src/HOL/Import/HOL4Setup.thy
 author wenzelm Mon Mar 16 18:24:30 2009 +0100 (2009-03-16) changeset 30549 d2d7874648bd parent 20326 cbf31171c147 child 31723 f5cafe803b55 permissions -rw-r--r--
simplified method setup;
```     1 (*  Title:      HOL/Import/HOL4Setup.thy
```
```     2     ID:         \$Id\$
```
```     3     Author:     Sebastian Skalberg (TU Muenchen)
```
```     4 *)
```
```     5
```
```     6 theory HOL4Setup imports MakeEqual ImportRecorder
```
```     7   uses ("proof_kernel.ML") ("replay.ML") ("hol4rews.ML") ("import_package.ML") begin
```
```     8
```
```     9 section {* General Setup *}
```
```    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
```
```    24 defs
```
```    25   ONE_ONE_DEF: "ONE_ONE f == ALL x y. f x = f y --> x = y"
```
```    26
```
```    27 lemma ONE_ONE_rew: "ONE_ONE f = inj_on f UNIV"
```
```    28   by (simp add: ONE_ONE_DEF inj_on_def)
```
```    29
```
```    30 lemma INFINITY_AX: "EX (f::ind \<Rightarrow> ind). (inj f & ~(surj f))"
```
```    31 proof (rule exI,safe)
```
```    32   show "inj Suc_Rep"
```
```    33     by (rule inj_Suc_Rep)
```
```    34 next
```
```    35   assume "surj Suc_Rep"
```
```    36   hence "ALL y. EX x. y = Suc_Rep x"
```
```    37     by (simp add: surj_def)
```
```    38   hence "EX x. Zero_Rep = Suc_Rep x"
```
```    39     by (rule spec)
```
```    40   thus False
```
```    41   proof (rule exE)
```
```    42     fix x
```
```    43     assume "Zero_Rep = Suc_Rep x"
```
```    44     hence "Suc_Rep x = Zero_Rep"
```
```    45       ..
```
```    46     with Suc_Rep_not_Zero_Rep
```
```    47     show False
```
```    48       ..
```
```    49   qed
```
```    50 qed
```
```    51
```
```    52 lemma EXISTS_DEF: "Ex P = P (Eps P)"
```
```    53 proof (rule iffI)
```
```    54   assume "Ex P"
```
```    55   thus "P (Eps P)"
```
```    56     ..
```
```    57 next
```
```    58   assume "P (Eps P)"
```
```    59   thus "Ex P"
```
```    60     ..
```
```    61 qed
```
```    62
```
```    63 consts
```
```    64   TYPE_DEFINITION :: "('a => bool) => ('b => 'a) => bool"
```
```    65
```
```    66 defs
```
```    67   TYPE_DEFINITION: "TYPE_DEFINITION p rep == ((ALL x y. (rep x = rep y) --> (x = y)) & (ALL x. (p x = (EX y. x = rep y))))"
```
```    68
```
```    69 lemma ex_imp_nonempty: "Ex P ==> EX x. x : (Collect P)"
```
```    70   by simp
```
```    71
```
```    72 lemma light_ex_imp_nonempty: "P t ==> EX x. x : (Collect P)"
```
```    73 proof -
```
```    74   assume "P t"
```
```    75   hence "EX x. P x"
```
```    76     ..
```
```    77   thus ?thesis
```
```    78     by (rule ex_imp_nonempty)
```
```    79 qed
```
```    80
```
```    81 lemma light_imp_as: "[| Q --> P; P --> Q |] ==> P = Q"
```
```    82   by blast
```
```    83
```
```    84 lemma typedef_hol2hol4:
```
```    85   assumes a: "type_definition (Rep::'a=>'b) Abs (Collect P)"
```
```    86   shows "EX rep. TYPE_DEFINITION P (rep::'a=>'b)"
```
```    87 proof -
```
```    88   from a
```
```    89   have td: "(ALL x. P (Rep x)) & (ALL x. Abs (Rep x) = x) & (ALL y. P y \<longrightarrow> Rep (Abs y) = y)"
```
```    90     by (simp add: type_definition_def)
```
```    91   have ed: "TYPE_DEFINITION P Rep"
```
```    92   proof (auto simp add: TYPE_DEFINITION)
```
```    93     fix x y
```
```    94     assume "Rep x = Rep y"
```
```    95     from td have "x = Abs (Rep x)"
```
```    96       by auto
```
```    97     also have "Abs (Rep x) = Abs (Rep y)"
```
```    98       by (simp add: prems)
```
```    99     also from td have "Abs (Rep y) = y"
```
```   100       by auto
```
```   101     finally show "x = y" .
```
```   102   next
```
```   103     fix x
```
```   104     assume "P x"
```
```   105     with td
```
```   106     have "Rep (Abs x) = x"
```
```   107       by auto
```
```   108     hence "x = Rep (Abs x)"
```
```   109       ..
```
```   110     thus "EX y. x = Rep y"
```
```   111       ..
```
```   112   next
```
```   113     fix y
```
```   114     from td
```
```   115     show "P (Rep y)"
```
```   116       by auto
```
```   117   qed
```
```   118   show ?thesis
```
```   119     apply (rule exI [of _ Rep])
```
```   120     apply (rule ed)
```
```   121     .
```
```   122 qed
```
```   123
```
```   124 lemma typedef_hol2hollight:
```
```   125   assumes a: "type_definition (Rep::'a=>'b) Abs (Collect P)"
```
```   126   shows "(Abs (Rep a) = a) & (P r = (Rep (Abs r) = r))"
```
```   127 proof
```
```   128   from a
```
```   129   show "Abs (Rep a) = a"
```
```   130     by (rule type_definition.Rep_inverse)
```
```   131 next
```
```   132   show "P r = (Rep (Abs r) = r)"
```
```   133   proof
```
```   134     assume "P r"
```
```   135     hence "r \<in> (Collect P)"
```
```   136       by simp
```
```   137     with a
```
```   138     show "Rep (Abs r) = r"
```
```   139       by (rule type_definition.Abs_inverse)
```
```   140   next
```
```   141     assume ra: "Rep (Abs r) = r"
```
```   142     from a
```
```   143     have "Rep (Abs r) \<in> (Collect P)"
```
```   144       by (rule type_definition.Rep)
```
```   145     thus "P r"
```
```   146       by (simp add: ra)
```
```   147   qed
```
```   148 qed
```
```   149
```
```   150 lemma termspec_help: "[| Ex P ; c == Eps P |] ==> P c"
```
```   151   apply simp
```
```   152   apply (rule someI_ex)
```
```   153   .
```
```   154
```
```   155 lemma typedef_helper: "EX x. P x \<Longrightarrow> EX x. x \<in> (Collect P)"
```
```   156   by simp
```
```   157
```
```   158 use "hol4rews.ML"
```
```   159
```
```   160 setup hol4_setup
```
```   161 parse_ast_translation smarter_trueprop_parsing
```
```   162
```
```   163 use "proof_kernel.ML"
```
```   164 use "replay.ML"
```
```   165 use "import_package.ML"
```
```   166
```
```   167 setup ImportPackage.setup
```
```   168
```
```   169 end
```