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FSet.thy
changeset 423 2f0ad33f0241
parent 420 dcfe009c98aa
child 430 123877af04ed
child 432 9c33c0809733 
--- a/FSet.thy	Fri Nov 27 18:38:44 2009 +0100
+++ b/FSet.thy	Sat Nov 28 02:54:24 2009 +0100
@@ -341,20 +341,64 @@
 apply (tactic {* lift_tac_fset @{context} @{thm append_assoc} 1 *})
 done
 
+ML {* fun r_mk_comb_tac_fset lthy = r_mk_comb_tac' lthy rty [quot] [rel_refl] [trans2] rsp_thms *}
+
 lemma cheat: "P" sorry
 
 lemma "\<lbrakk>P EMPTY; \<And>a x. P x \<Longrightarrow> P (INSERT a x)\<rbrakk> \<Longrightarrow> P l"
 apply(tactic {* procedure_tac @{context} @{thm list.induct} 1 *})
 apply(tactic {* regularize_tac @{context} [rel_eqv] [rel_refl] 1 *})
 prefer 2
-apply (tactic {* clean_tac @{context} [quot] defs 
-                 [(@{typ "('a list \<Rightarrow> bool)"},@{typ "('a fset \<Rightarrow> bool)"})] 1 *})
-apply(tactic {* r_mk_comb_tac' @{context} rty [quot] rel_refl trans2 rsp_thms 1*})
+apply(rule cheat)
+apply(tactic {* r_mk_comb_tac_fset @{context} 1*}) (* 3 *) (* Ball-Ball *)
+apply(tactic {* r_mk_comb_tac_fset @{context} 1*}) (* 9 *) (* Rep-Abs-elim - can be complex Rep-Abs *)
+apply(tactic {* r_mk_comb_tac_fset @{context} 1*}) (* 2 *) (* lam-lam-elim for R = (===>) *) 
+apply(tactic {* r_mk_comb_tac_fset @{context} 1*}) (* 3 *) (* Ball-Ball *)
+apply(tactic {* r_mk_comb_tac_fset @{context} 1*}) (* 9 *) (* Rep-Abs-elim - can be complex Rep-Abs *)
+apply(tactic {* r_mk_comb_tac_fset @{context} 1*}) (* 2 *) (* lam-lam-elim for R = (===>) *) 
+apply(tactic {* r_mk_comb_tac_fset @{context} 1*}) (* B *) (* Cong *)
+apply(tactic {* r_mk_comb_tac_fset @{context} 1*}) (* B *) (* Cong *)
+apply(tactic {* r_mk_comb_tac_fset @{context} 1*}) (* 8 *) (* = reflexivity arising from cong *)
+apply(tactic {* r_mk_comb_tac_fset @{context} 1*}) (* A *) (* application if type needs lifting *)
+apply(tactic {* r_mk_comb_tac_fset @{context} 1*}) (* 9 *) (* Rep-Abs-elim - can be complex Rep-Abs *)
+apply(tactic {* r_mk_comb_tac_fset @{context} 1*}) (* E *) (* R x y assumptions *)
+apply(tactic {* r_mk_comb_tac_fset @{context} 1*}) (* 9 *) (* Rep-Abs-elim - can be complex Rep-Abs *)
+apply(tactic {* r_mk_comb_tac_fset @{context} 1*}) (* D *) (* reflexivity of basic relations *)
+apply(tactic {* r_mk_comb_tac_fset @{context} 1*}) (* B *) (* Cong *)
+apply(tactic {* r_mk_comb_tac_fset @{context} 1*}) (* B *) (* Cong *)
+apply(tactic {* r_mk_comb_tac_fset @{context} 1*}) (* 8 *) (* = reflexivity arising from cong *)
+apply(tactic {* r_mk_comb_tac_fset @{context} 1*}) (* B *) (* Cong *)
+apply(tactic {* r_mk_comb_tac_fset @{context} 1*}) (* 8 *) (* = reflexivity arising from cong *)
+apply(tactic {* r_mk_comb_tac_fset @{context} 1*}) (* C *) (* = and extensionality *)
+apply(tactic {* r_mk_comb_tac_fset @{context} 1*}) (* 3 *) (* Ball-Ball *)
