src/HOL/BNF/Tools/bnf_gfp_tactics.ML
author blanchet
Sun, 23 Sep 2012 14:52:53 +0200
changeset 49543 53b3c532a082
parent 49542 b39354db8629
child 49544 24094fa47e0d
permissions -rw-r--r--
renamed low-level "map_unique" to have "ctor" or "dtor" in the name
Ignore whitespace changes - Everywhere: Within whitespace: At end of lines:
49509
163914705f8d renamed top-level theory from "Codatatype" to "BNF"
blanchet
parents: 49506
diff changeset
     1
(*  Title:      HOL/BNF/Tools/bnf_gfp_tactics.ML
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
     2
    Author:     Dmitriy Traytel, TU Muenchen
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
     3
    Author:     Andrei Popescu, TU Muenchen
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
     4
    Author:     Jasmin Blanchette, TU Muenchen
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
     5
    Copyright   2012
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
     6
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
     7
Tactics for the codatatype construction.
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
     8
*)
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
     9
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
    10
signature BNF_GFP_TACTICS =
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
    11
sig
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
    12
  val mk_Lev_sbd_tac: cterm option list -> thm list -> thm list -> thm list list -> tactic
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
    13
  val mk_bd_card_order_tac: thm -> tactic
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
    14
  val mk_bd_cinfinite_tac: thm -> tactic
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
    15
  val mk_bis_Gr_tac: thm -> thm list -> thm list -> thm list -> thm list ->
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
    16
    {prems: 'a, context: Proof.context} -> tactic
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
    17
  val mk_bis_O_tac: int -> thm -> thm list -> thm list -> tactic
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
    18
  val mk_bis_Union_tac: thm -> thm list -> {prems: 'a, context: Proof.context} -> tactic
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
    19
  val mk_bis_converse_tac: int -> thm -> thm list -> thm list -> tactic
49506
aeb0cc8889f2 renamed "rel" to "srel"
blanchet
parents: 49504
diff changeset
    20
  val mk_bis_srel_tac: int -> thm -> thm list -> thm list -> thm list -> thm list list -> tactic
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
    21
  val mk_carT_set_tac: int -> int -> thm -> thm -> thm -> thm ->
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
    22
    {prems: 'a, context: Proof.context} -> tactic
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
    23
  val mk_card_of_carT_tac: int -> thm list -> thm -> thm -> thm -> thm -> thm -> thm list -> tactic
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
    24
  val mk_coalgT_tac: int -> thm list -> thm list -> thm list list ->
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
    25
    {prems: 'a, context: Proof.context} -> tactic
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
    26
  val mk_coalg_final_tac: int -> thm -> thm list -> thm list -> thm list list -> thm list list ->
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
    27
    tactic
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
    28
  val mk_coalg_set_tac: thm -> tactic
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
    29
  val mk_coalg_thePull_tac: int -> thm -> thm list -> thm list list -> (int -> tactic) list ->
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
    30
    {prems: 'a, context: Proof.context} -> tactic
49104
6defdacd595a generate coinductive witnesses for codatatypes
traytel
parents: 49091
diff changeset
    31
  val mk_coind_wit_tac: thm -> thm list -> thm list -> thm list ->
6defdacd595a generate coinductive witnesses for codatatypes
traytel
parents: 49091
diff changeset
    32
    {prems: 'a, context: Proof.context} -> tactic
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
    33
  val mk_col_bd_tac: int -> int -> cterm option list -> thm list -> thm list -> thm -> thm ->
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
    34
    thm list list -> tactic
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
    35
  val mk_col_natural_tac: cterm option list -> thm list -> thm list -> thm list -> thm list list ->
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
    36
    {prems: 'a, context: Proof.context} -> tactic
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
    37
  val mk_congruent_str_final_tac: int -> thm -> thm -> thm -> thm list -> tactic
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
    38
  val mk_corec_tac: int -> thm list -> thm -> thm -> thm list ->
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
    39
    {prems: 'a, context: Proof.context} -> tactic
49501
acc9635a644a renamed "fld"/"unf" to "ctor"/"dtor"
blanchet
parents: 49499
diff changeset
    40
  val mk_dtor_coinduct_tac: int -> int list -> thm -> thm -> tactic
49516
d4859efc1096 renamed "rel_simp" to "dtor_rel" and similarly for "srel"
blanchet
parents: 49510
diff changeset
    41
  val mk_dtor_srel_tac: thm list -> int -> thm -> thm -> thm -> thm -> thm list -> thm -> thm ->
d4859efc1096 renamed "rel_simp" to "dtor_rel" and similarly for "srel"
blanchet
parents: 49510
diff changeset
    42
    thm list -> thm list -> thm list list -> tactic
49506
aeb0cc8889f2 renamed "rel" to "srel"
blanchet
parents: 49504
diff changeset
    43
  val mk_dtor_strong_coinduct_tac: int list -> ctyp option list -> cterm option list -> thm ->
aeb0cc8889f2 renamed "rel" to "srel"
blanchet
parents: 49504
diff changeset
    44
    thm -> thm -> tactic
49501
acc9635a644a renamed "fld"/"unf" to "ctor"/"dtor"
blanchet
parents: 49499
diff changeset
    45
  val mk_dtor_o_ctor_tac: thm -> thm -> thm -> thm -> thm list ->
acc9635a644a renamed "fld"/"unf" to "ctor"/"dtor"
blanchet
parents: 49499
diff changeset
    46
    {prems: 'a, context: Proof.context} -> tactic
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
    47
  val mk_equiv_lsbis_tac: thm -> thm -> thm -> thm -> thm -> thm -> tactic
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
    48
  val mk_hset_minimal_tac: int -> thm list -> thm -> {prems: 'a, context: Proof.context} -> tactic
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
    49
  val mk_hset_rec_minimal_tac: int -> cterm option list -> thm list -> thm list ->
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
    50
    {prems: 'a, context: Proof.context} -> tactic
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
    51
  val mk_in_bd_tac: thm -> thm list -> thm -> thm -> thm -> thm -> thm list -> thm -> thm -> thm ->
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
    52
    thm -> thm -> thm -> tactic
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
    53
  val mk_incl_lsbis_tac: int -> int -> thm -> tactic
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
    54
  val mk_isNode_hset_tac: int -> thm -> thm list -> {prems: 'a, context: Proof.context} -> tactic
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
    55
  val mk_length_Lev'_tac: thm -> tactic
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
    56
  val mk_length_Lev_tac: cterm option list -> thm list -> thm list -> tactic
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
    57
  val mk_map_comp_tac: int -> int -> thm list -> thm list -> thm list -> thm -> tactic
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
    58
  val mk_mcong_tac: int -> (int -> tactic) -> thm list -> thm list -> thm list -> thm list list ->
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
    59
    thm list list -> thm list list list -> tactic
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
    60
  val mk_map_id_tac: thm list -> thm -> thm -> tactic
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
    61
  val mk_map_tac: int -> int -> ctyp option -> thm -> thm -> thm -> tactic
49543
53b3c532a082 renamed low-level "map_unique" to have "ctor" or "dtor" in the name
blanchet
parents: 49542
diff changeset
    62
  val mk_dtor_map_unique_tac: thm -> thm list -> {prems: 'a, context: Proof.context} -> tactic
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
    63
  val mk_mor_Abs_tac: thm list -> thm list -> {prems: 'a, context: Proof.context} -> tactic
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
    64
  val mk_mor_Rep_tac: int -> thm list -> thm list -> thm list -> thm list list -> thm list ->
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
    65
    thm list -> {prems: 'a, context: Proof.context} -> tactic
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
    66
  val mk_mor_T_final_tac: thm -> thm list -> thm list -> tactic
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
    67
  val mk_mor_UNIV_tac: thm list -> thm -> tactic
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
    68
  val mk_mor_beh_tac: int -> thm -> thm -> thm list -> thm list -> thm list -> thm list ->
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
    69
    thm list list -> thm list list -> thm list -> thm list -> thm list -> thm list -> thm list ->
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
    70
    thm list -> thm list -> thm list -> thm list list -> thm list list list -> thm list list list ->
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
    71
    thm list list list -> thm list list -> thm list list -> thm list -> thm list -> thm list ->
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
    72
    {prems: 'a, context: Proof.context} -> tactic
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
    73
  val mk_mor_comp_tac: thm -> thm list -> thm list -> thm list -> tactic
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
    74
  val mk_mor_elim_tac: thm -> tactic
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
    75
  val mk_mor_hset_rec_tac: int -> int -> cterm option list -> int -> thm list -> thm list ->
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
    76
    thm list -> thm list list -> thm list list -> tactic
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
    77
  val mk_mor_hset_tac: thm -> thm -> tactic
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
    78
  val mk_mor_incl_tac: thm -> thm list -> tactic
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
    79
  val mk_mor_str_tac: 'a list -> thm -> tactic
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
    80
  val mk_mor_sum_case_tac: 'a list -> thm -> tactic
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
    81
  val mk_mor_thePull_fst_tac: int -> thm -> thm list -> thm list -> (int -> tactic) list ->
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
    82
    {prems: thm list, context: Proof.context} -> tactic
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
    83
  val mk_mor_thePull_snd_tac: int -> thm -> thm list -> thm list -> (int -> tactic) list ->
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
    84
    {prems: thm list, context: Proof.context} -> tactic
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
    85
  val mk_mor_thePull_pick_tac: thm -> thm list -> thm list ->
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
    86
    {prems: 'a, context: Proof.context} -> tactic
49504
df9b897fb254 renamed "iter"/"coiter" to "fold"/"unfold" (cf. Wadler)
blanchet
parents: 49501
diff changeset
    87
  val mk_mor_unfold_tac: int -> thm -> thm list -> thm list -> thm list -> thm list -> thm list ->
df9b897fb254 renamed "iter"/"coiter" to "fold"/"unfold" (cf. Wadler)
blanchet
parents: 49501
diff changeset
    88
    thm list -> tactic
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
    89
  val mk_prefCl_Lev_tac: cterm option list -> thm list -> thm list -> tactic
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
    90
  val mk_pickWP_assms_tac: thm list -> thm list -> thm -> (int -> tactic)
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
    91
  val mk_pick_col_tac: int -> int -> cterm option list -> thm list -> thm list -> thm list ->
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
    92
    thm list list -> thm list -> (int -> tactic) list -> {prems: 'a, context: Proof.context} ->
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
    93
    tactic
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
    94
  val mk_raw_coind_tac: thm -> thm -> thm -> thm -> thm -> thm -> thm -> thm -> thm -> thm list ->
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
    95
    thm list -> thm list -> thm -> thm list -> tactic
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
    96
  val mk_rv_last_tac: ctyp option list -> cterm option list -> thm list -> thm list -> tactic
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
    97
  val mk_sbis_lsbis_tac: thm list -> thm -> thm -> tactic
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
    98
  val mk_set_Lev_tac: cterm option list -> thm list -> thm list -> thm list -> thm list ->
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
    99
    thm list list -> tactic
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   100
  val mk_set_bd_tac: thm -> thm -> thm -> tactic
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   101
  val mk_set_hset_incl_hset_tac: int -> thm list -> thm -> int -> tactic
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   102
  val mk_set_image_Lev_tac: cterm option list -> thm list -> thm list -> thm list -> thm list ->
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   103
    thm list list -> thm list list -> tactic
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   104
  val mk_set_incl_hin_tac: thm list -> tactic
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   105
  val mk_set_incl_hset_tac: thm -> thm -> tactic
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   106
  val mk_set_le_tac: int -> thm -> thm list -> thm list list -> tactic
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   107
  val mk_set_natural_tac: thm -> thm -> tactic
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   108
  val mk_set_rv_Lev_tac: int -> cterm option list -> thm list -> thm list -> thm list -> thm list ->
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   109
    thm list list -> thm list list -> tactic
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   110
  val mk_set_simp_tac: int -> thm -> thm -> thm list -> tactic
49506
aeb0cc8889f2 renamed "rel" to "srel"
blanchet
parents: 49504
diff changeset
   111
  val mk_srel_coinduct_tac: 'a list -> thm -> thm -> tactic
aeb0cc8889f2 renamed "rel" to "srel"
blanchet
parents: 49504
diff changeset
   112
  val mk_srel_strong_coinduct_tac: int -> ctyp option list -> cterm option list -> thm ->
aeb0cc8889f2 renamed "rel" to "srel"
blanchet
parents: 49504
diff changeset
   113
    thm list -> thm list -> tactic
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   114
  val mk_strT_hset_tac: int -> int -> int -> ctyp option list -> ctyp option list ->
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   115
    cterm option list -> thm list -> thm list -> thm list -> thm list -> thm list list ->
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   116
    thm list list -> thm list list -> thm -> thm list list -> tactic
49504
df9b897fb254 renamed "iter"/"coiter" to "fold"/"unfold" (cf. Wadler)
blanchet
parents: 49501
diff changeset
   117
  val mk_unfold_unique_mor_tac: thm list -> thm -> thm -> thm list -> tactic
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   118
  val mk_unique_mor_tac: thm list -> thm -> tactic
49104
6defdacd595a generate coinductive witnesses for codatatypes
traytel
parents: 49091
diff changeset
   119
  val mk_wit_tac: int -> thm list -> thm list -> thm list -> thm list ->
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   120
    {prems: 'a, context: Proof.context} -> tactic
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   121
  val mk_wpull_tac: int -> thm -> thm -> thm -> thm -> thm -> thm list -> thm list -> tactic
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   122
end;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   123
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   124
structure BNF_GFP_Tactics : BNF_GFP_TACTICS =
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   125
struct
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   126
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   127
open BNF_Tactics
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   128
open BNF_Util
49457
1d2825673cec renamed "bnf_fp_util.ML" to "bnf_fp.ML"
blanchet
parents: 49456
diff changeset
   129
open BNF_FP
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   130
open BNF_GFP_Util
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   131
49305
8241f21d104b tuned antiquotations
blanchet
parents: 49104
diff changeset
   132
val fst_convol_fun_cong_sym = @{thm fst_convol} RS fun_cong RS sym;
49488
02eb07152998 use iffD* instead of (s)subst instantiated with identity; tuned antiquotations;
traytel
parents: 49463
diff changeset
   133
val list_inject_iffD1 = @{thm list.inject[THEN iffD1]};
49305
8241f21d104b tuned antiquotations
blanchet
parents: 49104
diff changeset
   134
val nat_induct = @{thm nat_induct};
8241f21d104b tuned antiquotations
blanchet
parents: 49104
diff changeset
   135
val o_apply_trans_sym = o_apply RS trans RS sym;
8241f21d104b tuned antiquotations
blanchet
parents: 49104
diff changeset
   136
val ord_eq_le_trans = @{thm ord_eq_le_trans};
8241f21d104b tuned antiquotations
blanchet
parents: 49104
diff changeset
   137
val ord_eq_le_trans_trans_fun_cong_image_id_id_apply =
8241f21d104b tuned antiquotations
blanchet
parents: 49104
diff changeset
   138
  @{thm ord_eq_le_trans[OF trans[OF fun_cong[OF image_id] id_apply]]};
8241f21d104b tuned antiquotations
blanchet
parents: 49104
diff changeset
   139
val ordIso_ordLeq_trans = @{thm ordIso_ordLeq_trans};
8241f21d104b tuned antiquotations
blanchet
parents: 49104
diff changeset
   140
val snd_convol_fun_cong_sym = @{thm snd_convol} RS fun_cong RS sym;
49328
a1c10b46fecd avoided duplicate lemma
blanchet
parents: 49305
diff changeset
   141
val sum_case_weak_cong = @{thm sum_case_weak_cong};
49305
8241f21d104b tuned antiquotations
blanchet
parents: 49104
diff changeset
   142
val trans_fun_cong_image_id_id_apply = @{thm trans[OF fun_cong[OF image_id] id_apply]};
8241f21d104b tuned antiquotations
blanchet
parents: 49104
diff changeset
   143
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   144
