src/FOL/FOL.thy
author wenzelm
Tue, 05 Nov 2019 14:28:00 +0100
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(*  Title:      FOL/FOL.thy
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    Author:     Lawrence C Paulson and Markus Wenzel
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*)
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section \<open>Classical first-order logic\<close>
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theory FOL
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imports IFOL
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keywords "print_claset" "print_induct_rules" :: diag
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begin
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ML_file \<open>~~/src/Provers/classical.ML\<close>
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ML_file \<open>~~/src/Provers/blast.ML\<close>
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ML_file \<open>~~/src/Provers/clasimp.ML\<close>
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subsection \<open>The classical axiom\<close>
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axiomatization where
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  classical: \<open>(\<not> P \<Longrightarrow> P) \<Longrightarrow> P\<close>
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subsection \<open>Lemmas and proof tools\<close>
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lemma ccontr: \<open>(\<not> P \<Longrightarrow> False) \<Longrightarrow> P\<close>
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  by (erule FalseE [THEN classical])
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subsubsection \<open>Classical introduction rules for \<open>\<or>\<close> and \<open>\<exists>\<close>\<close>
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lemma disjCI: \<open>(\<not> Q \<Longrightarrow> P) \<Longrightarrow> P \<or> Q\<close>
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  apply (rule classical)
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  apply (assumption | erule meta_mp | rule disjI1 notI)+
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  apply (erule notE disjI2)+
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  done
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text \<open>Introduction rule involving only \<open>\<exists>\<close>\<close>
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lemma ex_classical:
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  assumes r: \<open>\<not> (\<exists>x. P(x)) \<Longrightarrow> P(a)\<close>
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  shows \<open>\<exists>x. P(x)\<close>
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  apply (rule classical)
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  apply (rule exI, erule r)
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  done
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text \<open>Version of above, simplifying \<open>\<not>\<exists>\<close> to \<open>\<forall>\<not>\<close>.\<close>
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lemma exCI:
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  assumes r: \<open>\<forall>x. \<not> P(x) \<Longrightarrow> P(a)\<close>
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  shows \<open>\<exists>x. P(x)\<close>
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  apply (rule ex_classical)
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  apply (rule notI [THEN allI, THEN r])
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  apply (erule notE)
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  apply (erule exI)
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  done
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lemma excluded_middle: \<open>\<not> P \<or> P\<close>
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  apply (rule disjCI)
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  apply assumption
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  done
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lemma case_split [case_names True False]:
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  assumes r1: \<open>P \<Longrightarrow> Q\<close>
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    and r2: \<open>\<not> P \<Longrightarrow> Q\<close>
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  shows \<open>Q\<close>
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  apply (rule excluded_middle [THEN disjE])
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  apply (erule r2)
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  apply (erule r1)
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  done
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ML \<open>
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  fun case_tac ctxt a fixes =
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    Rule_Insts.res_inst_tac ctxt [((("P", 0), Position.none), a)] fixes @{thm case_split};
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\<close>
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method_setup case_tac = \<open>
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  Args.goal_spec -- Scan.lift (Args.embedded_inner_syntax -- Parse.for_fixes) >>
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    (fn (quant, (s, fixes)) => fn ctxt => SIMPLE_METHOD'' quant (case_tac ctxt s fixes))
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\<close> "case_tac emulation (dynamic instantiation!)"
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subsection \<open>Special elimination rules\<close>
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text \<open>Classical implies (\<open>\<longrightarrow>\<close>) elimination.\<close>
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lemma impCE:
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  assumes major: \<open>P \<longrightarrow> Q\<close>
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    and r1: \<open>\<not> P \<Longrightarrow> R\<close>
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    and r2: \<open>Q \<Longrightarrow> R\<close>
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  shows \<open>R\<close>
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  apply (rule excluded_middle [THEN disjE])
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   apply (erule r1)
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  apply (rule r2)
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  apply (erule major [THEN mp])
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  done
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text \<open>
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  This version of \<open>\<longrightarrow>\<close> elimination works on \<open>Q\<close> before \<open>P\<close>. It works best for those cases in which P holds ``almost everywhere''.
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  Can't install as default: would break old proofs.
