author | blanchet |
Mon, 20 Jan 2014 18:24:56 +0100 | |
changeset 55060 | 3105434fb02f |
parent 55058 | src/HOL/Tools/BNF/Tools/bnf_lfp_tactics.ML@4e700eb471d4 |
child 55061 | a0adf838e2d1 |
permissions | -rw-r--r-- |
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(* Title: HOL/BNF/Tools/bnf_lfp_tactics.ML |
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Author: Dmitriy Traytel, TU Muenchen |
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Author: Andrei Popescu, TU Muenchen |
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Copyright 2012 |
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Tactics for the datatype construction. |
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*) |
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signature BNF_LFP_TACTICS = |
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sig |
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val mk_alg_min_alg_tac: int -> thm -> thm list -> thm -> thm -> thm list list -> thm list -> |
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thm list -> tactic |
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val mk_alg_not_empty_tac: Proof.context -> thm -> thm list -> thm list -> tactic |
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val mk_alg_select_tac: thm -> {prems: 'a, context: Proof.context} -> tactic |
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val mk_alg_set_tac: thm -> tactic |
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val mk_bd_card_order_tac: thm list -> tactic |
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val mk_bd_limit_tac: int -> thm -> tactic |
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val mk_card_of_min_alg_tac: thm -> thm -> thm -> thm -> thm -> tactic |
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val mk_copy_alg_tac: thm list list -> thm list -> thm -> thm -> thm -> tactic |
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val mk_copy_str_tac: thm list list -> thm -> thm list -> tactic |
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val mk_ctor_induct_tac: Proof.context -> int -> thm list list -> thm -> thm list -> thm -> |
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thm list -> thm list -> thm list -> tactic |
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val mk_ctor_induct2_tac: ctyp option list -> cterm option list -> thm -> thm list -> |
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{prems: 'a, context: Proof.context} -> tactic |
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val mk_ctor_set_tac: thm -> thm -> thm list -> tactic |
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val mk_ctor_rel_tac: Proof.context -> thm list -> int -> thm -> thm -> thm -> thm -> thm list -> |
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thm -> thm -> thm list -> thm list -> thm list list -> tactic |
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val mk_dtor_o_ctor_tac: thm -> thm -> thm -> thm -> thm list -> tactic |
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val mk_ex_copy_alg_tac: int -> thm -> thm -> tactic |
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val mk_init_ex_mor_tac: thm -> thm -> thm -> thm list -> thm -> thm -> thm -> |
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{prems: 'a, context: Proof.context} -> tactic |
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val mk_init_induct_tac: int -> thm -> thm -> thm list -> thm list -> tactic |
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val mk_init_unique_mor_tac: int -> thm -> thm -> thm list -> thm list -> thm list -> thm list -> |
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thm list -> tactic |
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val mk_iso_alt_tac: thm list -> thm -> tactic |
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val mk_fold_unique_mor_tac: thm list -> thm list -> thm list -> thm -> thm -> thm -> tactic |
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val mk_fold_transfer_tac: int -> thm -> thm list -> thm list -> |
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{prems: thm list, context: Proof.context} -> tactic |
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val mk_least_min_alg_tac: thm -> thm -> tactic |
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val mk_le_rel_OO_tac: int -> thm -> thm list -> thm list -> thm list -> thm list -> |
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{prems: 'a, context: Proof.context} -> tactic |
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val mk_map_comp0_tac: thm list -> thm list -> thm -> int -> tactic |
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val mk_map_id0_tac: thm list -> thm -> tactic |
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val mk_map_tac: int -> int -> thm -> thm -> thm -> tactic |
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val mk_ctor_map_unique_tac: thm -> thm list -> Proof.context -> tactic |
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val mk_mcong_tac: (int -> tactic) -> thm list list list -> thm list -> thm list -> |
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{prems: 'a, context: Proof.context} -> tactic |
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val mk_min_algs_card_of_tac: ctyp -> cterm -> int -> thm -> thm list -> thm list -> thm -> thm -> |
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thm -> thm -> thm -> thm -> thm -> tactic |
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val mk_min_algs_least_tac: ctyp -> cterm -> thm -> thm list -> thm list -> tactic |
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val mk_min_algs_mono_tac: Proof.context -> thm -> tactic |
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val mk_min_algs_tac: thm -> thm list -> tactic |
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val mk_mor_Abs_tac: thm -> thm list -> thm list -> tactic |
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val mk_mor_Rep_tac: thm list -> thm -> thm list -> thm list -> thm list -> |
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{prems: 'a, context: Proof.context} -> tactic |
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val mk_mor_UNIV_tac: int -> thm list -> thm -> tactic |
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val mk_mor_comp_tac: thm -> thm list list -> thm list -> tactic |
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val mk_mor_convol_tac: 'a list -> thm -> tactic |
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val mk_mor_elim_tac: thm -> tactic |
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val mk_mor_incl_tac: thm -> thm list -> tactic |
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val mk_mor_inv_tac: thm -> thm -> thm list list -> thm list -> thm list -> thm list -> tactic |
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val mk_mor_fold_tac: ctyp -> cterm -> thm list -> thm -> thm -> tactic |
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val mk_mor_select_tac: thm -> thm -> thm -> thm -> thm -> thm -> thm list -> thm list list -> |
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thm list -> tactic |
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val mk_mor_str_tac: 'a list -> thm -> tactic |
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val mk_rel_induct_tac: int -> thm -> int list -> thm list -> thm list -> |
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{prems: thm list, context: Proof.context} -> tactic |
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val mk_rec_tac: thm list -> thm -> thm list -> {prems: 'a, context: Proof.context} -> tactic |
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(co)rec is (just as the (un)fold) the unique morphism;
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val mk_rec_unique_mor_tac: thm list -> thm list -> thm -> {prems: 'a, context: Proof.context} -> |
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tactic |
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val mk_set_bd_tac: int -> (int -> tactic) -> thm -> thm list list -> thm list -> int -> |
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Proof.context -> tactic |
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val mk_set_nat_tac: int -> (int -> tactic) -> thm list list -> thm list -> cterm list -> |
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thm list -> int -> {prems: 'a, context: Proof.context} -> tactic |
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val mk_set_map0_tac: thm -> tactic |
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val mk_set_tac: thm -> tactic |
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val mk_wit_tac: Proof.context -> int -> thm list -> thm list -> tactic |
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end; |
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structure BNF_LFP_Tactics : BNF_LFP_TACTICS = |
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struct |
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open BNF_Tactics |
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open BNF_LFP_Util |
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open BNF_Util |
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val fst_snd_convs = @{thms fst_conv snd_conv}; |
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val ord_eq_le_trans = @{thm ord_eq_le_trans}; |
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val subset_trans = @{thm subset_trans}; |
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val trans_fun_cong_image_id_id_apply = @{thm trans[OF fun_cong[OF image_id] id_apply]}; |
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val rev_bspec = Drule.rotate_prems 1 bspec; |
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val Un_cong = @{thm arg_cong2[of _ _ _ _ "op \<union>"]} |
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fun mk_alg_set_tac alg_def = |
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dtac (alg_def RS iffD1) 1 THEN |
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REPEAT_DETERM (etac conjE 1) THEN |
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EVERY' [etac bspec, rtac CollectI] 1 THEN |
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REPEAT_DETERM (etac conjI 1) THEN atac 1; |
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fun mk_alg_not_empty_tac ctxt alg_set alg_sets wits = |
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(EVERY' [rtac notI, hyp_subst_tac ctxt, ftac alg_set] THEN' |
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REPEAT_DETERM o FIRST' |
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[rtac subset_UNIV, |
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EVERY' [rtac @{thm subset_emptyI}, eresolve_tac wits], |
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EVERY' [rtac subsetI, rtac FalseE, eresolve_tac wits], |
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EVERY' [rtac subsetI, dresolve_tac wits, hyp_subst_tac ctxt, |
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FIRST' (map (fn thm => rtac thm THEN' atac) alg_sets)]] THEN' |
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etac @{thm emptyE}) 1; |
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fun mk_mor_elim_tac mor_def = |
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(dtac (subst OF [mor_def]) THEN' |
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REPEAT o etac conjE THEN' |
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TRY o rtac @{thm image_subsetI} THEN' |
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etac bspec THEN' |
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115 |