fun mk_coalg_set_tac coalg_def =
49488
02eb07152998 use iffD* instead of (s)subst instantiated with identity; tuned antiquotations;
traytel
parents: 49463
diff changeset
   145
  dtac (coalg_def RS iffD1) 1 THEN
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   146
  REPEAT_DETERM (etac conjE 1) THEN
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   147
  EVERY' [dtac @{thm rev_bspec}, atac] 1 THEN
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   148
  REPEAT_DETERM (eresolve_tac [CollectE, conjE] 1) THEN atac 1;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   149
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   150
fun mk_mor_elim_tac mor_def =
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   151
  (dtac (subst OF [mor_def]) THEN'
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   152
  REPEAT o etac conjE THEN'
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   153
  TRY o rtac @{thm image_subsetI} THEN'
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   154
  etac bspec THEN'
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   155
  atac) 1;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   156
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   157
fun mk_mor_incl_tac mor_def map_id's =
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   158
  (stac mor_def THEN'
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   159
  rtac conjI THEN'
49305
8241f21d104b tuned antiquotations
blanchet
parents: 49104
diff changeset
   160
  CONJ_WRAP' (K (EVERY' [rtac ballI, etac set_mp, stac @{thm id_apply}, atac]))
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   161
    map_id's THEN'
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   162
  CONJ_WRAP' (fn thm =>
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   163
   (EVERY' [rtac ballI, rtac (thm RS trans), rtac sym, rtac (@{thm id_apply} RS arg_cong)]))
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   164
  map_id's) 1;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   165
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   166
fun mk_mor_comp_tac mor_def mor_images morEs map_comp_ids =
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   167
  let
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   168
    fun fbetw_tac image = EVERY' [rtac ballI, stac o_apply, etac image, etac image, atac];
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   169
    fun mor_tac ((mor_image, morE), map_comp_id) =
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   170
      EVERY' [rtac ballI, stac o_apply, rtac trans, rtac (map_comp_id RS sym), rtac trans,
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   171
        etac (morE RS arg_cong), atac, etac morE, etac mor_image, atac];
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   172
  in
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   173
    (stac mor_def THEN' rtac conjI THEN'
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   174
    CONJ_WRAP' fbetw_tac mor_images THEN'
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   175
    CONJ_WRAP' mor_tac ((mor_images ~~ morEs) ~~ map_comp_ids)) 1
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   176
  end;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   177
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   178
fun mk_mor_UNIV_tac morEs mor_def =
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   179
  let
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   180
    val n = length morEs;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   181
    fun mor_tac morE = EVERY' [rtac ext, rtac trans, rtac o_apply, rtac trans, etac morE,
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   182
      rtac UNIV_I, rtac sym, rtac o_apply];
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   183
  in
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   184
    EVERY' [rtac iffI, CONJ_WRAP' mor_tac morEs,
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   185
    stac mor_def, rtac conjI, CONJ_WRAP' (K (rtac ballI THEN' rtac UNIV_I)) morEs,
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   186
    CONJ_WRAP' (fn i =>
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   187
      EVERY' [dtac (mk_conjunctN n i), rtac ballI, etac @{thm pointfreeE}]) (1 upto n)] 1
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   188
  end;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   189
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   190
fun mk_mor_str_tac ks mor_UNIV =
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   191
  (stac mor_UNIV THEN' CONJ_WRAP' (K (rtac refl)) ks) 1;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   192
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   193
fun mk_mor_sum_case_tac ks mor_UNIV =
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   194
  (stac mor_UNIV THEN' CONJ_WRAP' (K (rtac @{thm sum_case_comp_Inl[symmetric]})) ks) 1;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   195
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   196
fun mk_set_incl_hset_tac def rec_Suc =
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   197
  EVERY' (stac def ::
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   198
    map rtac [@{thm incl_UNION_I}, UNIV_I, @{thm ord_le_eq_trans}, @{thm Un_upper1},
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   199
      sym, rec_Suc]) 1;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   200
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   201
fun mk_set_hset_incl_hset_tac n defs rec_Suc i =
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   202
  EVERY' (map (TRY oo stac) defs @
49305
8241f21d104b tuned antiquotations
blanchet
parents: 49104
diff changeset
   203
    map rtac [@{thm UN_least}, subsetI, @{thm UN_I}, UNIV_I, set_mp, equalityD2, rec_Suc, UnI2,
49366
3edd1c90f6e6 renamed "mk_UnN" to "mk_UnIN"
blanchet
parents: 49328
diff changeset
   204
      mk_UnIN n i] @
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   205
    [etac @{thm UN_I}, atac]) 1;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   206
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   207
fun mk_set_incl_hin_tac incls =
49490
394870e51d18 tuned antiquotations
traytel
parents: 49488
diff changeset
   208
  if null incls then rtac subset_UNIV 1
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   209
  else EVERY' [rtac subsetI, rtac CollectI,
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   210
    CONJ_WRAP' (fn incl => EVERY' [rtac subset_trans, etac incl, atac]) incls] 1;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   211
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   212
fun mk_hset_rec_minimal_tac m cts rec_0s rec_Sucs {context = ctxt, prems = _} =
49305
8241f21d104b tuned antiquotations
blanchet
parents: 49104
diff changeset
   213
  EVERY' [rtac (Drule.instantiate' [] cts nat_induct),
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   214
    REPEAT_DETERM o rtac allI,
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   215
    CONJ_WRAP' (fn thm => EVERY'
49305
8241f21d104b tuned antiquotations
blanchet
parents: 49104
diff changeset
   216
      [rtac ord_eq_le_trans, rtac thm, rtac @{thm empty_subsetI}]) rec_0s,
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   217
    REPEAT_DETERM o rtac allI,
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   218
    CONJ_WRAP' (fn rec_Suc => EVERY'
49305
8241f21d104b tuned antiquotations
blanchet
parents: 49104
diff changeset
   219
      [rtac ord_eq_le_trans, rtac rec_Suc,
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   220
        if m = 0 then K all_tac
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   221
        else (rtac @{thm Un_least} THEN' Goal.assume_rule_tac ctxt),
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   222
        CONJ_WRAP_GEN' (rtac (Thm.permute_prems 0 1 @{thm Un_least}))
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   223
          (K (EVERY' [rtac @{thm UN_least}, REPEAT_DETERM o eresolve_tac [allE, conjE],
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   224
            rtac subset_trans, atac, Goal.assume_rule_tac ctxt])) rec_0s])
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   225
      rec_Sucs] 1;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   226
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   227
fun mk_hset_minimal_tac n hset_defs hset_rec_minimal {context = ctxt, prems = _} =
49305
8241f21d104b tuned antiquotations
blanchet
parents: 49104
diff changeset
   228
  (CONJ_WRAP' (fn def => (EVERY' [rtac ord_eq_le_trans, rtac def,
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   229
    rtac @{thm UN_least}, rtac rev_mp, rtac hset_rec_minimal,
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   230
    EVERY' (replicate ((n + 1) * n) (Goal.assume_rule_tac ctxt)), rtac impI,
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   231
    REPEAT_DETERM o eresolve_tac [allE, conjE], atac])) hset_defs) 1
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   232
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   233
fun mk_mor_hset_rec_tac m n cts j rec_0s rec_Sucs morEs set_naturalss coalg_setss =
49305
8241f21d104b tuned antiquotations
blanchet
parents: 49104
diff changeset
   234
  EVERY' [rtac (Drule.instantiate' [] cts nat_induct),
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   235
    REPEAT_DETERM o rtac allI,
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   236
    CONJ_WRAP' (fn thm => EVERY' (map rtac [impI, thm RS trans, thm RS sym])) rec_0s,
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   237
    REPEAT_DETERM o rtac allI,
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   238
    CONJ_WRAP'
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   239
      (fn (rec_Suc, (morE, ((passive_set_naturals, active_set_naturals), coalg_sets))) =>
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   240
        EVERY' [rtac impI, rtac (rec_Suc RS trans), rtac (rec_Suc RS trans RS sym),
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   241
          if m = 0 then K all_tac
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   242
          else EVERY' [rtac @{thm Un_cong}, rtac box_equals,
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   243
            rtac (nth passive_set_naturals (j - 1) RS sym),
49305
8241f21d104b tuned antiquotations
blanchet
parents: 49104
diff changeset
   244
            rtac trans_fun_cong_image_id_id_apply, etac (morE RS arg_cong), atac],
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   245
          CONJ_WRAP_GEN' (rtac (Thm.permute_prems 0 1 @{thm Un_cong}))
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   246
            (fn (i, (set_natural, coalg_set)) =>
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   247
              EVERY' [rtac sym, rtac trans, rtac (refl RSN (2, @{thm UN_cong})),
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   248
                etac (morE RS sym RS arg_cong RS trans), atac, rtac set_natural,
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   249
                rtac (@{thm UN_simps(10)} RS trans), rtac (refl RS @{thm UN_cong}),
49305
8241f21d104b tuned antiquotations
blanchet
parents: 49104
diff changeset
   250
                ftac coalg_set, atac, dtac set_mp, atac, rtac mp, rtac (mk_conjunctN n i),
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   251
                REPEAT_DETERM o etac allE, atac, atac])
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   252
            (rev ((1 upto n) ~~ (active_set_naturals ~~ coalg_sets)))])
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   253
      (rec_Sucs ~~ (morEs ~~ (map (chop m) set_naturalss ~~ map (drop m) coalg_setss)))] 1;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   254
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   255
fun mk_mor_hset_tac hset_def mor_hset_rec =
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   256
  EVERY' [rtac (hset_def RS trans), rtac (refl RS @{thm UN_cong} RS trans), etac mor_hset_rec,
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   257
    atac, atac, rtac (hset_def RS sym)] 1
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   258
49506
aeb0cc8889f2 renamed "rel" to "srel"
blanchet
parents: 49504
diff changeset
   259
fun mk_bis_srel_tac m bis_def srel_O_Grs map_comps map_congs set_naturalss =
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   260
  let
49506
aeb0cc8889f2 renamed "rel" to "srel"
blanchet
parents: 49504
diff changeset
   261
    val n = length srel_O_Grs;
aeb0cc8889f2 renamed "rel" to "srel"
blanchet
parents: 49504
diff changeset
   262
    val thms = ((1 upto n) ~~ map_comps ~~ map_congs ~~ set_naturalss ~~ srel_O_Grs);
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   263
49506
aeb0cc8889f2 renamed "rel" to "srel"
blanchet
parents: 49504
diff changeset
   264
    fun mk_if_tac ((((i, map_comp), map_cong), set_naturals), srel_O_Gr) =
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   265
      EVERY' [rtac allI, rtac allI, rtac impI, dtac (mk_conjunctN n i),
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   266
        etac allE, etac allE, etac impE, atac, etac bexE, etac conjE,
49506
aeb0cc8889f2 renamed "rel" to "srel"
blanchet
parents: 49504
diff changeset
   267
        rtac (srel_O_Gr RS equalityD2 RS set_mp),
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   268
        rtac @{thm relcompI}, rtac @{thm converseI},
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   269
        EVERY' (map (fn thm =>
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   270
          EVERY' [rtac @{thm GrI}, REPEAT_DETERM o eresolve_tac [CollectE, conjE],
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   271
            rtac CollectI,
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   272
            CONJ_WRAP' (fn (i, thm) =>
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   273
              if i <= m
49305
8241f21d104b tuned antiquotations
blanchet
parents: 49104
diff changeset
   274
              then EVERY' [rtac ord_eq_le_trans, rtac thm, rtac subset_trans,
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   275
                etac @{thm image_mono}, rtac @{thm image_subsetI}, etac @{thm diagI}]
49305
8241f21d104b tuned antiquotations
blanchet
parents: 49104
diff changeset
   276
              else EVERY' [rtac ord_eq_le_trans, rtac trans, rtac thm,
8241f21d104b tuned antiquotations
blanchet
parents: 49104
diff changeset
   277
                rtac trans_fun_cong_image_id_id_apply, atac])
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   278
            (1 upto (m + n) ~~ set_naturals),
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   279
            rtac trans, rtac trans, rtac map_comp, rtac map_cong, REPEAT_DETERM_N m o rtac thm,
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   280
            REPEAT_DETERM_N n o rtac (@{thm o_id} RS fun_cong), atac])
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   281
          @{thms fst_diag_id snd_diag_id})];
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   282
49506
aeb0cc8889f2 renamed "rel" to "srel"
blanchet
parents: 49504
diff changeset
   283
    fun mk_only_if_tac ((((i, map_comp), map_cong), set_naturals), srel_O_Gr) =
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   284
      EVERY' [dtac (mk_conjunctN n i), rtac allI, rtac allI, rtac impI,
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   285
        etac allE, etac allE, etac impE, atac,
49506
aeb0cc8889f2 renamed "rel" to "srel"
blanchet
parents: 49504
diff changeset
   286
        dtac (srel_O_Gr RS equalityD1 RS set_mp),
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   287
        REPEAT_DETERM o eresolve_tac [CollectE, @{thm relcompE}, @{thm converseE}],
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   288
        REPEAT_DETERM o eresolve_tac [@{thm GrE}, exE, conjE],
49488
02eb07152998 use iffD* instead of (s)subst instantiated with identity; tuned antiquotations;
traytel
parents: 49463
diff changeset
   289
        REPEAT_DETERM o dtac Pair_eqD,
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   290
        REPEAT_DETERM o etac conjE,
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   291
        hyp_subst_tac,
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   292
        REPEAT_DETERM o eresolve_tac [CollectE, conjE],
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   293
        rtac bexI, rtac conjI, rtac trans, rtac map_comp,
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   294
        REPEAT_DETERM_N m o stac @{thm id_o},
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   295
        REPEAT_DETERM_N n o stac @{thm o_id},
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   296
        etac sym, rtac trans, rtac map_comp,
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   297
        REPEAT_DETERM_N m o stac @{thm id_o},
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   298
        REPEAT_DETERM_N n o stac @{thm o_id},
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   299
        rtac trans, rtac map_cong,
49305
8241f21d104b tuned antiquotations
blanchet
parents: 49104
diff changeset
   300
        REPEAT_DETERM_N m o EVERY' [rtac @{thm diagE'}, etac set_mp, atac],
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   301
        REPEAT_DETERM_N n o rtac refl,
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   302
        etac sym, rtac CollectI,
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   303
        CONJ_WRAP' (fn (i, thm) =>
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   304
          if i <= m
49305
8241f21d104b tuned antiquotations
blanchet
parents: 49104
diff changeset
   305
          then EVERY' [rtac ord_eq_le_trans, rtac thm, rtac @{thm image_subsetI},
8241f21d104b tuned antiquotations
blanchet
parents: 49104
diff changeset
   306
            rtac @{thm diag_fst}, etac set_mp, atac]
8241f21d104b tuned antiquotations
blanchet
parents: 49104
diff changeset
   307
          else EVERY' [rtac ord_eq_le_trans, rtac trans, rtac thm,
8241f21d104b tuned antiquotations
blanchet
parents: 49104
diff changeset
   308
            rtac trans_fun_cong_image_id_id_apply, atac])
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   309
        (1 upto (m + n) ~~ set_naturals)];
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   310
  in
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   311
    EVERY' [rtac (bis_def RS trans),
