@48975
   821
                  REPEAT_DETERM o eresolve_tac [CollectE, exE, conjE] THEN'
traytel@49488
   822
                  dtac list_inject_iffD1 THEN' etac conjE THEN'
blanchet@48975
   823
                  (if k = i
blanchet@48975
   824
                  then EVERY' [dtac (mk_InN_inject n i),
traytel@49488
   825
                    dtac (Thm.permute_prems 0 2 (to_sbd_inj RS iffD1)),
wenzelm@51798
   826
                    atac, atac, hyp_subst_tac ctxt] THEN'
blanchet@48975
   827
                    CONJ_WRAP' (fn i'' =>
blanchet@48975
   828
                      EVERY' [rtac impI, dtac (sym RS trans),
blanchet@48975
   829
                        rtac (rv_Cons RS trans), rtac (mk_sum_casesN n i RS arg_cong RS trans),
blanchet@48975
   830
                        etac (from_to_sbd RS arg_cong),
blanchet@48975
   831
                        REPEAT_DETERM o etac allE,
blanchet@48975
   832
                        dtac (mk_conjunctN n i), dtac mp, atac,
blanchet@48975
   833
                        dtac (mk_conjunctN n i'), dtac mp, atac,
blanchet@48975
   834
                        dtac (mk_conjunctN n i''), etac mp, etac sym])
blanchet@48975
   835
                    ks
blanchet@48975
   836
                  else etac (mk_InN_not_InM i k RS notE)))
blanchet@48975
   837
                (rev ks))
blanchet@48975
   838
              ks)
blanchet@48975
   839
          (rev (ks ~~ (from_to_sbds ~~ to_sbd_injs)))])
blanchet@48975
   840
      ((Lev_Sucs ~~ rv_Conss) ~~ (from_to_sbdss ~~ to_sbd_injss))] 1
blanchet@48975
   841
  end;
blanchet@48975
   842
blanchet@48975
   843
fun mk_mor_beh_tac m mor_def mor_cong beh_defs carT_defs strT_defs isNode_defs
blanchet@48975
   844
  to_sbd_injss from_to_sbdss Lev_0s Lev_Sucs rv_Nils rv_Conss Lev_sbds length_Levs length_Lev's
blanchet@51766
   845
  prefCl_Levs rv_lastss set_rv_Levsss set_Levsss set_image_Levsss set_mapss coalg_setss
blanchet@51761
   846
  map_comp_ids map_cong0s map_arg_congs {context = ctxt, prems = _} =
blanchet@48975
   847
  let
blanchet@48975
   848
    val n = length beh_defs;
blanchet@48975
   849
    val ks = 1 upto n;
blanchet@48975
   850
blanchet@48975
   851
    fun fbetw_tac (i, (carT_def, (isNode_def, (Lev_0, (rv_Nil, (Lev_sbd,
blanchet@51766
   852
      ((length_Lev, length_Lev'), (prefCl_Lev, (rv_lasts, (set_maps,
blanchet@48975
   853
        (coalg_sets, (set_rv_Levss, (set_Levss, set_image_Levss))))))))))))) =
blanchet@49305
   854
      EVERY' [rtac ballI, rtac (carT_def RS equalityD2 RS set_mp),
blanchet@48975
   855
        rtac CollectI, REPEAT_DETERM o rtac exI, rtac conjI, rtac refl, rtac conjI,
blanchet@48975
   856
        rtac conjI,
blanchet@49305
   857
          rtac @{thm UN_I}, rtac UNIV_I, rtac (Lev_0 RS equalityD2 RS set_mp),
blanchet@48975
   858
          rtac @{thm singletonI},
blanchet@48975
   859
        rtac conjI,
blanchet@48975
   860
          rtac @{thm UN_least}, rtac Lev_sbd,
blanchet@48975
   861
        rtac conjI,
blanchet@48975
   862
          rtac @{thm prefCl_UN}, rtac ssubst, rtac @{thm PrefCl_def}, REPEAT_DETERM o rtac allI,
blanchet@48975
   863
          rtac impI, etac conjE, rtac exI, rtac conjI, rtac @{thm ord_le_eq_trans},
traytel@50058
   864
          etac @{thm prefixeq_length_le}, etac length_Lev, rtac prefCl_Lev, etac conjI, atac,
blanchet@48975
   865
        rtac conjI,
blanchet@48975
   866
          rtac ballI, etac @{thm UN_E}, rtac conjI,
blanchet@48975
   867
          if n = 1 then K all_tac else rtac (mk_sumEN n),
blanchet@51766
   868
          EVERY' (map6 (fn i => fn isNode_def => fn set_maps =>
blanchet@48975
   869
            fn set_rv_Levs => fn set_Levs => fn set_image_Levs =>
blanchet@48975
   870
            EVERY' [rtac (mk_disjIN n i), rtac (isNode_def RS ssubst),
blanchet@48975
   871
              rtac exI, rtac conjI,
blanchet@48975
   872
              (if n = 1 then rtac @{thm if_P} THEN' etac length_Lev'
blanchet@48975
   873
              else rtac (@{thm if_P} RS arg_cong RS trans) THEN' etac length_Lev' THEN'
blanchet@49328
   874
                etac (sum_case_weak_cong RS trans) THEN' rtac (mk_sum_casesN n i)),
blanchet@51766
   875
              EVERY' (map2 (fn set_map => fn set_rv_Lev =>
blanchet@51766
   876
                EVERY' [rtac conjI, rtac ord_eq_le_trans, rtac (set_map RS trans),
blanchet@49305
   877
                  rtac trans_fun_cong_image_id_id_apply,
blanchet@48975
   878
                  etac set_rv_Lev, TRY o atac, etac conjI, atac])
blanchet@51766
   879
              (take m set_maps) set_rv_Levs),
blanchet@51766
   880
              CONJ_WRAP' (fn (set_map, (set_Lev, set_image_Lev)) =>
blanchet@51766
   881
                EVERY' [rtac (set_map RS trans), rtac equalityI, rtac @{thm image_subsetI},
blanchet@48975
   882
                  rtac CollectI, rtac @{thm SuccI}, rtac @{thm UN_I}, rtac UNIV_I, etac set_Lev,
blanchet@48975
   883
                  if n = 1 then rtac refl else atac, atac, rtac subsetI,
blanchet@48975
   884
                  REPEAT_DETERM o eresolve_tac [CollectE, @{thm SuccE}, @{thm UN_E}],
wenzelm@51798
   885
                  rtac set_image_Lev, atac, dtac length_Lev, hyp_subst_tac ctxt, dtac length_Lev',
blanchet@48975
   886
                  etac @{thm set_mp[OF equalityD1[OF arg_cong[OF length_append_singleton]]]},
blanchet@48975
   887
                  if n = 1 then rtac refl else atac])
blanchet@51766
   888
              (drop m set_maps ~~ (set_Levs ~~ set_image_Levs))])
blanchet@51766
   889
          ks isNode_defs set_mapss set_rv_Levss set_Levss set_image_Levss),
blanchet@51766
   890
          CONJ_WRAP' (fn (i, (rv_last, (isNode_def, (set_maps,
blanchet@48975
   891
            (set_rv_Levs, (set_Levs, set_image_Levs)))))) =>
blanchet@48975
   892
            EVERY' [rtac ballI,
blanchet@48975
   893
              REPEAT_DETERM o eresolve_tac [CollectE, @{thm SuccE}, @{thm UN_E}],
blanchet@48975
   894
              rtac (rev_mp OF [rv_last, impI]), etac exE, rtac (isNode_def RS ssubst),
blanchet@48975
   895
              rtac exI, rtac conjI,
blanchet@48975
   896
              (if n = 1 then rtac @{thm if_P} THEN' etac length_Lev'
blanchet@48975
   897
              else rtac (@{thm if_P} RS trans) THEN' etac length_Lev' THEN'
blanchet@49328
   898
                etac (sum_case_weak_cong RS trans) THEN' rtac (mk_sum_casesN n i)),
blanchet@51766
   899
              EVERY' (map2 (fn set_map => fn set_rv_Lev =>
blanchet@51766
   900
                EVERY' [rtac conjI, rtac ord_eq_le_trans, rtac (set_map RS trans),
blanchet@49305
   901
                  rtac trans_fun_cong_image_id_id_apply,
blanchet@48975
   902
                  etac set_rv_Lev, TRY o atac, etac conjI, atac])
blanchet@51766
   903
              (take m set_maps) set_rv_Levs),
blanchet@51766
   904
              CONJ_WRAP' (fn (set_map, (set_Lev, set_image_Lev)) =>
blanchet@51766
   905
                EVERY' [rtac (set_map RS trans), rtac equalityI, rtac @{thm image_subsetI},
blanchet@48975
   906
                  rtac CollectI, rtac @{thm SuccI}, rtac @{thm UN_I}, rtac UNIV_I, etac set_Lev,
blanchet@48975
   907
                  if n = 1 then rtac refl else atac, atac, rtac subsetI,
blanchet@48975
   908
