src/HOL/Metis.thy
 author paulson Mon Feb 22 14:37:56 2016 +0000 (2016-02-22) changeset 62379 340738057c8c parent 60758 d8d85a8172b5 child 62672 068b430e678f permissions -rw-r--r--
An assortment of useful lemmas about sums, norm, etc. Also: norm_conv_dist [symmetric] is now a simprule!
```     1 (*  Title:      HOL/Metis.thy
```
```     2     Author:     Lawrence C. Paulson, Cambridge University Computer Laboratory
```
```     3     Author:     Jia Meng, Cambridge University Computer Laboratory and NICTA
```
```     4     Author:     Jasmin Blanchette, TU Muenchen
```
```     5 *)
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```     6
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```     7 section \<open>Metis Proof Method\<close>
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```     8
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```     9 theory Metis
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```    10 imports ATP
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```    11 begin
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```    12
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```    13 declare [[ML_print_depth = 0]]
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```    14 ML_file "~~/src/Tools/Metis/metis.ML"
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```    15 declare [[ML_print_depth = 10]]
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```    16
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```    17
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```    18 subsection \<open>Literal selection and lambda-lifting helpers\<close>
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```    19
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```    20 definition select :: "'a \<Rightarrow> 'a" where
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```    21 "select = (\<lambda>x. x)"
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```    22
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```    23 lemma not_atomize: "(\<not> A \<Longrightarrow> False) \<equiv> Trueprop A"
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```    24 by (cut_tac atomize_not [of "\<not> A"]) simp
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```    25
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```    26 lemma atomize_not_select: "(A \<Longrightarrow> select False) \<equiv> Trueprop (\<not> A)"
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```    27 unfolding select_def by (rule atomize_not)
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```    28
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```    29 lemma not_atomize_select: "(\<not> A \<Longrightarrow> select False) \<equiv> Trueprop A"
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```    30 unfolding select_def by (rule not_atomize)
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```    31
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```    32 lemma select_FalseI: "False \<Longrightarrow> select False" by simp
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```    33
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```    34 definition lambda :: "'a \<Rightarrow> 'a" where
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```    35 "lambda = (\<lambda>x. x)"
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```    36
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```    37 lemma eq_lambdaI: "x \<equiv> y \<Longrightarrow> x \<equiv> lambda y"
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```    38 unfolding lambda_def by assumption
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```    39
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```    40
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```    41 subsection \<open>Metis package\<close>
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```    42
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```    43 ML_file "Tools/Metis/metis_generate.ML"
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```    44 ML_file "Tools/Metis/metis_reconstruct.ML"
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```    45 ML_file "Tools/Metis/metis_tactic.ML"
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```    46
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```    47 hide_const (open) select fFalse fTrue fNot fComp fconj fdisj fimplies fAll fEx fequal lambda
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```    48 hide_fact (open) select_def not_atomize atomize_not_select not_atomize_select select_FalseI
```
```    49   fFalse_def fTrue_def fNot_def fconj_def fdisj_def fimplies_def fAll_def fEx_def fequal_def
```
```    50   fTrue_ne_fFalse fNot_table fconj_table fdisj_table fimplies_table fAll_table fEx_table
```
```    51   fequal_table fAll_table fEx_table fNot_law fComp_law fconj_laws fdisj_laws fimplies_laws
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```    52   fequal_laws fAll_law fEx_law lambda_def eq_lambdaI
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```    53
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```    54 end
```