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   312
      rtac iffI, etac conjE, etac conjI, CONJ_WRAP' mk_if_tac thms,
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   313
      etac conjE, etac conjI, CONJ_WRAP' mk_only_if_tac thms] 1
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   314
  end;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   315
49506
aeb0cc8889f2 renamed "rel" to "srel"
blanchet
parents: 49504
diff changeset
   316
fun mk_bis_converse_tac m bis_srel srel_congs srel_converses =
aeb0cc8889f2 renamed "rel" to "srel"
blanchet
parents: 49504
diff changeset
   317
  EVERY' [stac bis_srel, dtac (bis_srel RS iffD1),
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   318
    REPEAT_DETERM o etac conjE, rtac conjI,
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   319
    CONJ_WRAP' (K (EVERY' [rtac @{thm converse_shift}, etac subset_trans,
49506
aeb0cc8889f2 renamed "rel" to "srel"
blanchet
parents: 49504
diff changeset
   320
      rtac equalityD2, rtac @{thm converse_Times}])) srel_congs,
aeb0cc8889f2 renamed "rel" to "srel"
blanchet
parents: 49504
diff changeset
   321
    CONJ_WRAP' (fn (srel_cong, srel_converse) =>
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   322
      EVERY' [rtac allI, rtac allI, rtac impI, rtac @{thm set_mp[OF equalityD2]},
49506
aeb0cc8889f2 renamed "rel" to "srel"
blanchet
parents: 49504
diff changeset
   323
        rtac (srel_cong RS trans),
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   324
        REPEAT_DETERM_N m o rtac @{thm diag_converse},
49506
aeb0cc8889f2 renamed "rel" to "srel"
blanchet
parents: 49504
diff changeset
   325
        REPEAT_DETERM_N (length srel_congs) o rtac refl,
aeb0cc8889f2 renamed "rel" to "srel"
blanchet
parents: 49504
diff changeset
   326
        rtac srel_converse,
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   327
        REPEAT_DETERM o etac allE,
49506
aeb0cc8889f2 renamed "rel" to "srel"
blanchet
parents: 49504
diff changeset
   328
        rtac @{thm converseI}, etac mp, etac @{thm converseD}]) (srel_congs ~~ srel_converses)] 1;
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   329
49506
aeb0cc8889f2 renamed "rel" to "srel"
blanchet
parents: 49504
diff changeset
   330
fun mk_bis_O_tac m bis_srel srel_congs srel_Os =
aeb0cc8889f2 renamed "rel" to "srel"
blanchet
parents: 49504
diff changeset
   331
  EVERY' [stac bis_srel, REPEAT_DETERM o dtac (bis_srel RS iffD1),
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   332
    REPEAT_DETERM o etac conjE, rtac conjI,
49506
aeb0cc8889f2 renamed "rel" to "srel"
blanchet
parents: 49504
diff changeset
   333
    CONJ_WRAP' (K (EVERY' [etac @{thm relcomp_subset_Sigma}, atac])) srel_congs,
aeb0cc8889f2 renamed "rel" to "srel"
blanchet
parents: 49504
diff changeset
   334
    CONJ_WRAP' (fn (srel_cong, srel_O) =>
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   335
      EVERY' [rtac allI, rtac allI, rtac impI, rtac @{thm set_mp[OF equalityD2]},
49506
aeb0cc8889f2 renamed "rel" to "srel"
blanchet
parents: 49504
diff changeset
   336
        rtac (srel_cong RS trans),
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   337
        REPEAT_DETERM_N m o rtac @{thm diag_Comp},
49506
aeb0cc8889f2 renamed "rel" to "srel"
blanchet
parents: 49504
diff changeset
   338
        REPEAT_DETERM_N (length srel_congs) o rtac refl,
aeb0cc8889f2 renamed "rel" to "srel"
blanchet
parents: 49504
diff changeset
   339
        rtac srel_O,
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   340
        etac @{thm relcompE},
49488
02eb07152998 use iffD* instead of (s)subst instantiated with identity; tuned antiquotations;
traytel
parents: 49463
diff changeset
   341
        REPEAT_DETERM o dtac Pair_eqD,
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   342
        etac conjE, hyp_subst_tac,
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   343
        REPEAT_DETERM o etac allE, rtac @{thm relcompI},
49506
aeb0cc8889f2 renamed "rel" to "srel"
blanchet
parents: 49504
diff changeset
   344
        etac mp, atac, etac mp, atac]) (srel_congs ~~ srel_Os)] 1;
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   345
49506
aeb0cc8889f2 renamed "rel" to "srel"
blanchet
parents: 49504
diff changeset
   346
fun mk_bis_Gr_tac bis_srel srel_Grs mor_images morEs coalg_ins
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   347
  {context = ctxt, prems = _} =
49506
aeb0cc8889f2 renamed "rel" to "srel"
blanchet
parents: 49504
diff changeset
   348
  unfold_thms_tac ctxt (bis_srel :: @{thm diag_Gr} :: srel_Grs) THEN
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   349
  EVERY' [rtac conjI,
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   350
    CONJ_WRAP' (fn thm => rtac (@{thm Gr_incl} RS ssubst) THEN' etac thm) mor_images,
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   351
    CONJ_WRAP' (fn (coalg_in, morE) =>
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   352
      EVERY' [rtac allI, rtac allI, rtac impI, rtac @{thm GrI}, etac coalg_in,
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   353
        etac @{thm GrD1}, etac (morE RS trans), etac @{thm GrD1},
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   354
        etac (@{thm GrD2} RS arg_cong)]) (coalg_ins ~~ morEs)] 1;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   355
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   356
fun mk_bis_Union_tac bis_def in_monos {context = ctxt, prems = _} =
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   357
  let
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   358
    val n = length in_monos;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   359
    val ks = 1 upto n;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   360
  in
49504
df9b897fb254 renamed "iter"/"coiter" to "fold"/"unfold" (cf. Wadler)
blanchet
parents: 49501
diff changeset
   361
    unfold_thms_tac ctxt [bis_def] THEN
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   362
    EVERY' [rtac conjI,
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   363
      CONJ_WRAP' (fn i =>
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   364
        EVERY' [rtac @{thm UN_least}, dtac bspec, atac,
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   365
          dtac conjunct1, etac (mk_conjunctN n i)]) ks,
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   366
      CONJ_WRAP' (fn (i, in_mono) =>
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   367
        EVERY' [rtac allI, rtac allI, rtac impI, etac @{thm UN_E}, dtac bspec, atac,
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   368
          dtac conjunct2, dtac (mk_conjunctN n i), etac allE, etac allE, dtac mp,
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   369
          atac, etac bexE, rtac bexI, atac, rtac in_mono,
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   370
          REPEAT_DETERM_N n o etac @{thm incl_UNION_I[OF _ subset_refl]},
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   371
          atac]) (ks ~~ in_monos)] 1
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   372
  end;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   373
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   374
fun mk_sbis_lsbis_tac lsbis_defs bis_Union bis_cong =
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   375
  let
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   376
    val n = length lsbis_defs;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   377
  in
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   378
    EVERY' [rtac (Thm.permute_prems 0 1 bis_cong), EVERY' (map rtac lsbis_defs),
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   379
      rtac bis_Union, rtac ballI, REPEAT_DETERM o eresolve_tac [CollectE, conjE, exE],
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   380
      hyp_subst_tac, etac bis_cong, EVERY' (map (rtac o mk_nth_conv n) (1 upto n))] 1
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   381
  end;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   382
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   383
fun mk_incl_lsbis_tac n i lsbis_def =
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   384
  EVERY' [rtac @{thm xt1(3)}, rtac lsbis_def, rtac @{thm incl_UNION_I}, rtac CollectI,
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   385
    REPEAT_DETERM_N n o rtac exI, rtac conjI, rtac refl, atac, rtac equalityD2,
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   386
    rtac (mk_nth_conv n i)] 1;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   387
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   388
fun mk_equiv_lsbis_tac sbis_lsbis lsbis_incl incl_lsbis bis_diag bis_converse bis_O =
49488
02eb07152998 use iffD* instead of (s)subst instantiated with identity; tuned antiquotations;
traytel
parents: 49463
diff changeset
   389
  EVERY' [rtac (@{thm equiv_def} RS iffD2),
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   390
49488
02eb07152998 use iffD* instead of (s)subst instantiated with identity; tuned antiquotations;
traytel
parents: 49463
diff changeset
   391
    rtac conjI, rtac (@{thm refl_on_def} RS iffD2),
49305
8241f21d104b tuned antiquotations
blanchet
parents: 49104
diff changeset
   392
    rtac conjI, rtac lsbis_incl, rtac ballI, rtac set_mp,
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   393
    rtac incl_lsbis, rtac bis_diag, atac, etac @{thm diagI},
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   394
49488
02eb07152998 use iffD* instead of (s)subst instantiated with identity; tuned antiquotations;
traytel
parents: 49463
diff changeset
   395
    rtac conjI, rtac (@{thm sym_def} RS iffD2),
49305
8241f21d104b tuned antiquotations
blanchet
parents: 49104
diff changeset
   396
    rtac allI, rtac allI, rtac impI, rtac set_mp,
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   397
    rtac incl_lsbis, rtac bis_converse, rtac sbis_lsbis, etac @{thm converseI},
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   398
49488
02eb07152998 use iffD* instead of (s)subst instantiated with identity; tuned antiquotations;
traytel
parents: 49463
diff changeset
   399
    rtac (@{thm trans_def} RS iffD2),
49305
8241f21d104b tuned antiquotations
blanchet
parents: 49104
diff changeset
   400
    rtac allI, rtac allI, rtac allI, rtac impI, rtac impI, rtac set_mp,
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   401
    rtac incl_lsbis, rtac bis_O, rtac sbis_lsbis, rtac sbis_lsbis,
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   402
    etac @{thm relcompI}, atac] 1;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   403
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   404
fun mk_coalgT_tac m defs strT_defs set_naturalss {context = ctxt, prems = _} =
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   405
  let
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   406
    val n = length strT_defs;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   407
    val ks = 1 upto n;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   408
    fun coalg_tac (i, ((passive_sets, active_sets), def)) =
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   409
      EVERY' [rtac ballI, REPEAT_DETERM o eresolve_tac [CollectE, exE, conjE],
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   410
        hyp_subst_tac, rtac (def RS trans RS @{thm ssubst_mem}), etac (arg_cong RS trans),
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   411
        rtac (mk_sum_casesN n i), rtac CollectI,
49305
8241f21d104b tuned antiquotations
blanchet
parents: 49104
diff changeset
   412
        EVERY' (map (fn thm => EVERY' [rtac conjI, rtac (thm RS ord_eq_le_trans),
8241f21d104b tuned antiquotations
blanchet
parents: 49104
diff changeset
   413
          etac ((trans OF [@{thm image_id} RS fun_cong, @{thm id_apply}]) RS ord_eq_le_trans)])
8241f21d104b tuned antiquotations
blanchet
parents: 49104
diff changeset
   414
          passive_sets),
8241f21d104b tuned antiquotations
blanchet
parents: 49104
diff changeset
   415
        CONJ_WRAP' (fn (i, thm) => EVERY' [rtac (thm RS ord_eq_le_trans),
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   416
          rtac @{thm image_subsetI}, rtac CollectI, rtac exI, rtac exI, rtac conjI, rtac refl,
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   417
          rtac conjI,
49305
8241f21d104b tuned antiquotations
blanchet
parents: 49104
diff changeset
   418
          rtac conjI, etac @{thm empty_Shift}, dtac set_rev_mp,
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   419
            etac equalityD1, etac CollectD,
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   420
          rtac conjI, etac @{thm Shift_clists},
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   421
          rtac conjI, etac @{thm Shift_prefCl},
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   422
          rtac conjI, rtac ballI,
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   423
            rtac conjI, dtac @{thm iffD1[OF ball_conj_distrib]}, dtac conjunct1,
49504
df9b897fb254 renamed "iter"/"coiter" to "fold"/"unfold" (cf. Wadler)
blanchet
parents: 49501
diff changeset
   424
            SELECT_GOAL (unfold_thms_tac ctxt @{thms Succ_Shift shift_def}),
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   425
            etac bspec, etac @{thm ShiftD},
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   426
            CONJ_WRAP' (fn i => EVERY' [rtac ballI, etac CollectE, dtac @{thm ShiftD},
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   427
              dtac bspec, etac thin_rl, atac, dtac conjunct2, dtac (mk_conjunctN n i),
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   428
              dtac bspec, rtac CollectI, etac @{thm set_mp[OF equalityD1[OF Succ_Shift]]},
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   429
              REPEAT_DETERM o eresolve_tac [exE, conjE], rtac exI,
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   430
              rtac conjI, rtac (@{thm shift_def} RS fun_cong RS trans),
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   431
              rtac (@{thm append_Cons} RS sym RS arg_cong RS trans), atac,
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   432
              REPEAT_DETERM_N m o (rtac conjI THEN' atac),
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   433
              CONJ_WRAP' (K (EVERY' [etac trans, rtac @{thm Collect_cong},
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   434
                rtac @{thm eqset_imp_iff}, rtac sym, rtac trans, rtac @{thm Succ_Shift},
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   435
                rtac (@{thm append_Cons} RS sym RS arg_cong)])) ks]) ks,
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   436
          rtac allI, rtac impI, REPEAT_DETERM o eresolve_tac [allE, impE],
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   437
          etac @{thm not_in_Shift}, rtac trans, rtac (@{thm shift_def} RS fun_cong), atac,
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   438
          dtac bspec, atac, dtac conjunct2, dtac (mk_conjunctN n i), dtac bspec,
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   439
          etac @{thm set_mp[OF equalityD1]}, atac,
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   440
          REPEAT_DETERM o eresolve_tac [exE, conjE], rtac exI,
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   441
          rtac conjI, rtac (@{thm shift_def} RS fun_cong RS trans),
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   442
          etac (@{thm append_Nil} RS sym RS arg_cong RS trans),
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   443
          REPEAT_DETERM_N m o (rtac conjI THEN' atac),
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   444
          CONJ_WRAP' (K (EVERY' [etac trans, rtac @{thm Collect_cong},
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   445
            rtac @{thm eqset_imp_iff}, rtac sym, rtac trans, rtac @{thm Succ_Shift},
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   446
            rtac (@{thm append_Nil} RS sym RS arg_cong)])) ks]) (ks ~~ active_sets)];
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   447
  in
49504
df9b897fb254 renamed "iter"/"coiter" to "fold"/"unfold" (cf. Wadler)
blanchet
parents: 49501
diff changeset
   448
    unfold_thms_tac ctxt defs THEN
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   449
    CONJ_WRAP' coalg_tac (ks ~~ (map (chop m) set_naturalss ~~ strT_defs)) 1
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   450
  end;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   451
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   452
fun mk_card_of_carT_tac m isNode_defs sbd_sbd
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   453
  sbd_card_order sbd_Card_order sbd_Cinfinite sbd_Cnotzero in_sbds =
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   454
  let
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   455
    val n = length isNode_defs;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   456
  in
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   457
    EVERY' [rtac (Thm.permute_prems 0 1 ctrans),
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   458
      rtac @{thm card_of_Sigma_ordLeq_Cinfinite}, rtac @{thm Cinfinite_cexp},
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   459
      if m = 0 then rtac @{thm ordLeq_refl} else rtac @{thm ordLeq_csum2},
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   460
      rtac @{thm Card_order_ctwo}, rtac @{thm Cinfinite_cexp},
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   461
      rtac @{thm ctwo_ordLeq_Cinfinite}, rtac sbd_Cinfinite, rtac sbd_Cinfinite,
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   462
      rtac ctrans, rtac @{thm card_of_diff},
49305
8241f21d104b tuned antiquotations
blanchet
parents: 49104
diff changeset
   463
      rtac ordIso_ordLeq_trans, rtac @{thm card_of_Field_ordIso},
8241f21d104b tuned antiquotations
blanchet
parents: 49104
diff changeset
   464
      rtac @{thm Card_order_cpow}, rtac ordIso_ordLeq_trans,
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   465
      rtac @{thm cpow_cexp_ctwo}, rtac ctrans, rtac @{thm cexp_mono1_Cnotzero},
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   466
      if m = 0 then rtac @{thm ordLeq_refl} else rtac @{thm ordLeq_csum2},
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   467
      rtac @{thm Card_order_ctwo}, rtac @{thm ctwo_Cnotzero}, rtac @{thm Card_order_clists},
49305
8241f21d104b tuned antiquotations
blanchet
parents: 49104
diff changeset
   468