atac) 1; |
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diff
changeset
|
116 |
|
53285 | 117 |
fun mk_mor_incl_tac mor_def map_ids = |
48975
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|
118 |
(stac mor_def THEN' |
7f79f94a432c
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parents:
diff
changeset
|
119 |
rtac conjI THEN' |
53285 | 120 |
CONJ_WRAP' (K (EVERY' [rtac ballI, etac set_mp, stac id_apply, atac])) map_ids THEN' |
48975
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parents:
diff
changeset
|
121 |
CONJ_WRAP' (fn thm => |
53285 | 122 |
(EVERY' [rtac ballI, rtac trans, rtac id_apply, stac thm, rtac refl])) map_ids) 1; |
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parents:
diff
changeset
|
123 |
|
53290 | 124 |
fun mk_mor_comp_tac mor_def set_maps map_comp_ids = |
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|
125 |
let |
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parents:
diff
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|
126 |
val fbetw_tac = EVERY' [rtac ballI, stac o_apply, etac bspec, etac bspec, atac]; |
53290 | 127 |
fun mor_tac (set_map, map_comp_id) = |
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parents:
diff
changeset
|
128 |
EVERY' [rtac ballI, stac o_apply, rtac trans, |
52659
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parents:
52635
diff
changeset
|
129 |
rtac trans, dtac rev_bspec, atac, etac arg_cong, |
48975
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parents:
diff
changeset
|
130 |
REPEAT o eresolve_tac [CollectE, conjE], etac bspec, rtac CollectI] THEN' |
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parents:
diff
changeset
|
131 |
CONJ_WRAP' (fn thm => |
49306 | 132 |
FIRST' [rtac subset_UNIV, |
133 |
(EVERY' [rtac ord_eq_le_trans, rtac thm, rtac @{thm image_subsetI}, |
|
53290 | 134 |
etac bspec, etac set_mp, atac])]) set_map THEN' |
48975
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parents:
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changeset
|
135 |
rtac (map_comp_id RS arg_cong); |
7f79f94a432c
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parents:
diff
changeset
|
136 |
in |
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parents:
diff
changeset
|
137 |
(dtac (mor_def RS subst) THEN' dtac (mor_def RS subst) THEN' stac mor_def THEN' |
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parents:
diff
changeset
|
138 |
REPEAT o etac conjE THEN' |
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parents:
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changeset
|
139 |
rtac conjI THEN' |
53290 | 140 |
CONJ_WRAP' (K fbetw_tac) set_maps THEN' |
141 |
CONJ_WRAP' mor_tac (set_maps ~~ map_comp_ids)) 1 |
|
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|
142 |
end; |
7f79f94a432c
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parents:
diff
changeset
|
143 |
|
53290 | 144 |
fun mk_mor_inv_tac alg_def mor_def set_maps morEs map_comp_ids map_cong0Ls = |
48975
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parents:
diff
changeset
|
145 |
let |
49306 | 146 |
val fbetw_tac = EVERY' [rtac ballI, etac set_mp, etac imageI]; |
53290 | 147 |
fun Collect_tac set_map = |
48975
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parents:
diff
changeset
|
148 |
CONJ_WRAP' (fn thm => |
49306 | 149 |
FIRST' [rtac subset_UNIV, |
150 |
(EVERY' [rtac ord_eq_le_trans, rtac thm, rtac subset_trans, |
|
53290 | 151 |
etac @{thm image_mono}, atac])]) set_map; |
152 |
fun mor_tac (set_map, ((morE, map_comp_id), map_cong0L)) = |
|
52659
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parents:
52635
diff
changeset
|
153 |
EVERY' [rtac ballI, ftac rev_bspec, atac, |
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parents:
diff
changeset
|
154 |
REPEAT o eresolve_tac [CollectE, conjE], rtac sym, rtac trans, rtac sym, |
53290 | 155 |
etac @{thm inverE}, etac bspec, rtac CollectI, Collect_tac set_map, |
156 |
rtac trans, etac (morE RS arg_cong), rtac CollectI, Collect_tac set_map, |
|
51761
4c9f08836d87
renamed "map_cong" axiom to "map_cong0" in preparation for real "map_cong"
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parents:
51739
diff
changeset
|
157 |
rtac trans, rtac (map_comp_id RS arg_cong), rtac (map_cong0L RS arg_cong), |
48975
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parents:
diff
changeset
|
158 |
REPEAT_DETERM_N (length morEs) o |
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parents:
diff
changeset
|
159 |
(EVERY' [rtac subst, rtac @{thm inver_pointfree}, etac @{thm inver_mono}, atac])]; |
7f79f94a432c
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parents:
diff
changeset
|
160 |
in |
7f79f94a432c
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parents:
diff
changeset
|
161 |
(stac mor_def THEN' |
49488
02eb07152998
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parents:
49463
diff
changeset
|
162 |
dtac (alg_def RS iffD1) THEN' |
02eb07152998
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parents:
49463
diff
changeset
|
163 |
dtac (alg_def RS iffD1) THEN' |
48975
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parents:
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changeset
|
164 |
REPEAT o etac conjE THEN' |
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parents:
diff
changeset
|
165 |
rtac conjI THEN' |
53290 | 166 |
CONJ_WRAP' (K fbetw_tac) set_maps THEN' |
167 |
CONJ_WRAP' mor_tac (set_maps ~~ (morEs ~~ map_comp_ids ~~ map_cong0Ls))) 1 |
|
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changeset
|
168 |
end; |
7f79f94a432c
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parents:
diff
changeset
|
169 |
|
7f79f94a432c
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parents:
diff
changeset
|
170 |
fun mk_mor_str_tac ks mor_def = |
7f79f94a432c
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blanchet
parents:
diff
changeset
|
171 |
(stac mor_def THEN' rtac conjI THEN' |
7f79f94a432c
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blanchet
parents:
diff
changeset
|
172 |
CONJ_WRAP' (K (EVERY' [rtac ballI, rtac UNIV_I])) ks THEN' |
7f79f94a432c
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blanchet
parents:
diff
changeset
|
173 |
CONJ_WRAP' (K (EVERY' [rtac ballI, rtac refl])) ks) 1; |
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
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parents:
diff
changeset
|
174 |
|
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff
changeset
|
175 |
fun mk_mor_convol_tac ks mor_def = |
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff
changeset
|
176 |
(stac mor_def THEN' rtac conjI THEN' |
7f79f94a432c
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blanchet
parents:
diff
changeset
|
177 |
CONJ_WRAP' (K (EVERY' [rtac ballI, rtac UNIV_I])) ks THEN' |
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff
changeset
|
178 |
CONJ_WRAP' (K (EVERY' [rtac ballI, rtac trans, rtac @{thm fst_convol'}, rtac o_apply])) ks) 1; |
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff
changeset
|
179 |
|
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff
changeset
|
180 |
fun mk_mor_UNIV_tac m morEs mor_def = |
7f79f94a432c
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parents:
diff
changeset
|
181 |
let |
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff
changeset
|
182 |
val n = length morEs; |
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff
changeset
|
183 |
fun mor_tac morE = EVERY' [rtac ext, rtac trans, rtac o_apply, rtac trans, etac morE, |
49306 | 184 |
rtac CollectI, CONJ_WRAP' (K (rtac subset_UNIV)) (1 upto m + n), |
48975
7f79f94a432c
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parents:
diff
changeset
|
185 |
rtac sym, rtac o_apply]; |
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff
changeset
|
186 |
in |
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff
changeset
|
187 |
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
|
188 |
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
|
189 |
REPEAT_DETERM o etac conjE, REPEAT_DETERM_N n o dtac (@{thm fun_eq_iff} RS subst), |
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff
changeset
|
190 |
CONJ_WRAP' (K (EVERY' [rtac ballI, REPEAT_DETERM o etac allE, rtac trans, |
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff
changeset
|
191 |
etac (o_apply RS subst), rtac o_apply])) morEs] 1 |
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff
changeset
|
192 |
end; |
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff
changeset
|
193 |
|
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff
changeset
|
194 |
fun mk_iso_alt_tac mor_images mor_inv = |
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff
changeset
|
195 |
let |
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff
changeset
|
196 |
val n = length mor_images; |
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff
changeset
|
197 |
fun if_wrap_tac thm = |
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff
changeset
|
198 |
EVERY' [rtac ssubst, rtac @{thm bij_betw_iff_ex}, rtac exI, rtac conjI, |
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff
changeset
|
199 |
rtac @{thm inver_surj}, etac thm, etac thm, atac, etac conjI, atac] |
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff
changeset
|
200 |
val if_tac = |
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff
changeset
|
201 |
EVERY' [etac thin_rl, etac thin_rl, REPEAT o eresolve_tac [conjE, exE], |
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff
changeset
|
202 |
rtac conjI, atac, CONJ_WRAP' if_wrap_tac mor_images]; |
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff
changeset
|
203 |
val only_if_tac = |
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff
changeset
|
204 |
EVERY' [rtac conjI, etac conjunct1, EVERY' (map (fn thm => |
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff
changeset
|
205 |
EVERY' [rtac exE, rtac @{thm bij_betw_ex_weakE}, etac (conjunct2 RS thm)]) |
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff
changeset
|
206 |
(map (mk_conjunctN n) (1 upto n))), REPEAT o rtac exI, rtac conjI, rtac mor_inv, |
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff
changeset
|
207 |
etac conjunct1, atac, atac, REPEAT_DETERM_N n o atac, |
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff
changeset
|
208 |
CONJ_WRAP' (K (etac conjunct2)) mor_images]; |
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff
changeset
|
209 |
in |
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff
changeset
|
210 |
(rtac iffI THEN' if_tac THEN' only_if_tac) 1 |
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff
changeset
|
211 |
end; |
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff
changeset
|
212 |
|
53290 | 213 |
fun mk_copy_str_tac set_maps alg_def alg_sets = |
48975
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff
changeset
|
214 |
let |
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff
changeset
|
215 |
val n = length alg_sets; |
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff
changeset
|
216 |
val bij_betw_inv_tac = |
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff
changeset
|
217 |
EVERY' [etac thin_rl, REPEAT_DETERM_N n o EVERY' [dtac @{thm bij_betwI}, atac, atac], |
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff
changeset
|
218 |
REPEAT_DETERM_N (2 * n) o etac thin_rl, REPEAT_DETERM_N (n - 1) o etac conjI, atac]; |
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff
changeset
|
219 |
fun set_tac thms = |
49306 | 220 |
EVERY' [rtac ord_eq_le_trans, resolve_tac thms, rtac subset_trans, |
48975
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff
changeset
|
221 |