                  REPEAT_DETERM o eresolve_tac [CollectE, @{thm SuccE}, @{thm UN_E}],
blanchet@48975
   909
                  REPEAT_DETERM_N 4 o etac thin_rl,
blanchet@48975
   910
                  rtac set_image_Lev,
wenzelm@51798
   911
                  atac, dtac length_Lev, hyp_subst_tac ctxt, dtac length_Lev',
blanchet@48975
   912
                  etac @{thm set_mp[OF equalityD1[OF arg_cong[OF length_append_singleton]]]},
blanchet@48975
   913
                  if n = 1 then rtac refl else atac])
blanchet@51766
   914
              (drop m set_maps ~~ (set_Levs ~~ set_image_Levs))])
blanchet@51766
   915
          (ks ~~ (rv_lasts ~~ (isNode_defs ~~ (set_mapss ~~
blanchet@48975
   916
            (set_rv_Levss ~~ (set_Levss ~~ set_image_Levss)))))),
blanchet@48975
   917
        (**)
blanchet@48975
   918
          rtac allI, rtac impI, rtac @{thm if_not_P}, rtac notI,
blanchet@48975
   919
          etac notE, etac @{thm UN_I[OF UNIV_I]},
blanchet@48975
   920
        (*root isNode*)
blanchet@48975
   921
          rtac (isNode_def RS ssubst), rtac exI, rtac conjI, rtac (@{thm if_P} RS trans),
blanchet@49305
   922
          rtac length_Lev', rtac (Lev_0 RS equalityD2 RS set_mp), rtac @{thm singletonI},
blanchet@48975
   923
          CONVERSION (Conv.top_conv
blanchet@48975
   924
            (K (Conv.try_conv (Conv.rewr_conv (rv_Nil RS eq_reflection)))) ctxt),
blanchet@48975
   925
          if n = 1 then rtac refl else rtac (mk_sum_casesN n i),
blanchet@51766
   926
          EVERY' (map2 (fn set_map => fn coalg_set =>
blanchet@51766
   927
            EVERY' [rtac conjI, rtac ord_eq_le_trans, rtac (set_map RS trans),
blanchet@49305
   928
              rtac trans_fun_cong_image_id_id_apply, etac coalg_set, atac])
blanchet@51766
   929
            (take m set_maps) (take m coalg_sets)),
blanchet@51766
   930
          CONJ_WRAP' (fn (set_map, (set_Lev, set_image_Lev)) =>
blanchet@51766
   931
            EVERY' [rtac (set_map RS trans), rtac equalityI, rtac @{thm image_subsetI},
blanchet@48975
   932
              rtac CollectI, rtac @{thm SuccI}, rtac @{thm UN_I}, rtac UNIV_I, rtac set_Lev,
blanchet@49305
   933
              rtac (Lev_0 RS equalityD2 RS set_mp), rtac @{thm singletonI}, rtac rv_Nil,
blanchet@48975
   934
              atac, rtac subsetI,
blanchet@48975
   935
              REPEAT_DETERM o eresolve_tac [CollectE, @{thm SuccE}, @{thm UN_E}],
blanchet@49305
   936
              rtac set_image_Lev, rtac (Lev_0 RS equalityD2 RS set_mp),
blanchet@48975
   937
              rtac @{thm singletonI}, dtac length_Lev',
blanchet@48975
   938
              etac @{thm set_mp[OF equalityD1[OF arg_cong[OF
blanchet@48975
   939
                trans[OF length_append_singleton arg_cong[of _ _ Suc, OF list.size(3)]]]]]},
blanchet@48975
   940
              rtac rv_Nil])
blanchet@51766
   941
          (drop m set_maps ~~ (nth set_Levss (i - 1) ~~ nth set_image_Levss (i - 1)))];
blanchet@48975
   942
blanchet@48975
   943
    fun mor_tac (i, (strT_def, (((Lev_0, Lev_Suc), (rv_Nil, rv_Cons)),
blanchet@51761
   944
      ((map_comp_id, (map_cong0, map_arg_cong)), (length_Lev', (from_to_sbds, to_sbd_injs)))))) =
blanchet@48975
   945
      EVERY' [rtac ballI, rtac sym, rtac trans, rtac strT_def,
blanchet@48975
   946
        rtac (@{thm if_P} RS
blanchet@49328
   947
          (if n = 1 then map_arg_cong else sum_case_weak_cong) RS trans),
blanchet@49305
   948
        rtac (@{thm list.size(3)} RS arg_cong RS trans RS equalityD2 RS set_mp),
blanchet@48975
   949
        rtac Lev_0, rtac @{thm singletonI},
blanchet@48975
   950
        CONVERSION (Conv.top_conv
blanchet@48975
   951
          (K (Conv.try_conv (Conv.rewr_conv (rv_Nil RS eq_reflection)))) ctxt),
blanchet@48975
   952
        if n = 1 then K all_tac
blanchet@49328
   953
        else (rtac (sum_case_weak_cong RS trans) THEN'
blanchet@48975
   954
          rtac (mk_sum_casesN n i) THEN' rtac (mk_sum_casesN n i RS trans)),
blanchet@51761
   955
        rtac (map_comp_id RS trans), rtac (map_cong0 OF replicate m refl),
blanchet@48975
   956
        EVERY' (map3 (fn i' => fn to_sbd_inj => fn from_to_sbd =>
traytel@49488
   957
          DETERM o EVERY' [rtac trans, rtac o_apply, rtac Pair_eqI, rtac conjI,
blanchet@48975
   958
            rtac trans, rtac @{thm Shift_def},
blanchet@48975
   959
            rtac equalityI, rtac subsetI, etac thin_rl, etac thin_rl,
blanchet@48975
   960
            REPEAT_DETERM o eresolve_tac [CollectE, @{thm UN_E}], dtac length_Lev', dtac asm_rl,
blanchet@48975
   961
            etac thin_rl, dtac @{thm set_rev_mp[OF _ equalityD1]},
blanchet@48975
   962
            rtac (@{thm length_Cons} RS arg_cong RS trans), rtac Lev_Suc,
blanchet@48975
   963
            CONJ_WRAP_GEN' (etac (Thm.permute_prems 1 1 UnE)) (fn i'' =>
blanchet@48975
   964
              EVERY' [REPEAT_DETERM o eresolve_tac [CollectE, exE, conjE],
traytel@49488
   965
                dtac list_inject_iffD1, etac conjE,
blanchet@48975
   966
                if i' = i'' then EVERY' [dtac (mk_InN_inject n i'),
traytel@49488
   967
                  dtac (Thm.permute_prems 0 2 (to_sbd_inj RS iffD1)),
wenzelm@51798
   968
                  atac, atac, hyp_subst_tac ctxt, etac @{thm UN_I[OF UNIV_I]}]
blanchet@48975
   969
                else etac (mk_InN_not_InM i' i'' RS notE)])
blanchet@48975
   970
            (rev ks),
blanchet@48975
   971
            rtac @{thm UN_least}, rtac subsetI, rtac CollectI, rtac @{thm UN_I[OF UNIV_I]},
blanchet@49366
   972
            rtac (Lev_Suc RS equalityD2 RS set_mp), rtac (mk_UnIN n i'), rtac CollectI,
blanchet@48975
   973
            REPEAT_DETERM o rtac exI, rtac conjI, rtac refl, etac conjI, atac,
blanchet@48975
   974
            rtac trans, rtac @{thm shift_def}, rtac ssubst, rtac @{thm fun_eq_iff}, rtac allI,
blanchet@48975
   975
            rtac @{thm if_cong}, rtac (@{thm length_Cons} RS arg_cong RS trans), rtac iffI,
blanchet@48975
   976
            dtac asm_rl, dtac asm_rl, dtac asm_rl,
blanchet@49305
   977
            dtac (Lev_Suc RS equalityD1 RS set_mp),
blanchet@48975
   978
            CONJ_WRAP_GEN' (etac (Thm.permute_prems 1 1 UnE)) (fn i'' =>
blanchet@48975
   979
              EVERY' [REPEAT_DETERM o eresolve_tac [CollectE, exE, conjE],
traytel@49488
   980
                dtac list_inject_iffD1, etac conjE,
blanchet@48975
   981
                if i' = i'' then EVERY' [dtac (mk_InN_inject n i'),
traytel@49488
   982
                  dtac (Thm.permute_prems 0 2 (to_sbd_inj RS iffD1)),
wenzelm@51798
   983
                  atac, atac, hyp_subst_tac ctxt, atac]
blanchet@48975
   984
                else etac (mk_InN_not_InM i' i'' RS notE)])
blanchet@48975
   985
            (rev ks),
blanchet@49366
   986
            rtac (Lev_Suc RS equalityD2 RS set_mp), rtac (mk_UnIN n i'), rtac CollectI,
blanchet@48975
   987
            REPEAT_DETERM o rtac exI, rtac conjI, rtac refl, etac conjI, atac,
blanchet@48975
   988
            CONVERSION (Conv.top_conv
blanchet@48975
   989
              (K (Conv.try_conv (Conv.rewr_conv (rv_Cons RS eq_reflection)))) ctxt),
blanchet@48975
   990
            if n = 1 then K all_tac
blanchet@49328
   991
            else rtac sum_case_weak_cong THEN' rtac (mk_sum_casesN n i' RS trans),