      rtac @{thm cexp_mono2_Cnotzero}, rtac ordIso_ordLeq_trans,
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   469
      rtac @{thm clists_Cinfinite},
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   470
      if n = 1 then rtac sbd_Cinfinite else rtac (sbd_Cinfinite RS @{thm Cinfinite_csum1}),
49305
8241f21d104b tuned antiquotations
blanchet
parents: 49104
diff changeset
   471
      rtac ordIso_ordLeq_trans, rtac sbd_sbd, rtac @{thm infinite_ordLeq_cexp},
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   472
      rtac sbd_Cinfinite,
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   473
      if m = 0 then rtac @{thm ctwo_Cnotzero} else rtac @{thm csum_Cnotzero2[OF ctwo_Cnotzero]},
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   474
      rtac @{thm Cnotzero_clists},
49305
8241f21d104b tuned antiquotations
blanchet
parents: 49104
diff changeset
   475
      rtac ballI, rtac ordIso_ordLeq_trans, rtac @{thm card_of_Func_Ffunc},
8241f21d104b tuned antiquotations
blanchet
parents: 49104
diff changeset
   476
      rtac ordIso_ordLeq_trans, rtac @{thm Func_cexp},
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   477
      rtac ctrans, rtac @{thm cexp_mono},
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   478
      rtac @{thm ordLeq_ordIso_trans},
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   479
      CONJ_WRAP_GEN' (rtac (Thm.permute_prems 0 1
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   480
          (sbd_Cinfinite RS @{thm Cinfinite_cexp[OF ordLeq_csum2[OF Card_order_ctwo]]}
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   481
        RSN (3, @{thm Un_Cinfinite_bound}))))
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   482
        (fn thm => EVERY' [rtac ctrans, rtac @{thm card_of_image}, rtac thm]) (rev in_sbds),
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   483
      rtac @{thm cexp_cong1_Cnotzero}, rtac @{thm csum_cong1},
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   484
      REPEAT_DETERM_N m o rtac @{thm csum_cong2},
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   485
      CONJ_WRAP_GEN' (rtac @{thm csum_cong})
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   486
        (K (rtac (sbd_Card_order RS @{thm card_of_Field_ordIso}))) in_sbds,
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   487
      rtac sbd_Card_order,
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   488
      rtac @{thm csum_Cnotzero2}, rtac @{thm ctwo_Cnotzero},
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   489
      rtac @{thm csum_Cnotzero2}, rtac @{thm ctwo_Cnotzero},
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   490
      rtac @{thm ordLeq_ordIso_trans}, etac @{thm clists_bound},
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   491
      rtac @{thm clists_Cinfinite}, TRY o rtac @{thm Cinfinite_csum1}, rtac sbd_Cinfinite,
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   492
      rtac disjI2, rtac @{thm cone_ordLeq_cexp}, rtac @{thm cone_ordLeq_cexp},
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   493
      rtac ctrans, rtac @{thm cone_ordLeq_ctwo}, rtac @{thm ordLeq_csum2},
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   494
      rtac @{thm Card_order_ctwo}, rtac FalseE, etac @{thm cpow_clists_czero}, atac,
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   495
      rtac @{thm card_of_Card_order},
49305
8241f21d104b tuned antiquotations
blanchet
parents: 49104
diff changeset
   496
      rtac ordIso_ordLeq_trans, rtac @{thm cexp_cprod},
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   497
      rtac @{thm csum_Cnotzero2}, rtac @{thm ctwo_Cnotzero},
49305
8241f21d104b tuned antiquotations
blanchet
parents: 49104
diff changeset
   498
      rtac ordIso_ordLeq_trans, rtac @{thm cexp_cong2_Cnotzero},
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   499
      rtac @{thm ordIso_transitive}, rtac @{thm cprod_cong2}, rtac sbd_sbd,
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   500
      rtac @{thm cprod_infinite}, rtac sbd_Cinfinite,
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   501
      rtac @{thm csum_Cnotzero2}, rtac @{thm ctwo_Cnotzero}, rtac @{thm Card_order_cprod},
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   502
      rtac ctrans, rtac @{thm cexp_mono1_Cnotzero},
49305
8241f21d104b tuned antiquotations
blanchet
parents: 49104
diff changeset
   503
      rtac ordIso_ordLeq_trans, rtac @{thm ordIso_transitive}, rtac @{thm csum_cong1},
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   504
      rtac @{thm ordIso_transitive},
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   505
      REPEAT_DETERM_N m o rtac @{thm csum_cong2},
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   506
      rtac sbd_sbd,
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   507
      BNF_Tactics.mk_rotate_eq_tac (rtac @{thm ordIso_refl} THEN'
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   508
        FIRST' [rtac @{thm card_of_Card_order},
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   509
          rtac @{thm Card_order_csum}, rtac sbd_Card_order])
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   510
        @{thm ordIso_transitive} @{thm csum_assoc} @{thm csum_com} @{thm csum_cong}
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   511
        (1 upto m + 1) (m + 1 :: (1 upto m)),
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   512
      if m = 0 then K all_tac else EVERY' [rtac @{thm ordIso_transitive}, rtac @{thm csum_assoc}],
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   513
      rtac @{thm csum_com}, rtac @{thm csum_cexp'}, rtac sbd_Cinfinite,
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   514
      if m = 0 then rtac @{thm Card_order_ctwo} else rtac @{thm Card_order_csum},
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   515
      if m = 0 then rtac @{thm ordLeq_refl} else rtac @{thm ordLeq_csum2},
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   516
      rtac @{thm Card_order_ctwo},
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   517
      rtac @{thm csum_Cnotzero2}, rtac @{thm ctwo_Cnotzero}, rtac sbd_Card_order,
49305
8241f21d104b tuned antiquotations
blanchet
parents: 49104
diff changeset
   518
      rtac ordIso_ordLeq_trans, rtac @{thm cexp_cprod_ordLeq},
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   519
      if m = 0 then rtac @{thm ctwo_Cnotzero} else rtac @{thm csum_Cnotzero2[OF ctwo_Cnotzero]},
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   520
      rtac sbd_Cinfinite, rtac sbd_Cnotzero, rtac @{thm ordLeq_refl}, rtac sbd_Card_order,
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   521
      rtac @{thm cexp_mono2_Cnotzero}, rtac @{thm infinite_ordLeq_cexp},
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   522
      rtac sbd_Cinfinite,
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   523
      if m = 0 then rtac @{thm ctwo_Cnotzero} else rtac @{thm csum_Cnotzero2[OF ctwo_Cnotzero]},
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   524
      rtac sbd_Cnotzero,
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   525
      rtac @{thm card_of_mono1}, rtac subsetI,
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   526
      REPEAT_DETERM o eresolve_tac [CollectE, exE, conjE, @{thm prod_caseE}], hyp_subst_tac,
49305
8241f21d104b tuned antiquotations
blanchet
parents: 49104
diff changeset
   527
      rtac @{thm SigmaI}, rtac @{thm DiffI}, rtac set_mp, rtac equalityD2,
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   528
      rtac (@{thm cpow_def} RS arg_cong RS trans), rtac (@{thm Pow_def} RS arg_cong RS trans),
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   529
      rtac @{thm Field_card_of}, rtac CollectI, atac, rtac notI, etac @{thm singletonE},
49305
8241f21d104b tuned antiquotations
blanchet
parents: 49104
diff changeset
   530
      hyp_subst_tac, etac @{thm emptyE}, rtac (@{thm Ffunc_def} RS equalityD2 RS set_mp),
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   531
      rtac CollectI, rtac conjI, rtac ballI, dtac bspec, etac thin_rl, atac, dtac conjunct1,
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   532
      CONJ_WRAP_GEN' (etac disjE) (fn (i, def) => EVERY'
49488
02eb07152998 use iffD* instead of (s)subst instantiated with identity; tuned antiquotations;
traytel
parents: 49463
diff changeset
   533
        [rtac (mk_UnIN n i), dtac (def RS iffD1),
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   534
        REPEAT_DETERM o eresolve_tac [exE, conjE], rtac @{thm image_eqI}, atac, rtac CollectI,
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   535
        REPEAT_DETERM_N m o (rtac conjI THEN' atac),
49305
8241f21d104b tuned antiquotations
blanchet
parents: 49104
diff changeset
   536
        CONJ_WRAP' (K (EVERY' [etac ord_eq_le_trans, rtac subset_trans,
49490
394870e51d18 tuned antiquotations
traytel
parents: 49488
diff changeset
   537
          rtac subset_UNIV, rtac equalityD2, rtac @{thm Field_card_order},
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   538
          rtac sbd_card_order])) isNode_defs]) (1 upto n ~~ isNode_defs),
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   539
      atac] 1
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   540
  end;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   541
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   542
fun mk_carT_set_tac n i carT_def strT_def isNode_def set_natural {context = ctxt, prems = _}=
49305
8241f21d104b tuned antiquotations
blanchet
parents: 49104
diff changeset
   543
  EVERY' [dtac (carT_def RS equalityD1 RS set_mp),
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   544
    REPEAT_DETERM o eresolve_tac [CollectE, exE, conjE],
49488
02eb07152998 use iffD* instead of (s)subst instantiated with identity; tuned antiquotations;
traytel
parents: 49463
diff changeset
   545
    dtac Pair_eqD,
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   546
    etac conjE, hyp_subst_tac,
49488
02eb07152998 use iffD* instead of (s)subst instantiated with identity; tuned antiquotations;
traytel
parents: 49463
diff changeset
   547
    dtac (isNode_def RS iffD1),
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   548
    REPEAT_DETERM o eresolve_tac [exE, conjE],
49305
8241f21d104b tuned antiquotations
blanchet
parents: 49104
diff changeset
   549
    rtac (equalityD2 RS set_mp),
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   550
    rtac (strT_def RS arg_cong RS trans),
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   551
    etac (arg_cong RS trans),
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   552
    fo_rtac (mk_sum_casesN n i RS arg_cong RS trans) ctxt,
49305
8241f21d104b tuned antiquotations
blanchet
parents: 49104
diff changeset
   553
    rtac set_natural, rtac imageI, etac (equalityD2 RS set_mp), rtac CollectI,
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   554
    etac @{thm prefCl_Succ}, atac] 1;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   555
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   556
fun mk_strT_hset_tac n m j arg_cong_cTs cTs cts carT_defs strT_defs isNode_defs
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   557
  set_incl_hsets set_hset_incl_hsetss coalg_setss carT_setss coalgT set_naturalss =
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   558
  let
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   559
    val set_naturals = map (fn xs => nth xs (j - 1)) set_naturalss;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   560
    val ks = 1 upto n;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   561
    fun base_tac (i, (cT, (strT_def, (set_incl_hset, set_natural)))) =
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   562
      CONJ_WRAP' (fn (i', (carT_def, isNode_def)) => rtac impI THEN' etac conjE THEN'
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   563
        (if i = i'
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   564
        then EVERY' [rtac @{thm xt1(4)}, rtac set_incl_hset,
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   565
          rtac (strT_def RS arg_cong RS trans), etac (arg_cong RS trans),
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   566
          rtac (Thm.permute_prems 0 1 (set_natural RS box_equals)),
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   567
          rtac (trans OF [@{thm image_id} RS fun_cong, @{thm id_apply}]),
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   568
          rtac (mk_sum_casesN n i RS (Drule.instantiate' [cT] [] arg_cong) RS sym)]
49305
8241f21d104b tuned antiquotations
blanchet
parents: 49104
diff changeset
   569
        else EVERY' [dtac (carT_def RS equalityD1 RS set_mp),
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   570
          REPEAT_DETERM o eresolve_tac [CollectE, exE], etac conjE,
49488
02eb07152998 use iffD* instead of (s)subst instantiated with identity; tuned antiquotations;
traytel
parents: 49463
diff changeset
   571
          dtac conjunct2, dtac Pair_eqD, etac conjE,
02eb07152998 use iffD* instead of (s)subst instantiated with identity; tuned antiquotations;
traytel
parents: 49463
diff changeset
   572
          hyp_subst_tac, dtac (isNode_def RS iffD1),
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   573
          REPEAT_DETERM o eresolve_tac [exE, conjE],
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   574
          rtac (mk_InN_not_InM i i' RS notE), etac (sym RS trans), atac]))
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   575
      (ks ~~ (carT_defs ~~ isNode_defs));
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   576
    fun step_tac (i, (coalg_sets, (carT_sets, set_hset_incl_hsets))) =
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   577
      dtac (mk_conjunctN n i) THEN'
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   578
      CONJ_WRAP' (fn (coalg_set, (carT_set, set_hset_incl_hset)) =>
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   579
        EVERY' [rtac impI, etac conjE, etac impE, rtac conjI,
49305
8241f21d104b tuned antiquotations
blanchet
parents: 49104
diff changeset
   580
          rtac (coalgT RS coalg_set RS set_mp), atac, etac carT_set, atac, atac,
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   581
          etac (@{thm shift_def} RS fun_cong RS trans), etac subset_trans,
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   582
          rtac set_hset_incl_hset, etac carT_set, atac, atac])
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   583
      (coalg_sets ~~ (carT_sets ~~ set_hset_incl_hsets));
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   584
  in
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   585
    EVERY' [rtac (Drule.instantiate' cTs cts @{thm list.induct}),
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   586
      REPEAT_DETERM o rtac allI, rtac impI,
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   587
      CONJ_WRAP' base_tac
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   588
        (ks ~~ (arg_cong_cTs ~~ (strT_defs ~~ (set_incl_hsets ~~ set_naturals)))),
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   589
      REPEAT_DETERM o rtac allI, rtac impI,
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   590
      REPEAT_DETERM o eresolve_tac [allE, impE], etac @{thm ShiftI},
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   591
      CONJ_WRAP' (fn i => dtac (mk_conjunctN n i) THEN' rtac (mk_sumEN n) THEN'
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   592
        CONJ_WRAP_GEN' (K all_tac) step_tac
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   593
          (ks ~~ (drop m coalg_setss ~~ (carT_setss ~~ set_hset_incl_hsetss)))) ks] 1
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   594
  end;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   595
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   596
fun mk_isNode_hset_tac n isNode_def strT_hsets {context = ctxt, prems = _} =
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   597
  let
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   598
    val m = length strT_hsets;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   599
  in
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   600
    if m = 0 then atac 1
49504
df9b897fb254 renamed "iter"/"coiter" to "fold"/"unfold" (cf. Wadler)
blanchet
parents: 49501
diff changeset
   601
    else (unfold_thms_tac ctxt [isNode_def] THEN
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   602
      EVERY' [REPEAT_DETERM o eresolve_tac [CollectE, exE, conjE],
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   603
        rtac exI, rtac conjI, atac,
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   604
        CONJ_WRAP' (fn (thm, i) =>  if i > m then atac
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   605
          else EVERY' [rtac (thm RS subset_trans), atac, rtac conjI, atac, atac, atac])
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   606
        (strT_hsets @ (replicate n mp) ~~ (1 upto (m + n)))] 1)
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   607
  end;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   608
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   609
fun mk_Lev_sbd_tac cts Lev_0s Lev_Sucs to_sbdss =
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   610
  let
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   611
    val n = length Lev_0s;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   612
    val ks = 1 upto n;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   613
  in
49305
8241f21d104b tuned antiquotations
blanchet
parents: 49104
diff changeset
   614
    EVERY' [rtac (Drule.instantiate' [] cts nat_induct),
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   615
      REPEAT_DETERM o rtac allI,
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   616
      CONJ_WRAP' (fn Lev_0 =>
49305
8241f21d104b tuned antiquotations
blanchet
parents: 49104
diff changeset
   617
        EVERY' (map rtac [ord_eq_le_trans, Lev_0, @{thm Nil_clists}])) Lev_0s,
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   618
      REPEAT_DETERM o rtac allI,
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   619
      CONJ_WRAP' (fn (Lev_Suc, to_sbds) =>
49305
8241f21d104b tuned antiquotations
blanchet
parents: 49104
diff changeset
   620
        EVERY' [rtac ord_eq_le_trans, rtac Lev_Suc,
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   621
          CONJ_WRAP_GEN' (rtac (Thm.permute_prems 0 1 @{thm Un_least}))
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   622