etac @{thm image_mono}, rtac equalityD1, etac @{thm bij_betw_imageE}]; |
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff
changeset
|
222 |
val copy_str_tac = |
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff
changeset
|
223 |
CONJ_WRAP' (fn (thms, thm) => |
49306 | 224 |
EVERY' [rtac ballI, REPEAT_DETERM o eresolve_tac [CollectE, conjE], rtac set_mp, |
48975
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff
changeset
|
225 |
rtac equalityD1, etac @{thm bij_betw_imageE}, rtac imageI, etac thm, |
49306 | 226 |
REPEAT_DETERM o rtac subset_UNIV, REPEAT_DETERM_N n o (set_tac thms)]) |
53290 | 227 |
(set_maps ~~ alg_sets); |
48975
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff
changeset
|
228 |
in |
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff
changeset
|
229 |
(rtac rev_mp THEN' DETERM o bij_betw_inv_tac THEN' rtac impI THEN' |
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff
changeset
|
230 |
stac alg_def THEN' copy_str_tac) 1 |
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff
changeset
|
231 |
end; |
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff
changeset
|
232 |
|
53290 | 233 |
fun mk_copy_alg_tac set_maps alg_sets mor_def iso_alt copy_str = |
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234 |
let |
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|
235 |
val n = length alg_sets; |
7f79f94a432c
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|
236 |
val fbetw_tac = CONJ_WRAP' (K (etac @{thm bij_betwE})) alg_sets; |
7f79f94a432c
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|
237 |
fun set_tac thms = |
49306 | 238 |
EVERY' [rtac ord_eq_le_trans, resolve_tac thms, rtac subset_trans, |
48975
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|
239 |
REPEAT_DETERM o etac conjE, etac @{thm image_mono}, |
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|
240 |
rtac equalityD1, etac @{thm bij_betw_imageE}]; |
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|
241 |
val mor_tac = |
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|
242 |
CONJ_WRAP' (fn (thms, thm) => |
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parents:
diff
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|
243 |
EVERY' [rtac ballI, etac CollectE, etac @{thm inverE}, etac thm, |
49306 | 244 |
REPEAT_DETERM o rtac subset_UNIV, REPEAT_DETERM_N n o (set_tac thms)]) |
53290 | 245 |
(set_maps ~~ alg_sets); |
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|
246 |
in |
52904 | 247 |
(rtac (iso_alt RS iffD2) THEN' |
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|
248 |
etac copy_str THEN' REPEAT_DETERM o atac THEN' |
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|
249 |
rtac conjI THEN' stac mor_def THEN' rtac conjI THEN' fbetw_tac THEN' mor_tac THEN' |
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parents:
diff
changeset
|
250 |
CONJ_WRAP' (K atac) alg_sets) 1 |
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|
251 |
end; |
7f79f94a432c
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parents:
diff
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|
252 |
|
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|
253 |
fun mk_ex_copy_alg_tac n copy_str copy_alg = |
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added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
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parents:
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changeset
|
254 |
EVERY' [REPEAT_DETERM_N n o rtac exI, rtac conjI, etac copy_str, |
7f79f94a432c
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parents:
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|
255 |
REPEAT_DETERM_N n o atac, |
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parents:
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changeset
|
256 |
REPEAT_DETERM_N n o etac @{thm bij_betw_inver2}, |
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parents:
diff
changeset
|
257 |
REPEAT_DETERM_N n o etac @{thm bij_betw_inver1}, etac copy_alg, |
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parents:
diff
changeset
|
258 |
REPEAT_DETERM_N n o atac, |
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parents:
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changeset
|
259 |
REPEAT_DETERM_N n o etac @{thm bij_betw_inver2}, |
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parents:
diff
changeset
|
260 |
REPEAT_DETERM_N n o etac @{thm bij_betw_inver1}] 1; |
7f79f94a432c
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parents:
diff
changeset
|
261 |
|
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
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parents:
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changeset
|
262 |
fun mk_bd_limit_tac n bd_Cinfinite = |
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
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parents:
diff
changeset
|
263 |
EVERY' [REPEAT_DETERM o etac conjE, rtac rev_mp, rtac @{thm Cinfinite_limit_finite}, |
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
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parents:
diff
changeset
|
264 |
REPEAT_DETERM_N n o rtac @{thm finite.insertI}, rtac @{thm finite.emptyI}, |
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
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parents:
diff
changeset
|
265 |
REPEAT_DETERM_N n o etac @{thm insert_subsetI}, rtac @{thm empty_subsetI}, |
7f79f94a432c
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parents:
diff
changeset
|
266 |
rtac bd_Cinfinite, rtac impI, etac bexE, rtac bexI, |
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
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parents:
diff
changeset
|
267 |
CONJ_WRAP' (fn i => |
7f79f94a432c
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parents:
diff
changeset
|
268 |
EVERY' [etac bspec, REPEAT_DETERM_N i o rtac @{thm insertI2}, rtac @{thm insertI1}]) |
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
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parents:
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changeset
|
269 |
(0 upto n - 1), |
7f79f94a432c
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changeset
|
270 |
atac] 1; |
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parents:
diff
changeset
|
271 |
|
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parents:
diff
changeset
|
272 |
fun mk_min_algs_tac worel in_congs = |
7f79f94a432c
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changeset
|
273 |
let |
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
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parents:
diff
changeset
|
274 |
val minG_tac = EVERY' [rtac @{thm UN_cong}, rtac refl, dtac bspec, atac, etac arg_cong]; |
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
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parents:
diff
changeset
|
275 |
fun minH_tac thm = |
52659
58b87aa4dc3b
eliminate duplicated theorems (thanks to "Auto solve_direct" in jEdit)
traytel
parents:
52635
diff
changeset
|
276 |
EVERY' [rtac Un_cong, minG_tac, rtac @{thm image_cong}, rtac thm, |
48975
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parents:
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changeset
|
277 |
REPEAT_DETERM_N (length in_congs) o minG_tac, rtac refl]; |
7f79f94a432c
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parents:
diff
changeset
|
278 |
in |
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
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parents:
diff
changeset
|
279 |
(rtac (worel RS (@{thm wo_rel.worec_fixpoint} RS fun_cong)) THEN' rtac ssubst THEN' |
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
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parents:
diff
changeset
|
280 |
rtac meta_eq_to_obj_eq THEN' rtac (worel RS @{thm wo_rel.adm_wo_def}) THEN' |
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
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parents:
diff
changeset
|
281 |
REPEAT_DETERM_N 3 o rtac allI THEN' rtac impI THEN' |
49488
02eb07152998
use iffD* instead of (s)subst instantiated with identity; tuned antiquotations;
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parents:
49463
diff
changeset
|
282 |
CONJ_WRAP_GEN' (EVERY' [rtac Pair_eqI, rtac conjI]) minH_tac in_congs) 1 |
48975
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added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
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|
283 |
end; |
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
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parents:
diff
changeset
|
284 |
|
51798 | 285 |
fun mk_min_algs_mono_tac ctxt min_algs = EVERY' [stac @{thm relChain_def}, rtac allI, rtac allI, |
48975
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
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parents:
diff
changeset
|
286 |
rtac impI, rtac @{thm case_split}, rtac @{thm xt1(3)}, rtac min_algs, etac @{thm FieldI2}, |
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff
changeset
|
287 |
rtac subsetI, rtac UnI1, rtac @{thm UN_I}, etac @{thm underS_I}, atac, atac, |
51798 | 288 |
rtac equalityD1, dtac @{thm notnotD}, hyp_subst_tac ctxt, rtac refl] 1; |
48975
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff
changeset
|
289 |
|
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff
changeset
|
290 |
fun mk_min_algs_card_of_tac cT ct m worel min_algs in_bds bd_Card_order bd_Cnotzero |
51812 | 291 |
suc_Card_order suc_Cinfinite suc_Cnotzero suc_Asuc Asuc_Cinfinite = |
48975
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff
changeset
|
292 |
let |
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
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parents:
diff
changeset
|
293 |
val induct = worel RS |
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
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parents:
diff
changeset
|
294 |
Drule.instantiate' [SOME cT] [NONE, SOME ct] @{thm well_order_induct_imp}; |
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
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parents:
diff
changeset
|
295 |
val src = 1 upto m + 1; |
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff
changeset
|
296 |
val dest = (m + 1) :: (1 upto m); |
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff
changeset
|
297 |
val absorbAs_tac = 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
|
298 |
else EVERY' [rtac @{thm ordIso_transitive}, rtac @{thm csum_cong1}, |
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff
changeset
|
299 |
rtac @{thm ordIso_transitive}, |
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff
changeset
|
300 |
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
|
301 |
FIRST' [rtac @{thm card_of_Card_order}, rtac @{thm Card_order_csum}, |
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff
changeset
|
302 |
rtac @{thm Card_order_cexp}]) |
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff
changeset
|
303 |
@{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
|
304 |
src dest, |
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff
changeset
|
305 |
rtac @{thm csum_absorb1}, rtac Asuc_Cinfinite, rtac ctrans, rtac @{thm ordLeq_csum1}, |
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff
changeset
|
306 |
FIRST' [rtac @{thm Card_order_csum}, 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
|
307 |
rtac @{thm ordLeq_cexp1}, rtac suc_Cnotzero, rtac @{thm Card_order_csum}]; |
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff
changeset
|
308 |
|
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff
changeset
|