blanchet@49504
   992
            SELECT_GOAL (unfold_thms_tac ctxt [from_to_sbd]), rtac refl,
blanchet@48975
   993
            rtac refl])
blanchet@48975
   994
        ks to_sbd_injs from_to_sbds)];
blanchet@48975
   995
  in
blanchet@48975
   996
    (rtac mor_cong THEN'
blanchet@48975
   997
    EVERY' (map (fn thm => rtac (thm RS ext)) beh_defs) THEN'
blanchet@48975
   998
    stac mor_def THEN' rtac conjI THEN'
blanchet@48975
   999
    CONJ_WRAP' fbetw_tac
blanchet@48975
  1000
      (ks ~~ (carT_defs ~~ (isNode_defs ~~ (Lev_0s ~~ (rv_Nils ~~ (Lev_sbds ~~
blanchet@48975
  1001
        ((length_Levs ~~ length_Lev's) ~~ (prefCl_Levs ~~ (rv_lastss ~~
blanchet@51766
  1002
          (set_mapss ~~ (coalg_setss ~~
blanchet@48975
  1003
            (set_rv_Levsss ~~ (set_Levsss ~~ set_image_Levsss))))))))))))) THEN'
blanchet@48975
  1004
    CONJ_WRAP' mor_tac
blanchet@48975
  1005
      (ks ~~ (strT_defs ~~ (((Lev_0s ~~ Lev_Sucs) ~~ (rv_Nils ~~ rv_Conss)) ~~
blanchet@51761
  1006
        ((map_comp_ids ~~ (map_cong0s ~~ map_arg_congs)) ~~
blanchet@48975
  1007
          (length_Lev's ~~ (from_to_sbdss ~~ to_sbd_injss))))))) 1
blanchet@48975
  1008
  end;
blanchet@48975
  1009
blanchet@51761
  1010
fun mk_congruent_str_final_tac m lsbisE map_comp_id map_cong0 equiv_LSBISs =
blanchet@48975
  1011
  EVERY' [rtac @{thm congruentI}, dtac lsbisE,
blanchet@48975
  1012
    REPEAT_DETERM o eresolve_tac [CollectE, conjE, bexE], rtac (o_apply RS trans),
blanchet@48975
  1013
    etac (sym RS arg_cong RS trans), rtac (map_comp_id RS trans),
blanchet@51761
  1014
    rtac (map_cong0 RS trans), REPEAT_DETERM_N m o rtac refl,
blanchet@48975
  1015
    EVERY' (map (fn equiv_LSBIS =>
blanchet@49305
  1016
      EVERY' [rtac @{thm equiv_proj}, rtac equiv_LSBIS, etac set_mp, atac])
blanchet@48975
  1017
    equiv_LSBISs), rtac sym, rtac (o_apply RS trans),
blanchet@48975
  1018
    etac (sym RS arg_cong RS trans), rtac map_comp_id] 1;
blanchet@48975
  1019
blanchet@51766
  1020
fun mk_coalg_final_tac m coalg_def congruent_str_finals equiv_LSBISs set_mapss coalgT_setss =
blanchet@48975
  1021
  EVERY' [stac coalg_def,
blanchet@51766
  1022
    CONJ_WRAP' (fn ((set_maps, coalgT_sets), (equiv_LSBIS, congruent_str_final)) =>
blanchet@48975
  1023
      EVERY' [rtac @{thm univ_preserves}, rtac equiv_LSBIS, rtac congruent_str_final,
blanchet@48975
  1024
        rtac ballI, rtac @{thm ssubst_mem}, rtac o_apply, rtac CollectI,
blanchet@51766
  1025
        EVERY' (map2 (fn set_map => fn coalgT_set =>
blanchet@51766
  1026
          EVERY' [rtac conjI, rtac (set_map RS ord_eq_le_trans),
blanchet@49305
  1027
            rtac ord_eq_le_trans_trans_fun_cong_image_id_id_apply,
blanchet@48975
  1028
            etac coalgT_set])
blanchet@51766
  1029
        (take m set_maps) (take m coalgT_sets)),
blanchet@51766
  1030
        CONJ_WRAP' (fn (equiv_LSBIS, (set_map, coalgT_set)) =>
blanchet@51766
  1031
          EVERY' [rtac (set_map RS ord_eq_le_trans),
blanchet@48975
  1032
            rtac @{thm image_subsetI}, rtac ssubst, rtac @{thm proj_in_iff},
blanchet@49305
  1033
            rtac equiv_LSBIS, etac set_rev_mp, etac coalgT_set])
blanchet@51766
  1034
        (equiv_LSBISs ~~ drop m (set_maps ~~ coalgT_sets))])
blanchet@51766
  1035
    ((set_mapss ~~ coalgT_setss) ~~ (equiv_LSBISs ~~ congruent_str_finals))] 1;
blanchet@48975
  1036
blanchet@48975
  1037
fun mk_mor_T_final_tac mor_def congruent_str_finals equiv_LSBISs =
blanchet@48975
  1038
  EVERY' [stac mor_def, rtac conjI,
blanchet@48975
  1039
    CONJ_WRAP' (fn equiv_LSBIS =>
blanchet@48975
  1040
      EVERY' [rtac ballI, rtac ssubst, rtac @{thm proj_in_iff}, rtac equiv_LSBIS, atac])
blanchet@48975
  1041
    equiv_LSBISs,
blanchet@48975
  1042
    CONJ_WRAP' (fn (equiv_LSBIS, congruent_str_final) =>
blanchet@48975
  1043
      EVERY' [rtac ballI, rtac sym, rtac trans, rtac @{thm univ_commute}, rtac equiv_LSBIS,
blanchet@48975
  1044
        rtac congruent_str_final, atac, rtac o_apply])
blanchet@48975
  1045
    (equiv_LSBISs ~~ congruent_str_finals)] 1;
blanchet@48975
  1046
blanchet@51761
  1047
fun mk_mor_Rep_tac m defs Reps Abs_inverses coalg_final_setss map_comp_ids map_cong0Ls
blanchet@48975
  1048
  {context = ctxt, prems = _} =
blanchet@49504
  1049
  unfold_thms_tac ctxt defs THEN
blanchet@48975
  1050
  EVERY' [rtac conjI,
blanchet@48975
  1051
    CONJ_WRAP' (fn thm => rtac ballI THEN' rtac thm) Reps,
blanchet@51761
  1052
    CONJ_WRAP' (fn (Rep, ((map_comp_id, map_cong0L), coalg_final_sets)) =>
blanchet@51761
  1053
      EVERY' [rtac ballI, rtac (map_comp_id RS trans), rtac map_cong0L,
blanchet@48975
  1054
        EVERY' (map2 (fn Abs_inverse => fn coalg_final_set =>
blanchet@48975
  1055
          EVERY' [rtac ballI, rtac (o_apply RS trans), rtac Abs_inverse,
blanchet@49305
  1056
            etac set_rev_mp, rtac coalg_final_set, rtac Rep])
blanchet@48975
  1057
        Abs_inverses (drop m coalg_final_sets))])
blanchet@51761
  1058
    (Reps ~~ ((map_comp_ids ~~ map_cong0Ls) ~~ coalg_final_setss))] 1;
blanchet@48975
  1059
blanchet@48975
  1060
fun mk_mor_Abs_tac defs Abs_inverses {context = ctxt, prems = _} =
blanchet@49504
  1061
  unfold_thms_tac ctxt defs THEN
blanchet@48975
  1062
  EVERY' [rtac conjI,
blanchet@48975
  1063
    CONJ_WRAP' (K (rtac ballI THEN' rtac UNIV_I)) Abs_inverses,
blanchet@48975
  1064
    CONJ_WRAP' (fn thm => rtac ballI THEN' etac (thm RS arg_cong RS sym)) Abs_inverses] 1;
blanchet@48975
  1065
blanchet@51761
  1066
fun mk_mor_unfold_tac m mor_UNIV dtor_defs unfold_defs Abs_inverses morEs map_comp_ids map_cong0s =
traytel@49488
  1067
  EVERY' [rtac iffD2, rtac mor_UNIV,
blanchet@51761
  1068
    CONJ_WRAP' (fn ((Abs_inverse, morE), ((dtor_def, unfold_def), (map_comp_id, map_cong0))) =>
blanchet@49501
  1069
      EVERY' [rtac ext, rtac (o_apply RS trans RS sym), rtac (dtor_def RS trans),
blanchet@49504
  1070
        rtac (unfold_def RS arg_cong RS trans), rtac (Abs_inverse RS arg_cong RS trans),
blanchet@48975
  1071
        rtac (morE RS arg_cong RS trans), rtac (map_comp_id RS trans),
blanchet@51761
  1072
        rtac (o_apply RS trans RS sym), rtac map_cong0,
blanchet@48975
  1073
        REPEAT_DETERM_N m o rtac refl,
blanchet@49504
  1074
        EVERY' (map (fn thm => rtac (thm RS trans) THEN' rtac (o_apply RS sym)) unfold_defs)])
blanchet@51761
  1075
    ((Abs_inverses ~~ morEs) ~~ ((dtor_defs ~~ unfold_defs) ~~ (map_comp_ids ~~ map_cong0s)))] 1;
blanchet@48975
  1076
blanchet@48975
  1077
fun mk_raw_coind_tac bis_def bis_cong bis_O bis_converse bis_Gr tcoalg coalgT mor_T_final
blanchet@48975
  1078
  sbis_lsbis lsbis_incls incl_lsbiss equiv_LSBISs mor_Rep Rep_injects =
blanchet@48975
  1079
  let
blanchet@48975
  1080
    val n = length Rep_injects;
blanchet@48975
  1081
  in
traytel@49488
  1082
    EVERY' [rtac rev_mp, ftac (bis_def RS iffD1),
blanchet@48975
  1083
      REPEAT_DETERM o etac conjE, rtac bis_cong, rtac bis_O, rtac bis_converse,
blanchet@48975
  1084
      rtac bis_Gr, rtac tcoalg, rtac mor_Rep, rtac bis_O, atac, rtac bis_Gr, rtac tcoalg,
blanchet@48975
  1085
      rtac mor_Rep, REPEAT_DETERM_N n o etac @{thm relImage_Gr},
blanchet@48975
  1086
      rtac impI, rtac rev_mp, rtac bis_cong, rtac bis_O, rtac bis_Gr, rtac coalgT,