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\<close>
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lemma impCE':
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  assumes major: \<open>P \<longrightarrow> Q\<close>
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    and r1: \<open>Q \<Longrightarrow> R\<close>
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    and r2: \<open>\<not> P \<Longrightarrow> R\<close>
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  shows \<open>R\<close>
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  apply (rule excluded_middle [THEN disjE])
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   apply (erule r2)
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  apply (rule r1)
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  apply (erule major [THEN mp])
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  done
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text \<open>Double negation law.\<close>
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lemma notnotD: \<open>\<not> \<not> P \<Longrightarrow> P\<close>
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  apply (rule classical)
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  apply (erule notE)
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  apply assumption
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  done
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lemma contrapos2:  \<open>\<lbrakk>Q; \<not> P \<Longrightarrow> \<not> Q\<rbrakk> \<Longrightarrow> P\<close>
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  apply (rule classical)
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  apply (drule (1) meta_mp)
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  apply (erule (1) notE)
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  done
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subsubsection \<open>Tactics for implication and contradiction\<close>
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text \<open>
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  Classical \<open>\<longleftrightarrow>\<close> elimination. Proof substitutes \<open>P = Q\<close> in
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  \<open>\<not> P \<Longrightarrow> \<not> Q\<close> and \<open>P \<Longrightarrow> Q\<close>.
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\<close>
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lemma iffCE:
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  assumes major: \<open>P \<longleftrightarrow> Q\<close>
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    and r1: \<open>\<lbrakk>P; Q\<rbrakk> \<Longrightarrow> R\<close>
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    and r2: \<open>\<lbrakk>\<not> P; \<not> Q\<rbrakk> \<Longrightarrow> R\<close>
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  shows \<open>R\<close>
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  apply (rule major [unfolded iff_def, THEN conjE])
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  apply (elim impCE)
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     apply (erule (1) r2)
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    apply (erule (1) notE)+
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  apply (erule (1) r1)
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  done
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(*Better for fast_tac: needs no quantifier duplication!*)
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lemma alt_ex1E:
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  assumes major: \<open>\<exists>! x. P(x)\<close>
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    and r: \<open>\<And>x. \<lbrakk>P(x);  \<forall>y y'. P(y) \<and> P(y') \<longrightarrow> y = y'\<rbrakk> \<Longrightarrow> R\<close>
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  shows \<open>R\<close>
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  using major
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proof (rule ex1E)
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  fix x
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  assume * : \<open>\<forall>y. P(y) \<longrightarrow> y = x\<close>
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  assume \<open>P(x)\<close>
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  then show \<open>R\<close>
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  proof (rule r)
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    {
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      fix y y'
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      assume \<open>P(y)\<close> and \<open>P(y')\<close>
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      with * have \<open>x = y\<close> and \<open>x = y'\<close>
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        by - (tactic "IntPr.fast_tac \<^context> 1")+
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      then have \<open>y = y'\<close> by (rule subst)
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    } note r' = this
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    show \<open>\<forall>y y'. P(y) \<and> P(y') \<longrightarrow> y = y'\<close>
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      by (intro strip, elim conjE) (rule r')
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  qed
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qed
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lemma imp_elim: \<open>P \<longrightarrow> Q \<Longrightarrow> (\<not> R \<Longrightarrow> P) \<Longrightarrow> (Q \<Longrightarrow> R) \<Longrightarrow> R\<close>
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  by (rule classical) iprover
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lemma swap: \<open>\<not> P \<Longrightarrow> (\<not> R \<Longrightarrow> P) \<Longrightarrow> R\<close>
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  by (rule classical) iprover
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section \<open>Classical Reasoner\<close>
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ML \<open>
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structure Cla = Classical
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(