            (fn (i, to_sbd) => EVERY' [rtac subsetI,
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   623
              REPEAT_DETERM o eresolve_tac [CollectE, exE, conjE], hyp_subst_tac,
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   624
              rtac @{thm Cons_clists}, rtac (mk_InN_Field n i), etac to_sbd,
49305
8241f21d104b tuned antiquotations
blanchet
parents: 49104
diff changeset
   625
              etac set_rev_mp, REPEAT_DETERM o etac allE,
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   626
              etac (mk_conjunctN n i)])
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   627
          (rev (ks ~~ to_sbds))])
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   628
      (Lev_Sucs ~~ to_sbdss)] 1
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   629
  end;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   630
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   631
fun mk_length_Lev_tac cts Lev_0s Lev_Sucs =
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   632
  let
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   633
    val n = length Lev_0s;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   634
    val ks = n downto 1;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   635
  in
49305
8241f21d104b tuned antiquotations
blanchet
parents: 49104
diff changeset
   636
    EVERY' [rtac (Drule.instantiate' [] cts nat_induct),
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   637
      REPEAT_DETERM o rtac allI,
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   638
      CONJ_WRAP' (fn Lev_0 =>
49305
8241f21d104b tuned antiquotations
blanchet
parents: 49104
diff changeset
   639
        EVERY' [rtac impI, dtac (Lev_0 RS equalityD1 RS set_mp),
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   640
          etac @{thm singletonE}, etac ssubst, rtac @{thm list.size(3)}]) Lev_0s,
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   641
      REPEAT_DETERM o rtac allI,
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   642
      CONJ_WRAP' (fn Lev_Suc =>
49305
8241f21d104b tuned antiquotations
blanchet
parents: 49104
diff changeset
   643
        EVERY' [rtac impI, dtac (Lev_Suc RS equalityD1 RS set_mp),
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   644
          CONJ_WRAP_GEN' (etac (Thm.permute_prems 1 1 UnE))
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   645
            (fn i => EVERY' [REPEAT_DETERM o eresolve_tac [CollectE, exE, conjE], hyp_subst_tac,
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   646
              rtac trans, rtac @{thm length_Cons}, rtac @{thm arg_cong[of _ _ Suc]},
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   647
              REPEAT_DETERM o etac allE, dtac (mk_conjunctN n i), etac mp, atac]) ks])
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   648
      Lev_Sucs] 1
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   649
  end;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   650
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   651
fun mk_length_Lev'_tac length_Lev =
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   652
  EVERY' [ftac length_Lev, etac ssubst, atac] 1;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   653
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   654
fun mk_prefCl_Lev_tac cts Lev_0s Lev_Sucs =
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   655
  let
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   656
    val n = length Lev_0s;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   657
    val ks = n downto 1;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   658
  in
49305
8241f21d104b tuned antiquotations
blanchet
parents: 49104
diff changeset
   659
    EVERY' [rtac (Drule.instantiate' [] cts nat_induct),
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   660
      REPEAT_DETERM o rtac allI,
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   661
      CONJ_WRAP' (fn Lev_0 =>
49305
8241f21d104b tuned antiquotations
blanchet
parents: 49104
diff changeset
   662
        EVERY' [rtac impI, etac conjE, dtac (Lev_0 RS equalityD1 RS set_mp),
49091
0da7116b1b23 reverted (accidentally commited) changes from changeset fd4aef9bc7a9
Christian Sternagel
parents: 49086
diff changeset
   663
          etac @{thm singletonE}, hyp_subst_tac, dtac @{thm prefix_Nil[THEN subst, of "%x. x"]},
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   664
          hyp_subst_tac, rtac @{thm set_mp[OF equalityD2[OF trans[OF arg_cong[OF list.size(3)]]]]},
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   665
          rtac Lev_0, rtac @{thm singletonI}]) Lev_0s,
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   666
      REPEAT_DETERM o rtac allI,
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   667
      CONJ_WRAP' (fn (Lev_0, Lev_Suc) =>
49305
8241f21d104b tuned antiquotations
blanchet
parents: 49104
diff changeset
   668
        EVERY' [rtac impI, etac conjE, dtac (Lev_Suc RS equalityD1 RS set_mp),
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   669
          CONJ_WRAP_GEN' (etac (Thm.permute_prems 1 1 UnE))
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   670
            (fn i => EVERY' [REPEAT_DETERM o eresolve_tac [CollectE, exE, conjE], hyp_subst_tac,
49091
0da7116b1b23 reverted (accidentally commited) changes from changeset fd4aef9bc7a9
Christian Sternagel
parents: 49086
diff changeset
   671
              dtac @{thm prefix_Cons[THEN subst, of "%x. x"]}, etac disjE, hyp_subst_tac,
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   672
              rtac @{thm set_mp[OF equalityD2[OF trans[OF arg_cong[OF list.size(3)]]]]},
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   673
              rtac Lev_0, rtac @{thm singletonI},
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   674
              REPEAT_DETERM o eresolve_tac [exE, conjE], hyp_subst_tac,
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   675
              rtac @{thm set_mp[OF equalityD2[OF trans[OF arg_cong[OF length_Cons]]]]},
49366
3edd1c90f6e6 renamed "mk_UnN" to "mk_UnIN"
blanchet
parents: 49328
diff changeset
   676
              rtac Lev_Suc, rtac (mk_UnIN n i), rtac CollectI, REPEAT_DETERM o rtac exI, rtac conjI,
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   677
              rtac refl, etac conjI, REPEAT_DETERM o etac allE, dtac (mk_conjunctN n i),
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   678
              etac mp, etac conjI, atac]) ks])
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   679
      (Lev_0s ~~ Lev_Sucs)] 1
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   680
  end;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   681
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   682
fun mk_rv_last_tac cTs cts rv_Nils rv_Conss =
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   683
  let
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   684
    val n = length rv_Nils;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   685
    val ks = 1 upto n;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   686
  in
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   687
    EVERY' [rtac (Drule.instantiate' cTs cts @{thm list.induct}),
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   688
      REPEAT_DETERM o rtac allI,
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   689
      CONJ_WRAP' (fn rv_Cons =>
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   690
        CONJ_WRAP' (fn (i, rv_Nil) => (EVERY' [rtac exI,
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   691
          rtac (@{thm append_Nil} RS arg_cong RS trans),
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   692
          rtac (rv_Cons RS trans), rtac (mk_sum_casesN n i RS arg_cong RS trans), rtac rv_Nil]))
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   693
        (ks ~~ rv_Nils))
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   694
      rv_Conss,
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   695
      REPEAT_DETERM o rtac allI, rtac (mk_sumEN n),
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   696
      EVERY' (map (fn i =>
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   697
        CONJ_WRAP' (fn rv_Cons => EVERY' [REPEAT_DETERM o etac allE, dtac (mk_conjunctN n i),
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   698
          CONJ_WRAP' (fn i' => EVERY' [dtac (mk_conjunctN n i'), etac exE, rtac exI,
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   699
            rtac (@{thm append_Cons} RS arg_cong RS trans),
49328
a1c10b46fecd avoided duplicate lemma
blanchet
parents: 49305
diff changeset
   700
            rtac (rv_Cons RS trans), etac (sum_case_weak_cong RS arg_cong RS trans),
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   701
            rtac (mk_sum_casesN n i RS arg_cong RS trans), atac])
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   702
          ks])
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   703
        rv_Conss)
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   704
      ks)] 1
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   705
  end;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   706
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   707
fun mk_set_rv_Lev_tac m cts Lev_0s Lev_Sucs rv_Nils rv_Conss coalg_setss from_to_sbdss =
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   708
  let
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   709
    val n = length Lev_0s;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   710
    val ks = 1 upto n;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   711
  in
49305
8241f21d104b tuned antiquotations
blanchet
parents: 49104
diff changeset
   712
    EVERY' [rtac (Drule.instantiate' [] cts nat_induct),
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   713
      REPEAT_DETERM o rtac allI,
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   714
      CONJ_WRAP' (fn (i, ((Lev_0, rv_Nil), coalg_sets)) =>
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   715
        EVERY' [rtac impI, REPEAT_DETERM o etac conjE,
49305
8241f21d104b tuned antiquotations
blanchet
parents: 49104
diff changeset
   716
          dtac (Lev_0 RS equalityD1 RS set_mp), etac @{thm singletonE}, etac ssubst,
49488
02eb07152998 use iffD* instead of (s)subst instantiated with identity; tuned antiquotations;
traytel
parents: 49463
diff changeset
   717
          rtac (rv_Nil RS arg_cong RS iffD2),
02eb07152998 use iffD* instead of (s)subst instantiated with identity; tuned antiquotations;
traytel
parents: 49463
diff changeset
   718
          rtac (mk_sum_casesN n i RS iffD2),
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   719
          CONJ_WRAP' (fn thm => etac thm THEN' atac) (take m coalg_sets)])
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   720
      (ks ~~ ((Lev_0s ~~ rv_Nils) ~~ coalg_setss)),
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   721
      REPEAT_DETERM o rtac allI,
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   722
      CONJ_WRAP' (fn ((Lev_Suc, rv_Cons), (from_to_sbds, coalg_sets)) =>
49305
8241f21d104b tuned antiquotations
blanchet
parents: 49104
diff changeset
   723
        EVERY' [rtac impI, etac conjE, dtac (Lev_Suc RS equalityD1 RS set_mp),
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   724
          CONJ_WRAP_GEN' (etac (Thm.permute_prems 1 1 UnE))
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   725
            (fn (i, (from_to_sbd, coalg_set)) =>
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   726
              EVERY' [REPEAT_DETERM o eresolve_tac [CollectE, exE, conjE], hyp_subst_tac,
49488
02eb07152998 use iffD* instead of (s)subst instantiated with identity; tuned antiquotations;
traytel
parents: 49463
diff changeset
   727
              rtac (rv_Cons RS arg_cong RS iffD2),
02eb07152998 use iffD* instead of (s)subst instantiated with identity; tuned antiquotations;
traytel
parents: 49463
diff changeset
   728
              rtac (mk_sum_casesN n i RS arg_cong RS trans RS iffD2),
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   729
              etac (from_to_sbd RS arg_cong), REPEAT_DETERM o etac allE,
49305
8241f21d104b tuned antiquotations
blanchet
parents: 49104
diff changeset
   730
              dtac (mk_conjunctN n i), etac mp, etac conjI, etac set_rev_mp,
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   731
              etac coalg_set, atac])
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   732
          (rev (ks ~~ (from_to_sbds ~~ drop m coalg_sets)))])
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   733
      ((Lev_Sucs ~~ rv_Conss) ~~ (from_to_sbdss ~~ coalg_setss))] 1
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   734
  end;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   735
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   736
fun mk_set_Lev_tac cts Lev_0s Lev_Sucs rv_Nils rv_Conss from_to_sbdss =
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   737
  let
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   738
    val n = length Lev_0s;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   739
    val ks = 1 upto n;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   740
  in
49305
8241f21d104b tuned antiquotations
blanchet
parents: 49104
diff changeset
   741
    EVERY' [rtac (Drule.instantiate' [] cts nat_induct),
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   742
      REPEAT_DETERM o rtac allI,
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   743
      CONJ_WRAP' (fn ((i, (Lev_0, Lev_Suc)), rv_Nil) =>
49305
8241f21d104b tuned antiquotations
blanchet
parents: 49104
diff changeset
   744
        EVERY' [rtac impI, dtac (Lev_0 RS equalityD1 RS set_mp),
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   745
          etac @{thm singletonE}, hyp_subst_tac,
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   746
          CONJ_WRAP' (fn i' => rtac impI THEN' dtac (sym RS trans) THEN' rtac rv_Nil THEN'
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   747
            (if i = i'
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   748
            then EVERY' [dtac (mk_InN_inject n i), hyp_subst_tac,
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   749
              CONJ_WRAP' (fn (i'', Lev_0'') =>
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   750
                EVERY' [rtac impI, rtac @{thm ssubst_mem[OF append_Nil]},
49366
3edd1c90f6e6 renamed "mk_UnN" to "mk_UnIN"
blanchet
parents: 49328
diff changeset
   751
                  rtac (Lev_Suc RS equalityD2 RS set_mp), rtac (mk_UnIN n i''),
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   752
                  rtac CollectI, REPEAT_DETERM o rtac exI, rtac conjI, rtac refl,
49305
8241f21d104b tuned antiquotations
blanchet
parents: 49104
diff changeset
   753
                  etac conjI, rtac (Lev_0'' RS equalityD2 RS set_mp),
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   754
                  rtac @{thm singletonI}])
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   755
              (ks ~~ Lev_0s)]
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   756
            else etac (mk_InN_not_InM i' i RS notE)))
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   757
          ks])
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   758
      ((ks ~~ (Lev_0s ~~ Lev_Sucs)) ~~ rv_Nils),
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   759
      REPEAT_DETERM o rtac allI,
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   760
      CONJ_WRAP' (fn ((Lev_Suc, rv_Cons), from_to_sbds) =>
49305
8241f21d104b tuned antiquotations
blanchet
parents: 49104
diff changeset
   761
        EVERY' [rtac impI, dtac (Lev_Suc RS equalityD1 RS set_mp),
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   762
          CONJ_WRAP_GEN' (etac (Thm.permute_prems 1 1 UnE))
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   763
            (fn (i, from_to_sbd) =>
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   764
              EVERY' [REPEAT_DETERM o eresolve_tac [CollectE, exE, conjE], hyp_subst_tac,
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   765
                CONJ_WRAP' (fn i' => rtac impI THEN'
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   766
                  CONJ_WRAP' (fn i'' =>
49305
8241f21d104b tuned antiquotations
blanchet
parents: 49104
diff changeset
   767
                    EVERY' [rtac impI, rtac (Lev_Suc RS equalityD2 RS set_mp),
49366
3edd1c90f6e6 renamed "mk_UnN" to "mk_UnIN"
blanchet
parents: 49328
diff changeset
   768
                      rtac @{thm ssubst_mem[OF append_Cons]}, rtac (mk_UnIN n i),
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   769
                      rtac CollectI, REPEAT_DETERM o rtac exI, rtac conjI, rtac refl,
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   770
                      rtac conjI, atac, dtac (sym RS trans RS sym),
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   771
                      rtac (rv_Cons RS trans), rtac (mk_sum_casesN n i RS trans),
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   772
                      etac (from_to_sbd RS arg_cong), REPEAT_DETERM o etac allE,
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   773
                      dtac (mk_conjunctN n i), dtac mp, atac,
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   774
                      dtac (mk_conjunctN n i'), dtac mp, atac,
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   775
                      dtac (mk_conjunctN n i''), etac mp, atac])
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   776
                  ks)
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   777
                ks])
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   778
          (rev (ks ~~ from_to_sbds))])
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   779
      ((Lev_Sucs ~~ rv_Conss) ~~ from_to_sbdss)] 1
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   780
  end;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   781
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   782
fun mk_set_image_Lev_tac cts Lev_0s Lev_Sucs rv_Nils rv_Conss from_to_sbdss to_sbd_injss =
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   783
  let
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   784
    val n = length Lev_0s;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   785
    val ks = 1 upto n;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   786
  in
49305
8241f21d104b tuned antiquotations
