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first monitor proof without sorries.

This commit is contained in:
Burkhart Wolff 2024-04-03 20:51:21 +02:00
parent c2eea7696b
commit 2b12e53cf4
1 changed files with 22 additions and 34 deletions
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Isabelle_DOF/ontologies/technical_report/technical_report.thy
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@ -81,8 +81,7 @@ doc_class report =
bibliography ~~
\<lbrakk>index\<rbrakk> ~~ \<lbrace>annex\<rbrace>\<^sup>* )"
ML\<open>ML_Syntax.print_string\<close>
ML\<open>ML_Syntax.atomic\<close>
(*
ML\<open>@{doc_class "report"}\<close>
*)
@ -94,6 +93,8 @@ ML\<open> fun get_class_2_ML ctxt (str,_) =
setup\<open>ML_Antiquotation.inline \<^binding>\<open>doc_class2\<close>
(fn (ctxt,toks) => (AttributeAccess.parse_cid >> get_class_2_ML ctxt) (ctxt, toks))\<close>
ML\<open>@{term \<open>a + b\<close>}\<close>
ML\<open>@{doc_class2 "report"}\<close>
ML\<open>fun constant_def (decl, spec, prems, params) = #2 o Specification.definition decl params prems spec\<close>
@ -138,47 +139,34 @@ notation Plus (infixr "||" 55)
notation Times (infixr "~~" 60)
notation Atom ("\<lfloor>_\<rfloor>" 65)
lemma seq_cancel : "Lang (a ~~ b) \<subseteq> Lang (a ~~ c) = (Lang (b) \<subseteq> Lang (c))"
apply auto
thm subsetCE
apply(drule_tac c=x in subsetCE)
prefer 3 apply assumption
find_theorems subset_eq elim
prefer 2
sledgehammer
sorry
lemma opt_star_incl:"Lang (opt a) \<subseteq> Lang (Star a)" by (simp add: opt_def subset_iff)
lemma rep1_star_incl:"Lang (rep1 a) \<subseteq> Lang (Star a)"
unfolding rep1_def
apply(subst L_Star)
apply(subst L_Conc)
by force
lemma regexp_unit_right : "Lang (a) = Lang (a ~~ One) " by simp
lemma regexp_unit_left : "Lang (a) = Lang (One ~~ a) " by simp
lemma regexp_seq_mono :
"Lang(a) \<subseteq> Lang (a') \<Longrightarrow> Lang(b) \<subseteq> Lang (b') \<Longrightarrow> Lang(a ~~ b) \<subseteq> Lang(a' ~~ b')"
by auto
lemma seq_d1 : "Lang (opt b ~~ a) \<subseteq> Lang ( c) = (Lang (a) \<subseteq> Lang (c))" sorry
lemma seq_d2 : "Lang (rep1 b ~~ a) \<subseteq> Lang ( c) = (Lang (a) \<subseteq> Lang (c))" sorry
lemma seq_d3 : "Lang (a) \<subseteq> Lang (opt b ~~ c) = (Lang (a) \<subseteq> Lang (c))" sorry
lemma seq_d4 : "Lang (a) \<subseteq> Lang (Star b ~~ c) = (Lang (a) \<subseteq> Lang (c))" sorry
lemma regexp_unit_right : "Lang (a) = Lang (a ~~ One) " by simp
lemma regexp_unit_left : "Lang (a) = Lang (One ~~ a) " by simp
lemma opt_star_incl :"Lang (opt a) \<subseteq> Lang (Star a)" by (simp add: opt_def subset_iff)
lemma rep1_star_incl:"Lang (rep1 a) \<subseteq> Lang (Star a)"
unfolding rep1_def by(subst L_Star, subst L_Conc)(force)
lemma cancel_rep1 : "Lang (a) \<subseteq> Lang (rep1 a)"
unfolding rep1_def by auto
lemma seq_cancel_opt : "Lang (a) \<subseteq> Lang (c) \<Longrightarrow> Lang (a) \<subseteq> Lang (opt b ~~ c)"
by(subst regexp_unit_left, rule regexp_seq_mono)(simp_all add: opt_def)
lemma seq_cancel_Star : "Lang (a) \<subseteq> Lang (c) \<Longrightarrow> Lang (a) \<subseteq> Lang (Star b ~~ c)"
by auto
text\<open>Not a terribly deep theorem, but an interesting property of consistency between
ontologies - so, a lemma that shouldn't break if the involved ontologies were changed:
the structural language of articles should be included in the structural language of reports,
that is to say, reports should just have a richer structure than ordinary papers: \<close>
the structural language of articles should be included in the structural language of
reports, that is to say, reports should just have a richer structure than ordinary papers. \<close>
theorem articles_sub_reports: \<open>(Lang article_monitor) \<subseteq> Lang report_monitor\<close>
theorem articles_sub_reports: \<open>(Lang article_monitor) \<subseteq> Lang report_monitor\<close>
unfolding article_monitor_def report_monitor_def
apply(simp only: seq_cancel seq_d1 seq_d2 seq_d3)
apply(rule regexp_seq_mono[OF subset_refl] | rule seq_cancel_opt | rule subset_refl)+
done