src/HOL/Import/HOL4Setup.thy
 author haftmann Mon Nov 29 13:44:54 2010 +0100 (2010-11-29) changeset 40815 6e2d17cc0d1d parent 34208 a7acd6c68d9b child 41550 efa734d9b221 permissions -rw-r--r--
equivI has replaced equiv.intro
```     1 (*  Title:      HOL/Import/HOL4Setup.thy
```
```     2     Author:     Sebastian Skalberg (TU Muenchen)
```
```     3 *)
```
```     4
```
```     5 theory HOL4Setup imports MakeEqual ImportRecorder
```
```     6   uses ("proof_kernel.ML") ("replay.ML") ("hol4rews.ML") ("import.ML") begin
```
```     7
```
```     8 section {* General Setup *}
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```     9
```
```    10 lemma eq_imp: "P = Q \<Longrightarrow> P \<longrightarrow> Q"
```
```    11   by auto
```
```    12
```
```    13 lemma HOLallI: "(!! bogus. P bogus) \<Longrightarrow> (ALL bogus. P bogus)"
```
```    14 proof -
```
```    15   assume "!! bogus. P bogus"
```
```    16   thus "ALL x. P x"
```
```    17     ..
```
```    18 qed
```
```    19
```
```    20 consts
```
```    21   ONE_ONE :: "('a => 'b) => bool"
```
```    22
```
```    23 defs
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```    24   ONE_ONE_DEF: "ONE_ONE f == ALL x y. f x = f y --> x = y"
```
```    25
```
```    26 lemma ONE_ONE_rew: "ONE_ONE f = inj_on f UNIV"
```
```    27   by (simp add: ONE_ONE_DEF inj_on_def)
```
```    28
```
```    29 lemma INFINITY_AX: "EX (f::ind \<Rightarrow> ind). (inj f & ~(surj f))"
```
```    30 proof (rule exI,safe)
```
```    31   show "inj Suc_Rep"
```
```    32     by (rule injI) (rule Suc_Rep_inject)
```
```    33 next
```
```    34   assume "surj Suc_Rep"
```
```    35   hence "ALL y. EX x. y = Suc_Rep x"
```
```    36     by (simp add: surj_def)
```
```    37   hence "EX x. Zero_Rep = Suc_Rep x"
```
```    38     by (rule spec)
```
```    39   thus False
```
```    40   proof (rule exE)
```
```    41     fix x
```
```    42     assume "Zero_Rep = Suc_Rep x"
```
```    43     hence "Suc_Rep x = Zero_Rep"
```
```    44       ..
```
```    45     with Suc_Rep_not_Zero_Rep
```
```    46     show False
```
```    47       ..
```
```    48   qed
```
```    49 qed
```
```    50
```
```    51 lemma EXISTS_DEF: "Ex P = P (Eps P)"
```
```    52 proof (rule iffI)
```
```    53   assume "Ex P"
```
```    54   thus "P (Eps P)"
```
```    55     ..
```
```    56 next
```
```    57   assume "P (Eps P)"
```
```    58   thus "Ex P"
```
```    59     ..
```
```    60 qed
```
```    61
```
```    62 consts
```
```    63   TYPE_DEFINITION :: "('a => bool) => ('b => 'a) => bool"
```
```    64
```
```    65 defs
```
```    66   TYPE_DEFINITION: "TYPE_DEFINITION p rep == ((ALL x y. (rep x = rep y) --> (x = y)) & (ALL x. (p x = (EX y. x = rep y))))"
```
```    67
```
```    68 lemma ex_imp_nonempty: "Ex P ==> EX x. x : (Collect P)"
```
```    69   by simp
```
```    70
```
```    71 lemma light_ex_imp_nonempty: "P t ==> EX x. x : (Collect P)"
```
```    72 proof -
```
```    73   assume "P t"
```
```    74   hence "EX x. P x"
```
```    75     ..
