src/HOL/Metis_Examples/Clausify.thy
 author blanchet Thu Apr 14 11:24:04 2011 +0200 (2011-04-14) changeset 42338 802f2fe7a0c9 child 42340 4e4f0665e5be permissions -rw-r--r--
started clausifier examples
```     1 (*  Title:      HOL/Metis_Examples/Clausifier.thy
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```     2     Author:     Jasmin Blanchette, TU Muenchen
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```     3
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```     4 Testing Metis's clausifier.
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```     5 *)
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```     6
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```     7 theory Clausifier
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```     8 imports Complex_Main
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```     9 begin
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```    10
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```    11
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```    12 text {* Definitional CNF for goal *}
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```    13
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```    14 (* FIXME: shouldn't need this *)
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```    15 declare [[unify_search_bound = 100]]
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```    16 declare [[unify_trace_bound = 100]]
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```    17
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```    18 axiomatization p :: "nat \<Rightarrow> nat \<Rightarrow> bool" where
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```    19 pax: "\<exists>b. \<forall>a. ((p b a \<and> p 0 0 \<and> p 1 a) \<or> (p 0 1 \<and> p 1 0 \<and> p a b))"
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```    20
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```    21 declare [[metis_new_skolemizer = false]]
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```    22
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```    23 lemma "\<exists>b. \<forall>a. \<exists>x. (p b a \<or> x) \<and> (p 0 0 \<or> x) \<and> (p 1 a \<or> x) \<and>
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```    24                    (p 0 1 \<or> \<not> x) \<and> (p 1 0 \<or> \<not> x) \<and> (p a b \<or> \<not> x)"
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```    25 by (metis pax)
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```    26
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```    27 lemma "\<exists>b. \<forall>a. \<exists>x. (p b a \<or> x) \<and> (p 0 0 \<or> x) \<and> (p 1 a \<or> x) \<and>
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```    28                    (p 0 1 \<or> \<not> x) \<and> (p 1 0 \<or> \<not> x) \<and> (p a b \<or> \<not> x)"
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```    29 by (metisFT pax)
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```    30
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```    31 declare [[metis_new_skolemizer]]
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```    32
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```    33 lemma "\<exists>b. \<forall>a. \<exists>x. (p b a \<or> x) \<and> (p 0 0 \<or> x) \<and> (p 1 a \<or> x) \<and>
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```    34                    (p 0 1 \<or> \<not> x) \<and> (p 1 0 \<or> \<not> x) \<and> (p a b \<or> \<not> x)"
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```    35 by (metis pax)
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```    36
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```    37 lemma "\<exists>b. \<forall>a. \<exists>x. (p b a \<or> x) \<and> (p 0 0 \<or> x) \<and> (p 1 a \<or> x) \<and>
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```    38                    (p 0 1 \<or> \<not> x) \<and> (p 1 0 \<or> \<not> x) \<and> (p a b \<or> \<not> x)"
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```    39 by (metisFT pax)
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```    40
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```    41
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```    42 text {* New Skolemizer *}
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```    43
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```    44 declare [[metis_new_skolemizer]]
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```    45
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```    46 lemma
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```    47   fixes x :: real
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```    48   assumes fn_le: "!!n. f n \<le> x" and 1: "f----> lim f"
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```    49   shows "lim f \<le> x"
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```    50 by (metis 1 LIMSEQ_le_const2 fn_le)
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```    51
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```    52 definition
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```    53   bounded :: "'a::metric_space set \<Rightarrow> bool" where
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```    54   "bounded S \<longleftrightarrow> (\<exists>x eee. \<forall>y\<in>S. dist x y \<le> eee)"
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```    55
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```    56 lemma "bounded T \<Longrightarrow> S \<subseteq> T ==> bounded S"
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```    57 by (metis bounded_def subset_eq)
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```    58
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```    59 lemma
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```    60   assumes a: "Quotient R Abs Rep"
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```    61   shows "symp R"
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```    62 using a unfolding Quotient_def using sympI
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```    63 by metisFT
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```    64
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```    65 lemma
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```    66   "(\<exists>x \<in> set xs. P x) \<longleftrightarrow>
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```    67    (\<exists>ys x zs. xs = ys@x#zs \<and> P x \<and> (\<forall>z \<in> set zs. \<not> P z))"
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```    68 by (metis split_list_last_prop [where P = P] in_set_conv_decomp)
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```    69
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```    70 end
```