blanchet
parents: 49104
diff changeset
   787
    EVERY' [rtac (Drule.instantiate' [] cts nat_induct),
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   788
      REPEAT_DETERM o rtac allI,
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   789
      CONJ_WRAP' (fn ((i, (Lev_0, Lev_Suc)), rv_Nil) =>
49305
8241f21d104b tuned antiquotations
blanchet
parents: 49104
diff changeset
   790
        EVERY' [rtac impI, dtac (Lev_0 RS equalityD1 RS set_mp),
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   791
          etac @{thm singletonE}, hyp_subst_tac,
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   792
          CONJ_WRAP' (fn i' => rtac impI THEN'
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   793
            CONJ_WRAP' (fn i'' => rtac impI  THEN' dtac (sym RS trans) THEN' rtac rv_Nil THEN'
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   794
              (if i = i''
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   795
              then EVERY' [dtac @{thm ssubst_mem[OF sym[OF append_Nil]]},
49305
8241f21d104b tuned antiquotations
blanchet
parents: 49104
diff changeset
   796
                dtac (Lev_Suc RS equalityD1 RS set_mp), dtac (mk_InN_inject n i),
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   797
                hyp_subst_tac,
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   798
                CONJ_WRAP_GEN' (etac (Thm.permute_prems 1 1 UnE))
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   799
                  (fn k => REPEAT_DETERM o eresolve_tac [CollectE, exE, conjE] THEN'
49488
02eb07152998 use iffD* instead of (s)subst instantiated with identity; tuned antiquotations;
traytel
parents: 49463
diff changeset
   800
                    dtac list_inject_iffD1 THEN' etac conjE THEN'
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   801
                    (if k = i'
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   802
                    then EVERY' [dtac (mk_InN_inject n k), hyp_subst_tac, etac imageI]
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   803
                    else etac (mk_InN_not_InM i' k RS notE)))
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   804
                (rev ks)]
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   805
              else etac (mk_InN_not_InM i'' i RS notE)))
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   806
            ks)
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   807
          ks])
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   808
      ((ks ~~ (Lev_0s ~~ Lev_Sucs)) ~~ rv_Nils),
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   809
      REPEAT_DETERM o rtac allI,
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   810
      CONJ_WRAP' (fn ((Lev_Suc, rv_Cons), (from_to_sbds, to_sbd_injs)) =>
49305
8241f21d104b tuned antiquotations
blanchet
parents: 49104
diff changeset
   811
        EVERY' [rtac impI, dtac (Lev_Suc RS equalityD1 RS set_mp),
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   812
          CONJ_WRAP_GEN' (etac (Thm.permute_prems 1 1 UnE))
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   813
            (fn (i, (from_to_sbd, to_sbd_inj)) =>
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   814
              REPEAT_DETERM o eresolve_tac [CollectE, exE, conjE] THEN' hyp_subst_tac THEN'
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   815
              CONJ_WRAP' (fn i' => rtac impI THEN'
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   816
                dtac @{thm ssubst_mem[OF sym[OF append_Cons]]} THEN'
49305
8241f21d104b tuned antiquotations
blanchet
parents: 49104
diff changeset
   817
                dtac (Lev_Suc RS equalityD1 RS set_mp) THEN'
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   818
                CONJ_WRAP_GEN' (etac (Thm.permute_prems 1 1 UnE)) (fn k =>
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   819
                  REPEAT_DETERM o eresolve_tac [CollectE, exE, conjE] THEN'
49488
02eb07152998 use iffD* instead of (s)subst instantiated with identity; tuned antiquotations;
traytel
parents: 49463
diff changeset
   820
                  dtac list_inject_iffD1 THEN' etac conjE THEN'
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   821
                  (if k = i
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   822
                  then EVERY' [dtac (mk_InN_inject n i),
49488
02eb07152998 use iffD* instead of (s)subst instantiated with identity; tuned antiquotations;
traytel
parents: 49463
diff changeset
   823
                    dtac (Thm.permute_prems 0 2 (to_sbd_inj RS iffD1)),
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   824
                    atac, atac, hyp_subst_tac] THEN'
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   825
                    CONJ_WRAP' (fn i'' =>
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   826
                      EVERY' [rtac impI, dtac (sym RS trans),
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   827
                        rtac (rv_Cons RS trans), rtac (mk_sum_casesN n i RS arg_cong RS trans),
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   828
                        etac (from_to_sbd RS arg_cong),
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   829
                        REPEAT_DETERM o etac allE,
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   830
                        dtac (mk_conjunctN n i), dtac mp, atac,
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   831
                        dtac (mk_conjunctN n i'), dtac mp, atac,
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   832
                        dtac (mk_conjunctN n i''), etac mp, etac sym])
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   833
                    ks
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   834
                  else etac (mk_InN_not_InM i k RS notE)))
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   835
                (rev ks))
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   836
              ks)
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   837
          (rev (ks ~~ (from_to_sbds ~~ to_sbd_injs)))])
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   838
      ((Lev_Sucs ~~ rv_Conss) ~~ (from_to_sbdss ~~ to_sbd_injss))] 1
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   839
  end;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   840
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   841
fun mk_mor_beh_tac m mor_def mor_cong beh_defs carT_defs strT_defs isNode_defs
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   842
  to_sbd_injss from_to_sbdss Lev_0s Lev_Sucs rv_Nils rv_Conss Lev_sbds length_Levs length_Lev's
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   843
  prefCl_Levs rv_lastss set_rv_Levsss set_Levsss set_image_Levsss set_naturalss coalg_setss
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   844
  map_comp_ids map_congs map_arg_congs {context = ctxt, prems = _} =
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   845
  let
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   846
    val n = length beh_defs;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   847
    val ks = 1 upto n;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   848
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   849
    fun fbetw_tac (i, (carT_def, (isNode_def, (Lev_0, (rv_Nil, (Lev_sbd,
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   850
      ((length_Lev, length_Lev'), (prefCl_Lev, (rv_lasts, (set_naturals,
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   851
        (coalg_sets, (set_rv_Levss, (set_Levss, set_image_Levss))))))))))))) =
49305
8241f21d104b tuned antiquotations
blanchet
parents: 49104
diff changeset
   852
      EVERY' [rtac ballI, rtac (carT_def RS equalityD2 RS set_mp),
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   853
        rtac CollectI, REPEAT_DETERM o rtac exI, rtac conjI, rtac refl, rtac conjI,
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   854
        rtac conjI,
49305
8241f21d104b tuned antiquotations
blanchet
parents: 49104
diff changeset
   855
          rtac @{thm UN_I}, rtac UNIV_I, rtac (Lev_0 RS equalityD2 RS set_mp),
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   856
          rtac @{thm singletonI},
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   857
        rtac conjI,
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   858
          rtac @{thm UN_least}, rtac Lev_sbd,
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   859
        rtac conjI,
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   860
          rtac @{thm prefCl_UN}, rtac ssubst, rtac @{thm PrefCl_def}, REPEAT_DETERM o rtac allI,
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   861
          rtac impI, etac conjE, rtac exI, rtac conjI, rtac @{thm ord_le_eq_trans},
49091
0da7116b1b23 reverted (accidentally commited) changes from changeset fd4aef9bc7a9
Christian Sternagel
parents: 49086
diff changeset
   862
          etac @{thm prefix_length_le}, etac length_Lev, rtac prefCl_Lev, etac conjI, atac,
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   863
        rtac conjI,
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   864
          rtac ballI, etac @{thm UN_E}, rtac conjI,
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   865
          if n = 1 then K all_tac else rtac (mk_sumEN n),
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   866
          EVERY' (map6 (fn i => fn isNode_def => fn set_naturals =>
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   867
            fn set_rv_Levs => fn set_Levs => fn set_image_Levs =>
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   868
            EVERY' [rtac (mk_disjIN n i), rtac (isNode_def RS ssubst),
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   869
              rtac exI, rtac conjI,
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   870
              (if n = 1 then rtac @{thm if_P} THEN' etac length_Lev'
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   871
              else rtac (@{thm if_P} RS arg_cong RS trans) THEN' etac length_Lev' THEN'
49328
a1c10b46fecd avoided duplicate lemma
blanchet
parents: 49305
diff changeset
   872
                etac (sum_case_weak_cong RS trans) THEN' rtac (mk_sum_casesN n i)),
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   873
              EVERY' (map2 (fn set_natural => fn set_rv_Lev =>
49305
8241f21d104b tuned antiquotations
blanchet
parents: 49104
diff changeset
   874
                EVERY' [rtac conjI, rtac ord_eq_le_trans, rtac (set_natural RS trans),
8241f21d104b tuned antiquotations
blanchet
parents: 49104
diff changeset
   875
                  rtac trans_fun_cong_image_id_id_apply,
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   876
                  etac set_rv_Lev, TRY o atac, etac conjI, atac])
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   877
              (take m set_naturals) set_rv_Levs),
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   878
              CONJ_WRAP' (fn (set_natural, (set_Lev, set_image_Lev)) =>
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   879
                EVERY' [rtac (set_natural RS trans), rtac equalityI, rtac @{thm image_subsetI},
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   880
                  rtac CollectI, rtac @{thm SuccI}, rtac @{thm UN_I}, rtac UNIV_I, etac set_Lev,
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   881
                  if n = 1 then rtac refl else atac, atac, rtac subsetI,
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   882
                  REPEAT_DETERM o eresolve_tac [CollectE, @{thm SuccE}, @{thm UN_E}],
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   883
                  rtac set_image_Lev, atac, dtac length_Lev, hyp_subst_tac, dtac length_Lev',
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   884
                  etac @{thm set_mp[OF equalityD1[OF arg_cong[OF length_append_singleton]]]},
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   885
                  if n = 1 then rtac refl else atac])
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   886
              (drop m set_naturals ~~ (set_Levs ~~ set_image_Levs))])
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   887
          ks isNode_defs set_naturalss set_rv_Levss set_Levss set_image_Levss),
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   888
          CONJ_WRAP' (fn (i, (rv_last, (isNode_def, (set_naturals,
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   889
            (set_rv_Levs, (set_Levs, set_image_Levs)))))) =>
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   890
            EVERY' [rtac ballI,
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   891
              REPEAT_DETERM o eresolve_tac [CollectE, @{thm SuccE}, @{thm UN_E}],
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   892
              rtac (rev_mp OF [rv_last, impI]), etac exE, rtac (isNode_def RS ssubst),
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   893
              rtac exI, rtac conjI,
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   894
              (if n = 1 then rtac @{thm if_P} THEN' etac length_Lev'
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   895
              else rtac (@{thm if_P} RS trans) THEN' etac length_Lev' THEN'
49328
a1c10b46fecd avoided duplicate lemma
blanchet
parents: 49305
diff changeset
   896
                etac (sum_case_weak_cong RS trans) THEN' rtac (mk_sum_casesN n i)),
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   897
              EVERY' (map2 (fn set_natural => fn set_rv_Lev =>
49305
8241f21d104b tuned antiquotations
blanchet
parents: 49104
diff changeset
   898
                EVERY' [rtac conjI, rtac ord_eq_le_trans, rtac (set_natural RS trans),
8241f21d104b tuned antiquotations
blanchet
parents: 49104
diff changeset
   899
                  rtac trans_fun_cong_image_id_id_apply,
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   900
                  etac set_rv_Lev, TRY o atac, etac conjI, atac])
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   901
              (take m set_naturals) set_rv_Levs),
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   902
              CONJ_WRAP' (fn (set_natural, (set_Lev, set_image_Lev)) =>
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   903
                EVERY' [rtac (set_natural RS trans), rtac equalityI, rtac @{thm image_subsetI},
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   904
                  rtac CollectI, rtac @{thm SuccI}, rtac @{thm UN_I}, rtac UNIV_I, etac set_Lev,
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   905
                  if n = 1 then rtac refl else atac, atac, rtac subsetI,
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   906
                  REPEAT_DETERM o eresolve_tac [CollectE, @{thm SuccE}, @{thm UN_E}],
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   907
                  REPEAT_DETERM_N 4 o etac thin_rl,
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   908
                  rtac set_image_Lev,
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   909
                  atac, dtac length_Lev, hyp_subst_tac, dtac length_Lev',
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   910
                  etac @{thm set_mp[OF equalityD1[OF arg_cong[OF length_append_singleton]]]},
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   911
                  if n = 1 then rtac refl else atac])
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   912
              (drop m set_naturals ~~ (set_Levs ~~ set_image_Levs))])
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   913
          (ks ~~ (rv_lasts ~~ (isNode_defs ~~ (set_naturalss ~~
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   914
            (set_rv_Levss ~~ (set_Levss ~~ set_image_Levss)))))),
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   915
        (**)
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   916
          rtac allI, rtac impI, rtac @{thm if_not_P}, rtac notI,
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   917
          etac notE, etac @{thm UN_I[OF UNIV_I]},
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   918
        (*root isNode*)
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   919
          rtac (isNode_def RS ssubst), rtac exI, rtac conjI, rtac (@{thm if_P} RS trans),
49305
8241f21d104b tuned antiquotations
blanchet
parents: 49104
diff changeset
   920
          rtac length_Lev', rtac (Lev_0 RS equalityD2 RS set_mp), rtac @{thm singletonI},
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   921
          CONVERSION (Conv.top_conv
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   922
            (K (Conv.try_conv (Conv.rewr_conv (rv_Nil RS eq_reflection)))) ctxt),
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   923
          if n = 1 then rtac refl else rtac (mk_sum_casesN n i),
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   924
          EVERY' (map2 (fn set_natural => fn coalg_set =>
49305
8241f21d104b tuned antiquotations
blanchet
parents: 49104
diff changeset
   925
            EVERY' [rtac conjI, rtac ord_eq_le_trans, rtac (set_natural RS trans),
8241f21d104b tuned antiquotations
blanchet
parents: 49104
diff changeset
   926
              rtac trans_fun_cong_image_id_id_apply, etac coalg_set, atac])
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   927
            (take m set_naturals) (take m coalg_sets)),
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   928
          CONJ_WRAP' (fn (set_natural, (set_Lev, set_image_Lev)) =>
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   929
            EVERY' [rtac (set_natural RS trans), rtac equalityI, rtac @{thm image_subsetI},
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   930
              rtac CollectI, rtac @{thm SuccI}, rtac @{thm UN_I}, rtac UNIV_I, rtac set_Lev,
49305
8241f21d104b tuned antiquotations
blanchet
parents: 49104
diff changeset
   931
              rtac (Lev_0 RS equalityD2 RS set_mp), rtac @{thm singletonI}, rtac rv_Nil,
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   932
              atac, rtac subsetI,
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   933
              REPEAT_DETERM o eresolve_tac [CollectE, @{thm SuccE}, @{thm UN_E}],
49305
8241f21d104b tuned antiquotations
blanchet
parents: 49104
diff changeset
   934
              rtac set_image_Lev, rtac (Lev_0 RS equalityD2 RS set_mp),