```
```    76   thus ?thesis
```
```    77     by (rule ex_imp_nonempty)
```
```    78 qed
```
```    79
```
```    80 lemma light_imp_as: "[| Q --> P; P --> Q |] ==> P = Q"
```
```    81   by blast
```
```    82
```
```    83 lemma typedef_hol2hol4:
```
```    84   assumes a: "type_definition (Rep::'a=>'b) Abs (Collect P)"
```
```    85   shows "EX rep. TYPE_DEFINITION P (rep::'a=>'b)"
```
```    86 proof -
```
```    87   from a
```
```    88   have td: "(ALL x. P (Rep x)) & (ALL x. Abs (Rep x) = x) & (ALL y. P y \<longrightarrow> Rep (Abs y) = y)"
```
```    89     by (simp add: type_definition_def)
```
```    90   have ed: "TYPE_DEFINITION P Rep"
```
```    91   proof (auto simp add: TYPE_DEFINITION)
```
```    92     fix x y
```
```    93     assume "Rep x = Rep y"
```
```    94     from td have "x = Abs (Rep x)"
```
```    95       by auto
```
```    96     also have "Abs (Rep x) = Abs (Rep y)"
```
```    97       by (simp add: prems)
```
```    98     also from td have "Abs (Rep y) = y"
```
```    99       by auto
```
```   100     finally show "x = y" .
```
```   101   next
```
```   102     fix x
```
```   103     assume "P x"
```
```   104     with td
```
```   105     have "Rep (Abs x) = x"
```
```   106       by auto
```
```   107     hence "x = Rep (Abs x)"
```
```   108       ..
```
```   109     thus "EX y. x = Rep y"
```
```   110       ..
```
```   111   next
```
```   112     fix y
```
```   113     from td
```
```   114     show "P (Rep y)"
```
```   115       by auto
```
```   116   qed
```
```   117   show ?thesis
```
```   118     apply (rule exI [of _ Rep])
```
```   119     apply (rule ed)
```
```   120     .
```
```   121 qed
```
```   122
```
```   123 lemma typedef_hol2hollight:
```
```   124   assumes a: "type_definition (Rep::'a=>'b) Abs (Collect P)"
```
```   125   shows "(Abs (Rep a) = a) & (P r = (Rep (Abs r) = r))"
```
```   126 proof
```
```   127   from a
```
```   128   show "Abs (Rep a) = a"
```
```   129     by (rule type_definition.Rep_inverse)
```
```   130 next
```
```   131   show "P r = (Rep (Abs r) = r)"
```
```   132   proof
```
```   133     assume "P r"
```
```   134     hence "r \<in> (Collect P)"
```
```   135       by simp
```
```   136     with a
```
```   137     show "Rep (Abs r) = r"
```
```   138       by (rule type_definition.Abs_inverse)
```
```   139   next
```
```   140     assume ra: "Rep (Abs r) = r"
```
```   141     from a
```
```   142     have "Rep (Abs r) \<in> (Collect P)"
```
```   143       by (rule type_definition.Rep)
```
```   144     thus "P r"
```
```   145       by (simp add: ra)
```
```   146   qed
```
```   147 qed
```
```   148
```
```   149 lemma termspec_help: "[| Ex P ; c == Eps P |] ==> P c"
```
```   150   apply simp
```
```   151   apply (rule someI_ex)
```
```   152   .
```
```   153
```
```   154 lemma typedef_helper: "EX x. P x \<Longrightarrow> EX x. x \<in> (Collect P)"
```
```   155   by simp
```
```   156
```
```   157 use "hol4rews.ML"
```
```   158
```
```   159 setup hol4_setup
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```   160 parse_ast_translation smarter_trueprop_parsing
```
```   161
```
```   162 use "proof_kernel.ML"
```
```   163 use "replay.ML"
```
```   164 use "import.ML"
```
```   165
```
```   166 setup Import.setup
```
```   167
```
```   168 end
```