blanchet@48975
  1087
      rtac mor_T_final, rtac bis_O, rtac sbis_lsbis, rtac bis_converse, rtac bis_Gr, rtac coalgT,
blanchet@48975
  1088
      rtac mor_T_final, EVERY' (map (fn thm => rtac (thm RS @{thm relInvImage_Gr})) lsbis_incls),
blanchet@48975
  1089
      rtac impI,
blanchet@48975
  1090
      CONJ_WRAP' (fn (Rep_inject, (equiv_LSBIS , (incl_lsbis, lsbis_incl))) =>
blanchet@48975
  1091
        EVERY' [rtac subset_trans, rtac @{thm relInvImage_UNIV_relImage}, rtac subset_trans,
blanchet@48975
  1092
          rtac @{thm relInvImage_mono}, rtac subset_trans, etac incl_lsbis,
blanchet@49305
  1093
          rtac ord_eq_le_trans, rtac @{thm sym[OF relImage_relInvImage]},
blanchet@48975
  1094
          rtac @{thm xt1(3)}, rtac @{thm Sigma_cong},
blanchet@48975
  1095
          rtac @{thm proj_image}, rtac @{thm proj_image}, rtac lsbis_incl,
blanchet@48975
  1096
          rtac subset_trans, rtac @{thm relImage_mono}, rtac incl_lsbis, atac,
traytel@51447
  1097
          rtac @{thm relImage_proj}, rtac equiv_LSBIS, rtac @{thm relInvImage_Id_on},
blanchet@48975
  1098
          rtac Rep_inject])
blanchet@48975
  1099
      (Rep_injects ~~ (equiv_LSBISs ~~ (incl_lsbiss ~~ lsbis_incls)))] 1
blanchet@48975
  1100
  end;
blanchet@48975
  1101
blanchet@48975
  1102
fun mk_unique_mor_tac raw_coinds bis =
blanchet@48975
  1103
  CONJ_WRAP' (fn raw_coind =>
blanchet@49305
  1104
    EVERY' [rtac impI, rtac (bis RS raw_coind RS set_mp RS @{thm IdD}), atac,
blanchet@48975
  1105
      etac conjunct1, atac, etac conjunct2, rtac @{thm image2_eqI}, rtac refl, rtac refl, atac])
blanchet@48975
  1106
  raw_coinds 1;
blanchet@48975
  1107
blanchet@49504
  1108
fun mk_unfold_unique_mor_tac raw_coinds bis mor unfold_defs =
blanchet@49504
  1109
  CONJ_WRAP' (fn (raw_coind, unfold_def) =>
blanchet@49305
  1110
    EVERY' [rtac ext, etac (bis RS raw_coind RS set_mp RS @{thm IdD}), rtac mor,
blanchet@49504
  1111
      rtac @{thm image2_eqI}, rtac refl, rtac (unfold_def RS arg_cong RS trans),
blanchet@49504
  1112
      rtac (o_apply RS sym), rtac UNIV_I]) (raw_coinds ~~ unfold_defs) 1;
blanchet@48975
  1113
blanchet@51761
  1114
fun mk_dtor_o_ctor_tac ctor_def unfold map_comp_id map_cong0L unfold_o_dtors
blanchet@48975
  1115
  {context = ctxt, prems = _} =
blanchet@49504
  1116
  unfold_thms_tac ctxt [ctor_def] THEN EVERY' [rtac ext, rtac trans, rtac o_apply,
blanchet@51761
  1117
    rtac trans, rtac unfold, rtac trans, rtac map_comp_id, rtac trans, rtac map_cong0L,
blanchet@48975
  1118
    EVERY' (map (fn thm =>
blanchet@49585
  1119
      rtac ballI THEN' rtac (trans OF [thm RS fun_cong, id_apply])) unfold_o_dtors),
blanchet@49585
  1120
    rtac sym, rtac id_apply] 1;
blanchet@48975
  1121
blanchet@51761
  1122
fun mk_corec_tac m corec_defs unfold map_cong0 corec_Inls {context = ctxt, prems = _} =
blanchet@49504
  1123
  unfold_thms_tac ctxt corec_defs THEN EVERY' [rtac trans, rtac (o_apply RS arg_cong),
blanchet@51761
  1124
    rtac trans, rtac unfold, fo_rtac (@{thm sum.cases(2)} RS arg_cong RS trans) ctxt, rtac map_cong0,
blanchet@48975
  1125
    REPEAT_DETERM_N m o rtac refl,
blanchet@48975
  1126
    EVERY' (map (fn thm => rtac @{thm sum_case_expand_Inr} THEN' rtac thm) corec_Inls)] 1;
blanchet@48975
  1127
traytel@51739
  1128
fun mk_corec_unique_mor_tac corec_defs corec_Inls unfold_unique_mor {context = ctxt, prems = _} =
traytel@51739
  1129
  unfold_thms_tac ctxt
traytel@51739
  1130
    (corec_defs @ map (fn thm => thm RS @{thm sum_case_expand_Inr'}) corec_Inls) THEN
traytel@51739
  1131
  etac unfold_unique_mor 1;
traytel@51739
  1132
blanchet@49545
  1133
fun mk_dtor_srel_coinduct_tac ks raw_coind bis_srel =
blanchet@49506
  1134
  EVERY' [rtac rev_mp, rtac raw_coind, rtac ssubst, rtac bis_srel, rtac conjI,
blanchet@48975
  1135
    CONJ_WRAP' (K (rtac @{thm ord_le_eq_trans[OF subset_UNIV UNIV_Times_UNIV[THEN sym]]})) ks,
blanchet@48975
  1136
    CONJ_WRAP' (K (EVERY' [rtac allI, rtac allI, rtac impI,
blanchet@48975
  1137
      REPEAT_DETERM o etac allE, etac mp, etac CollectE, etac @{thm splitD}])) ks,
blanchet@48975
  1138
    rtac impI, REPEAT_DETERM o etac conjE,
blanchet@49305
  1139
    CONJ_WRAP' (K (EVERY' [rtac impI, rtac @{thm IdD}, etac set_mp,
blanchet@48975
  1140
      rtac CollectI, etac @{thm prod_caseI}])) ks] 1;
blanchet@48975
  1141
wenzelm@51798
  1142
fun mk_dtor_srel_strong_coinduct_tac ctxt m cTs cts dtor_srel_coinduct srel_monos srel_Ids =
blanchet@49545
  1143
  EVERY' [rtac rev_mp, rtac (Drule.instantiate' cTs cts dtor_srel_coinduct),
blanchet@49506
  1144
    EVERY' (map2 (fn srel_mono => fn srel_Id =>
blanchet@48975
  1145
      EVERY' [REPEAT_DETERM o resolve_tac [allI, impI], REPEAT_DETERM o etac allE,
wenzelm@51798
  1146
        etac disjE, etac mp, atac, hyp_subst_tac ctxt, rtac (srel_mono RS set_mp),
blanchet@48975
  1147
        REPEAT_DETERM_N m o rtac @{thm subset_refl},
blanchet@49506
  1148
        REPEAT_DETERM_N (length srel_monos) o rtac @{thm Id_subset},
blanchet@49506
  1149
        rtac (srel_Id RS equalityD2 RS set_mp), rtac @{thm IdI}])
blanchet@49506
  1150
    srel_monos srel_Ids),
blanchet@48975
  1151
    rtac impI, REPEAT_DETERM o etac conjE,
blanchet@49506
  1152
    CONJ_WRAP' (K (rtac impI THEN' etac mp THEN' etac disjI1)) srel_Ids] 1;
blanchet@48975
  1153
blanchet@49581
  1154
fun mk_dtor_map_coinduct_tac m ks raw_coind bis_def =
blanchet@48975
  1155
  let
blanchet@48975
  1156
    val n = length ks;
blanchet@48975
  1157
  in
blanchet@48975
  1158
    EVERY' [rtac rev_mp, rtac raw_coind, rtac ssubst, rtac bis_def, rtac conjI,
blanchet@48975
  1159
      CONJ_WRAP' (K (rtac @{thm ord_le_eq_trans[OF subset_UNIV UNIV_Times_UNIV[THEN sym]]})) ks,
blanchet@48975
  1160
      CONJ_WRAP' (fn i => EVERY' [select_prem_tac n (dtac asm_rl) i, REPEAT_DETERM o rtac allI,
blanchet@48975
  1161
        rtac impI, REPEAT_DETERM o dtac @{thm meta_spec}, etac CollectE, etac @{thm meta_impE},
blanchet@48975
  1162
        atac, etac exE, etac conjE, etac conjE, rtac bexI, rtac conjI,
blanchet@48975
  1163
        etac @{thm fst_conv[THEN subst]}, etac @{thm snd_conv[THEN subst]},
traytel@49490
  1164
        rtac CollectI, REPEAT_DETERM_N m o (rtac conjI THEN' rtac subset_UNIV),
blanchet@48975
  1165
        CONJ_WRAP' (fn i' => EVERY' [rtac subsetI, rtac CollectI, dtac (mk_conjunctN n i'),
blanchet@48975
  1166
          REPEAT_DETERM o etac allE, etac mp, rtac @{thm ssubst_mem[OF pair_collapse]}, atac])
blanchet@48975
  1167
        ks])
blanchet@48975
  1168
      ks,
blanchet@48975
  1169
      rtac impI,
blanchet@48975
  1170
      CONJ_WRAP' (fn i => EVERY' [rtac impI, dtac (mk_conjunctN n i),
blanchet@49305
  1171
        rtac @{thm subst[OF pair_in_Id_conv]}, etac set_mp,
blanchet@48975
  1172
        rtac CollectI, etac (refl RSN (2, @{thm subst_Pair}))]) ks] 1
blanchet@48975
  1173
  end;
blanchet@48975
  1174
traytel@51447
  1175
fun mk_dtor_map_strong_coinduct_tac ks cTs cts dtor_map_coinduct bis_def bis_Id_on =
blanchet@49581
  1176
  EVERY' [rtac rev_mp, rtac (Drule.instantiate' cTs cts dtor_map_coinduct),
blanchet@48975
  1177
    EVERY' (map (fn i =>
blanchet@49585
  1178
      EVERY' [etac disjE, REPEAT_DETERM o dtac @{thm meta_spec}, etac meta_mp,
traytel@51447