309 |
val minG_tac = EVERY' [rtac @{thm UNION_Cinfinite_bound}, rtac @{thm ordLess_imp_ordLeq}, |
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff
changeset
|
310 |
rtac @{thm ordLess_transitive}, rtac @{thm card_of_underS}, rtac suc_Card_order, |
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff
changeset
|
311 |
atac, rtac suc_Asuc, rtac ballI, etac allE, dtac mp, etac @{thm underS_E}, |
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff
changeset
|
312 |
dtac mp, etac @{thm underS_Field}, REPEAT o etac conjE, atac, rtac Asuc_Cinfinite] |
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff
changeset
|
313 |
|
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff
changeset
|
314 |
fun mk_minH_tac (min_alg, in_bd) = EVERY' [rtac @{thm ordIso_ordLeq_trans}, |
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff
changeset
|
315 |
rtac @{thm card_of_ordIso_subst}, etac min_alg, rtac @{thm Un_Cinfinite_bound}, |
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff
changeset
|
316 |
minG_tac, rtac ctrans, rtac @{thm card_of_image}, rtac ctrans, rtac in_bd, rtac ctrans, |
51782
84e7225f5ab6
removed unnecessary assumptions in some theorems about cardinal exponentiation
traytel
parents:
51766
diff
changeset
|
317 |
rtac @{thm cexp_mono1}, rtac @{thm csum_mono1}, |
48975
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff
changeset
|
318 |
REPEAT_DETERM_N m o rtac @{thm csum_mono2}, |
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff
changeset
|
319 |
CONJ_WRAP_GEN' (rtac @{thm csum_cinfinite_bound}) (K minG_tac) min_algs, |
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff
changeset
|
320 |
REPEAT_DETERM o FIRST' |
51782
84e7225f5ab6
removed unnecessary assumptions in some theorems about cardinal exponentiation
traytel
parents:
51766
diff
changeset
|
321 |
[rtac @{thm card_of_Card_order}, rtac @{thm Card_order_csum}, |
84e7225f5ab6
removed unnecessary assumptions in some theorems about cardinal exponentiation
traytel
parents:
51766
diff
changeset
|
322 |
rtac Asuc_Cinfinite, rtac bd_Card_order], |
84e7225f5ab6
removed unnecessary assumptions in some theorems about cardinal exponentiation
traytel
parents:
51766
diff
changeset
|
323 |
rtac @{thm ordIso_ordLeq_trans}, rtac @{thm cexp_cong1}, absorbAs_tac, |
48975
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff
changeset
|
324 |
rtac @{thm csum_absorb1}, rtac Asuc_Cinfinite, rtac @{thm ctwo_ordLeq_Cinfinite}, |
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff
changeset
|
325 |
rtac Asuc_Cinfinite, rtac bd_Card_order, |
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff
changeset
|
326 |
rtac @{thm ordIso_imp_ordLeq}, rtac @{thm cexp_cprod_ordLeq}, |
51782
84e7225f5ab6
removed unnecessary assumptions in some theorems about cardinal exponentiation
traytel
parents:
51766
diff
changeset
|
327 |
resolve_tac @{thms Card_order_csum Card_order_ctwo}, rtac suc_Cinfinite, |
48975
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff
changeset
|
328 |
rtac bd_Cnotzero, rtac @{thm cardSuc_ordLeq}, rtac bd_Card_order, rtac Asuc_Cinfinite]; |
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff
changeset
|
329 |
in |
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff
changeset
|
330 |
(rtac induct THEN' |
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff
changeset
|
331 |
rtac impI THEN' |
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff
changeset
|
332 |
CONJ_WRAP' mk_minH_tac (min_algs ~~ in_bds)) 1 |
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff
changeset
|
333 |
end; |
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff
changeset
|
334 |
|
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff
changeset
|
335 |
fun mk_min_algs_least_tac cT ct worel min_algs alg_sets = |
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff
changeset
|
336 |
let |
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff
changeset
|
337 |
val induct = worel RS |
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff
changeset
|
338 |
Drule.instantiate' [SOME cT] [NONE, SOME ct] @{thm well_order_induct_imp}; |
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff
changeset
|
339 |
|
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff
changeset
|
340 |
val minG_tac = EVERY' [rtac @{thm UN_least}, etac allE, dtac mp, etac @{thm underS_E}, |
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff
changeset
|
341 |
dtac mp, etac @{thm underS_Field}, REPEAT_DETERM o etac conjE, atac]; |
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff
changeset
|
342 |
|
49306 | 343 |
fun mk_minH_tac (min_alg, alg_set) = EVERY' [rtac ord_eq_le_trans, etac min_alg, |
48975
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff
changeset
|
344 |
rtac @{thm Un_least}, minG_tac, rtac @{thm image_subsetI}, |
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff
changeset
|
345 |
REPEAT_DETERM o eresolve_tac [CollectE, conjE], etac alg_set, |
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff
changeset
|
346 |
REPEAT_DETERM o FIRST' [atac, etac subset_trans THEN' minG_tac]]; |
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff
changeset
|
347 |
in |
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff
changeset
|
348 |
(rtac induct THEN' |
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff
changeset
|
349 |
rtac impI THEN' |
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff
changeset
|
350 |
CONJ_WRAP' mk_minH_tac (min_algs ~~ alg_sets)) 1 |
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff
changeset
|
351 |
end; |
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff
changeset
|
352 |
|
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff
changeset
|
353 |
fun mk_alg_min_alg_tac m alg_def min_alg_defs bd_limit bd_Cinfinite |
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff
changeset
|
354 |
set_bdss min_algs min_alg_monos = |
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff
changeset
|
355 |
let |
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff
changeset
|
356 |
val n = length min_algs; |
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff
changeset
|
357 |
fun mk_cardSuc_UNION_tac set_bds (mono, def) = EVERY' |
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff
changeset
|
358 |
[rtac bexE, rtac @{thm cardSuc_UNION_Cinfinite}, rtac bd_Cinfinite, rtac mono, |
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff
changeset
|
359 |
etac (def RSN (2, @{thm subset_trans[OF _ equalityD1]})), resolve_tac set_bds]; |
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff
changeset
|
360 |
fun mk_conjunct_tac (set_bds, (min_alg, min_alg_def)) = |
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff
changeset
|
361 |
EVERY' [rtac ballI, 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
|
362 |
EVERY' (map (mk_cardSuc_UNION_tac set_bds) (min_alg_monos ~~ min_alg_defs)), rtac bexE, |
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff
changeset
|
363 |
rtac bd_limit, REPEAT_DETERM_N (n - 1) o etac conjI, atac, |
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff
changeset
|
364 |
rtac (min_alg_def RS @{thm set_mp[OF equalityD2]}), |
49306 | 365 |
rtac @{thm UN_I}, REPEAT_DETERM_N (m + 3 * n) o etac thin_rl, atac, rtac set_mp, |
48975
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff
changeset
|
366 |
rtac equalityD2, rtac min_alg, atac, rtac UnI2, rtac @{thm image_eqI}, rtac refl, |
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff
changeset
|
367 |
rtac CollectI, REPEAT_DETERM_N m o dtac asm_rl, REPEAT_DETERM_N n o etac thin_rl, |
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff
changeset
|
368 |
REPEAT_DETERM o etac conjE, |
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff
changeset
|
369 |
CONJ_WRAP' (K (FIRST' [atac, |
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff
changeset
|
370 |
EVERY' [etac subset_trans, rtac subsetI, rtac @{thm UN_I}, |
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff
changeset
|
371 |
etac @{thm underS_I}, atac, atac]])) |
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff
changeset
|
372 |
set_bds]; |
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff
changeset
|
373 |
in |
52904 | 374 |
(rtac (alg_def RS iffD2) THEN' |
48975
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff
changeset
|
375 |
CONJ_WRAP' mk_conjunct_tac (set_bdss ~~ (min_algs ~~ min_alg_defs))) 1 |
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff
changeset
|
376 |
end; |
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff
changeset
|
377 |
|
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff
changeset
|
378 |
fun mk_card_of_min_alg_tac min_alg_def card_of suc_Card_order suc_Asuc Asuc_Cinfinite = |
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff
changeset
|
379 |
EVERY' [stac min_alg_def, rtac @{thm UNION_Cinfinite_bound}, |
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff
changeset
|
380 |
rtac @{thm ordIso_ordLeq_trans}, rtac @{thm card_of_Field_ordIso}, rtac suc_Card_order, |
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff
changeset
|
381 |
rtac @{thm ordLess_imp_ordLeq}, rtac suc_Asuc, rtac ballI, dtac rev_mp, rtac card_of, |
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff
changeset
|
382 |
REPEAT_DETERM o etac conjE, atac, rtac Asuc_Cinfinite] 1; |
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff
changeset
|
383 |
|
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff
changeset
|
384 |
fun mk_least_min_alg_tac min_alg_def least = |
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff
changeset
|
385 |
EVERY' [stac min_alg_def, rtac @{thm UN_least}, dtac least, dtac mp, atac, |
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff
changeset
|
386 |
REPEAT_DETERM o etac conjE, atac] 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_alg_select_tac Abs_inverse {context = ctxt, prems = _} = |
51798 | 389 |
EVERY' [rtac ballI, REPEAT_DETERM o eresolve_tac [CollectE, exE, conjE], hyp_subst_tac ctxt] 1 THEN |
49504
df9b897fb254
renamed "iter"/"coiter" to "fold"/"unfold" (cf. Wadler)
blanchet
parents:
49502
diff
changeset
|
390 |
unfold_thms_tac ctxt (Abs_inverse :: fst_snd_convs) THEN atac 1; |
48975
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff
changeset
|
391 |
|
53290 | 392 |
fun mk_mor_select_tac mor_def mor_cong mor_comp mor_incl_min_alg alg_def alg_select alg_sets |
393 |
set_maps str_init_defs = |
|
48975
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff
changeset
|
394 |
let |
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff
changeset
|
395 |
val n = length alg_sets; |
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff
changeset
|
396 |
val fbetw_tac = |
52659
58b87aa4dc3b
eliminate duplicated theorems (thanks to "Auto solve_direct" in jEdit)
traytel
parents:
52635
diff
changeset
|
397 |
CONJ_WRAP' (K (EVERY' [rtac ballI, etac rev_bspec, etac CollectE, atac])) alg_sets; |
48975
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff
changeset
|
398 |
val mor_tac = |
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff
changeset
|
399 |
CONJ_WRAP' (fn thm => EVERY' [rtac ballI, rtac thm]) str_init_defs; |
53290 | 400 |
fun alg_epi_tac ((alg_set, str_init_def), set_map) = |
48975
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff
changeset
|
401 |
EVERY' [rtac ballI, REPEAT_DETERM o eresolve_tac [CollectE, conjE], rtac CollectI, |
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff
changeset
|
402 |
rtac ballI, ftac (alg_select RS bspec), stac str_init_def, etac alg_set, |
49306 | 403 |
REPEAT_DETERM o FIRST' [rtac subset_UNIV, |
53290 | 404 |
EVERY' [rtac ord_eq_le_trans, resolve_tac set_map, rtac subset_trans, |
48975
