src/HOL/Import/HOL4Setup.thy
 author skalberg Fri Apr 02 17:37:45 2004 +0200 (2004-04-02) changeset 14516 a183dec876ab child 14620 1be590fd2422 permissions -rw-r--r--
```     1 theory HOL4Setup = MakeEqual
```
```     2   files ("proof_kernel.ML") ("replay.ML") ("hol4rews.ML") ("import_package.ML"):
```
```     3
```
```     4 section {* General Setup *}
```
```     5
```
```     6 lemma eq_imp: "P = Q \<Longrightarrow> P \<longrightarrow> Q"
```
```     7   by auto
```
```     8
```
```     9 lemma HOLallI: "(!! bogus. P bogus) \<Longrightarrow> (ALL bogus. P bogus)"
```
```    10 proof -
```
```    11   assume "!! bogus. P bogus"
```
```    12   thus "ALL x. P x"
```
```    13     ..
```
```    14 qed
```
```    15
```
```    16 consts
```
```    17   ONE_ONE :: "('a => 'b) => bool"
```
```    18   ONTO    :: "('a => 'b) => bool"
```
```    19
```
```    20 defs
```
```    21   ONE_ONE_DEF: "ONE_ONE f == ALL x y. f x = f y --> x = y"
```
```    22   ONTO_DEF   : "ONTO f == ALL y. EX x. y = f x"
```
```    23
```
```    24 lemma ONE_ONE_rew: "ONE_ONE f = inj_on f UNIV"
```
```    25   by (simp add: ONE_ONE_DEF inj_on_def)
```
```    26
```
```    27 lemma INFINITY_AX: "EX (f::ind \<Rightarrow> ind). (inj f & ~(ONTO f))"
```
```    28 proof (rule exI,safe)
```
```    29   show "inj Suc_Rep"
```
```    30     by (rule inj_Suc_Rep)
```
```    31 next
```
```    32   assume "ONTO Suc_Rep"
```
```    33   hence "ALL y. EX x. y = Suc_Rep x"
```
```    34     by (simp add: ONTO_DEF surj_def)
```
```    35   hence "EX x. Zero_Rep = Suc_Rep x"
```
```    36     by (rule spec)
```
```    37   thus False
```
```    38   proof (rule exE)
```
```    39     fix x
```
```    40     assume "Zero_Rep = Suc_Rep x"
```
```    41     hence "Suc_Rep x = Zero_Rep"
```
```    42       ..
```
```    43     with Suc_Rep_not_Zero_Rep
```
```    44     show False
```
```    45       ..
```
```    46   qed
```
```    47 qed
```
```    48
```
```    49 lemma EXISTS_DEF: "Ex P = P (Eps P)"
```
```    50 proof (rule iffI)
```
```    51   assume "Ex P"
```
```    52   thus "P (Eps P)"
```
```    53     ..
```
```    54 next
```
```    55   assume "P (Eps P)"
```
```    56   thus "Ex P"
```
```    57     ..
```
```    58 qed
```
```    59
```
```    60 consts
```
```    61   TYPE_DEFINITION :: "('a => bool) => ('b => 'a) => bool"
```
```    62
```
```    63 defs
```
```    64   TYPE_DEFINITION: "TYPE_DEFINITION p rep == ((ALL x y. (rep x = rep y) --> (x = y)) & (ALL x. (p x = (EX y. x = rep y))))"
```
```    65
```
```    66 lemma ex_imp_nonempty: "Ex P ==> EX x. x : (Collect P)"
```
```    67   by simp
```
```    68
```
```    69 lemma light_ex_imp_nonempty: "P t ==> EX x. x : (Collect P)"
```
```    70 proof -
```
```    71   assume "P t"
```
```    72   hence "EX x. P x"
```
```    73     ..
```
```    74   thus ?thesis
```
```    75     by (rule ex_imp_nonempty)
```
```    76 qed
```
```    77
```
```    78 lemma light_imp_as: "[| Q --> P; P --> Q |] ==> P = Q"
```
```    79   by blast
```
```    80
```
```    81 lemma typedef_hol2hol4:
```
```    82   assumes a: "type_definition (Rep::'a=>'b) Abs (Collect P)"
```
```    83   shows "EX rep. TYPE_DEFINITION P (rep::'a=>'b)"
```
```    84 proof -
```
```    85   from a
```
```    86   have td: "(ALL x. P (Rep x)) & (ALL x. Abs (Rep x) = x) & (ALL y. P y \<longrightarrow> Rep (Abs y) = y)"
```
```    87     by (simp add: type_definition_def)
```
```    88   have ed: "TYPE_DEFINITION P Rep"
```
```    89   proof (auto simp add: TYPE_DEFINITION)
```
```    90     fix x y
```
```    91     assume "Rep x = Rep y"
```
```    92     from td have "x = Abs (Rep x)"
```
```    93       by auto
```
```    94     also have "Abs (Rep x) = Abs (Rep y)"
```
```    95       by (simp add: prems)
```
```    96     also from td have "Abs (Rep y) = y"
```
```    97       by auto
```
```    98     finally show "x = y" .
```
```    99   next
```
```   100     fix x
```
```   101     assume "P x"
```
```   102     with td
```
```   103     have "Rep (Abs x) = x"
```
```   104       by auto
```
```   105     hence "x = Rep (Abs x)"
```
```   106       ..
```
```   107     thus "EX y. x = Rep y"
```
```   108       ..
```
```   109   next
```
```   110     fix y
```
```   111     from td
```
```   112     show "P (Rep y)"
```
```   113       by auto
```
```   114   qed
```
```   115   show ?thesis
```
```   116     apply (rule exI [of _ Rep])
```
```   117     apply (rule ed)
```
```   118     .
```
```   119 qed
```
```   120
```
```   121 lemma typedef_hol2hollight:
```
```   122   assumes a: "type_definition (Rep::'a=>'b) Abs (Collect P)"
```
```   123   shows "(Abs (Rep a) = a) & (P r = (Rep (Abs r) = r))"
```
```   124 proof
```
```   125   from a
```
```   126   show "Abs (Rep a) = a"
```
```   127     by (rule type_definition.Rep_inverse)
```
```   128 next
```
```   129   show "P r = (Rep (Abs r) = r)"
```
```   130   proof
```
```   131     assume "P r"
```
```   132     hence "r \<in> (Collect P)"
```
```   133       by simp
```
```   134     with a
```
```   135     show "Rep (Abs r) = r"
```
```   136       by (rule type_definition.Abs_inverse)
```
```   137   next
```
```   138     assume ra: "Rep (Abs r) = r"
```
```   139     from a
```
```   140     have "Rep (Abs r) \<in> (Collect P)"
```
```   141       by (rule type_definition.Rep)
```
```   142     thus "P r"
```
```   143       by (simp add: ra)
```
```   144   qed
```
```   145 qed
```
```   146
```
```   147 lemma termspec_help: "[| Ex P ; c == Eps P |] ==> P c"
```
```   148   apply simp
```
```   149   apply (rule someI_ex)
```
```   150   .
```
```   151
```
```   152 lemma typedef_helper: "EX x. P x \<Longrightarrow> EX x. x \<in> (Collect P)"
```
```   153   by simp
```
```   154
```
```   155 use "hol4rews.ML"
```
```   156
```
```   157 setup hol4_setup
```
```   158 parse_ast_translation smarter_trueprop_parsing
```
```   159
```
```   160 use "proof_kernel.ML"
```
```   161 use "replay.ML"
```
```   162 use "import_package.ML"
```
```   163
```
```   164 setup ImportPackage.setup
```
```   165
```
```   166 end
```