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  val imp_elim = @{thm imp_elim}
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  val not_elim = @{thm notE}
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  val swap = @{thm swap}
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  val classical = @{thm classical}
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  val sizef = size_of_thm
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  val hyp_subst_tacs = [hyp_subst_tac]
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);
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structure Basic_Classical: BASIC_CLASSICAL = Cla;
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open Basic_Classical;
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\<close>
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(*Propositional rules*)
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lemmas [intro!] = refl TrueI conjI disjCI impI notI iffI
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  and [elim!] = conjE disjE impCE FalseE iffCE
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ML \<open>val prop_cs = claset_of \<^context>\<close>
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(*Quantifier rules*)
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lemmas [intro!] = allI ex_ex1I
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  and [intro] = exI
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  and [elim!] = exE alt_ex1E
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  and [elim] = allE
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ML \<open>val FOL_cs = claset_of \<^context>\<close>
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ML \<open>
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  structure Blast = Blast
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  (
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    structure Classical = Cla
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    val Trueprop_const = dest_Const \<^const>\<open>Trueprop\<close>
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    val equality_name = \<^const_name>\<open>eq\<close>
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    val not_name = \<^const_name>\<open>Not\<close>
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    val notE = @{thm notE}
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    val ccontr = @{thm ccontr}
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    val hyp_subst_tac = Hypsubst.blast_hyp_subst_tac
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  );
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  val blast_tac = Blast.blast_tac;
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\<close>
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lemma ex1_functional: \<open>\<lbrakk>\<exists>! z. P(a,z); P(a,b); P(a,c)\<rbrakk> \<Longrightarrow> b = c\<close>
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  by blast
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text \<open>Elimination of \<open>True\<close> from assumptions:\<close>
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lemma True_implies_equals: \<open>(True \<Longrightarrow> PROP P) \<equiv> PROP P\<close>
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proof
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  assume \<open>True \<Longrightarrow> PROP P\<close>
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  from this and TrueI show \<open>PROP P\<close> .
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next
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  assume \<open>PROP P\<close>
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  then show \<open>PROP P\<close> .
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qed
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lemma uncurry: \<open>P \<longrightarrow> Q \<longrightarrow> R \<Longrightarrow> P \<and> Q \<longrightarrow> R\<close>
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  by blast
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lemma iff_allI: \<open>(\<And>x. P(x) \<longleftrightarrow> Q(x)) \<Longrightarrow> (\<forall>x. P(x)) \<longleftrightarrow> (\<forall>x. Q(x))\<close>
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  by blast
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lemma iff_exI: \<open>(\<And>x. P(x) \<longleftrightarrow> Q(x)) \<Longrightarrow> (\<exists>x. P(x)) \<longleftrightarrow> (\<exists>x. Q(x))\<close>
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  by blast
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lemma all_comm: \<open>(\<forall>x y. P(x,y)) \<longleftrightarrow> (\<forall>y x. P(x,y))\<close>
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  by blast
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lemma ex_comm: \<open>(\<exists>x y. P(x,y)) \<longleftrightarrow> (\<exists>y x. P(x,y))\<close>
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  by blast
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subsection \<open>Classical simplification rules\<close>
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text \<open>
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  Avoids duplication of subgoals after \<open>expand_if\<close>, when the true and
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  false cases boil down to the same thing.
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\<close>
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lemma cases_simp: \<open>(P \<longrightarrow> Q) \<and> (\<not> P \<longrightarrow> Q) \<longleftrightarrow> Q\<close>
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  by blast
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subsubsection \<open>Miniscoping: pushing quantifiers in\<close>
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text \<open>
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  We do NOT distribute of \<open>\<forall>\<close> over \<open>\<and>\<close>, or dually that of
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  \<open>\<exists>\<close> over \<open>\<or>\<close>.
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  Baaz and Leitsch, On Skolemization and Proof Complexity (1994) show that
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  this step can increase proof length!