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff
changeset
|
405 |
etac @{thm image_mono}, rtac @{thm image_Collect_subsetI}, etac bspec, atac]]]; |
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff
changeset
|
406 |
in |
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff
changeset
|
407 |
(rtac mor_cong THEN' REPEAT_DETERM_N n o (rtac sym THEN' rtac @{thm o_id}) THEN' |
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff
changeset
|
408 |
rtac (Thm.permute_prems 0 1 mor_comp) THEN' etac (Thm.permute_prems 0 1 mor_comp) THEN' |
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff
changeset
|
409 |
stac mor_def THEN' rtac conjI THEN' fbetw_tac THEN' mor_tac THEN' rtac mor_incl_min_alg THEN' |
53290 | 410 |
stac alg_def THEN' CONJ_WRAP' alg_epi_tac ((alg_sets ~~ str_init_defs) ~~ set_maps)) 1 |
48975
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff
changeset
|
411 |
end; |
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff
changeset
|
412 |
|
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff
changeset
|
413 |
fun mk_init_ex_mor_tac Abs_inverse copy_alg_ex alg_min_alg card_of_min_algs |
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff
changeset
|
414 |
mor_comp mor_select mor_incl_min_alg {context = ctxt, prems = _} = |
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff
changeset
|
415 |
let |
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff
changeset
|
416 |
val n = length card_of_min_algs; |
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff
changeset
|
417 |
val card_of_ordIso_tac = EVERY' [rtac ssubst, rtac @{thm card_of_ordIso}, |
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff
changeset
|
418 |
rtac @{thm ordIso_symmetric}, rtac conjunct1, rtac conjunct2, atac]; |
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff
changeset
|
419 |
fun internalize_tac card_of = EVERY' [rtac subst, rtac @{thm internalize_card_of_ordLeq2}, |
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff
changeset
|
420 |
rtac @{thm ordLeq_ordIso_trans}, rtac card_of, rtac subst, |
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff
changeset
|
421 |
rtac @{thm Card_order_iff_ordIso_card_of}, rtac @{thm Card_order_cexp}]; |
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff
changeset
|
422 |
in |
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff
changeset
|
423 |
(rtac rev_mp THEN' |
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff
changeset
|
424 |
REPEAT_DETERM_N (2 * n) o (rtac mp THEN' rtac @{thm ex_mono} THEN' rtac impI) THEN' |
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff
changeset
|
425 |
REPEAT_DETERM_N (n + 1) o etac thin_rl THEN' rtac (alg_min_alg RS copy_alg_ex) THEN' |
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff
changeset
|
426 |
REPEAT_DETERM_N n o atac THEN' |
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff
changeset
|
427 |
REPEAT_DETERM_N n o card_of_ordIso_tac THEN' |
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff
changeset
|
428 |
EVERY' (map internalize_tac card_of_min_algs) THEN' |
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff
changeset
|
429 |
rtac impI THEN' |
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff
changeset
|
430 |
REPEAT_DETERM o eresolve_tac [exE, conjE] THEN' |
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff
changeset
|
431 |
REPEAT_DETERM o rtac exI THEN' |
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff
changeset
|
432 |
rtac mor_select THEN' atac THEN' rtac CollectI THEN' |
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff
changeset
|
433 |
REPEAT_DETERM o rtac exI THEN' |
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff
changeset
|
434 |
rtac conjI THEN' rtac refl THEN' atac THEN' |
49504
df9b897fb254
renamed "iter"/"coiter" to "fold"/"unfold" (cf. Wadler)
blanchet
parents:
49502
diff
changeset
|
435 |
K (unfold_thms_tac ctxt (Abs_inverse :: fst_snd_convs)) THEN' |
48975
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff
changeset
|
436 |
etac mor_comp THEN' etac mor_incl_min_alg) 1 |
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff
changeset
|
437 |
end; |
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff
changeset
|
438 |
|
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff
changeset
|
439 |
fun mk_init_unique_mor_tac m |
51761
4c9f08836d87
renamed "map_cong" axiom to "map_cong0" in preparation for real "map_cong"
blanchet
parents:
51739
diff
changeset
|
440 |
alg_def alg_min_alg least_min_algs in_monos alg_sets morEs map_cong0s = |
48975
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff
changeset
|
441 |
let |
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff
changeset
|
442 |
val n = length least_min_algs; |
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff
changeset
|
443 |
val ks = (1 upto n); |
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff
changeset
|
444 |
|
49306 | 445 |
fun mor_tac morE in_mono = EVERY' [etac morE, rtac set_mp, rtac in_mono, |
48975
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff
changeset
|
446 |
REPEAT_DETERM_N n o rtac @{thm Collect_restrict}, rtac CollectI, |
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff
changeset
|
447 |
REPEAT_DETERM_N (m + n) o (TRY o rtac conjI THEN' atac)]; |
51761
4c9f08836d87
renamed "map_cong" axiom to "map_cong0" in preparation for real "map_cong"
blanchet
parents:
51739
diff
changeset
|
448 |
fun cong_tac map_cong0 = EVERY' [rtac (map_cong0 RS arg_cong), |
48975
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff
changeset
|
449 |
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
|
450 |
REPEAT_DETERM_N n o (etac @{thm prop_restrict} THEN' atac)]; |
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff
changeset
|
451 |
|
51761
4c9f08836d87
renamed "map_cong" axiom to "map_cong0" in preparation for real "map_cong"
blanchet
parents:
51739
diff
changeset
|
452 |
fun mk_alg_tac (alg_set, (in_mono, (morE, map_cong0))) = EVERY' [rtac ballI, rtac CollectI, |
48975
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff
changeset
|
453 |
REPEAT_DETERM o eresolve_tac [CollectE, conjE], rtac conjI, rtac (alg_min_alg RS alg_set), |
49306 | 454 |
REPEAT_DETERM_N m o rtac subset_UNIV, |
455 |
REPEAT_DETERM_N n o (etac subset_trans THEN' rtac @{thm Collect_restrict}), |
|
48975
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff
changeset
|
456 |
rtac trans, mor_tac morE in_mono, |
51761
4c9f08836d87
renamed "map_cong" axiom to "map_cong0" in preparation for real "map_cong"
blanchet
parents:
51739
diff
changeset
|
457 |
rtac trans, cong_tac map_cong0, |
48975
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff
changeset
|
458 |
rtac sym, mor_tac morE in_mono]; |
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff
changeset
|
459 |
|
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff
changeset
|
460 |
fun mk_unique_tac (k, least_min_alg) = |
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff
changeset
|
461 |
select_prem_tac n (etac @{thm prop_restrict}) k THEN' rtac least_min_alg THEN' |
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff
changeset
|
462 |
stac alg_def THEN' |
51761
4c9f08836d87
renamed "map_cong" axiom to "map_cong0" in preparation for real "map_cong"
blanchet
parents:
51739
diff
changeset
|
463 |
CONJ_WRAP' mk_alg_tac (alg_sets ~~ (in_monos ~~ (morEs ~~ map_cong0s))); |
48975
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff
changeset
|
464 |
in |
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff
changeset
|
465 |
CONJ_WRAP' mk_unique_tac (ks ~~ least_min_algs) 1 |
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff
changeset
|
466 |
end; |
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff
changeset
|
467 |
|
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff
changeset
|
468 |
fun mk_init_induct_tac m alg_def alg_min_alg least_min_algs alg_sets = |
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff
changeset
|
469 |
let |
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff
changeset
|
470 |
val n = length least_min_algs; |
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff
changeset
|
471 |
|
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff
changeset
|
472 |
fun mk_alg_tac alg_set = EVERY' [rtac ballI, rtac CollectI, |
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff
changeset
|
473 |
REPEAT_DETERM o eresolve_tac [CollectE, conjE], rtac conjI, rtac (alg_min_alg RS alg_set), |
49306 | 474 |
REPEAT_DETERM_N m o rtac subset_UNIV, |
475 |
REPEAT_DETERM_N n o (etac subset_trans THEN' rtac @{thm Collect_restrict}), |
|
48975
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff
changeset
|
476 |
rtac mp, etac bspec, rtac CollectI, |
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff
changeset
|
477 |
REPEAT_DETERM_N m o (rtac conjI THEN' atac), |
49306 | 478 |
CONJ_WRAP' (K (etac subset_trans THEN' rtac @{thm Collect_restrict})) alg_sets, |
48975
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff
changeset
|
479 |
CONJ_WRAP' (K (rtac ballI THEN' etac @{thm prop_restrict} THEN' atac)) alg_sets]; |
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff
changeset
|
480 |
|
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff
changeset
|
481 |
fun mk_induct_tac least_min_alg = |
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff
changeset
|
482 |
rtac ballI THEN' etac @{thm prop_restrict} THEN' rtac least_min_alg THEN' |
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff
changeset
|
483 |
stac alg_def THEN' |
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff
changeset
|
484 |
CONJ_WRAP' mk_alg_tac alg_sets; |
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff
changeset
|
485 |
in |
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff
changeset
|
486 |
CONJ_WRAP' mk_induct_tac least_min_algs 1 |
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff
changeset
|
487 |
end; |
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff
changeset
|
488 |
|
49501 | 489 |
fun mk_mor_Rep_tac ctor_defs copy bijs inver_Abss inver_Reps {context = ctxt, prems = _} = |
49504
df9b897fb254
renamed "iter"/"coiter" to "fold"/"unfold" (cf. Wadler)
blanchet
parents:
49502
diff
changeset
|
490 |
(K (unfold_thms_tac ctxt ctor_defs) THEN' rtac conjunct1 THEN' rtac copy THEN' |
48975
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff
changeset
|
491 |
EVERY' (map (fn bij => EVERY' [rtac bij, atac, etac bexI, rtac UNIV_I]) bijs) THEN' |
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff
changeset
|
492 |
EVERY' (map rtac inver_Abss) THEN' |
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff
changeset
|
493 |
EVERY' (map rtac inver_Reps)) 1; |
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff
changeset
|
494 |
|
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff
changeset
|
495 |
fun mk_mor_Abs_tac inv inver_Abss inver_Reps = |
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff
changeset
|
496 |
(rtac inv THEN' |
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff
changeset
|
497 |
EVERY' (map2 (fn inver_Abs => fn inver_Rep => |
49306 | 498 |
EVERY' [rtac conjI, rtac subset_UNIV, rtac conjI, rtac inver_Rep, rtac inver_Abs]) |
48975
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff
changeset
|
499 |
inver_Abss inver_Reps)) 1; |
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff
changeset
|
500 |
|
49504
df9b897fb254
renamed "iter"/"coiter" to "fold"/"unfold" (cf. Wadler)
blanchet
parents:
49502
diff
changeset
|
501 |
fun mk_mor_fold_tac cT ct fold_defs ex_mor mor = |
df9b897fb254
renamed "iter"/"coiter" to "fold"/"unfold" (cf. Wadler)
blanchet
parents:
49502
diff
changeset
|
502 |