+apply(tactic {* r_mk_comb_tac_fset @{context} 1*}) (* 9 *) (* Rep-Abs-elim - can be complex Rep-Abs *)
+apply(tactic {* r_mk_comb_tac_fset @{context} 1*}) (* 2 *) (* lam-lam-elim for R = (===>) *) 
+apply(tactic {* r_mk_comb_tac_fset @{context} 1*}) (* B *) (* Cong *)
+apply(tactic {* r_mk_comb_tac_fset @{context} 1*}) (* B *) (* Cong *)
+apply(tactic {* r_mk_comb_tac_fset @{context} 1*}) (* 8 *) (* = reflexivity arising from cong *)
+apply(tactic {* r_mk_comb_tac_fset @{context} 1*}) (* A *) (* application if type needs lifting *)
+apply(tactic {* r_mk_comb_tac_fset @{context} 1*}) (* 9 *) (* Rep-Abs-elim - can be complex Rep-Abs *)
+apply(tactic {* r_mk_comb_tac_fset @{context} 1*}) (* E *) (* R x y assumptions *)
+apply(tactic {* r_mk_comb_tac_fset @{context} 1*}) (* 9 *) (* Rep-Abs-elim - can be complex Rep-Abs *)
+apply(tactic {* r_mk_comb_tac_fset @{context} 1*}) (* E *) (* R x y assumptions *)
+apply(tactic {* r_mk_comb_tac_fset @{context} 1*}) (* A *) (* application if type needs lifting *)
+apply(tactic {* r_mk_comb_tac_fset @{context} 1*}) (* 9 *) (* Rep-Abs-elim - can be complex Rep-Abs *)
+apply(tactic {* r_mk_comb_tac_fset @{context} 1*}) (* E *) (* R x y assumptions *)
+apply(tactic {* r_mk_comb_tac_fset @{context} 1*}) (* 9 *) (* Rep-Abs-elim - can be complex Rep-Abs *)
+apply(tactic {* r_mk_comb_tac_fset @{context} 1*}) (* A *) (* application if type needs lifting *)
+apply(tactic {* r_mk_comb_tac_fset @{context} 1*}) (* A *) (* application if type needs lifting *)
+apply(tactic {* r_mk_comb_tac_fset @{context} 1*}) (* 7 *) (* respectfulness *)
+apply(tactic {* r_mk_comb_tac_fset @{context} 1*}) (* 8 *) (* = reflexivity arising from cong *)
+apply(tactic {* r_mk_comb_tac_fset @{context} 1*}) (* 9 *) (* Rep-Abs-elim - can be complex Rep-Abs *)
+apply(tactic {* r_mk_comb_tac_fset @{context} 1*}) (* E *) (* R x y assumptions *)
+apply(tactic {* r_mk_comb_tac_fset @{context} 1*}) (* A *) (* application if type needs lifting *)
+apply(tactic {* r_mk_comb_tac_fset @{context} 1*}) (* 9 *) (* Rep-Abs-elim - can be complex Rep-Abs *)
+apply(tactic {* r_mk_comb_tac_fset @{context} 1*}) (* E *) (* R x y assumptions *)
+apply(tactic {* r_mk_comb_tac_fset @{context} 1*}) (* 9 *) (* Rep-Abs-elim - can be complex Rep-Abs *)
+apply(tactic {* r_mk_comb_tac_fset @{context} 1*}) (* E *) (* R x y assumptions *)
 done
 
 
-
-
 quotient_def
   fset_rec::"'a \<Rightarrow> ('b \<Rightarrow> 'b fset \<Rightarrow> 'a \<Rightarrow> 'a) \<Rightarrow> 'b fset \<Rightarrow> 'a"
 where
@@ -400,12 +444,8 @@
   apply (assumption)
   done
 
-
 ML {* fun r_mk_comb_tac_fset lthy = r_mk_comb_tac lthy rty [quot] [rel_refl] [trans2] rsp_thms *}
 
-
-
-
 (* Construction site starts here *)
 lemma "P (x :: 'a list) (EMPTY :: 'c fset) \<Longrightarrow> (\<And>e t. P x t \<Longrightarrow> P x (INSERT e t)) \<Longrightarrow> P x l"
 apply (tactic {* procedure_tac @{context} @{thm list_induct_part} 1 *})
nominal2