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