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   935
              rtac @{thm singletonI}, dtac length_Lev',
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   936
              etac @{thm set_mp[OF equalityD1[OF arg_cong[OF
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   937
                trans[OF length_append_singleton arg_cong[of _ _ Suc, OF list.size(3)]]]]]},
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   938
              rtac rv_Nil])
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   939
          (drop m set_naturals ~~ (nth set_Levss (i - 1) ~~ nth set_image_Levss (i - 1)))];
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   940
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   941
    fun mor_tac (i, (strT_def, (((Lev_0, Lev_Suc), (rv_Nil, rv_Cons)),
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   942
      ((map_comp_id, (map_cong, map_arg_cong)), (length_Lev', (from_to_sbds, to_sbd_injs)))))) =
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   943
      EVERY' [rtac ballI, rtac sym, rtac trans, rtac strT_def,
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   944
        rtac (@{thm if_P} RS
49328
a1c10b46fecd avoided duplicate lemma
blanchet
parents: 49305
diff changeset
   945
          (if n = 1 then map_arg_cong else sum_case_weak_cong) RS trans),
49305
8241f21d104b tuned antiquotations
blanchet
parents: 49104
diff changeset
   946
        rtac (@{thm list.size(3)} RS arg_cong RS trans RS equalityD2 RS set_mp),
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   947
        rtac Lev_0, rtac @{thm singletonI},
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   948
        CONVERSION (Conv.top_conv
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   949
          (K (Conv.try_conv (Conv.rewr_conv (rv_Nil RS eq_reflection)))) ctxt),
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   950
        if n = 1 then K all_tac
49328
a1c10b46fecd avoided duplicate lemma
blanchet
parents: 49305
diff changeset
   951
        else (rtac (sum_case_weak_cong RS trans) THEN'
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   952
          rtac (mk_sum_casesN n i) THEN' rtac (mk_sum_casesN n i RS trans)),
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   953
        rtac (map_comp_id RS trans), rtac (map_cong OF replicate m refl),
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   954
        EVERY' (map3 (fn i' => fn to_sbd_inj => fn from_to_sbd =>
49488
02eb07152998 use iffD* instead of (s)subst instantiated with identity; tuned antiquotations;
traytel
parents: 49463
diff changeset
   955
          DETERM o EVERY' [rtac trans, rtac o_apply, rtac Pair_eqI, rtac conjI,
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   956
            rtac trans, rtac @{thm Shift_def},
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   957
            rtac equalityI, rtac subsetI, etac thin_rl, etac thin_rl,
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   958
            REPEAT_DETERM o eresolve_tac [CollectE, @{thm UN_E}], dtac length_Lev', dtac asm_rl,
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   959
            etac thin_rl, dtac @{thm set_rev_mp[OF _ equalityD1]},
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   960
            rtac (@{thm length_Cons} RS arg_cong RS trans), rtac Lev_Suc,
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   961
            CONJ_WRAP_GEN' (etac (Thm.permute_prems 1 1 UnE)) (fn i'' =>
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   962
              EVERY' [REPEAT_DETERM o eresolve_tac [CollectE, exE, conjE],
49488
02eb07152998 use iffD* instead of (s)subst instantiated with identity; tuned antiquotations;
traytel
parents: 49463
diff changeset
   963
                dtac list_inject_iffD1, etac conjE,
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   964
                if i' = i'' then EVERY' [dtac (mk_InN_inject n i'),
49488
02eb07152998 use iffD* instead of (s)subst instantiated with identity; tuned antiquotations;
traytel
parents: 49463
diff changeset
   965
                  dtac (Thm.permute_prems 0 2 (to_sbd_inj RS iffD1)),
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   966
                  atac, atac, hyp_subst_tac, etac @{thm UN_I[OF UNIV_I]}]
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   967
                else etac (mk_InN_not_InM i' i'' RS notE)])
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   968
            (rev ks),
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   969
            rtac @{thm UN_least}, rtac subsetI, rtac CollectI, rtac @{thm UN_I[OF UNIV_I]},
49366
3edd1c90f6e6 renamed "mk_UnN" to "mk_UnIN"
blanchet
parents: 49328
diff changeset
   970
            rtac (Lev_Suc RS equalityD2 RS set_mp), rtac (mk_UnIN n i'), rtac CollectI,
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   971
            REPEAT_DETERM o rtac exI, rtac conjI, rtac refl, etac conjI, atac,
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   972
            rtac trans, rtac @{thm shift_def}, rtac ssubst, rtac @{thm fun_eq_iff}, rtac allI,
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   973
            rtac @{thm if_cong}, rtac (@{thm length_Cons} RS arg_cong RS trans), rtac iffI,
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   974
            dtac asm_rl, dtac asm_rl, dtac asm_rl,
49305
8241f21d104b tuned antiquotations
blanchet
parents: 49104
diff changeset
   975
            dtac (Lev_Suc RS equalityD1 RS set_mp),
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   976
            CONJ_WRAP_GEN' (etac (Thm.permute_prems 1 1 UnE)) (fn i'' =>
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   977
              EVERY' [REPEAT_DETERM o eresolve_tac [CollectE, exE, conjE],
49488
02eb07152998 use iffD* instead of (s)subst instantiated with identity; tuned antiquotations;
traytel
parents: 49463
diff changeset
   978
                dtac list_inject_iffD1, etac conjE,
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   979
                if i' = i'' then EVERY' [dtac (mk_InN_inject n i'),
49488
02eb07152998 use iffD* instead of (s)subst instantiated with identity; tuned antiquotations;
traytel
parents: 49463
diff changeset
   980
                  dtac (Thm.permute_prems 0 2 (to_sbd_inj RS iffD1)),
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   981
                  atac, atac, hyp_subst_tac, atac]
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   982
                else etac (mk_InN_not_InM i' i'' RS notE)])
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   983
            (rev ks),
49366
3edd1c90f6e6 renamed "mk_UnN" to "mk_UnIN"
blanchet
parents: 49328
diff changeset
   984
            rtac (Lev_Suc RS equalityD2 RS set_mp), rtac (mk_UnIN n i'), rtac CollectI,
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   985
            REPEAT_DETERM o rtac exI, rtac conjI, rtac refl, etac conjI, atac,
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   986
            CONVERSION (Conv.top_conv
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   987
              (K (Conv.try_conv (Conv.rewr_conv (rv_Cons RS eq_reflection)))) ctxt),
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   988
            if n = 1 then K all_tac
49328
a1c10b46fecd avoided duplicate lemma
blanchet
parents: 49305
diff changeset
   989
            else rtac sum_case_weak_cong THEN' rtac (mk_sum_casesN n i' RS trans),
49504
df9b897fb254 renamed "iter"/"coiter" to "fold"/"unfold" (cf. Wadler)
blanchet
parents: 49501
diff changeset
   990
            SELECT_GOAL (unfold_thms_tac ctxt [from_to_sbd]), rtac refl,
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   991
            rtac refl])
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   992
        ks to_sbd_injs from_to_sbds)];
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   993
  in
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   994
    (rtac mor_cong THEN'
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   995
    EVERY' (map (fn thm => rtac (thm RS ext)) beh_defs) THEN'
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   996
    stac mor_def THEN' rtac conjI THEN'
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   997
    CONJ_WRAP' fbetw_tac
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   998
      (ks ~~ (carT_defs ~~ (isNode_defs ~~ (Lev_0s ~~ (rv_Nils ~~ (Lev_sbds ~~
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   999
        ((length_Levs ~~ length_Lev's) ~~ (prefCl_Levs ~~ (rv_lastss ~~
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1000
          (set_naturalss ~~ (coalg_setss ~~
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1001
            (set_rv_Levsss ~~ (set_Levsss ~~ set_image_Levsss))))))))))))) THEN'
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1002
    CONJ_WRAP' mor_tac
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1003
      (ks ~~ (strT_defs ~~ (((Lev_0s ~~ Lev_Sucs) ~~ (rv_Nils ~~ rv_Conss)) ~~
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1004
        ((map_comp_ids ~~ (map_congs ~~ map_arg_congs)) ~~
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1005
          (length_Lev's ~~ (from_to_sbdss ~~ to_sbd_injss))))))) 1
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1006
  end;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1007
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1008
fun mk_congruent_str_final_tac m lsbisE map_comp_id map_cong equiv_LSBISs =
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1009
  EVERY' [rtac @{thm congruentI}, dtac lsbisE,
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1010
    REPEAT_DETERM o eresolve_tac [CollectE, conjE, bexE], rtac (o_apply RS trans),
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1011
    etac (sym RS arg_cong RS trans), rtac (map_comp_id RS trans),
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1012
    rtac (map_cong RS trans), REPEAT_DETERM_N m o rtac refl,
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1013
    EVERY' (map (fn equiv_LSBIS =>
49305
8241f21d104b tuned antiquotations
blanchet
parents: 49104
diff changeset
  1014
      EVERY' [rtac @{thm equiv_proj}, rtac equiv_LSBIS, etac set_mp, atac])
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1015
    equiv_LSBISs), rtac sym, rtac (o_apply RS trans),
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1016
    etac (sym RS arg_cong RS trans), rtac map_comp_id] 1;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1017
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1018
fun mk_coalg_final_tac m coalg_def congruent_str_finals equiv_LSBISs set_naturalss coalgT_setss =
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1019
  EVERY' [stac coalg_def,
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1020
    CONJ_WRAP' (fn ((set_naturals, coalgT_sets), (equiv_LSBIS, congruent_str_final)) =>
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1021
      EVERY' [rtac @{thm univ_preserves}, rtac equiv_LSBIS, rtac congruent_str_final,
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1022
        rtac ballI, rtac @{thm ssubst_mem}, rtac o_apply, rtac CollectI,
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1023
        EVERY' (map2 (fn set_natural => fn coalgT_set =>
49305
8241f21d104b tuned antiquotations
blanchet
parents: 49104
diff changeset
  1024
          EVERY' [rtac conjI, rtac (set_natural RS ord_eq_le_trans),
8241f21d104b tuned antiquotations
blanchet
parents: 49104
diff changeset
  1025
            rtac ord_eq_le_trans_trans_fun_cong_image_id_id_apply,
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1026
            etac coalgT_set])
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1027
        (take m set_naturals) (take m coalgT_sets)),
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1028
        CONJ_WRAP' (fn (equiv_LSBIS, (set_natural, coalgT_set)) =>
49305
8241f21d104b tuned antiquotations
blanchet
parents: 49104
diff changeset
  1029
          EVERY' [rtac (set_natural RS ord_eq_le_trans),
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1030
            rtac @{thm image_subsetI}, rtac ssubst, rtac @{thm proj_in_iff},
49305
8241f21d104b tuned antiquotations
blanchet
parents: 49104
diff changeset
  1031
            rtac equiv_LSBIS, etac set_rev_mp, etac coalgT_set])
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1032
        (equiv_LSBISs ~~ drop m (set_naturals ~~ coalgT_sets))])
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1033
    ((set_naturalss ~~ coalgT_setss) ~~ (equiv_LSBISs ~~ congruent_str_finals))] 1;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1034
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1035
fun mk_mor_T_final_tac mor_def congruent_str_finals equiv_LSBISs =
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1036
  EVERY' [stac mor_def, rtac conjI,
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1037
    CONJ_WRAP' (fn equiv_LSBIS =>
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1038
      EVERY' [rtac ballI, rtac ssubst, rtac @{thm proj_in_iff}, rtac equiv_LSBIS, atac])
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1039
    equiv_LSBISs,
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1040
    CONJ_WRAP' (fn (equiv_LSBIS, congruent_str_final) =>
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1041
      EVERY' [rtac ballI, rtac sym, rtac trans, rtac @{thm univ_commute}, rtac equiv_LSBIS,
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1042
        rtac congruent_str_final, atac, rtac o_apply])
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1043
    (equiv_LSBISs ~~ congruent_str_finals)] 1;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1044
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1045
fun mk_mor_Rep_tac m defs Reps Abs_inverses coalg_final_setss map_comp_ids map_congLs
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1046
  {context = ctxt, prems = _} =
49504
df9b897fb254 renamed "iter"/"coiter" to "fold"/"unfold" (cf. Wadler)
blanchet
parents: 49501
diff changeset
  1047
  unfold_thms_tac ctxt defs THEN
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1048
  EVERY' [rtac conjI,
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1049
    CONJ_WRAP' (fn thm => rtac ballI THEN' rtac thm) Reps,
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1050
    CONJ_WRAP' (fn (Rep, ((map_comp_id, map_congL), coalg_final_sets)) =>
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1051
      EVERY' [rtac ballI, rtac (map_comp_id RS trans), rtac map_congL,
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1052
        EVERY' (map2 (fn Abs_inverse => fn coalg_final_set =>
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1053
          EVERY' [rtac ballI, rtac (o_apply RS trans), rtac Abs_inverse,
49305
8241f21d104b tuned antiquotations
blanchet
parents: 49104
diff changeset
  1054
            etac set_rev_mp, rtac coalg_final_set, rtac Rep])
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1055
        Abs_inverses (drop m coalg_final_sets))])
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1056
    (Reps ~~ ((map_comp_ids ~~ map_congLs) ~~ coalg_final_setss))] 1;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1057
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1058
fun mk_mor_Abs_tac defs Abs_inverses {context = ctxt, prems = _} =
49504
df9b897fb254 renamed "iter"/"coiter" to "fold"/"unfold" (cf. Wadler)
blanchet
parents: 49501
diff changeset
  1059
  unfold_thms_tac ctxt defs THEN
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1060
  EVERY' [rtac conjI,
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1061
    CONJ_WRAP' (K (rtac ballI THEN' rtac UNIV_I)) Abs_inverses,
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1062
    CONJ_WRAP' (fn thm => rtac ballI THEN' etac (thm RS arg_cong RS sym)) Abs_inverses] 1;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1063
49504
df9b897fb254 renamed "iter"/"coiter" to "fold"/"unfold" (cf. Wadler)
blanchet
parents: 49501
diff changeset
  1064
fun mk_mor_unfold_tac m mor_UNIV dtor_defs unfold_defs Abs_inverses morEs map_comp_ids map_congs =
49488
02eb07152998 use iffD* instead of (s)subst instantiated with identity; tuned antiquotations;
traytel
parents: 49463
diff changeset
  1065
  EVERY' [rtac iffD2, rtac mor_UNIV,
49504
df9b897fb254 renamed "iter"/"coiter" to "fold"/"unfold" (cf. Wadler)
blanchet
parents: 49501
diff changeset
  1066
    CONJ_WRAP' (fn ((Abs_inverse, morE), ((dtor_def, unfold_def), (map_comp_id, map_cong))) =>
49501
acc9635a644a renamed "fld"/"unf" to "ctor"/"dtor"
blanchet
parents: 49499
diff changeset
  1067
      EVERY' [rtac ext, rtac (o_apply RS trans RS sym), rtac (dtor_def RS trans),
49504
df9b897fb254 renamed "iter"/"coiter" to "fold"/"unfold" (cf. Wadler)
blanchet
parents: 49501
diff changeset
  1068
        rtac (unfold_def RS arg_cong RS trans), rtac (Abs_inverse RS arg_cong RS trans),
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1069
        rtac (morE RS arg_cong RS trans), rtac (map_comp_id RS trans),
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1070
        rtac (o_apply RS trans RS sym), rtac map_cong,
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1071
        REPEAT_DETERM_N m o rtac refl,
49504
df9b897fb254 renamed "iter"/"coiter" to "fold"/"unfold" (cf. Wadler)
blanchet
parents: 49501
diff changeset
  1072
        EVERY' (map (fn thm => rtac (thm RS trans) THEN' rtac (o_apply RS sym)) unfold_defs)])
df9b897fb254 renamed "iter"/"coiter" to "fold"/"unfold" (cf. Wadler)
blanchet
parents: 49501
diff changeset
  1073
    ((Abs_inverses ~~ morEs) ~~ ((dtor_defs ~~ unfold_defs) ~~ (map_comp_ids ~~ map_congs)))] 1;
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1074
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1075
fun mk_raw_coind_tac bis_def bis_cong bis_O bis_converse bis_Gr tcoalg coalgT mor_T_final
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1076
  sbis_lsbis lsbis_incls incl_lsbiss equiv_LSBISs mor_Rep Rep_injects =
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1077
  let
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1078
    val n = length Rep_injects;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1079
  in
49488
02eb07152998 use iffD* instead of (s)subst instantiated with identity; tuned antiquotations;
traytel
parents: 49463
diff changeset
  1080
    EVERY' [rtac rev_mp, ftac (bis_def RS iffD1),
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1081
      REPEAT_DETERM o etac conjE, rtac bis_cong, rtac bis_O, rtac bis_converse,
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1082