  1179
        atac, rtac rev_mp, rtac subst, rtac bis_def, rtac bis_Id_on,
blanchet@48975
  1180
        rtac impI, dtac conjunct2, dtac (mk_conjunctN (length ks) i), REPEAT_DETERM o etac allE,
traytel@51447
  1181
        etac impE, etac @{thm Id_on_UNIV_I}, REPEAT_DETERM o eresolve_tac [bexE, conjE, CollectE],
blanchet@48975
  1182
        rtac exI, rtac conjI, etac conjI, atac,
blanchet@48975
  1183
        CONJ_WRAP' (K (EVERY' [REPEAT_DETERM o resolve_tac [allI, impI],
traytel@51447
  1184
          rtac disjI2, rtac @{thm Id_onD}, etac set_mp, atac])) ks])
blanchet@48975
  1185
    ks),
blanchet@48975
  1186
    rtac impI, REPEAT_DETERM o etac conjE,
blanchet@48975
  1187
    CONJ_WRAP' (K (rtac impI THEN' etac mp THEN' etac disjI1)) ks] 1;
blanchet@48975
  1188
blanchet@51761
  1189
fun mk_map_tac m n cT unfold map_comp' map_cong0 =
blanchet@48975
  1190
  EVERY' [rtac ext, rtac (o_apply RS trans RS sym), rtac (o_apply RS trans RS sym),
blanchet@51761
  1191
    rtac (unfold RS trans), rtac (Thm.permute_prems 0 1 (map_comp' RS box_equals)), rtac map_cong0,
blanchet@48975
  1192
    REPEAT_DETERM_N m o rtac (@{thm id_o} RS fun_cong),
blanchet@48975
  1193
    REPEAT_DETERM_N n o rtac (@{thm o_id} RS fun_cong),
blanchet@48975
  1194
    rtac (o_apply RS (Drule.instantiate' [cT] [] arg_cong) RS sym)] 1;
blanchet@48975
  1195
blanchet@48975
  1196
fun mk_set_le_tac n hset_minimal set_hsets set_hset_hsetss =
blanchet@48975
  1197
  EVERY' [rtac hset_minimal,
blanchet@48975
  1198
    REPEAT_DETERM_N n o rtac @{thm Un_upper1},
blanchet@48975
  1199
    REPEAT_DETERM_N n o
blanchet@48975
  1200
      EVERY' (map3 (fn i => fn set_hset => fn set_hset_hsets =>
blanchet@49366
  1201
        EVERY' [rtac subsetI, rtac @{thm UnI2}, rtac (mk_UnIN n i), etac @{thm UN_I},
blanchet@48975
  1202
          etac UnE, etac set_hset, REPEAT_DETERM_N (n - 1) o etac UnE,
blanchet@48975
  1203
          EVERY' (map (fn thm => EVERY' [etac @{thm UN_E}, etac thm, atac]) set_hset_hsets)])
blanchet@48975
  1204
      (1 upto n) set_hsets set_hset_hsetss)] 1;
blanchet@48975
  1205
blanchet@49585
  1206
fun mk_dtor_set_tac n set_le set_incl_hset set_hset_incl_hsets =
blanchet@48975
  1207
  EVERY' [rtac equalityI, rtac set_le, rtac @{thm Un_least}, rtac set_incl_hset,
blanchet@48975
  1208
    REPEAT_DETERM_N (n - 1) o rtac @{thm Un_least},
blanchet@48975
  1209
    EVERY' (map (fn thm => rtac @{thm UN_least} THEN' etac thm) set_hset_incl_hsets)] 1;
blanchet@48975
  1210
blanchet@49504
  1211
fun mk_map_id_tac maps unfold_unique unfold_dtor =
blanchet@49504
  1212
  EVERY' [rtac (unfold_unique RS trans), EVERY' (map (fn thm => rtac (thm RS sym)) maps),
blanchet@49504
  1213
    rtac unfold_dtor] 1;
blanchet@48975
  1214
blanchet@51761
  1215
fun mk_map_comp_tac m n maps map_comps map_cong0s unfold_unique =
blanchet@49504
  1216
  EVERY' [rtac unfold_unique,
blanchet@51761
  1217
    EVERY' (map3 (fn map_thm => fn map_comp => fn map_cong0 =>
blanchet@48975
  1218
      EVERY' (map rtac
blanchet@48975
  1219
        ([@{thm o_assoc} RS trans,
blanchet@48975
  1220
        @{thm arg_cong2[of _ _ _ _ "op o"]} OF [map_comp RS sym, refl] RS trans,
blanchet@48975
  1221
        @{thm o_assoc} RS trans RS sym,
blanchet@48975
  1222
        @{thm arg_cong2[of _ _ _ _ "op o"]} OF [map_thm, refl] RS trans,
blanchet@48975
  1223
        @{thm o_assoc} RS sym RS trans, map_thm RS arg_cong RS trans, @{thm o_assoc} RS trans,
blanchet@48975
  1224
        @{thm arg_cong2[of _ _ _ _ "op o"]} OF [map_comp RS sym, refl] RS trans,
blanchet@51761
  1225
        ext, o_apply RS trans,  o_apply RS trans RS sym, map_cong0] @
blanchet@48975
  1226
        replicate m (@{thm id_o} RS fun_cong) @
blanchet@48975
  1227
        replicate n (@{thm o_id} RS fun_cong))))
blanchet@51761
  1228
    maps map_comps map_cong0s)] 1;
blanchet@48975
  1229
wenzelm@51798
  1230
fun mk_mcong_tac ctxt m coinduct_tac map_comp's dtor_maps map_cong0s set_mapss set_hsetss
blanchet@48975
  1231
  set_hset_hsetsss =
blanchet@48975
  1232
  let
blanchet@48975
  1233
    val n = length map_comp's;
blanchet@48975
  1234
    val ks = 1 upto n;
blanchet@48975
  1235
  in
blanchet@48975
  1236
    EVERY' ([rtac rev_mp,
blanchet@48975
  1237
      coinduct_tac] @
blanchet@51766
  1238
      maps (fn (((((map_comp'_trans, dtor_maps_trans), map_cong0), set_maps), set_hsets),
blanchet@48975
  1239
        set_hset_hsetss) =>
wenzelm@51798
  1240
        [REPEAT_DETERM o eresolve_tac [exE, conjE], hyp_subst_tac ctxt, rtac exI, rtac conjI,
wenzelm@51798
  1241
         rtac conjI, rtac map_comp'_trans, rtac sym, rtac dtor_maps_trans, rtac map_cong0,
blanchet@49585
  1242
         REPEAT_DETERM_N m o (rtac o_apply_trans_sym THEN' rtac id_apply),
blanchet@48975
  1243
         REPEAT_DETERM_N n o rtac fst_convol_fun_cong_sym,
blanchet@51761
  1244
         rtac map_comp'_trans, rtac sym, rtac dtor_maps_trans, rtac map_cong0,
blanchet@48975
  1245
         EVERY' (maps (fn set_hset =>
blanchet@49585
  1246
           [rtac o_apply_trans_sym, rtac (id_apply RS trans), etac CollectE,
blanchet@48975
  1247
           REPEAT_DETERM o etac conjE, etac bspec, etac set_hset]) set_hsets),
blanchet@48975
  1248
         REPEAT_DETERM_N n o rtac snd_convol_fun_cong_sym,
blanchet@51766
  1249
         CONJ_WRAP' (fn (set_map, set_hset_hsets) =>
blanchet@48975
  1250
           EVERY' [REPEAT_DETERM o rtac allI, rtac impI, rtac @{thm image_convolD},
blanchet@51766
  1251
             etac set_rev_mp, rtac ord_eq_le_trans, rtac set_map,
blanchet@48975
  1252
             rtac @{thm image_mono}, rtac subsetI, rtac CollectI, etac CollectE,
blanchet@48975
  1253
             REPEAT_DETERM o etac conjE,
blanchet@48975
  1254
             CONJ_WRAP' (fn set_hset_hset =>
blanchet@48975
  1255
               EVERY' [rtac ballI, etac bspec, etac set_hset_hset, atac]) set_hset_hsets])
blanchet@51766
  1256
           (drop m set_maps ~~ set_hset_hsetss)])
blanchet@49541
  1257
        (map (fn th => th RS trans) map_comp's ~~ map (fn th => th RS trans) dtor_maps ~~
blanchet@51766
  1258
          map_cong0s ~~ set_mapss ~~ set_hsetss ~~ set_hset_hsetsss) @
blanchet@48975
  1259
      [rtac impI,
blanchet@48975
  1260
       CONJ_WRAP' (fn k =>
blanchet@48975
  1261
         EVERY' [rtac impI, dtac (mk_conjunctN n k), etac mp, rtac exI, rtac conjI, etac CollectI,
blanchet@48975
  1262
           rtac conjI, rtac refl, rtac refl]) ks]) 1
blanchet@48975
  1263
  end
blanchet@48975
  1264
blanchet@49543
  1265
fun mk_dtor_map_unique_tac unfold_unique map_comps {context = ctxt, prems = _} =
blanchet@49504
  1266
  rtac unfold_unique 1 THEN
blanchet@49504
  1267
  unfold_thms_tac ctxt (map (fn thm => thm RS sym) map_comps @ @{thms o_assoc id_o o_id}) THEN
blanchet@48975
  1268
  ALLGOALS (etac sym);
blanchet@48975
  1269
blanchet@51766
  1270
fun mk_col_natural_tac cts rec_0s rec_Sucs dtor_maps set_mapss
blanchet@48975
  1271
  {context = ctxt, prems = _} =
blanchet@48975
  1272
  let
blanchet@49541
  1273
    val n = length dtor_maps;
blanchet@48975
  1274
  in
blanchet@49305
  1275
    EVERY' [rtac (Drule.instantiate' [] cts nat_induct),
blanchet@49504
  1276
      REPEAT_DETERM o rtac allI, SELECT_GOAL (unfold_thms_tac ctxt rec_0s),
blanchet@48975
