nicer presentation of proofs, closer to automation.
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@ -218,56 +218,55 @@ print_doc_classes
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text\<open>All Class-Id's --- should be generated.\<close>
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lemmas class_ids =
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SML_def code_def annex_def title_def figure_def chapter_def article_def theorem_def
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paragraph_def tech_code_def assumption_def definition_def hypothesis_def eng_example_def
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text_element_def math_content_def tech_example_def subsubsection_def tech_definition_def
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engineering_content_def data_def float_def axiom_def LATEX_def author_def listing_def example_def
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abstract_def assertion_def technical_def background_def evaluation_def math_proof_def
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math_formal_def bibliography_def math_example_def text_section_def conclusion_stmt_def
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math_explanation_def ISAR_def frame_def lemma_def index_def report_def section_def premise_def
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subtitle_def corollary_def subsection_def conclusion_def experiment_def consequence_def
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proposition_def introduction_def related_work_def front_matter_def math_motivation_def
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table_of_contents_def
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SML_def code_def annex_def title_def figure_def chapter_def article_def theorem_def
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paragraph_def tech_code_def assumption_def definition_def hypothesis_def
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eng_example_def text_element_def math_content_def tech_example_def subsubsection_def
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engineering_content_def data_def float_def axiom_def LATEX_def author_def listing_def
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abstract_def assertion_def technical_def background_def evaluation_def math_proof_def
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math_formal_def bibliography_def math_example_def text_section_def conclusion_stmt_def
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math_explanation_def ISAR_def frame_def lemma_def index_def report_def section_def
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subtitle_def corollary_def subsection_def conclusion_def experiment_def consequence_def
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proposition_def introduction_def related_work_def front_matter_def math_motivation_def
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example_def table_of_contents_def tech_definition_def premise_def
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term\<open>{
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SML,code, annex, title ,figure,chapter, article , theorem ,paragraph,tech_code,
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assumption, definition , hypothesis ,eng_example ,text_element,math_content,tech_example,
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subsubsection,tech_definition,engineering_content,data,float,axiom,LATEX,author,listing,
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example,abstract,assertion,technical,background,evaluation,math_proof,math_formal,
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bibliography,math_example,text_section,conclusion_stmt,math_explanation,ISAR,frame,
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lemma,index,report,section,premise,subtitle,corollary,subsection,conclusion,experiment,
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consequence,proposition,introduction,related_work,front_matter,math_motivation,table_of_contents}
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\<close>
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definition allClasses
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where \<open>allClasses \<equiv> {SML, code, annex, title,figure,chapter, article, theorem, paragraph,
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tech_code, assumption, definition, hypothesis, eng_example, text_element,
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math_content,tech_example, subsubsection,tech_definition,
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engineering_content,data,float,axiom,LATEX,author,listing, example,abstract,
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assertion,technical,background,evaluation,math_proof,math_formal,bibliography,
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math_example,text_section,conclusion_stmt,math_explanation,ISAR,frame,
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lemma,index,report,section,premise,subtitle,corollary,subsection,conclusion,
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experiment, consequence,proposition,introduction,related_work,front_matter,
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math_motivation,table_of_contents}
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\<close>
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where \<open>allClasses \<equiv>
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{SML, code, annex, title,figure,chapter, article, theorem, paragraph,
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tech_code, assumption, definition, hypothesis, eng_example, text_element,
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math_content,tech_example, subsubsection,tech_definition,
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engineering_content,data,float,axiom,LATEX,author,listing, example,abstract,
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assertion,technical,background,evaluation,math_proof,math_formal,bibliography,
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math_example,text_section,conclusion_stmt,math_explanation,ISAR,frame,
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lemma,index,report,section,premise,subtitle,corollary,subsection,conclusion,
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experiment, consequence,proposition,introduction,related_work,front_matter,
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math_motivation,table_of_contents}\<close>
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text\<open>A rudimentary fragment of the class hierarchy re-modeled on classid's :\<close>
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definition cid_of where \<open>cid_of = inv Regular_Exp.Atom\<close>
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lemma Atom_inverse[simp]:\<open>cid_of (Regular_Exp.Atom a) = a\<close>
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unfolding cid_of_def by (meson UNIV_I f_inv_into_f image_eqI rexp.inject(1))
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definition doc_class_rel
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where \<open>doc_class_rel \<equiv> {(proposition,math_content),
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(listing,float),
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(figure,float)} \<close>
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where \<open>doc_class_rel \<equiv> {(cid_of proposition,cid_of math_content),
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(cid_of listing,cid_of float),
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(cid_of figure,cid_of float)} \<close>
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instantiation "doc_class" :: ord
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begin
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definition
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le_class_def: "x \<le> y \<longleftrightarrow> (x,y) \<in> doc_class_rel\<^sup>*"
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less_eq_doc_class: "x \<le> y \<longleftrightarrow> (x,y) \<in> doc_class_rel\<^sup>*"
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definition
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less_class_def: "(x::doc_class) < y \<longleftrightarrow> (x \<le> y \<and> \<not> y \<le> x)"
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less_doc_class: "(x::doc_class) < y \<longleftrightarrow> (x \<le> y \<and> \<not> y \<le> x)"
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instance ..
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@ -275,13 +274,12 @@ end
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lemma drc_acyclic : "acyclic doc_class_rel"
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proof -
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let ?measure = " (\<lambda>x.3::int)(float := 0, math_content := 0,
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listing := 1, figure := 1,
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proposition := 1)"
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let ?measure = "(\<lambda>x.3::int)(cid_of float := 0, cid_of math_content := 0,
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cid_of listing := 1, cid_of figure := 1, cid_of proposition := 1)"
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show ?thesis
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unfolding doc_class_rel_def
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apply(rule_tac f = "?measure" in acyclicI_order)
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by auto
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unfolding doc_class_rel_def
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apply(rule_tac f = "?measure" in acyclicI_order)
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by(simp only: class_ids)(auto)
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qed
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@ -291,11 +289,11 @@ instance
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proof
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fix x::"doc_class"
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show \<open>x \<le> x\<close>
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unfolding le_class_def by simp
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unfolding less_eq_doc_class by simp
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next
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fix x y z:: "doc_class"
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show \<open>x \<le> y \<Longrightarrow> y \<le> z \<Longrightarrow> x \<le> z\<close>
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unfolding le_class_def
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unfolding less_eq_doc_class
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by force
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next
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fix x y::"doc_class"
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@ -303,12 +301,11 @@ instance
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by (simp add: acyclic_impl_antisym_rtrancl drc_acyclic)
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show \<open>x \<le> y \<Longrightarrow> y \<le> x \<Longrightarrow> x = y\<close>
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apply(insert antisymD[OF *])
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unfolding le_class_def
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by auto
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using less_eq_doc_class by auto
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next
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fix x y::"doc_class"
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show \<open>(x < y) = (x \<le> y \<and> \<not> y \<le> x)\<close>
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by(simp add: less_class_def )
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by(simp add: less_doc_class)
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qed
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end
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