--- a/Unused.thy	Tue Jan 26 20:07:50 2010 +0100
+++ /dev/null	Thu Jan 01 00:00:00 1970 +0000
@@ -1,161 +0,0 @@
-(*notation ( output) "prop" ("#_" [1000] 1000) *)
-notation ( output) "Trueprop" ("#_" [1000] 1000)
-
-lemma regularize_to_injection:
-  shows "(QUOT_TRUE l \<Longrightarrow> y) \<Longrightarrow> (l = r) \<longrightarrow> y"
-  by(auto simp add: QUOT_TRUE_def)
-
-syntax
-  "Bexeq" :: "id \<Rightarrow> ('a \<Rightarrow> 'a \<Rightarrow> bool) \<Rightarrow> ('a \<Rightarrow> bool) \<Rightarrow> bool" ("(3\<exists>!!_\<in>_./ _)" [0, 0, 10] 10)
-translations
-  "\<exists>!!x\<in>A. P"  == "Bexeq A (%x. P)"
-
-
-(* Atomize infrastructure *)
-(* FIXME/TODO: is this really needed? *)
-(*
-lemma atomize_eqv:
-  shows "(Trueprop A \<equiv> Trueprop B) \<equiv> (A \<equiv> B)"
-proof
-  assume "A \<equiv> B"
-  then show "Trueprop A \<equiv> Trueprop B" by unfold
-next
-  assume *: "Trueprop A \<equiv> Trueprop B"
-  have "A = B"
-  proof (cases A)
-    case True
-    have "A" by fact
-    then show "A = B" using * by simp
-  next
-    case False
-    have "\<not>A" by fact
-    then show "A = B" using * by auto
-  qed
-  then show "A \<equiv> B" by (rule eq_reflection)
-qed
-*)
-
-
-ML {*
-  fun dest_cbinop t =
-    let
-      val (t2, rhs) = Thm.dest_comb t;
-      val (bop, lhs) = Thm.dest_comb t2;
-    in
-      (bop, (lhs, rhs))
-    end
-*}
-
-ML {*
-  fun dest_ceq t =
-    let
-      val (bop, pair) = dest_cbinop t;
-      val (bop_s, _) = Term.dest_Const (Thm.term_of bop);
-    in
-      if bop_s = "op =" then pair else (raise CTERM ("Not an equality", [t]))
-    end
-*}
-
-ML {*
-  fun split_binop_conv t =
-    let
-      val (lhs, rhs) = dest_ceq t;
-      val (bop, _) = dest_cbinop lhs;
-      val [clT, cr2] = bop |> Thm.ctyp_of_term |> Thm.dest_ctyp;
-      val [cmT, crT] = Thm.dest_ctyp cr2;
-    in
-      Drule.instantiate' [SOME clT, SOME cmT, SOME crT] [NONE, NONE, NONE, NONE, SOME bop] @{thm arg_cong2}
-    end
-*}
-
-
-ML {*
-  fun split_arg_conv t =
-    let
-      val (lhs, rhs) = dest_ceq t;
-      val (lop, larg) = Thm.dest_comb lhs;
-      val [caT, crT] = lop |> Thm.ctyp_of_term |> Thm.dest_ctyp;
-    in
-      Drule.instantiate' [SOME caT, SOME crT] [NONE, NONE, SOME lop] @{thm arg_cong}
-    end
-*}
-
-ML {*
-  fun split_binop_tac n thm =
-    let
-      val concl = Thm.cprem_of thm n;
-      val (_, cconcl) = Thm.dest_comb concl;
-      val rewr = split_binop_conv cconcl;
-    in
-      rtac rewr n thm
-    end
-      handle CTERM _ => Seq.empty
-*}
-
-
-ML {*
-  fun split_arg_tac n thm =
-    let
-      val concl = Thm.cprem_of thm n;
-      val (_, cconcl) = Thm.dest_comb concl;
-      val rewr = split_arg_conv cconcl;
-    in
-      rtac rewr n thm
-    end
-      handle CTERM _ => Seq.empty
-*}
-
-
-lemma trueprop_cong:
-  shows "(a \<equiv> b) \<Longrightarrow> (Trueprop a \<equiv> Trueprop b)"
-  by auto
-
-lemma list_induct_hol4:
-  fixes P :: "'a list \<Rightarrow> bool"
-  assumes a: "((P []) \<and> (\<forall>t. (P t) \<longrightarrow> (\<forall>h. (P (h # t)))))"
-  shows "\<forall>l. (P l)"
-  using a
-  apply (rule_tac allI)
-  apply (induct_tac "l")
-  apply (simp)
-  apply (metis)
-  done
-
-ML {*
-val no_vars = Thm.rule_attribute (fn context => fn th =>
-  let
-    val ctxt = Variable.set_body false (Context.proof_of context);
-    val ((_, [th']), _) = Variable.import true [th] ctxt;
-  in th' end);
-*}
-
-(*lemma equality_twice:
-  "a = c \<Longrightarrow> b = d \<Longrightarrow> (a = b \<longrightarrow> c = d)"
-by auto*)
-
-
-(*interpretation code *)
-(*val bindd = ((Binding.make ("", Position.none)), ([]: Attrib.src list))
-  val ((_, [eqn1pre]), lthy5) = Variable.import true [ABS_def] lthy4;
-  val eqn1i = Thm.prop_of (symmetric eqn1pre)
-  val ((_, [eqn2pre]), lthy6) = Variable.import true [REP_def] lthy5;
-  val eqn2i = Thm.prop_of (symmetric eqn2pre)
-
-  val exp_morphism = ProofContext.export_morphism lthy6 (ProofContext.init (ProofContext.theory_of lthy6));
-  val exp_term = Morphism.term exp_morphism;
-  val exp = Morphism.thm exp_morphism;
-
-  val mthd = Method.SIMPLE_METHOD ((rtac quot_thm 1) THEN
-    ALLGOALS (simp_tac (HOL_basic_ss addsimps [(symmetric (exp ABS_def)), (symmetric (exp REP_def))])))
-  val mthdt = Method.Basic (fn _ => mthd)
-  val bymt = Proof.global_terminal_proof (mthdt, NONE)
-  val exp_i = [(@{const_name QUOT_TYPE}, ((("QUOT_TYPE_I_" ^ (Binding.name_of qty_name)), true),
-    Expression.Named [("R", rel), ("Abs", abs), ("Rep", rep) ]))]*)
-
-(*||> Local_Theory.theory (fn thy =>
-      let
-        val global_eqns = map exp_term [eqn2i, eqn1i];
-        (* Not sure if the following context should not be used *)
-        val (global_eqns2, lthy7) = Variable.import_terms true global_eqns lthy6;
-        val global_eqns3 = map (fn t => (bindd, t)) global_eqns2;
-      in ProofContext.theory_of (bymt (Expression.interpretation (exp_i, []) global_eqns3 thy)) end)*)