(EVERY' (map stac fold_defs) THEN' EVERY' [rtac rev_mp, rtac ex_mor, rtac impI] THEN' |
df9b897fb254
renamed "iter"/"coiter" to "fold"/"unfold" (cf. Wadler)
blanchet
parents:
49502
diff
changeset
|
503 |
REPEAT_DETERM_N (length fold_defs) o etac exE THEN' |
48975
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff
changeset
|
504 |
rtac (Drule.instantiate' [SOME cT] [SOME ct] @{thm someI}) THEN' etac mor) 1; |
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff
changeset
|
505 |
|
49504
df9b897fb254
renamed "iter"/"coiter" to "fold"/"unfold" (cf. Wadler)
blanchet
parents:
49502
diff
changeset
|
506 |
fun mk_fold_unique_mor_tac type_defs init_unique_mors Reps mor_comp mor_Abs mor_fold = |
48975
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff
changeset
|
507 |
let |
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff
changeset
|
508 |
fun mk_unique type_def = |
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff
changeset
|
509 |
EVERY' [rtac @{thm surj_fun_eq}, rtac (type_def RS @{thm type_definition.Abs_image}), |
49227 | 510 |
rtac ballI, resolve_tac init_unique_mors, |
511 |
EVERY' (map (fn thm => atac ORELSE' rtac thm) Reps), |
|
48975
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff
changeset
|
512 |
rtac mor_comp, rtac mor_Abs, atac, |
49504
df9b897fb254
renamed "iter"/"coiter" to "fold"/"unfold" (cf. Wadler)
blanchet
parents:
49502
diff
changeset
|
513 |
rtac mor_comp, rtac mor_Abs, rtac mor_fold]; |
48975
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff
changeset
|
514 |
in |
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff
changeset
|
515 |
CONJ_WRAP' mk_unique type_defs 1 |
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff
changeset
|
516 |
end; |
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff
changeset
|
517 |
|
51761
4c9f08836d87
renamed "map_cong" axiom to "map_cong0" in preparation for real "map_cong"
blanchet
parents:
51739
diff
changeset
|
518 |
fun mk_dtor_o_ctor_tac dtor_def foldx map_comp_id map_cong0L ctor_o_folds = |
49504
df9b897fb254
renamed "iter"/"coiter" to "fold"/"unfold" (cf. Wadler)
blanchet
parents:
49502
diff
changeset
|
519 |
EVERY' [stac dtor_def, rtac ext, rtac trans, rtac o_apply, rtac trans, rtac foldx, |
51761
4c9f08836d87
renamed "map_cong" axiom to "map_cong0" in preparation for real "map_cong"
blanchet
parents:
51739
diff
changeset
|
520 |
rtac trans, rtac map_comp_id, rtac trans, rtac map_cong0L, |
49306 | 521 |
EVERY' (map (fn thm => rtac ballI THEN' rtac (trans OF [thm RS fun_cong, id_apply])) |
49504
df9b897fb254
renamed "iter"/"coiter" to "fold"/"unfold" (cf. Wadler)
blanchet
parents:
49502
diff
changeset
|
522 |
ctor_o_folds), |
49306 | 523 |
rtac sym, rtac id_apply] 1; |
48975
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff
changeset
|
524 |
|
49504
df9b897fb254
renamed "iter"/"coiter" to "fold"/"unfold" (cf. Wadler)
blanchet
parents:
49502
diff
changeset
|
525 |
fun mk_rec_tac rec_defs foldx fst_recs {context = ctxt, prems = _}= |
df9b897fb254
renamed "iter"/"coiter" to "fold"/"unfold" (cf. Wadler)
blanchet
parents:
49502
diff
changeset
|
526 |
unfold_thms_tac ctxt |
48975
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff
changeset
|
527 |
(rec_defs @ map (fn thm => thm RS @{thm convol_expand_snd}) fst_recs) THEN |
49504
df9b897fb254
renamed "iter"/"coiter" to "fold"/"unfold" (cf. Wadler)
blanchet
parents:
49502
diff
changeset
|
528 |
EVERY' [rtac trans, rtac o_apply, rtac trans, rtac (foldx RS @{thm arg_cong[of _ _ snd]}), |
48975
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff
changeset
|
529 |
rtac @{thm snd_convol'}] 1; |
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff
changeset
|
530 |
|
51739
3514b90d0a8b
(co)rec is (just as the (un)fold) the unique morphism;
traytel
parents:
49585
diff
changeset
|
531 |
fun mk_rec_unique_mor_tac rec_defs fst_recs fold_unique_mor {context = ctxt, prems = _} = |
3514b90d0a8b
(co)rec is (just as the (un)fold) the unique morphism;
traytel
parents:
49585
diff
changeset
|
532 |
unfold_thms_tac ctxt |
3514b90d0a8b
(co)rec is (just as the (un)fold) the unique morphism;
traytel
parents:
49585
diff
changeset
|
533 |
(rec_defs @ map (fn thm => thm RS @{thm convol_expand_snd'}) fst_recs) THEN |
3514b90d0a8b
(co)rec is (just as the (un)fold) the unique morphism;
traytel
parents:
49585
diff
changeset
|
534 |
etac fold_unique_mor 1; |
3514b90d0a8b
(co)rec is (just as the (un)fold) the unique morphism;
traytel
parents:
49585
diff
changeset
|
535 |
|
53290 | 536 |
fun mk_ctor_induct_tac ctxt m set_mapss init_induct morEs mor_Abs Rep_invs Abs_invs Reps = |
48975
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff
changeset
|
537 |
let |
53290 | 538 |
val n = length set_mapss; |
48975
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff
changeset
|
539 |
val ks = 1 upto n; |
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff
changeset
|
540 |
|
53290 | 541 |
fun mk_IH_tac Rep_inv Abs_inv set_map = |
49306 | 542 |
DETERM o EVERY' [dtac meta_mp, rtac (Rep_inv RS arg_cong RS subst), etac bspec, |
53290 | 543 |
dtac set_rev_mp, rtac equalityD1, rtac set_map, etac imageE, |
51798 | 544 |
hyp_subst_tac ctxt, rtac (Abs_inv RS ssubst), etac set_mp, atac, atac]; |
48975
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff
changeset
|
545 |
|
53290 | 546 |
fun mk_closed_tac (k, (morE, set_maps)) = |
48975
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff
changeset
|
547 |
EVERY' [select_prem_tac n (dtac asm_rl) k, rtac ballI, rtac impI, |
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff
changeset
|
548 |
rtac (mor_Abs RS morE RS arg_cong RS ssubst), atac, |
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff
changeset
|
549 |
REPEAT_DETERM o eresolve_tac [CollectE, conjE], dtac @{thm meta_spec}, |
53290 | 550 |
EVERY' (map3 mk_IH_tac Rep_invs Abs_invs (drop m set_maps)), atac]; |
48975
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff
changeset
|
551 |
|
49227 | 552 |
fun mk_induct_tac (Rep, Rep_inv) = |
553 |
EVERY' [rtac (Rep_inv RS arg_cong RS subst), etac (Rep RSN (2, bspec))]; |
|
48975
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff
changeset
|
554 |
in |
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff
changeset
|
555 |
(rtac mp THEN' rtac impI THEN' |
49227 | 556 |
DETERM o CONJ_WRAP_GEN' (etac conjE THEN' rtac conjI) mk_induct_tac (Reps ~~ Rep_invs) THEN' |
48975
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff
changeset
|
557 |
rtac init_induct THEN' |
53290 | 558 |
DETERM o CONJ_WRAP' mk_closed_tac (ks ~~ (morEs ~~ set_mapss))) 1 |
48975
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff
changeset
|
559 |
end; |
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff
changeset
|
560 |
|
49501 | 561 |
fun mk_ctor_induct2_tac cTs cts ctor_induct weak_ctor_inducts {context = ctxt, prems = _} = |
48975
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff
changeset
|
562 |
let |
49501 | 563 |
val n = length weak_ctor_inducts; |
48975
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff
changeset
|
564 |
val ks = 1 upto n; |
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff
changeset
|
565 |
fun mk_inner_induct_tac induct i = |
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff
changeset
|
566 |
EVERY' [rtac allI, fo_rtac induct ctxt, |
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff
changeset
|
567 |
select_prem_tac n (dtac @{thm meta_spec2}) i, |
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff
changeset
|
568 |
REPEAT_DETERM_N n o |
54742
7a86358a3c0b
proper context for basic Simplifier operations: rewrite_rule, rewrite_goals_rule, rewrite_goals_tac etc.;
wenzelm
parents:
53290
diff
changeset
|
569 |
EVERY' [dtac meta_mp THEN_ALL_NEW Goal.norm_hhf_tac ctxt, |
49306 | 570 |
REPEAT_DETERM o dtac @{thm meta_spec}, etac (spec RS meta_mp), atac], |
48975
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff
changeset
|
571 |
atac]; |
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff
changeset
|
572 |
in |
49501 | 573 |
EVERY' [rtac rev_mp, rtac (Drule.instantiate' cTs cts ctor_induct), |
574 |
EVERY' (map2 mk_inner_induct_tac weak_ctor_inducts ks), rtac impI, |
|
48975
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff
changeset
|
575 |
REPEAT_DETERM o eresolve_tac [conjE, allE], |
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff
changeset
|
576 |
CONJ_WRAP' (K atac) ks] 1 |
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff
changeset
|
577 |
end; |
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff
changeset
|
578 |
|
51761
4c9f08836d87
renamed "map_cong" axiom to "map_cong0" in preparation for real "map_cong"
blanchet
parents:
51739
diff
changeset
|
579 |
fun mk_map_tac m n foldx map_comp_id map_cong0 = |
49504
df9b897fb254
renamed "iter"/"coiter" to "fold"/"unfold" (cf. Wadler)
blanchet
parents:
49502
diff
changeset
|
580 |
EVERY' [rtac ext, rtac trans, rtac o_apply, rtac trans, rtac foldx, rtac trans, rtac o_apply, |
51761
4c9f08836d87
renamed "map_cong" axiom to "map_cong0" in preparation for real "map_cong"
blanchet
parents:
51739
diff
changeset
|
581 |
rtac trans, rtac (map_comp_id RS arg_cong), rtac trans, rtac (map_cong0 RS arg_cong), |
48975
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff
changeset
|
582 |
REPEAT_DETERM_N m o rtac refl, |
49306 | 583 |
REPEAT_DETERM_N n o (EVERY' (map rtac [trans, o_apply, id_apply])), |
48975
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff
changeset
|
584 |
rtac sym, rtac o_apply] 1; |
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff
changeset
|
585 |
|
54841
af71b753c459
express weak pullback property of bnfs only in terms of the relator
traytel
parents:
54793
diff
changeset
|
586 |
fun mk_ctor_map_unique_tac fold_unique sym_map_comps ctxt = |
52911 | 587 |
rtac fold_unique 1 THEN |
588 |
unfold_thms_tac ctxt (sym_map_comps @ @{thms o_assoc[symmetric] id_o o_id}) THEN |
|
589 |
ALLGOALS atac; |
|
48975
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff
changeset
|
590 |
|
49504
df9b897fb254
renamed "iter"/"coiter" to "fold"/"unfold" (cf. Wadler)
blanchet
parents:
49502
diff
changeset
|
591 |
fun mk_set_tac foldx = EVERY' [rtac ext, rtac trans, rtac o_apply, |
df9b897fb254
renamed "iter"/"coiter" to "fold"/"unfold" (cf. Wadler)
blanchet
parents:
49502
diff
changeset
|
592 |
rtac trans, rtac foldx, rtac sym, rtac o_apply] 1; |
48975
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff
changeset
|
593 |
|
53290 | 594 |
fun mk_ctor_set_tac set set_map set_maps = |
48975
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff
changeset
|
595 |
let |
53290 | 596 |
val n = length set_maps; |
48975
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff
changeset
|
597 |
fun mk_UN thm = rtac (thm RS @{thm arg_cong[of _ _ Union]} RS trans) THEN' |
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff
changeset
|
598 |
rtac @{thm Union_image_eq}; |
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff
changeset
|
599 |
in |
52659
58b87aa4dc3b
eliminate duplicated theorems (thanks to "Auto solve_direct" in jEdit)
traytel
parents:
52635
diff
changeset
|
600 |
EVERY' [rtac (set RS @{thm comp_eq_dest} RS trans), rtac Un_cong, |
53290 | 601 |
rtac (trans OF [set_map, trans_fun_cong_image_id_id_apply]), |
52659
58b87aa4dc3b
eliminate duplicated theorems (thanks to "Auto solve_direct" in jEdit)
traytel
parents:
52635
diff
changeset
|
602 |
REPEAT_DETERM_N (n - 1) o rtac Un_cong, |
53290 | 603 |
EVERY' (map mk_UN set_maps)] 1 |
48975
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff
changeset
|
604 |
end; |
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff
changeset
|
605 |
|
53290 | 606 |
fun mk_set_nat_tac m induct_tac set_mapss |
49542
b39354db8629