  1277
      CONJ_WRAP' (K (rtac @{thm image_empty})) rec_0s,
blanchet@48975
  1278
      REPEAT_DETERM o rtac allI,
blanchet@49541
  1279
      CONJ_WRAP' (fn (rec_Suc, (dtor_map, set_nats)) => EVERY'
blanchet@49504
  1280
        [SELECT_GOAL (unfold_thms_tac ctxt
blanchet@49541
  1281
          (rec_Suc :: dtor_map :: set_nats @ @{thms image_Un image_UN UN_simps(10)})),
blanchet@48975
  1282
        rtac @{thm Un_cong}, rtac refl,
blanchet@48975
  1283
        CONJ_WRAP_GEN' (rtac (Thm.permute_prems 0 1 @{thm Un_cong}))
blanchet@48975
  1284
          (fn i => EVERY' [rtac @{thm UN_cong[OF refl]},
blanchet@48975
  1285
            REPEAT_DETERM o etac allE, etac (mk_conjunctN n i)]) (n downto 1)])
blanchet@51766
  1286
      (rec_Sucs ~~ (dtor_maps ~~ set_mapss))] 1
blanchet@48975
  1287
  end;
blanchet@48975
  1288
blanchet@51766
  1289
fun mk_set_map_tac hset_def col_natural =
blanchet@48975
  1290
  EVERY' (map rtac [ext, (o_apply RS trans), (hset_def RS trans), sym,
blanchet@48975
  1291
    (o_apply RS trans), (@{thm image_cong} OF [hset_def, refl] RS trans),
blanchet@48975
  1292
    (@{thm image_UN} RS trans), (refl RS @{thm UN_cong}), col_natural]) 1;
blanchet@48975
  1293
blanchet@48975
  1294
fun mk_col_bd_tac m j cts rec_0s rec_Sucs sbd_Card_order sbd_Cinfinite set_sbdss =
blanchet@48975
  1295
  let
blanchet@48975
  1296
    val n = length rec_0s;
blanchet@48975
  1297
  in
blanchet@49305
  1298
    EVERY' [rtac (Drule.instantiate' [] cts nat_induct),
blanchet@48975
  1299
      REPEAT_DETERM o rtac allI,
blanchet@49305
  1300
      CONJ_WRAP' (fn rec_0 => EVERY' (map rtac [ordIso_ordLeq_trans,
blanchet@48975
  1301
        @{thm card_of_ordIso_subst}, rec_0, @{thm Card_order_empty}, sbd_Card_order])) rec_0s,
blanchet@48975
  1302
      REPEAT_DETERM o rtac allI,
blanchet@48975
  1303
      CONJ_WRAP' (fn (rec_Suc, set_sbds) => EVERY'
blanchet@49305
  1304
        [rtac ordIso_ordLeq_trans, rtac @{thm card_of_ordIso_subst}, rtac rec_Suc,
blanchet@48975
  1305
        rtac (sbd_Cinfinite RSN (3, @{thm Un_Cinfinite_bound})), rtac (nth set_sbds (j - 1)),
blanchet@48975
  1306
        REPEAT_DETERM_N (n - 1) o rtac (sbd_Cinfinite RSN (3, @{thm Un_Cinfinite_bound})),
blanchet@48975
  1307
        EVERY' (map2 (fn i => fn set_sbd => EVERY' [rtac @{thm UNION_Cinfinite_bound},
blanchet@48975
  1308
          rtac set_sbd, rtac ballI, REPEAT_DETERM o etac allE,
blanchet@48975
  1309
          etac (mk_conjunctN n i), rtac sbd_Cinfinite]) (1 upto n) (drop m set_sbds))])
blanchet@48975
  1310
      (rec_Sucs ~~ set_sbdss)] 1
blanchet@48975
  1311
  end;
blanchet@48975
  1312
blanchet@48975
  1313
fun mk_set_bd_tac sbd_Cinfinite hset_def col_bd =
blanchet@49305
  1314
  EVERY' (map rtac [ordIso_ordLeq_trans, @{thm card_of_ordIso_subst}, hset_def,
blanchet@49305
  1315
    ctrans, @{thm UNION_Cinfinite_bound}, ordIso_ordLeq_trans, @{thm card_of_nat},
blanchet@48975
  1316
    @{thm natLeq_ordLeq_cinfinite}, sbd_Cinfinite, ballI, col_bd, sbd_Cinfinite,
blanchet@48975
  1317
    ctrans, @{thm infinite_ordLeq_cexp}, sbd_Cinfinite, @{thm cexp_ordLeq_ccexp}]) 1;
blanchet@48975
  1318
wenzelm@51798
  1319
fun mk_in_bd_tac ctxt isNode_hset isNode_hsets carT_def card_of_carT mor_image Rep_inverse mor_hsets
blanchet@48975
  1320
  sbd_Cnotzero sbd_Card_order mor_Rep coalgT mor_T_final tcoalg =
blanchet@48975
  1321
  let
blanchet@48975
  1322
    val n = length isNode_hsets;
blanchet@48975
  1323
    val in_hin_tac = rtac CollectI THEN'
blanchet@48975
  1324
      CONJ_WRAP' (fn mor_hset => EVERY' (map etac
blanchet@49305
  1325
        [mor_hset OF [coalgT, mor_T_final] RS sym RS ord_eq_le_trans,
blanchet@49305
  1326
        arg_cong RS sym RS ord_eq_le_trans,
blanchet@49305
  1327
        mor_hset OF [tcoalg, mor_Rep, UNIV_I] RS ord_eq_le_trans])) mor_hsets;
blanchet@48975
  1328
  in
blanchet@48975
  1329
    EVERY' [rtac (Thm.permute_prems 0 1 @{thm ordLeq_transitive}), rtac ctrans,
blanchet@49305
  1330
      rtac @{thm card_of_image}, rtac ordIso_ordLeq_trans,
blanchet@48975
  1331
      rtac @{thm card_of_ordIso_subst}, rtac @{thm sym[OF proj_image]}, rtac ctrans,
blanchet@48975
  1332
      rtac @{thm card_of_image}, rtac ctrans, rtac card_of_carT, rtac @{thm cexp_mono2_Cnotzero},
traytel@51782
  1333
      rtac @{thm cexp_ordLeq_ccexp}, rtac @{thm Card_order_csum},
blanchet@48975
  1334
      rtac @{thm Cnotzero_cexp}, rtac sbd_Cnotzero, rtac sbd_Card_order,
blanchet@48975
  1335
      rtac @{thm card_of_mono1}, rtac subsetI, rtac @{thm image_eqI}, rtac sym,
blanchet@48975
  1336
      rtac Rep_inverse, REPEAT_DETERM o eresolve_tac [CollectE, conjE],
blanchet@49305
  1337
      rtac set_mp, rtac equalityD2, rtac @{thm sym[OF proj_image]}, rtac imageE,
blanchet@49305
  1338
      rtac set_rev_mp, rtac mor_image, rtac mor_Rep, rtac UNIV_I, rtac equalityD2,
blanchet@48975
  1339
      rtac @{thm proj_image},  rtac @{thm image_eqI}, atac,
blanchet@49305
  1340
      ftac (carT_def RS equalityD1 RS set_mp),
wenzelm@51798
  1341
      REPEAT_DETERM o eresolve_tac [CollectE, exE, conjE], hyp_subst_tac ctxt,
blanchet@49305
  1342
      rtac (carT_def RS equalityD2 RS set_mp), rtac CollectI, REPEAT_DETERM o rtac exI,
blanchet@48975
  1343
      rtac conjI, rtac refl, rtac conjI, etac conjI, etac conjI, etac conjI, rtac conjI,
blanchet@48975
  1344
      rtac ballI, dtac bspec, atac, REPEAT_DETERM o etac conjE, rtac conjI,
blanchet@48975
  1345
      CONJ_WRAP_GEN' (etac disjE) (fn (i, isNode_hset) =>
blanchet@48975
  1346
        EVERY' [rtac (mk_disjIN n i), rtac isNode_hset, atac, atac, atac, in_hin_tac])
blanchet@48975
  1347
      (1 upto n ~~ isNode_hsets),
blanchet@48975
  1348
      CONJ_WRAP' (fn isNode_hset =>
blanchet@48975
  1349
        EVERY' [rtac ballI, rtac isNode_hset, atac, ftac CollectD, etac @{thm SuccD},
blanchet@48975
  1350
          etac bspec, atac, in_hin_tac])
blanchet@48975
  1351
      isNode_hsets,
blanchet@48975
  1352
      atac, rtac isNode_hset, atac, atac, atac, in_hin_tac] 1
blanchet@48975
  1353
  end;
blanchet@48975
  1354
blanchet@48975
  1355
fun mk_bd_card_order_tac sbd_card_order =
blanchet@48975
  1356
  EVERY' (map rtac [@{thm card_order_ccexp}, sbd_card_order, sbd_card_order]) 1;
blanchet@48975
  1357
blanchet@48975
  1358
fun mk_bd_cinfinite_tac sbd_Cinfinite =
blanchet@48975
  1359
  EVERY' (map rtac [@{thm cinfinite_ccexp}, @{thm ctwo_ordLeq_Cinfinite},
blanchet@48975
  1360
    sbd_Cinfinite, sbd_Cinfinite]) 1;
blanchet@48975
  1361
blanchet@48975
  1362
fun mk_pickWP_assms_tac set_incl_hsets set_incl_hins map_eq =
blanchet@48975
  1363
  let
blanchet@48975
  1364
    val m = length set_incl_hsets;
blanchet@48975
  1365
  in
blanchet@48975
  1366
    EVERY' [REPEAT_DETERM o eresolve_tac [CollectE, conjE], rtac CollectI,
blanchet@48975
  1367
      EVERY' (map (fn thm => rtac conjI THEN' etac (thm RS @{thm subset_trans})) set_incl_hsets),
blanchet@48975
  1368
      CONJ_WRAP' (fn thm => rtac thm THEN' REPEAT_DETERM_N m o atac) set_incl_hins,
blanchet@48975
  1369
      REPEAT_DETERM o eresolve_tac [CollectE, conjE], rtac CollectI,
blanchet@48975
  1370
      EVERY' (map (fn thm => rtac conjI THEN' etac (thm RS @{thm subset_trans})) set_incl_hsets),
blanchet@48975
  1371
