src/HOL/Import/HOL4Setup.thy
 author obua Mon Sep 12 15:52:00 2005 +0200 (2005-09-12) changeset 17322 781abf7011e6 parent 16417 9bc16273c2d4 child 17801 30cbd2685e73 permissions -rw-r--r--
```     1 (*  Title:      HOL/Import/HOL4Setup.thy
```
```     2     ID:         \$Id\$
```
```     3     Author:     Sebastian Skalberg (TU Muenchen)
```
```     4 *)
```
```     5
```
```     6 theory HOL4Setup imports MakeEqual
```
```     7   uses ("proof_kernel.ML") ("replay.ML") ("hol4rews.ML") ("import_package.ML") begin
```
```     8
```
```     9 section {* General Setup *}
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```    10
```
```    11 lemma eq_imp: "P = Q \<Longrightarrow> P \<longrightarrow> Q"
```
```    12   by auto
```
```    13
```
```    14 lemma HOLallI: "(!! bogus. P bogus) \<Longrightarrow> (ALL bogus. P bogus)"
```
```    15 proof -
```
```    16   assume "!! bogus. P bogus"
```
```    17   thus "ALL x. P x"
```
```    18     ..
```
```    19 qed
```
```    20
```
```    21 consts
```
```    22   ONE_ONE :: "('a => 'b) => bool"
```
```    23   ONTO    :: "('a => 'b) => bool"
```
```    24
```
```    25 defs
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```    26   ONE_ONE_DEF: "ONE_ONE f == ALL x y. f x = f y --> x = y"
```
```    27
```
```    28 lemma ONE_ONE_rew: "ONE_ONE f = inj_on f UNIV"
```
```    29   by (simp add: ONE_ONE_DEF inj_on_def)
```
```    30
```
```    31 lemma INFINITY_AX: "EX (f::ind \<Rightarrow> ind). (inj f & ~(surj f))"
```
```    32 proof (rule exI,safe)
```
```    33   show "inj Suc_Rep"
```
```    34     by (rule inj_Suc_Rep)
```
```    35 next
```
```    36   assume "surj Suc_Rep"
```
```    37   hence "ALL y. EX x. y = Suc_Rep x"
```
```    38     by (simp add: surj_def)
```
```    39   hence "EX x. Zero_Rep = Suc_Rep x"
```
```    40     by (rule spec)
```
```    41   thus False
```
```    42   proof (rule exE)
```
```    43     fix x
```
```    44     assume "Zero_Rep = Suc_Rep x"
```
```    45     hence "Suc_Rep x = Zero_Rep"
```
```    46       ..
```
```    47     with Suc_Rep_not_Zero_Rep
```
```    48     show False
```
```    49       ..
```
```    50   qed
```
```    51 qed
```
```    52
```
```    53 lemma EXISTS_DEF: "Ex P = P (Eps P)"
```
```    54 proof (rule iffI)
```
```    55   assume "Ex P"
```
```    56   thus "P (Eps P)"
```
```    57     ..
```
```    58 next
```
```    59   assume "P (Eps P)"
```
```    60   thus "Ex P"
```
```    61     ..
```
```    62 qed
```
```    63
```
```    64 consts
```
```    65   TYPE_DEFINITION :: "('a => bool) => ('b => 'a) => bool"
```
```    66
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```    67 defs
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```    68   TYPE_DEFINITION: "TYPE_DEFINITION p rep == ((ALL x y. (rep x = rep y) --> (x = y)) & (ALL x. (p x = (EX y. x = rep y))))"
```
```    69
```
```    70 lemma ex_imp_nonempty: "Ex P ==> EX x. x : (Collect P)"
```
```    71   by simp
```
```    72
```
```    73 lemma light_ex_imp_nonempty: "P t ==> EX x. x : (Collect P)"
```
```    74 proof -
```
```    75   assume "P t"
```
```    76   hence "EX x. P x"
```
```    77     ..