renamed low-level "set_simps" and "set_induct" to have "ctor" or "dtor" in the name
blanchet
parents:
49541
diff
changeset
|
607 |
ctor_maps csets ctor_sets i {context = ctxt, prems = _} = |
48975
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff
changeset
|
608 |
let |
49541 | 609 |
val n = length ctor_maps; |
48975
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff
changeset
|
610 |
|
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff
changeset
|
611 |
fun useIH set_nat = EVERY' [rtac trans, rtac @{thm image_UN}, rtac trans, rtac @{thm UN_cong}, |
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff
changeset
|
612 |
rtac refl, Goal.assume_rule_tac ctxt, rtac sym, rtac trans, rtac @{thm UN_cong}, |
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff
changeset
|
613 |
rtac set_nat, rtac refl, rtac @{thm UN_simps(10)}]; |
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff
changeset
|
614 |
|
49585
5c4a12550491
generate high-level "maps", "sets", and "rels" properties
blanchet
parents:
49544
diff
changeset
|
615 |
fun mk_set_nat cset ctor_map ctor_set set_nats = |
5c4a12550491
generate high-level "maps", "sets", and "rels" properties
blanchet
parents:
49544
diff
changeset
|
616 |
EVERY' [rtac trans, rtac @{thm image_cong}, rtac ctor_set, rtac refl, |
5c4a12550491
generate high-level "maps", "sets", and "rels" properties
blanchet
parents:
49544
diff
changeset
|
617 |
rtac sym, rtac (trans OF [ctor_map RS HOL_arg_cong cset, ctor_set RS trans]), |
52659
58b87aa4dc3b
eliminate duplicated theorems (thanks to "Auto solve_direct" in jEdit)
traytel
parents:
52635
diff
changeset
|
618 |
rtac sym, EVERY' (map rtac [trans, @{thm image_Un}, Un_cong]), |
48975
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff
changeset
|
619 |
rtac sym, rtac (nth set_nats (i - 1)), |
52659
58b87aa4dc3b
eliminate duplicated theorems (thanks to "Auto solve_direct" in jEdit)
traytel
parents:
52635
diff
changeset
|
620 |
REPEAT_DETERM_N (n - 1) o EVERY' (map rtac [trans, @{thm image_Un}, Un_cong]), |
48975
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff
changeset
|
621 |
EVERY' (map useIH (drop m set_nats))]; |
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff
changeset
|
622 |
in |
53290 | 623 |
(induct_tac THEN' EVERY' (map4 mk_set_nat csets ctor_maps ctor_sets set_mapss)) 1 |
48975
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff
changeset
|
624 |
end; |
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff
changeset
|
625 |
|
54841
af71b753c459
express weak pullback property of bnfs only in terms of the relator
traytel
parents:
54793
diff
changeset
|
626 |
fun mk_set_bd_tac m induct_tac bd_Cinfinite set_bdss ctor_sets i ctxt = |
48975
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff
changeset
|
627 |
let |
49542
b39354db8629
renamed low-level "set_simps" and "set_induct" to have "ctor" or "dtor" in the name
blanchet
parents:
49541
diff
changeset
|
628 |
val n = length ctor_sets; |
48975
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff
changeset
|
629 |
|
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff
changeset
|
630 |
fun useIH set_bd = EVERY' [rtac @{thm UNION_Cinfinite_bound}, rtac set_bd, rtac ballI, |
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff
changeset
|
631 |
Goal.assume_rule_tac ctxt, rtac bd_Cinfinite]; |
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff
changeset
|
632 |
|
49585
5c4a12550491
generate high-level "maps", "sets", and "rels" properties
blanchet
parents:
49544
diff
changeset
|
633 |
fun mk_set_nat ctor_set set_bds = |
5c4a12550491
generate high-level "maps", "sets", and "rels" properties
blanchet
parents:
49544
diff
changeset
|
634 |
EVERY' [rtac @{thm ordIso_ordLeq_trans}, rtac @{thm card_of_ordIso_subst}, rtac ctor_set, |
48975
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff
changeset
|
635 |
rtac (bd_Cinfinite RSN (3, @{thm Un_Cinfinite_bound})), rtac (nth set_bds (i - 1)), |
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff
changeset
|
636 |
REPEAT_DETERM_N (n - 1) o rtac (bd_Cinfinite 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
|
637 |
EVERY' (map useIH (drop m set_bds))]; |
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff
changeset
|
638 |
in |
49542
b39354db8629
renamed low-level "set_simps" and "set_induct" to have "ctor" or "dtor" in the name
blanchet
parents:
49541
diff
changeset
|
639 |
(induct_tac THEN' EVERY' (map2 mk_set_nat ctor_sets set_bdss)) 1 |
48975
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff
changeset
|
640 |
end; |
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff
changeset
|
641 |
|
51761
4c9f08836d87
renamed "map_cong" axiom to "map_cong0" in preparation for real "map_cong"
blanchet
parents:
51739
diff
changeset
|
642 |
fun mk_mcong_tac induct_tac set_setsss map_cong0s ctor_maps {context = ctxt, prems = _} = |
48975
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff
changeset
|
643 |
let |
49306 | 644 |
fun use_asm thm = EVERY' [etac bspec, etac set_rev_mp, rtac thm]; |
48975
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff
changeset
|
645 |
|
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff
changeset
|
646 |
fun useIH set_sets = EVERY' [rtac mp, Goal.assume_rule_tac ctxt, |
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff
changeset
|
647 |
CONJ_WRAP' (fn thm => |
49306 | 648 |
EVERY' [rtac ballI, etac bspec, etac set_rev_mp, etac thm]) set_sets]; |
48975
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff
changeset
|
649 |
|
51761
4c9f08836d87
renamed "map_cong" axiom to "map_cong0" in preparation for real "map_cong"
blanchet
parents:
51739
diff
changeset
|
650 |
fun mk_map_cong0 ctor_map map_cong0 set_setss = |
48975
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff
changeset
|
651 |
EVERY' [rtac impI, REPEAT_DETERM o etac conjE, |
51761
4c9f08836d87
renamed "map_cong" axiom to "map_cong0" in preparation for real "map_cong"
blanchet
parents:
51739
diff
changeset
|
652 |
rtac trans, rtac ctor_map, rtac trans, rtac (map_cong0 RS arg_cong), |
48975
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff
changeset
|
653 |
EVERY' (map use_asm (map hd set_setss)), |
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff
changeset
|
654 |
EVERY' (map useIH (transpose (map tl set_setss))), |
49541 | 655 |
rtac sym, rtac ctor_map]; |
48975
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff
changeset
|
656 |
in |
51761
4c9f08836d87
renamed "map_cong" axiom to "map_cong0" in preparation for real "map_cong"
blanchet
parents:
51739
diff
changeset
|
657 |
(induct_tac THEN' EVERY' (map3 mk_map_cong0 ctor_maps map_cong0s set_setsss)) 1 |
48975
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff
changeset
|
658 |
end; |
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff
changeset
|
659 |
|
54841
af71b753c459
express weak pullback property of bnfs only in terms of the relator
traytel
parents:
54793
diff
changeset
|
660 |
fun mk_le_rel_OO_tac m induct ctor_nchotomys ctor_Irels rel_mono_strongs rel_OOs |
af71b753c459
express weak pullback property of bnfs only in terms of the relator
traytel
parents:
54793
diff
changeset
|
661 |
{context = ctxt, prems = _} = |
af71b753c459
express weak pullback property of bnfs only in terms of the relator
traytel
parents:
54793
diff
changeset
|
662 |
EVERY' (rtac induct :: |
af71b753c459
express weak pullback property of bnfs only in terms of the relator
traytel
parents:
54793
diff
changeset
|
663 |
map4 (fn nchotomy => fn Irel => fn rel_mono => fn rel_OO => |
af71b753c459
express weak pullback property of bnfs only in terms of the relator
traytel
parents:
54793
diff
changeset
|
664 |
EVERY' [rtac impI, etac (nchotomy RS @{thm nchotomy_relcomppE}), |
af71b753c459
express weak pullback property of bnfs only in terms of the relator
traytel
parents:
54793
diff
changeset
|
665 |
REPEAT_DETERM_N 2 o dtac (Irel RS iffD1), rtac (Irel RS iffD2), |
af71b753c459
express weak pullback property of bnfs only in terms of the relator
traytel
parents:
54793
diff
changeset
|
666 |
rtac rel_mono, rtac (rel_OO RS @{thm predicate2_eqD} RS iffD2), |
af71b753c459
express weak pullback property of bnfs only in terms of the relator
traytel
parents:
54793
diff
changeset
|
667 |
rtac @{thm relcomppI}, atac, atac, |
af71b753c459
express weak pullback property of bnfs only in terms of the relator
traytel
parents:
54793
diff
changeset
|
668 |
REPEAT_DETERM_N m o EVERY' [rtac ballI, rtac ballI, rtac impI, atac], |
af71b753c459
express weak pullback property of bnfs only in terms of the relator
traytel
parents:
54793
diff
changeset
|
669 |
REPEAT_DETERM_N (length rel_OOs) o |
af71b753c459
express weak pullback property of bnfs only in terms of the relator
traytel
parents:
54793
diff
changeset
|
670 |
EVERY' [rtac ballI, rtac ballI, Goal.assume_rule_tac ctxt]]) |
af71b753c459
express weak pullback property of bnfs only in terms of the relator
traytel
parents:
54793
diff
changeset
|
671 |
ctor_nchotomys ctor_Irels rel_mono_strongs rel_OOs) 1; |
48975
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff
changeset
|
672 |
|
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff
changeset
|
673 |
(* BNF tactics *) |
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff
changeset
|
674 |
|
53270 | 675 |
fun mk_map_id0_tac map_id0s unique = |
48975
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff
changeset
|
676 |
(rtac sym THEN' rtac unique THEN' |
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff
changeset
|
677 |
EVERY' (map (fn thm => |
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff
changeset
|
678 |
EVERY' [rtac trans, rtac @{thm id_o}, rtac trans, rtac sym, rtac @{thm o_id}, |
53270 | 679 |
rtac (thm RS sym RS arg_cong)]) map_id0s)) 1; |
48975
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff
changeset
|
680 |
|
53287 | 681 |
fun mk_map_comp0_tac map_comp0s ctor_maps unique iplus1 = |
48975
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff
changeset
|
682 |
let |
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff
changeset
|
683 |
val i = iplus1 - 1; |
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff
changeset
|
684 |
val unique' = Thm.permute_prems 0 i unique; |
53288 | 685 |
val map_comp0s' = drop i map_comp0s @ take i map_comp0s; |
49541 | 686 |
val ctor_maps' = drop i ctor_maps @ take i ctor_maps; |
48975
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff
changeset
|
687 |
fun mk_comp comp simp = |
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff
changeset
|
688 |
EVERY' [rtac ext, rtac trans, rtac o_apply, rtac trans, rtac o_apply, |
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff
changeset
|
689 |
rtac trans, rtac (simp RS arg_cong), rtac trans, rtac simp, |
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff
changeset
|
690 |
rtac trans, rtac (comp RS arg_cong), rtac sym, rtac o_apply]; |
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff
changeset
|
691 |
in |
53288 | 692 |
(rtac sym THEN' rtac unique' THEN' EVERY' (map2 mk_comp map_comp0s' ctor_maps')) 1 |
48975
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff
changeset
|
693 |
end; |
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff
changeset
|
694 |
|
53289 | 695 |
fun mk_set_map0_tac set_nat = |
48975
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff
changeset
|
696 |
EVERY' (map rtac [ext, trans, o_apply, sym, trans, o_apply, set_nat]) 1; |
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff
changeset
|
697 |
|
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff
changeset
|
698 |
fun mk_bd_card_order_tac bd_card_orders = |
54793 | 699 |
CONJ_WRAP_GEN' (rtac @{thm card_order_csum}) rtac bd_card_orders 1; |