      CONJ_WRAP' (fn thm => rtac thm THEN' REPEAT_DETERM_N m o atac) set_incl_hins,
blanchet@48975
  1372
      REPEAT_DETERM o eresolve_tac [CollectE, conjE], etac map_eq]
blanchet@48975
  1373
  end;
blanchet@48975
  1374
blanchet@51766
  1375
fun mk_coalg_thePull_tac m coalg_def map_wpulls set_mapss pickWP_assms_tacs
blanchet@48975
  1376
  {context = ctxt, prems = _} =
blanchet@49504
  1377
  unfold_thms_tac ctxt [coalg_def] THEN
blanchet@51766
  1378
  CONJ_WRAP' (fn (map_wpull, (pickWP_assms_tac, set_maps)) =>
blanchet@48975
  1379
    EVERY' [rtac ballI, dtac @{thm set_mp[OF equalityD1[OF thePull_def]]},
blanchet@48975
  1380
      REPEAT_DETERM o eresolve_tac [CollectE, @{thm prod_caseE}],
wenzelm@51798
  1381
      hyp_subst_tac ctxt, rtac rev_mp, rtac (map_wpull RS @{thm pickWP(1)}),
blanchet@48975
  1382
      EVERY' (map (etac o mk_conjunctN m) (1 upto m)),
blanchet@48975
  1383
      pickWP_assms_tac,
blanchet@49504
  1384
      SELECT_GOAL (unfold_thms_tac ctxt @{thms o_apply prod.cases}), rtac impI,
blanchet@48975
  1385
      REPEAT_DETERM o eresolve_tac [CollectE, conjE],
blanchet@48975
  1386
      rtac CollectI,
traytel@49490
  1387
      REPEAT_DETERM_N m o (rtac conjI THEN' rtac subset_UNIV),
blanchet@51766
  1388
      CONJ_WRAP' (fn set_map =>
blanchet@51766
  1389
        EVERY' [rtac ord_eq_le_trans, rtac trans, rtac set_map,
blanchet@49305
  1390
          rtac trans_fun_cong_image_id_id_apply, atac])
blanchet@51766
  1391
      (drop m set_maps)])
blanchet@51766
  1392
  (map_wpulls ~~ (pickWP_assms_tacs ~~ set_mapss)) 1;
blanchet@48975
  1393
blanchet@48975
  1394
fun mk_mor_thePull_nth_tac conv pick m mor_def map_wpulls map_comps pickWP_assms_tacs
traytel@51070
  1395
  {context = ctxt, prems = _: thm list} =
blanchet@48975
  1396
  let
blanchet@48975
  1397
    val n = length map_comps;
blanchet@48975
  1398
  in
blanchet@49504
  1399
    unfold_thms_tac ctxt [mor_def] THEN
blanchet@48975
  1400
    EVERY' [rtac conjI,
blanchet@48975
  1401
      CONJ_WRAP' (K (rtac ballI THEN' rtac UNIV_I)) (1 upto n),
blanchet@48975
  1402
      CONJ_WRAP' (fn (map_wpull, (pickWP_assms_tac, map_comp)) =>
blanchet@48975
  1403
        EVERY' [rtac ballI, dtac @{thm set_mp[OF equalityD1[OF thePull_def]]},
blanchet@48975
  1404
          REPEAT_DETERM o eresolve_tac [CollectE, @{thm prod_caseE}, conjE],
wenzelm@51798
  1405
          hyp_subst_tac ctxt,
blanchet@49504
  1406
          SELECT_GOAL (unfold_thms_tac ctxt @{thms o_apply prod.cases}),
blanchet@48975
  1407
          rtac (map_comp RS trans),
blanchet@49504
  1408
          SELECT_GOAL (unfold_thms_tac ctxt (conv :: @{thms o_id id_o})),
blanchet@48975
  1409
          rtac (map_wpull RS pick), REPEAT_DETERM_N m o atac,
blanchet@48975
  1410
          pickWP_assms_tac])
blanchet@48975
  1411
      (map_wpulls ~~ (pickWP_assms_tacs ~~ map_comps))] 1
blanchet@48975
  1412
  end;
blanchet@48975
  1413
blanchet@48975
  1414
val mk_mor_thePull_fst_tac = mk_mor_thePull_nth_tac @{thm fst_conv} @{thm pickWP(2)};
blanchet@48975
  1415
val mk_mor_thePull_snd_tac = mk_mor_thePull_nth_tac @{thm snd_conv} @{thm pickWP(3)};
blanchet@48975
  1416
blanchet@49504
  1417
fun mk_mor_thePull_pick_tac mor_def unfolds map_comps {context = ctxt, prems = _} =
blanchet@49504
  1418
  unfold_thms_tac ctxt [mor_def, @{thm thePull_def}] THEN rtac conjI 1 THEN
blanchet@49504
  1419
  CONJ_WRAP' (K (rtac ballI THEN' rtac UNIV_I)) unfolds 1 THEN
blanchet@49504
  1420
  CONJ_WRAP' (fn (unfold, map_comp) =>
blanchet@48975
  1421
    EVERY' [rtac ballI, REPEAT_DETERM o eresolve_tac [CollectE, @{thm prod_caseE}, conjE],
wenzelm@51798
  1422
      hyp_subst_tac ctxt,
blanchet@49504
  1423
      SELECT_GOAL (unfold_thms_tac ctxt (unfold :: map_comp :: @{thms comp_def id_def})),
blanchet@48975
  1424
      rtac refl])
blanchet@49504
  1425
  (unfolds ~~ map_comps) 1;
blanchet@48975
  1426
blanchet@51766
  1427
fun mk_pick_col_tac m j cts rec_0s rec_Sucs unfolds set_mapss map_wpulls pickWP_assms_tacs
blanchet@48975
  1428
  {context = ctxt, prems = _} =
blanchet@48975
  1429
  let
blanchet@48975
  1430
    val n = length rec_0s;
blanchet@48975
  1431
    val ks = n downto 1;
blanchet@48975
  1432
  in
blanchet@49305
  1433
    EVERY' [rtac (Drule.instantiate' [] cts nat_induct),
blanchet@48975
  1434
      REPEAT_DETERM o rtac allI,
blanchet@48975
  1435
      CONJ_WRAP' (fn thm => EVERY'
blanchet@49305
  1436
        [rtac impI, rtac ord_eq_le_trans, rtac thm, rtac @{thm empty_subsetI}]) rec_0s,
blanchet@48975
  1437
      REPEAT_DETERM o rtac allI,
blanchet@51766
  1438
      CONJ_WRAP' (fn (rec_Suc, ((unfold, set_maps), (map_wpull, pickWP_assms_tac))) =>
blanchet@48975
  1439
        EVERY' [rtac impI, dtac @{thm set_mp[OF equalityD1[OF thePull_def]]},
blanchet@48975
  1440
          REPEAT_DETERM o eresolve_tac [CollectE, @{thm prod_caseE}],
wenzelm@51798
  1441
          hyp_subst_tac ctxt, rtac rev_mp, rtac (map_wpull RS @{thm pickWP(1)}),
blanchet@48975
  1442
          EVERY' (map (etac o mk_conjunctN m) (1 upto m)),
blanchet@48975
  1443
          pickWP_assms_tac,
blanchet@48975
  1444
          rtac impI, REPEAT_DETERM o eresolve_tac [CollectE, conjE],
blanchet@49305
  1445
          rtac ord_eq_le_trans, rtac rec_Suc,
blanchet@48975
  1446
          rtac @{thm Un_least},
blanchet@51766
  1447
          SELECT_GOAL (unfold_thms_tac ctxt [unfold, nth set_maps (j - 1),
blanchet@48975
  1448
            @{thm prod.cases}]),
blanchet@49305
  1449
          etac ord_eq_le_trans_trans_fun_cong_image_id_id_apply,
blanchet@51766
  1450
          CONJ_WRAP_GEN' (rtac (Thm.permute_prems 0 1 @{thm Un_least})) (fn (i, set_map) =>
blanchet@48975
  1451
            EVERY' [rtac @{thm UN_least},
blanchet@51766
  1452
              SELECT_GOAL (unfold_thms_tac ctxt [unfold, set_map, @{thm prod.cases}]),
wenzelm@51798
  1453
              etac imageE, hyp_subst_tac ctxt, REPEAT_DETERM o etac allE,
blanchet@49305
  1454
              dtac (mk_conjunctN n i), etac mp, etac set_mp, atac])
blanchet@51766
  1455
          (ks ~~ rev (drop m set_maps))])
blanchet@51766
  1456
      (rec_Sucs ~~ ((unfolds ~~ set_mapss) ~~ (map_wpulls ~~ pickWP_assms_tacs)))] 1
blanchet@48975
  1457
  end;
blanchet@48975
  1458
blanchet@48975
  1459
fun mk_wpull_tac m coalg_thePull mor_thePull_fst mor_thePull_snd mor_thePull_pick
blanchet@48975
  1460
  mor_unique pick_cols hset_defs =
traytel@49488
  1461
  EVERY' [rtac (@{thm wpull_def} RS iffD2), REPEAT_DETERM o rtac allI, rtac impI,
blanchet@48975
  1462
    REPEAT_DETERM o etac conjE, rtac bexI, rtac conjI,
blanchet@48975
  1463
    rtac box_equals, rtac mor_unique,
blanchet@48975
  1464
    rtac coalg_thePull, REPEAT_DETERM_N (m - 1) o etac conjI, atac,
blanchet@48975
  1465
    rtac mor_thePull_pick, REPEAT_DETERM_N (m - 1) o etac conjI, atac,
blanchet@48975
  1466
    rtac mor_thePull_fst, REPEAT_DETERM_N (m - 1) o etac conjI, atac,
blanchet@48975
  1467
    rtac @{thm set_mp[OF equalityD2[OF thePull_def]]}, rtac CollectI,
blanchet@48975
  1468
    rtac @{thm prod_caseI}, etac conjI, etac conjI, atac, rtac o_apply, rtac @{thm fst_conv},
blanchet@48975
  1469
    rtac box_equals, rtac mor_unique,
blanchet@48975
  1470
    rtac coalg_thePull, REPEAT_DETERM_N (m - 1) o etac conjI, atac,
blanchet@48975