```
```    78   thus ?thesis
```
```    79     by (rule ex_imp_nonempty)
```
```    80 qed
```
```    81
```
```    82 lemma light_imp_as: "[| Q --> P; P --> Q |] ==> P = Q"
```
```    83   by blast
```
```    84
```
```    85 lemma typedef_hol2hol4:
```
```    86   assumes a: "type_definition (Rep::'a=>'b) Abs (Collect P)"
```
```    87   shows "EX rep. TYPE_DEFINITION P (rep::'a=>'b)"
```
```    88 proof -
```
```    89   from a
```
```    90   have td: "(ALL x. P (Rep x)) & (ALL x. Abs (Rep x) = x) & (ALL y. P y \<longrightarrow> Rep (Abs y) = y)"
```
```    91     by (simp add: type_definition_def)
```
```    92   have ed: "TYPE_DEFINITION P Rep"
```
```    93   proof (auto simp add: TYPE_DEFINITION)
```
```    94     fix x y
```
```    95     assume "Rep x = Rep y"
```
```    96     from td have "x = Abs (Rep x)"
```
```    97       by auto
```
```    98     also have "Abs (Rep x) = Abs (Rep y)"
```
```    99       by (simp add: prems)
```
```   100     also from td have "Abs (Rep y) = y"
```
```   101       by auto
```
```   102     finally show "x = y" .
```
```   103   next
```
```   104     fix x
```
```   105     assume "P x"
```
```   106     with td
```
```   107     have "Rep (Abs x) = x"
```
```   108       by auto
```
```   109     hence "x = Rep (Abs x)"
```
```   110       ..
```
```   111     thus "EX y. x = Rep y"
```
```   112       ..
```
```   113   next
```
```   114     fix y
```
```   115     from td
```
```   116     show "P (Rep y)"
```
```   117       by auto
```
```   118   qed
```
```   119   show ?thesis
```
```   120     apply (rule exI [of _ Rep])
```
```   121     apply (rule ed)
```
```   122     .
```
```   123 qed
```
```   124
```
```   125 lemma typedef_hol2hollight:
```
```   126   assumes a: "type_definition (Rep::'a=>'b) Abs (Collect P)"
```
```   127   shows "(Abs (Rep a) = a) & (P r = (Rep (Abs r) = r))"
```
```   128 proof
```
```   129   from a
```
```   130   show "Abs (Rep a) = a"
```
```   131     by (rule type_definition.Rep_inverse)
```
```   132 next
```
```   133   show "P r = (Rep (Abs r) = r)"
```
```   134   proof
```
```   135     assume "P r"
```
```   136     hence "r \<in> (Collect P)"
```
```   137       by simp
```
```   138     with a
```
```   139     show "Rep (Abs r) = r"
```
```   140       by (rule type_definition.Abs_inverse)
```
```   141   next
```
```   142     assume ra: "Rep (Abs r) = r"
```
```   143     from a
```
```   144     have "Rep (Abs r) \<in> (Collect P)"
```
```   145       by (rule type_definition.Rep)
```
```   146     thus "P r"
```
```   147       by (simp add: ra)
```
```   148   qed
```
```   149 qed
```
```   150
```
```   151 lemma termspec_help: "[| Ex P ; c == Eps P |] ==> P c"
```
```   152   apply simp
```
```   153   apply (rule someI_ex)
```
```   154   .
```
```   155
```
```   156 lemma typedef_helper: "EX x. P x \<Longrightarrow> EX x. x \<in> (Collect P)"
```
```   157   by simp
```
```   158
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```   159 use "hol4rews.ML"
```
```   160
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```   161 setup hol4_setup
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```   162 parse_ast_translation smarter_trueprop_parsing
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```   163
```
```   164 use "proof_kernel.ML"
```
```   165 use "replay.ML"
```
```   166 use "import_package.ML"
```
```   167
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```   168 setup ImportPackage.setup
```
```   169
```
```   170 end
```