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\<close>
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text \<open>Existential miniscoping.\<close>
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lemma int_ex_simps:
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  \<open>\<And>P Q. (\<exists>x. P(x) \<and> Q) \<longleftrightarrow> (\<exists>x. P(x)) \<and> Q\<close>
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  \<open>\<And>P Q. (\<exists>x. P \<and> Q(x)) \<longleftrightarrow> P \<and> (\<exists>x. Q(x))\<close>
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  \<open>\<And>P Q. (\<exists>x. P(x) \<or> Q) \<longleftrightarrow> (\<exists>x. P(x)) \<or> Q\<close>
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  \<open>\<And>P Q. (\<exists>x. P \<or> Q(x)) \<longleftrightarrow> P \<or> (\<exists>x. Q(x))\<close>
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  by iprover+
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text \<open>Classical rules.\<close>
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lemma cla_ex_simps:
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  \<open>\<And>P Q. (\<exists>x. P(x) \<longrightarrow> Q) \<longleftrightarrow> (\<forall>x. P(x)) \<longrightarrow> Q\<close>
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  \<open>\<And>P Q. (\<exists>x. P \<longrightarrow> Q(x)) \<longleftrightarrow> P \<longrightarrow> (\<exists>x. Q(x))\<close>
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  by blast+
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lemmas ex_simps = int_ex_simps cla_ex_simps
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text \<open>Universal miniscoping.\<close>
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lemma int_all_simps:
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  \<open>\<And>P Q. (\<forall>x. P(x) \<and> Q) \<longleftrightarrow> (\<forall>x. P(x)) \<and> Q\<close>
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  \<open>\<And>P Q. (\<forall>x. P \<and> Q(x)) \<longleftrightarrow> P \<and> (\<forall>x. Q(x))\<close>
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  \<open>\<And>P Q. (\<forall>x. P(x) \<longrightarrow> Q) \<longleftrightarrow> (\<exists> x. P(x)) \<longrightarrow> Q\<close>
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  \<open>\<And>P Q. (\<forall>x. P \<longrightarrow> Q(x)) \<longleftrightarrow> P \<longrightarrow> (\<forall>x. Q(x))\<close>
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  by iprover+
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text \<open>Classical rules.\<close>
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lemma cla_all_simps:
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  \<open>\<And>P Q. (\<forall>x. P(x) \<or> Q) \<longleftrightarrow> (\<forall>x. P(x)) \<or> Q\<close>
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  \<open>\<And>P Q. (\<forall>x. P \<or> Q(x)) \<longleftrightarrow> P \<or> (\<forall>x. Q(x))\<close>
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  by blast+
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lemmas all_simps = int_all_simps cla_all_simps
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subsubsection \<open>Named rewrite rules proved for IFOL\<close>
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lemma imp_disj1: \<open>(P \<longrightarrow> Q) \<or> R \<longleftrightarrow> (P \<longrightarrow> Q \<or> R)\<close> by blast
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lemma imp_disj2: \<open>Q \<or> (P \<longrightarrow> R) \<longleftrightarrow> (P \<longrightarrow> Q \<or> R)\<close> by blast
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lemma de_Morgan_conj: \<open>(\<not> (P \<and> Q)) \<longleftrightarrow> (\<not> P \<or> \<not> Q)\<close> by blast
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lemma not_imp: \<open>\<not> (P \<longrightarrow> Q) \<longleftrightarrow> (P \<and> \<not> Q)\<close> by blast
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lemma not_iff: \<open>\<not> (P \<longleftrightarrow> Q) \<longleftrightarrow> (P \<longleftrightarrow> \<not> Q)\<close> by blast
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lemma not_all: \<open>(\<not> (\<forall>x. P(x))) \<longleftrightarrow> (\<exists>x. \<not> P(x))\<close> by blast
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lemma imp_all: \<open>((\<forall>x. P(x)) \<longrightarrow> Q) \<longleftrightarrow> (\<exists>x. P(x) \<longrightarrow> Q)\<close> by blast
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lemmas meta_simps =
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  triv_forall_equality  \<comment> \<open>prunes params\<close>
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  True_implies_equals  \<comment> \<open>prune asms \<open>True\<close>\<close>
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lemmas IFOL_simps =
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  refl [THEN P_iff_T] conj_simps disj_simps not_simps
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  imp_simps iff_simps quant_simps
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lemma notFalseI: \<open>\<not> False\<close> by iprover
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lemma cla_simps_misc:
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  \<open>\<not> (P \<and> Q) \<longleftrightarrow> \<not> P \<or> \<not> Q\<close>
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  \<open>P \<or> \<not> P\<close>
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  \<open>\<not> P \<or> P\<close>
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  \<open>\<not> \<not> P \<longleftrightarrow> P\<close>
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  \<open>(\<not> P \<longrightarrow> P) \<longleftrightarrow> P\<close>
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  \<open>(\<not> P \<longleftrightarrow> \<not> Q) \<longleftrightarrow> (P \<longleftrightarrow> Q)\<close> by blast+
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lemmas cla_simps =
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  de_Morgan_conj de_Morgan_disj imp_disj1 imp_disj2
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   335
  not_imp not_all not_ex cases_simp cla_simps_misc
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   336
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   337
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ML_file \<open>simpdata.ML\<close>
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simproc_setup defined_Ex (\<open>\<exists>x. P(x)\<close>) = \<open>fn _ => Quantifier1.rearrange_ex\<close>
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simproc_setup defined_All (\<open>\<forall>x. P(x)\<close>) = \<open>fn _ => Quantifier1.rearrange_all\<close>
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ML \<open>
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(*intuitionistic simprules only*)
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val IFOL_ss =
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  put_simpset FOL_basic_ss \<^context>
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  addsimps @{thms meta_simps IFOL_simps int_ex_simps int_all_simps}
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  addsimprocs [\<^simproc>\<open>defined_All\<close>, \<^simproc>\<open>defined_Ex\<close>]
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  |> Simplifier.add_cong @{thm imp_cong}
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  |> simpset_of;
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cd5005020f4e clarified simpset setup;
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(*classical simprules too*)
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val FOL_ss =
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  put_simpset IFOL_ss \<^context>
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  addsimps @{thms cla_simps cla_ex_simps cla_all_simps}
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  |> simpset_of;
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\<close>
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   359
setup \<open>
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  map_theory_simpset (put_simpset FOL_ss) #>
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   361
  Simplifier.method_setup Splitter.split_modifiers
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\<close>
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   364
ML_file \<open>~~/src/Tools/eqsubst.ML\<close>
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fc075ae929e4 the new subst tactic, by Lucas Dixon
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subsection \<open>Other simple lemmas\<close>
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lemma [simp]: \<open>((P \<longrightarrow> R) \<longleftrightarrow> (Q \<longrightarrow> R)) \<longleftrightarrow> ((P \<longleftrightarrow> Q) \<or> R)\<close>
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  by blast
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lemma [simp]: \<open>((P \<longrightarrow> Q) \<longleftrightarrow> (P \<longrightarrow> R)) \<longleftrightarrow> (P \<longrightarrow> (Q \<longleftrightarrow> R))\<close>
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  by blast
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lemma not_disj_iff_imp: \<open>\<not> P \<or> Q \<longleftrightarrow> (P \<longrightarrow> Q)\<close>
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  by blast
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subsubsection \<open>Monotonicity of implications\<close>
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   381
lemma conj_mono: \<open>\<lbrakk>P1 \<longrightarrow> Q1; P2 \<longrightarrow> Q2\<rbrakk> \<Longrightarrow> (P1 \<and> P2) \<longrightarrow> (Q1 \<and> Q2)\<close>
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  by fast (*or (IntPr.fast_tac 1)*)
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diff changeset
   383
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   384
lemma disj_mono: \<open>\<lbrakk>P1 \<longrightarrow> Q1; P2 \<longrightarrow> Q2\<rbrakk> \<Longrightarrow> (P1 \<or> P2) \<longrightarrow> (Q1 \<or> Q2)\<close>
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   385
  by fast (*or (IntPr.fast_tac 1)*)
14085
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diff changeset
   386
69590
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diff changeset
   387
lemma imp_mono: \<open>\<lbrakk>Q1 \<longrightarrow> P1; P2 \<longrightarrow> Q2\<rbrakk> \<Longrightarrow> (P1 \<longrightarrow> P2) \<longrightarrow> (Q1 \<longrightarrow> Q2)\<close>