48975
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff
changeset
|
700 |
|
51798 | 701 |
fun mk_wit_tac ctxt n ctor_set wit = |
48975
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff
changeset
|
702 |
REPEAT_DETERM (atac 1 ORELSE |
49585
5c4a12550491
generate high-level "maps", "sets", and "rels" properties
blanchet
parents:
49544
diff
changeset
|
703 |
EVERY' [dtac set_rev_mp, rtac equalityD1, resolve_tac ctor_set, |
48975
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff
changeset
|
704 |
REPEAT_DETERM o |
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff
changeset
|
705 |
(TRY o REPEAT_DETERM o etac UnE THEN' TRY o etac @{thm UN_E} THEN' |
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff
changeset
|
706 |
(eresolve_tac wit ORELSE' |
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff
changeset
|
707 |
(dresolve_tac wit THEN' |
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff
changeset
|
708 |
(etac FalseE ORELSE' |
51798 | 709 |
EVERY' [hyp_subst_tac ctxt, dtac set_rev_mp, rtac equalityD1, resolve_tac ctor_set, |
48975
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff
changeset
|
710 |
REPEAT_DETERM_N n o etac UnE]))))] 1); |
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff
changeset
|
711 |
|
53287 | 712 |
fun mk_ctor_rel_tac ctxt in_Irels i in_rel map_comp0 map_cong0 ctor_map ctor_sets ctor_inject |
53289 | 713 |
ctor_dtor set_map0s ctor_set_incls ctor_set_set_inclss = |
48975
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff
changeset
|
714 |
let |
49544
24094fa47e0d
renamed "set_incl" etc. to have "ctor" or "dtor" in the name
blanchet
parents:
49543
diff
changeset
|
715 |
val m = length ctor_set_incls; |
24094fa47e0d
renamed "set_incl" etc. to have "ctor" or "dtor" in the name
blanchet
parents:
49543
diff
changeset
|
716 |
val n = length ctor_set_set_inclss; |
48975
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff
changeset
|
717 |
|
53289 | 718 |
val (passive_set_map0s, active_set_map0s) = chop m set_map0s; |
51893
596baae88a88
got rid of the set based relator---use (binary) predicate based relator instead
traytel
parents:
51812
diff
changeset
|
719 |
val in_Irel = nth in_Irels (i - 1); |
49501 | 720 |
val le_arg_cong_ctor_dtor = ctor_dtor RS arg_cong RS ord_eq_le_trans; |
721 |
val eq_arg_cong_ctor_dtor = ctor_dtor 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
|
722 |
val if_tac = |
51893
596baae88a88
got rid of the set based relator---use (binary) predicate based relator instead
traytel
parents:
51812
diff
changeset
|
723 |
EVERY' [dtac (in_Irel RS iffD1), REPEAT_DETERM o eresolve_tac [exE, conjE, CollectE], |
596baae88a88
got rid of the set based relator---use (binary) predicate based relator instead
traytel
parents:
51812
diff
changeset
|
724 |
rtac (in_rel RS iffD2), rtac exI, rtac conjI, rtac CollectI, |
53289 | 725 |
EVERY' (map2 (fn set_map0 => fn ctor_set_incl => |
726 |
EVERY' [rtac conjI, rtac ord_eq_le_trans, rtac set_map0, |
|
49306 | 727 |
rtac ord_eq_le_trans, rtac trans_fun_cong_image_id_id_apply, |
49544
24094fa47e0d
renamed "set_incl" etc. to have "ctor" or "dtor" in the name
blanchet
parents:
49543
diff
changeset
|
728 |
rtac (ctor_set_incl RS subset_trans), etac le_arg_cong_ctor_dtor]) |
53289 | 729 |
passive_set_map0s ctor_set_incls), |
730 |
CONJ_WRAP' (fn (in_Irel, (set_map0, ctor_set_set_incls)) => |
|
731 |
EVERY' [rtac ord_eq_le_trans, rtac set_map0, rtac @{thm image_subsetI}, rtac CollectI, |
|
51893
596baae88a88
got rid of the set based relator---use (binary) predicate based relator instead
traytel
parents:
51812
diff
changeset
|
732 |
rtac @{thm prod_caseI}, rtac (in_Irel RS iffD2), rtac exI, rtac conjI, rtac CollectI, |
48975
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff
changeset
|
733 |
CONJ_WRAP' (fn thm => |
49501 | 734 |
EVERY' (map etac [thm RS subset_trans, le_arg_cong_ctor_dtor])) |
49544
24094fa47e0d
renamed "set_incl" etc. to have "ctor" or "dtor" in the name
blanchet
parents:
49543
diff
changeset
|
735 |
ctor_set_set_incls, |
48975
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff
changeset
|
736 |
rtac conjI, rtac refl, rtac refl]) |
53289 | 737 |
(in_Irels ~~ (active_set_map0s ~~ ctor_set_set_inclss)), |
48975
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff
changeset
|
738 |
CONJ_WRAP' (fn conv => |
53287 | 739 |
EVERY' [rtac trans, rtac map_comp0, rtac trans, rtac map_cong0, |
48975
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff
changeset
|
740 |
REPEAT_DETERM_N m o rtac @{thm fun_cong[OF o_id]}, |
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff
changeset
|
741 |
REPEAT_DETERM_N n o EVERY' (map rtac [trans, o_apply, conv]), |
49541 | 742 |
rtac (ctor_inject RS iffD1), rtac trans, rtac sym, rtac ctor_map, |
49501 | 743 |
etac eq_arg_cong_ctor_dtor]) |
49306 | 744 |
fst_snd_convs]; |
48975
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff
changeset
|
745 |
val only_if_tac = |
51893
596baae88a88
got rid of the set based relator---use (binary) predicate based relator instead
traytel
parents:
51812
diff
changeset
|
746 |
EVERY' [dtac (in_rel RS iffD1), REPEAT_DETERM o eresolve_tac [exE, conjE, CollectE], |
596baae88a88
got rid of the set based relator---use (binary) predicate based relator instead
traytel
parents:
51812
diff
changeset
|
747 |
rtac (in_Irel RS iffD2), rtac exI, rtac conjI, rtac CollectI, |
53289 | 748 |
CONJ_WRAP' (fn (ctor_set, passive_set_map0) => |
49585
5c4a12550491
generate high-level "maps", "sets", and "rels" properties
blanchet
parents:
49544
diff
changeset
|
749 |
EVERY' [rtac ord_eq_le_trans, rtac ctor_set, rtac @{thm Un_least}, |
49306 | 750 |
rtac ord_eq_le_trans, rtac @{thm box_equals[OF _ refl]}, |
53289 | 751 |
rtac passive_set_map0, 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
|
752 |
CONJ_WRAP_GEN' (rtac (Thm.permute_prems 0 1 @{thm Un_least})) |
53289 | 753 |
(fn (active_set_map0, in_Irel) => EVERY' [rtac ord_eq_le_trans, |
754 |
rtac @{thm UN_cong[OF _ refl]}, rtac active_set_map0, rtac @{thm UN_least}, |
|
49306 | 755 |
dtac set_rev_mp, etac @{thm image_mono}, etac imageE, |
51893
596baae88a88
got rid of the set based relator---use (binary) predicate based relator instead
traytel
parents:
51812
diff
changeset
|
756 |
dtac @{thm ssubst_mem[OF pair_collapse]}, |
596baae88a88
got rid of the set based relator---use (binary) predicate based relator instead
traytel
parents:
51812
diff
changeset
|
757 |
REPEAT_DETERM o eresolve_tac (CollectE :: conjE :: |
596baae88a88
got rid of the set based relator---use (binary) predicate based relator instead
traytel
parents:
51812
diff
changeset
|
758 |
@{thms prod_caseE iffD1[OF Pair_eq, elim_format]}), |
596baae88a88
got rid of the set based relator---use (binary) predicate based relator instead
traytel
parents:
51812
diff
changeset
|
759 |
hyp_subst_tac ctxt, |
596baae88a88
got rid of the set based relator---use (binary) predicate based relator instead
traytel
parents:
51812
diff
changeset
|
760 |
dtac (in_Irel RS iffD1), dtac @{thm someI_ex}, REPEAT_DETERM o etac conjE, |
596baae88a88
got rid of the set based relator---use (binary) predicate based relator instead
traytel
parents:
51812
diff
changeset
|
761 |
TRY o |
596baae88a88
got rid of the set based relator---use (binary) predicate based relator instead
traytel
parents:
51812
diff
changeset
|
762 |
EVERY' [dtac (Thm.permute_prems 0 1 @{thm ssubst_mem}), atac, hyp_subst_tac ctxt], |
596baae88a88
got rid of the set based relator---use (binary) predicate based relator instead
traytel
parents:
51812
diff
changeset
|
763 |
REPEAT_DETERM o eresolve_tac [CollectE, conjE], atac]) |
53289 | 764 |
(rev (active_set_map0s ~~ in_Irels))]) |
765 |
(ctor_sets ~~ passive_set_map0s), |
|
48975
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff
changeset
|
766 |
rtac conjI, |
49541 | 767 |
REPEAT_DETERM_N 2 o EVERY' [rtac trans, rtac ctor_map, rtac (ctor_inject RS iffD2), |
53287 | 768 |
rtac trans, rtac map_comp0, rtac trans, rtac map_cong0, |
48975
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff
changeset
|
769 |
REPEAT_DETERM_N m o rtac @{thm fun_cong[OF o_id]}, |
51893
596baae88a88
got rid of the set based relator---use (binary) predicate based relator instead
traytel
parents:
51812
diff
changeset
|
770 |
EVERY' (map (fn in_Irel => EVERY' [rtac trans, rtac o_apply, dtac set_rev_mp, atac, |
596baae88a88
got rid of the set based relator---use (binary) predicate based relator instead
traytel
parents:
51812
diff
changeset
|
771 |
dtac @{thm ssubst_mem[OF pair_collapse]}, |
596baae88a88
got rid of the set based relator---use (binary) predicate based relator instead
traytel
parents:
51812
diff
changeset
|
772 |
REPEAT_DETERM o |
596baae88a88
got rid of the set based relator---use (binary) predicate based relator instead
traytel
parents:
51812
diff
changeset
|
773 |
eresolve_tac (CollectE :: conjE :: @{thms prod_caseE iffD1[OF Pair_eq, elim_format]}), |
596baae88a88
got rid of the set based relator---use (binary) predicate based relator instead
traytel
parents:
51812
diff
changeset
|
774 |
hyp_subst_tac ctxt, |
596baae88a88
got rid of the set based relator---use (binary) predicate based relator instead
traytel
parents:
51812
diff
changeset
|
775 |
dtac (in_Irel RS iffD1), dtac @{thm someI_ex}, REPEAT_DETERM o etac conjE, atac]) |
596baae88a88
got rid of the set based relator---use (binary) predicate based relator instead
traytel
parents:
51812
diff
changeset
|
776 |
in_Irels), |
48975
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff
changeset
|
777 |
atac]] |
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff
changeset
|
778 |
in |
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff
changeset
|
779 |
EVERY' [rtac iffI, if_tac, only_if_tac] 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 |
|
52506 | 782 |
fun mk_rel_induct_tac m ctor_induct2 ks ctor_rels rel_mono_strongs {context = ctxt, prems = IHs} = |
51918 | 783 |
let val n = length ks; |
784 |
in |
|
54998 | 785 |
unfold_tac ctxt @{thms le_fun_def le_bool_def all_simps(1,2)[symmetric]} THEN |
51918 | 786 |
EVERY' [REPEAT_DETERM o rtac allI, rtac ctor_induct2, |
52506 | 787 |
EVERY' (map3 (fn IH => fn ctor_rel => fn rel_mono_strong => |
788 |
EVERY' [rtac impI, dtac (ctor_rel RS iffD1), rtac (IH RS @{thm spec2} RS mp), |
|
789 |
etac rel_mono_strong, |
|
51918 | 790 |
REPEAT_DETERM_N m o rtac @{thm ballI[OF ballI[OF imp_refl]]}, |
791 |
EVERY' (map (fn j => |
|
792 |
EVERY' [select_prem_tac n (dtac asm_rl) j, rtac @{thm ballI[OF ballI]}, |
|
793 |
Goal.assume_rule_tac ctxt]) ks)]) |
|
52506 | 794 |
IHs ctor_rels rel_mono_strongs)] 1 |
51918 | 795 |
end; |
796 |
||
52731 | 797 |
fun mk_fold_transfer_tac m rel_induct map_transfers folds {context = ctxt, prems = _} = |
798 |
let |
|
799 |
val n = length map_transfers; |
|
800 |
in |
|
801 |
unfold_thms_tac ctxt |
|
802 |
@{thms fun_rel_def_butlast all_conj_distrib[symmetric] imp_conjR[symmetric]} THEN |
|
803 |
unfold_thms_tac ctxt @{thms fun_rel_iff_leq_vimage2p} THEN |
|
804 |
HEADGOAL (EVERY' |
|
805 |
[REPEAT_DETERM o resolve_tac [allI, impI], rtac rel_induct, |
|
806 |
EVERY' (map (fn map_transfer => EVERY' |
|
807 |
[REPEAT_DETERM o resolve_tac [allI, impI, @{thm vimage2pI}], |
|
808 |
SELECT_GOAL (unfold_thms_tac ctxt folds), |
|
809 |
etac @{thm predicate2D_vimage2p}, |
|
810 |
rtac (funpow (m + n + 1) (fn thm => thm RS @{thm fun_relD}) map_transfer), |
|
811 |
REPEAT_DETERM_N m o rtac @{thm id_transfer}, |
|
812 |
REPEAT_DETERM_N n o rtac @{thm vimage2p_fun_rel}, |
|
813 |
atac]) |
|
814 |
map_transfers)]) |
|
815 |
end; |
|
816 |
||
48975
7f79f94a432c
added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff
changeset
|
817 |
end; |