  1471
    rtac mor_thePull_pick, REPEAT_DETERM_N (m - 1) o etac conjI, atac,
blanchet@48975
  1472
    rtac mor_thePull_snd, REPEAT_DETERM_N (m - 1) o etac conjI, atac,
blanchet@48975
  1473
    rtac @{thm set_mp[OF equalityD2[OF thePull_def]]}, rtac CollectI,
blanchet@48975
  1474
    rtac @{thm prod_caseI}, etac conjI, etac conjI, atac, rtac o_apply, rtac @{thm snd_conv},
blanchet@48975
  1475
    rtac CollectI,
blanchet@48975
  1476
    CONJ_WRAP' (fn (pick, def) =>
blanchet@49305
  1477
      EVERY' [rtac (def RS ord_eq_le_trans), rtac @{thm UN_least},
blanchet@48975
  1478
        rtac pick, REPEAT_DETERM_N (m - 1) o etac conjI, atac,
blanchet@48975
  1479
        rtac @{thm set_mp[OF equalityD2[OF thePull_def]]}, rtac CollectI,
blanchet@48975
  1480
        rtac @{thm prod_caseI}, etac conjI, etac conjI, atac])
blanchet@48975
  1481
    (pick_cols ~~ hset_defs)] 1;
blanchet@48975
  1482
blanchet@49585
  1483
fun mk_wit_tac n dtor_ctors dtor_set wit coind_wits {context = ctxt, prems = _} =
traytel@49104
  1484
  ALLGOALS (TRY o (eresolve_tac coind_wits THEN' rtac refl)) THEN
blanchet@48975
  1485
  REPEAT_DETERM (atac 1 ORELSE
blanchet@49585
  1486
    EVERY' [dtac set_rev_mp, rtac equalityD1, resolve_tac dtor_set,
blanchet@49504
  1487
    K (unfold_thms_tac ctxt dtor_ctors),
blanchet@48975
  1488
    REPEAT_DETERM_N n o etac UnE,
blanchet@48975
  1489
    REPEAT_DETERM o
blanchet@48975
  1490
      (TRY o REPEAT_DETERM o etac UnE THEN' TRY o etac @{thm UN_E} THEN'
blanchet@48975
  1491
        (eresolve_tac wit ORELSE'
blanchet@48975
  1492
        (dresolve_tac wit THEN'
blanchet@48975
  1493
          (etac FalseE ORELSE'
wenzelm@51798
  1494
          EVERY' [hyp_subst_tac ctxt, dtac set_rev_mp, rtac equalityD1, resolve_tac dtor_set,
blanchet@49504
  1495
            K (unfold_thms_tac ctxt dtor_ctors), REPEAT_DETERM_N n o etac UnE]))))] 1);
blanchet@48975
  1496
blanchet@49504
  1497
fun mk_coind_wit_tac induct unfolds set_nats wits {context = ctxt, prems = _} =
wenzelm@51798
  1498
  rtac induct 1 THEN ALLGOALS (TRY o rtac impI THEN' TRY o hyp_subst_tac ctxt) THEN
blanchet@49504
  1499
  unfold_thms_tac ctxt (unfolds @ set_nats @ @{thms image_id id_apply}) THEN
wenzelm@51798
  1500
  ALLGOALS (REPEAT_DETERM o etac imageE THEN' TRY o hyp_subst_tac ctxt) THEN
traytel@49104
  1501
  ALLGOALS (TRY o
traytel@49104
  1502
    FIRST' [rtac TrueI, rtac refl, etac (refl RSN (2, mp)), dresolve_tac wits THEN' etac FalseE])
traytel@49104
  1503
wenzelm@51798
  1504
fun mk_dtor_srel_tac ctxt in_Jsrels i in_srel map_comp map_cong0 dtor_map dtor_sets dtor_inject
wenzelm@51798
  1505
    dtor_ctor set_maps dtor_set_incls dtor_set_set_inclss =
blanchet@48975
  1506
  let
blanchet@49544
  1507
    val m = length dtor_set_incls;
blanchet@49544
  1508
    val n = length dtor_set_set_inclss;
blanchet@51766
  1509
    val (passive_set_maps, active_set_maps) = chop m set_maps;
blanchet@49506
  1510
    val in_Jsrel = nth in_Jsrels (i - 1);
blanchet@48975
  1511
    val if_tac =
blanchet@49506
  1512
      EVERY' [dtac (in_Jsrel RS iffD1), REPEAT_DETERM o eresolve_tac [exE, conjE, CollectE],
blanchet@49506
  1513
        rtac (in_srel RS iffD2), rtac exI, rtac conjI, rtac CollectI,
blanchet@51766
  1514
        EVERY' (map2 (fn set_map => fn set_incl =>
blanchet@51766
  1515
          EVERY' [rtac conjI, rtac ord_eq_le_trans, rtac set_map,
blanchet@49305
  1516
            rtac ord_eq_le_trans, rtac trans_fun_cong_image_id_id_apply,
blanchet@48975
  1517
            etac (set_incl RS @{thm subset_trans})])
blanchet@51766
  1518
        passive_set_maps dtor_set_incls),
blanchet@51766
  1519
        CONJ_WRAP' (fn (in_Jsrel, (set_map, dtor_set_set_incls)) =>
blanchet@51766
  1520
          EVERY' [rtac ord_eq_le_trans, rtac set_map, rtac @{thm image_subsetI},
blanchet@49506
  1521
            rtac (in_Jsrel RS iffD2), rtac exI, rtac conjI, rtac CollectI,
blanchet@49544
  1522
            CONJ_WRAP' (fn thm => etac (thm RS @{thm subset_trans}) THEN' atac) dtor_set_set_incls,
blanchet@48975
  1523
            rtac conjI, rtac refl, rtac refl])
blanchet@51766
  1524
        (in_Jsrels ~~ (active_set_maps ~~ dtor_set_set_inclss)),
blanchet@48975
  1525
        CONJ_WRAP' (fn conv =>
blanchet@51761
  1526
          EVERY' [rtac trans, rtac map_comp, rtac trans, rtac map_cong0,
blanchet@48975
  1527
          REPEAT_DETERM_N m o rtac @{thm fun_cong[OF o_id]},
blanchet@48975
  1528
          REPEAT_DETERM_N n o EVERY' (map rtac [trans, o_apply, conv]),
blanchet@49541
  1529
          rtac trans, rtac sym, rtac dtor_map, rtac (dtor_inject RS iffD2), atac])
blanchet@48975
  1530
        @{thms fst_conv snd_conv}];
blanchet@48975
  1531
    val only_if_tac =
blanchet@49506
  1532
      EVERY' [dtac (in_srel RS iffD1), REPEAT_DETERM o eresolve_tac [exE, conjE, CollectE],
blanchet@49506
  1533
        rtac (in_Jsrel RS iffD2), rtac exI, rtac conjI, rtac CollectI,
blanchet@51766
  1534
        CONJ_WRAP' (fn (dtor_set, passive_set_map) =>
blanchet@49585
  1535
          EVERY' [rtac ord_eq_le_trans, rtac dtor_set, rtac @{thm Un_least},
blanchet@51766
  1536
            rtac ord_eq_le_trans, rtac box_equals, rtac passive_set_map,
blanchet@49501
  1537
            rtac (dtor_ctor RS sym RS arg_cong), rtac trans_fun_cong_image_id_id_apply, atac,
blanchet@48975
  1538
            CONJ_WRAP_GEN' (rtac (Thm.permute_prems 0 1 @{thm Un_least}))
blanchet@51766
  1539
              (fn (active_set_map, in_Jsrel) => EVERY' [rtac ord_eq_le_trans,
blanchet@48975
  1540
                rtac @{thm UN_cong[OF _ refl]}, rtac @{thm box_equals[OF _ _ refl]},
blanchet@51766
  1541
                rtac active_set_map, rtac (dtor_ctor RS sym RS arg_cong), rtac @{thm UN_least},
blanchet@49305
  1542
                dtac set_rev_mp, etac @{thm image_mono}, etac imageE,
blanchet@49506
  1543
                dtac @{thm ssubst_mem[OF pair_collapse]}, dtac (in_Jsrel RS iffD1),
blanchet@48975
  1544
                dtac @{thm someI_ex}, REPEAT_DETERM o etac conjE,
blanchet@48975
  1545
                dtac (Thm.permute_prems 0 1 @{thm ssubst_mem}), atac,
wenzelm@51798
  1546
                hyp_subst_tac ctxt, REPEAT_DETERM o eresolve_tac [CollectE, conjE], atac])
blanchet@51766
  1547
            (rev (active_set_maps ~~ in_Jsrels))])
blanchet@51766
  1548
        (dtor_sets ~~ passive_set_maps),
blanchet@48975
  1549
        rtac conjI,
blanchet@49541
  1550
        REPEAT_DETERM_N 2 o EVERY'[rtac (dtor_inject RS iffD1), rtac trans, rtac dtor_map,
blanchet@49501
  1551
          rtac box_equals, rtac map_comp, rtac (dtor_ctor RS sym RS arg_cong), rtac trans,
blanchet@51761
  1552
          rtac map_cong0, REPEAT_DETERM_N m o rtac @{thm fun_cong[OF o_id]},
blanchet@49506
  1553
          EVERY' (map (fn in_Jsrel => EVERY' [rtac trans, rtac o_apply, dtac set_rev_mp, atac,
blanchet@49506
  1554
            dtac @{thm ssubst_mem[OF pair_collapse]}, dtac (in_Jsrel RS iffD1),
blanchet@49506
  1555
            dtac @{thm someI_ex}, REPEAT_DETERM o etac conjE, atac]) in_Jsrels),
blanchet@48975
  1556
          atac]]
blanchet@48975
  1557
  in
blanchet@48975
  1558
    EVERY' [rtac iffI, if_tac, only_if_tac] 1
blanchet@48975
  1559
  end;
blanchet@48975
  1560
blanchet@48975
  1561
end;