61487
f8cb97e0fd0b more symbols, with swapped defaults: old-style ASCII syntax uses "ASCII" print mode;
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diff changeset
   388
  by fast (*or (IntPr.fast_tac 1)*)
14085
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paulson
parents: 13550
diff changeset
   389
69590
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diff changeset
   390
lemma imp_refl: \<open>P \<longrightarrow> P\<close>
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diff changeset
   391
  by (rule impI)
14085
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paulson
parents: 13550
diff changeset
   392
61487
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diff changeset
   393
text \<open>The quantifier monotonicity rules are also intuitionistically valid.\<close>
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diff changeset
   394
lemma ex_mono: \<open>(\<And>x. P(x) \<longrightarrow> Q(x)) \<Longrightarrow> (\<exists>x. P(x)) \<longrightarrow> (\<exists>x. Q(x))\<close>
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diff changeset
   395
  by blast
14085
8dc3e532959a moved some lemmas here from ZF
paulson
parents: 13550
diff changeset
   396
69590
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diff changeset
   397
lemma all_mono: \<open>(\<And>x. P(x) \<longrightarrow> Q(x)) \<Longrightarrow> (\<forall>x. P(x)) \<longrightarrow> (\<forall>x. Q(x))\<close>
61487
f8cb97e0fd0b more symbols, with swapped defaults: old-style ASCII syntax uses "ASCII" print mode;
wenzelm
parents: 60770
diff changeset
   398
  by blast
14085
8dc3e532959a moved some lemmas here from ZF
paulson
parents: 13550
diff changeset
   399
11678
6aa3e2d26683 moved atomize stuff to theory IFOL;
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diff changeset
   400
60770
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diff changeset
   401
subsection \<open>Proof by cases and induction\<close>
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diff changeset
   402
60770
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diff changeset
   403
text \<open>Proper handling of non-atomic rule statements.\<close>
11678
6aa3e2d26683 moved atomize stuff to theory IFOL;
wenzelm
parents: 11096
diff changeset
   404
59940
087d81f5213e local setup of induction tools, with restricted access to auxiliary consts;
wenzelm
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diff changeset
   405
context
087d81f5213e local setup of induction tools, with restricted access to auxiliary consts;
wenzelm
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diff changeset
   406
begin
087d81f5213e local setup of induction tools, with restricted access to auxiliary consts;
wenzelm
parents: 59780
diff changeset
   407
69590
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diff changeset
   408
qualified definition \<open>induct_forall(P) \<equiv> \<forall>x. P(x)\<close>
e65314985426 isabelle update_inner_syntax_cartouches;
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diff changeset
   409
qualified definition \<open>induct_implies(A, B) \<equiv> A \<longrightarrow> B\<close>
e65314985426 isabelle update_inner_syntax_cartouches;
wenzelm
parents: 63120
diff changeset
   410
qualified definition \<open>induct_equal(x, y) \<equiv> x = y\<close>
e65314985426 isabelle update_inner_syntax_cartouches;
wenzelm
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diff changeset
   411
qualified definition \<open>induct_conj(A, B) \<equiv> A \<and> B\<close>
11678
6aa3e2d26683 moved atomize stuff to theory IFOL;
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diff changeset
   412
69590
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diff changeset
   413
lemma induct_forall_eq: \<open>(\<And>x. P(x)) \<equiv> Trueprop(induct_forall(\<lambda>x. P(x)))\<close>
18816
aebd7f315b92 tuned proofs;
wenzelm
parents: 18595
diff changeset
   414
  unfolding atomize_all induct_forall_def .
11678
6aa3e2d26683 moved atomize stuff to theory IFOL;
wenzelm
parents: 11096
diff changeset
   415
69590
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wenzelm
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diff changeset
   416
lemma induct_implies_eq: \<open>(A \<Longrightarrow> B) \<equiv> Trueprop(induct_implies(A, B))\<close>
18816
aebd7f315b92 tuned proofs;
wenzelm
parents: 18595
diff changeset
   417
  unfolding atomize_imp induct_implies_def .
11678
6aa3e2d26683 moved atomize stuff to theory IFOL;
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diff changeset
   418
69590
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diff changeset
   419
lemma induct_equal_eq: \<open>(x \<equiv> y) \<equiv> Trueprop(induct_equal(x, y))\<close>
18816
aebd7f315b92 tuned proofs;
wenzelm
parents: 18595
diff changeset
   420
  unfolding atomize_eq induct_equal_def .
11678
6aa3e2d26683 moved atomize stuff to theory IFOL;
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diff changeset
   421
69590
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diff changeset
   422
lemma induct_conj_eq: \<open>(A &&& B) \<equiv> Trueprop(induct_conj(A, B))\<close>
18816
aebd7f315b92 tuned proofs;
wenzelm
parents: 18595
diff changeset
   423
  unfolding atomize_conj induct_conj_def .