      rtac bis_Gr, rtac tcoalg, rtac mor_Rep, rtac bis_O, atac, rtac bis_Gr, rtac tcoalg,
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1083
      rtac mor_Rep, REPEAT_DETERM_N n o etac @{thm relImage_Gr},
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1084
      rtac impI, rtac rev_mp, rtac bis_cong, rtac bis_O, rtac bis_Gr, rtac coalgT,
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1085
      rtac mor_T_final, rtac bis_O, rtac sbis_lsbis, rtac bis_converse, rtac bis_Gr, rtac coalgT,
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1086
      rtac mor_T_final, EVERY' (map (fn thm => rtac (thm RS @{thm relInvImage_Gr})) lsbis_incls),
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1087
      rtac impI,
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1088
      CONJ_WRAP' (fn (Rep_inject, (equiv_LSBIS , (incl_lsbis, lsbis_incl))) =>
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1089
        EVERY' [rtac subset_trans, rtac @{thm relInvImage_UNIV_relImage}, rtac subset_trans,
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1090
          rtac @{thm relInvImage_mono}, rtac subset_trans, etac incl_lsbis,
49305
8241f21d104b tuned antiquotations
blanchet
parents: 49104
diff changeset
  1091
          rtac ord_eq_le_trans, rtac @{thm sym[OF relImage_relInvImage]},
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1092
          rtac @{thm xt1(3)}, rtac @{thm Sigma_cong},
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1093
          rtac @{thm proj_image}, rtac @{thm proj_image}, rtac lsbis_incl,
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1094
          rtac subset_trans, rtac @{thm relImage_mono}, rtac incl_lsbis, atac,
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1095
          rtac @{thm relImage_proj}, rtac equiv_LSBIS, rtac @{thm relInvImage_diag},
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1096
          rtac Rep_inject])
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1097
      (Rep_injects ~~ (equiv_LSBISs ~~ (incl_lsbiss ~~ lsbis_incls)))] 1
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1098
  end;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1099
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1100
fun mk_unique_mor_tac raw_coinds bis =
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1101
  CONJ_WRAP' (fn raw_coind =>
49305
8241f21d104b tuned antiquotations
blanchet
parents: 49104
diff changeset
  1102
    EVERY' [rtac impI, rtac (bis RS raw_coind RS set_mp RS @{thm IdD}), atac,
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1103
      etac conjunct1, atac, etac conjunct2, rtac @{thm image2_eqI}, rtac refl, rtac refl, atac])
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1104
  raw_coinds 1;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1105
49504
df9b897fb254 renamed "iter"/"coiter" to "fold"/"unfold" (cf. Wadler)
blanchet
parents: 49501
diff changeset
  1106
fun mk_unfold_unique_mor_tac raw_coinds bis mor unfold_defs =
df9b897fb254 renamed "iter"/"coiter" to "fold"/"unfold" (cf. Wadler)
blanchet
parents: 49501
diff changeset
  1107
  CONJ_WRAP' (fn (raw_coind, unfold_def) =>
49305
8241f21d104b tuned antiquotations
blanchet
parents: 49104
diff changeset
  1108
    EVERY' [rtac ext, etac (bis RS raw_coind RS set_mp RS @{thm IdD}), rtac mor,
49504
df9b897fb254 renamed "iter"/"coiter" to "fold"/"unfold" (cf. Wadler)
blanchet
parents: 49501
diff changeset
  1109
      rtac @{thm image2_eqI}, rtac refl, rtac (unfold_def RS arg_cong RS trans),
df9b897fb254 renamed "iter"/"coiter" to "fold"/"unfold" (cf. Wadler)
blanchet
parents: 49501
diff changeset
  1110
      rtac (o_apply RS sym), rtac UNIV_I]) (raw_coinds ~~ unfold_defs) 1;
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1111
49504
df9b897fb254 renamed "iter"/"coiter" to "fold"/"unfold" (cf. Wadler)
blanchet
parents: 49501
diff changeset
  1112
fun mk_dtor_o_ctor_tac ctor_def unfold map_comp_id map_congL unfold_o_dtors
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1113
  {context = ctxt, prems = _} =
49504
df9b897fb254 renamed "iter"/"coiter" to "fold"/"unfold" (cf. Wadler)
blanchet
parents: 49501
diff changeset
  1114
  unfold_thms_tac ctxt [ctor_def] THEN EVERY' [rtac ext, rtac trans, rtac o_apply,
df9b897fb254 renamed "iter"/"coiter" to "fold"/"unfold" (cf. Wadler)
blanchet
parents: 49501
diff changeset
  1115
    rtac trans, rtac unfold, rtac trans, rtac map_comp_id, rtac trans, rtac map_congL,
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1116
    EVERY' (map (fn thm =>
49504
df9b897fb254 renamed "iter"/"coiter" to "fold"/"unfold" (cf. Wadler)
blanchet
parents: 49501
diff changeset
  1117
      rtac ballI THEN' rtac (trans OF [thm RS fun_cong, @{thm id_apply}])) unfold_o_dtors),
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1118
    rtac sym, rtac @{thm id_apply}] 1;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1119
49504
df9b897fb254 renamed "iter"/"coiter" to "fold"/"unfold" (cf. Wadler)
blanchet
parents: 49501
diff changeset
  1120
fun mk_corec_tac m corec_defs unfold map_cong corec_Inls {context = ctxt, prems = _} =
df9b897fb254 renamed "iter"/"coiter" to "fold"/"unfold" (cf. Wadler)
blanchet
parents: 49501
diff changeset
  1121
  unfold_thms_tac ctxt corec_defs THEN EVERY' [rtac trans, rtac (o_apply RS arg_cong),
df9b897fb254 renamed "iter"/"coiter" to "fold"/"unfold" (cf. Wadler)
blanchet
parents: 49501
diff changeset
  1122
    rtac trans, rtac unfold, fo_rtac (@{thm sum.cases(2)} RS arg_cong RS trans) ctxt, rtac map_cong,
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1123
    REPEAT_DETERM_N m o rtac refl,
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1124
    EVERY' (map (fn thm => rtac @{thm sum_case_expand_Inr} THEN' rtac thm) corec_Inls)] 1;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1125
49506
aeb0cc8889f2 renamed "rel" to "srel"
blanchet
parents: 49504
diff changeset
  1126
fun mk_srel_coinduct_tac ks raw_coind bis_srel =
aeb0cc8889f2 renamed "rel" to "srel"
blanchet
parents: 49504
diff changeset
  1127
  EVERY' [rtac rev_mp, rtac raw_coind, rtac ssubst, rtac bis_srel, rtac conjI,
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1128
    CONJ_WRAP' (K (rtac @{thm ord_le_eq_trans[OF subset_UNIV UNIV_Times_UNIV[THEN sym]]})) ks,
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1129
    CONJ_WRAP' (K (EVERY' [rtac allI, rtac allI, rtac impI,
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1130
      REPEAT_DETERM o etac allE, etac mp, etac CollectE, etac @{thm splitD}])) ks,
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1131
    rtac impI, REPEAT_DETERM o etac conjE,
49305
8241f21d104b tuned antiquotations
blanchet
parents: 49104
diff changeset
  1132
    CONJ_WRAP' (K (EVERY' [rtac impI, rtac @{thm IdD}, etac set_mp,
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1133
      rtac CollectI, etac @{thm prod_caseI}])) ks] 1;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1134
49506
aeb0cc8889f2 renamed "rel" to "srel"
blanchet
parents: 49504
diff changeset
  1135
fun mk_srel_strong_coinduct_tac m cTs cts srel_coinduct srel_monos srel_Ids =
aeb0cc8889f2 renamed "rel" to "srel"
blanchet
parents: 49504
diff changeset
  1136
  EVERY' [rtac rev_mp, rtac (Drule.instantiate' cTs cts srel_coinduct),
aeb0cc8889f2 renamed "rel" to "srel"
blanchet
parents: 49504
diff changeset
  1137
    EVERY' (map2 (fn srel_mono => fn srel_Id =>
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1138
      EVERY' [REPEAT_DETERM o resolve_tac [allI, impI], REPEAT_DETERM o etac allE,
49506
aeb0cc8889f2 renamed "rel" to "srel"
blanchet
parents: 49504
diff changeset
  1139
        etac disjE, etac mp, atac, hyp_subst_tac, rtac (srel_mono RS set_mp),
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1140
        REPEAT_DETERM_N m o rtac @{thm subset_refl},
49506
aeb0cc8889f2 renamed "rel" to "srel"
blanchet
parents: 49504
diff changeset
  1141
        REPEAT_DETERM_N (length srel_monos) o rtac @{thm Id_subset},
aeb0cc8889f2 renamed "rel" to "srel"
blanchet
parents: 49504
diff changeset
  1142
        rtac (srel_Id RS equalityD2 RS set_mp), rtac @{thm IdI}])
aeb0cc8889f2 renamed "rel" to "srel"
blanchet
parents: 49504
diff changeset
  1143
    srel_monos srel_Ids),
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1144
    rtac impI, REPEAT_DETERM o etac conjE,
49506
aeb0cc8889f2 renamed "rel" to "srel"
blanchet
parents: 49504
diff changeset
  1145
    CONJ_WRAP' (K (rtac impI THEN' etac mp THEN' etac disjI1)) srel_Ids] 1;
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1146
49501
acc9635a644a renamed "fld"/"unf" to "ctor"/"dtor"
blanchet
parents: 49499
diff changeset
  1147
fun mk_dtor_coinduct_tac m ks raw_coind bis_def =
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1148
  let
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1149
    val n = length ks;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1150
  in
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1151
    EVERY' [rtac rev_mp, rtac raw_coind, rtac ssubst, rtac bis_def, rtac conjI,
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1152
      CONJ_WRAP' (K (rtac @{thm ord_le_eq_trans[OF subset_UNIV UNIV_Times_UNIV[THEN sym]]})) ks,
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1153
      CONJ_WRAP' (fn i => EVERY' [select_prem_tac n (dtac asm_rl) i, REPEAT_DETERM o rtac allI,
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1154
        rtac impI, REPEAT_DETERM o dtac @{thm meta_spec}, etac CollectE, etac @{thm meta_impE},
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1155
        atac, etac exE, etac conjE, etac conjE, rtac bexI, rtac conjI,
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1156
        etac @{thm fst_conv[THEN subst]}, etac @{thm snd_conv[THEN subst]},
49490
394870e51d18 tuned antiquotations
traytel
parents: 49488
diff changeset
  1157
        rtac CollectI, REPEAT_DETERM_N m o (rtac conjI THEN' rtac subset_UNIV),
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1158
        CONJ_WRAP' (fn i' => EVERY' [rtac subsetI, rtac CollectI, dtac (mk_conjunctN n i'),
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1159
          REPEAT_DETERM o etac allE, etac mp, rtac @{thm ssubst_mem[OF pair_collapse]}, atac])
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1160
        ks])
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1161
      ks,
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1162
      rtac impI,
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1163
      CONJ_WRAP' (fn i => EVERY' [rtac impI, dtac (mk_conjunctN n i),
49305
8241f21d104b tuned antiquotations
blanchet
parents: 49104
diff changeset
  1164
        rtac @{thm subst[OF pair_in_Id_conv]}, etac set_mp,
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1165
        rtac CollectI, etac (refl RSN (2, @{thm subst_Pair}))]) ks] 1
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1166
  end;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1167
49501
acc9635a644a renamed "fld"/"unf" to "ctor"/"dtor"
blanchet
parents: 49499
diff changeset
  1168
fun mk_dtor_strong_coinduct_tac ks cTs cts dtor_coinduct bis_def bis_diag =
acc9635a644a renamed "fld"/"unf" to "ctor"/"dtor"
blanchet
parents: 49499
diff changeset
  1169
  EVERY' [rtac rev_mp, rtac (Drule.instantiate' cTs cts dtor_coinduct),
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1170
    EVERY' (map (fn i =>
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1171
      EVERY' [etac disjE, REPEAT_DETERM o dtac @{thm meta_spec}, etac @{thm meta_mp},
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1172
        atac, rtac rev_mp, rtac subst, rtac bis_def, rtac bis_diag,
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1173
        rtac impI, dtac conjunct2, dtac (mk_conjunctN (length ks) i), REPEAT_DETERM o etac allE,
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1174
        etac impE, etac @{thm diag_UNIV_I}, REPEAT_DETERM o eresolve_tac [bexE, conjE, CollectE],
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1175
        rtac exI, rtac conjI, etac conjI, atac,
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1176
        CONJ_WRAP' (K (EVERY' [REPEAT_DETERM o resolve_tac [allI, impI],
49305
8241f21d104b tuned antiquotations
blanchet
parents: 49104
diff changeset
  1177
          rtac disjI2, rtac @{thm diagE}, etac set_mp, atac])) ks])
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1178
    ks),
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1179
    rtac impI, REPEAT_DETERM o etac conjE,
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1180
    CONJ_WRAP' (K (rtac impI THEN' etac mp THEN' etac disjI1)) ks] 1;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1181
49504
df9b897fb254 renamed "iter"/"coiter" to "fold"/"unfold" (cf. Wadler)
blanchet
parents: 49501
diff changeset
  1182
fun mk_map_tac m n cT unfold map_comp' map_cong =
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1183
  EVERY' [rtac ext, rtac (o_apply RS trans RS sym), rtac (o_apply RS trans RS sym),
49504
df9b897fb254 renamed "iter"/"coiter" to "fold"/"unfold" (cf. Wadler)
blanchet
parents: 49501
diff changeset
  1184
    rtac (unfold RS trans), rtac (Thm.permute_prems 0 1 (map_comp' RS box_equals)), rtac map_cong,
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1185
    REPEAT_DETERM_N m o rtac (@{thm id_o} RS fun_cong),
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1186
    REPEAT_DETERM_N n o rtac (@{thm o_id} RS fun_cong),
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1187
    rtac (o_apply RS (Drule.instantiate' [cT] [] arg_cong) RS sym)] 1;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1188
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1189
fun mk_set_le_tac n hset_minimal set_hsets set_hset_hsetss =
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1190
  EVERY' [rtac hset_minimal,
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1191
    REPEAT_DETERM_N n o rtac @{thm Un_upper1},
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1192
    REPEAT_DETERM_N n o
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1193
      EVERY' (map3 (fn i => fn set_hset => fn set_hset_hsets =>
49366
3edd1c90f6e6 renamed "mk_UnN" to "mk_UnIN"
blanchet
parents: 49328
diff changeset
  1194
        EVERY' [rtac subsetI, rtac @{thm UnI2}, rtac (mk_UnIN n i), etac @{thm UN_I},
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1195
          etac UnE, etac set_hset, REPEAT_DETERM_N (n - 1) o etac UnE,
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1196
          EVERY' (map (fn thm => EVERY' [etac @{thm UN_E}, etac thm, atac]) set_hset_hsets)])
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1197
      (1 upto n) set_hsets set_hset_hsetss)] 1;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1198
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1199
fun mk_set_simp_tac n set_le set_incl_hset set_hset_incl_hsets =
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1200
  EVERY' [rtac equalityI, rtac set_le, rtac @{thm Un_least}, rtac set_incl_hset,
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1201
    REPEAT_DETERM_N (n - 1) o rtac @{thm Un_least},
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1202
    EVERY' (map (fn thm => rtac @{thm UN_least} THEN' etac thm) set_hset_incl_hsets)] 1;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1203
49504
df9b897fb254 renamed "iter"/"coiter" to "fold"/"unfold" (cf. Wadler)
blanchet
parents: 49501
diff changeset
  1204
fun mk_map_id_tac maps unfold_unique unfold_dtor =
df9b897fb254 renamed "iter"/"coiter" to "fold"/"unfold" (cf. Wadler)
blanchet
parents: 49501
diff changeset
  1205
  EVERY' [rtac (unfold_unique RS trans), EVERY' (map (fn thm => rtac (thm RS sym)) maps),
df9b897fb254 renamed "iter"/"coiter" to "fold"/"unfold" (cf. Wadler)
blanchet
parents: 49501
diff changeset
  1206
    rtac unfold_dtor] 1;
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1207
49504
df9b897fb254 renamed "iter"/"coiter" to "fold"/"unfold" (cf. Wadler)
blanchet
parents: 49501
diff changeset
  1208
fun mk_map_comp_tac m n maps map_comps map_congs unfold_unique =
df9b897fb254 renamed "iter"/"coiter" to "fold"/"unfold" (cf. Wadler)
blanchet
parents: 49501
diff changeset
  1209
  EVERY' [rtac unfold_unique,
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1210
    EVERY' (map3 (fn map_thm => fn map_comp => fn map_cong =>
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1211
      EVERY' (map rtac
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1212
        ([@{thm o_assoc} RS trans,
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1213
        @{thm arg_cong2[of _ _ _ _ "op o"]} OF [map_comp RS sym, refl] RS trans,
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1214
        @{thm o_assoc} RS trans RS sym,
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1215
        @{thm arg_cong2[of _ _ _ _ "op o"]} OF [map_thm, refl] RS trans,
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1216
        @{thm o_assoc} RS sym RS trans, map_thm RS arg_cong RS trans, @{thm o_assoc} RS trans,
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1217
        @{thm arg_cong2[of _ _ _ _ "op o"]} OF [map_comp RS sym, refl] RS trans,
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1218
        ext, o_apply RS trans,  o_apply RS trans RS sym, map_cong] @
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1219
        replicate m (@{thm id_o} RS fun_cong) @
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1220
        replicate n (@{thm o_id} RS fun_cong))))
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1221
    maps map_comps map_congs)] 1;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1222
49541
32fb6e4c7f4b renamed "map_simps" to "{c,d}tor_maps"
blanchet
parents: 49516
diff changeset
  1223
fun mk_mcong_tac m coinduct_tac map_comp's dtor_maps map_congs set_naturalss set_hsetss
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1224
  set_hset_hsetsss =
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1225
  let
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1226
    val n = length map_comp's;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1227
    val ks = 1 upto n;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1228
  in
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1229
    EVERY' ([rtac rev_mp,
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1230
      coinduct_tac] @
49541
32fb6e4c7f4b renamed "map_simps" to "{c,d}tor_maps"
blanchet
parents: 49516
diff changeset
  1231
      maps (fn (((((map_comp'_trans, dtor_maps_trans), map_cong), set_naturals), set_hsets),
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1232
        set_hset_hsetss) =>