11988
8340fb172607 induct_impliesI;
wenzelm
parents: 11848
diff changeset
   424
18456
8cc35e95450a updated auxiliary facts for induct method;
wenzelm
parents: 16417
diff changeset
   425
lemmas induct_atomize = induct_forall_eq induct_implies_eq induct_equal_eq induct_conj_eq
45594
wenzelm
parents: 43560
diff changeset
   426
lemmas induct_rulify [symmetric] = induct_atomize
18456
8cc35e95450a updated auxiliary facts for induct method;
wenzelm
parents: 16417
diff changeset
   427
lemmas induct_rulify_fallback =
8cc35e95450a updated auxiliary facts for induct method;
wenzelm
parents: 16417
diff changeset
   428
  induct_forall_def induct_implies_def induct_equal_def induct_conj_def
11678
6aa3e2d26683 moved atomize stuff to theory IFOL;
wenzelm
parents: 11096
diff changeset
   429
60770
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diff changeset
   430
text \<open>Method setup.\<close>
11678
6aa3e2d26683 moved atomize stuff to theory IFOL;
wenzelm
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diff changeset
   431
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diff changeset
   432
ML_file \<open>~~/src/Tools/induct.ML\<close>
60770
240563fbf41d isabelle update_cartouches;
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diff changeset
   433
ML \<open>
32171
220abde9962b renamed functor InductFun to Induct;
wenzelm
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diff changeset
   434
  structure Induct = Induct
24830
a7b3ab44d993 moved Pure/Isar/induct_attrib.ML and Provers/induct_method.ML to Tools/induct.ML;
wenzelm
parents: 24097
diff changeset
   435
  (
22139
539a63b98f76 tuned ML setup;
wenzelm
parents: 21539
diff changeset
   436
    val cases_default = @{thm case_split}
539a63b98f76 tuned ML setup;
wenzelm
parents: 21539
diff changeset
   437
    val atomize = @{thms induct_atomize}
539a63b98f76 tuned ML setup;
wenzelm
parents: 21539
diff changeset
   438
    val rulify = @{thms induct_rulify}
539a63b98f76 tuned ML setup;
wenzelm
parents: 21539
diff changeset
   439
    val rulify_fallback = @{thms induct_rulify_fallback}
34989
b5c6e59e2cd7 Adapted to changes in setup of cases method.
berghofe
parents: 34914
diff changeset
   440
    val equal_def = @{thm induct_equal_def}
34914
e391c3de0f6b Adapted to changes in setup of induct method.
berghofe
parents: 32960
diff changeset
   441
    fun dest_def _ = NONE
58957
c9e744ea8a38 proper context for match_tac etc.;
wenzelm
parents: 58889
diff changeset
   442
    fun trivial_tac _ _ = no_tac
24830
a7b3ab44d993 moved Pure/Isar/induct_attrib.ML and Provers/induct_method.ML to Tools/induct.ML;
wenzelm
parents: 24097
diff changeset
   443
  );
60770
240563fbf41d isabelle update_cartouches;
wenzelm
parents: 59990
diff changeset
   444
\<close>
11678
6aa3e2d26683 moved atomize stuff to theory IFOL;
wenzelm
parents: 11096
diff changeset
   445
24830
a7b3ab44d993 moved Pure/Isar/induct_attrib.ML and Provers/induct_method.ML to Tools/induct.ML;
wenzelm
parents: 24097
diff changeset
   446
declare case_split [cases type: o]
11678
6aa3e2d26683 moved atomize stuff to theory IFOL;
wenzelm
parents: 11096
diff changeset
   447
59940
087d81f5213e local setup of induction tools, with restricted access to auxiliary consts;
wenzelm
parents: 59780
diff changeset
   448
end
087d81f5213e local setup of induction tools, with restricted access to auxiliary consts;
wenzelm
parents: 59780
diff changeset
   449
69605
a96320074298 isabelle update -u path_cartouches;
wenzelm
parents: 69597
diff changeset
   450
ML_file \<open>~~/src/Tools/case_product.ML\<close>
41827
98eda7ffde79 setup case_product attribute in HOL and FOL
noschinl
parents: 41779
diff changeset
   451
41310
65631ca437c9 proper identifiers for consts and types;
wenzelm
parents: 36866
diff changeset
   452
65631ca437c9 proper identifiers for consts and types;
wenzelm
parents: 36866
diff changeset
   453
hide_const (open) eq
65631ca437c9 proper identifiers for consts and types;
wenzelm
parents: 36866
diff changeset
   454
4854
d1850e0964f2 tuned setup;
wenzelm
parents: 4793
diff changeset
   455
end