--- a/QuotMain.thy Thu Oct 22 10:45:33 2009 +0200
+++ b/QuotMain.thy Thu Oct 22 11:43:12 2009 +0200
@@ -1018,9 +1018,32 @@
val insts = Thm.match (pat, concl)
in
rtac (Drule.instantiate insts thm) 1
-end)
+end
+handle _ => no_tac
+)
*}
+ML {*
+fun r_mk_comb_tac ctxt quot_thm reflex_thm trans_thm =
+ (FIRST' [
+ rtac @{thm FUN_QUOTIENT},
+ rtac quot_thm,
+ rtac @{thm IDENTITY_QUOTIENT},
+ rtac @{thm card1_rsp},
+ rtac @{thm ext},
+ rtac trans_thm,
+ instantiate_tac @{thm REP_ABS_RSP(1)} ctxt,
+ instantiate_tac @{thm APPLY_RSP} ctxt,
+ rtac reflex_thm,
+ Cong_Tac.cong_tac @{thm cong},
+ atac
+ ])
+*}
+
+ML {*
+fun r_mk_comb_tac_fset ctxt =
+ r_mk_comb_tac ctxt @{thm QUOTIENT_fset} @{thm list_eq_refl} @{thm QUOT_TYPE_I_fset.R_trans2}
+*}
ML {* val thm = @{thm list_induct_r} OF [atomize_thm @{thm list_induct_hol4}] *}
@@ -1031,21 +1054,12 @@
apply (atomize(full))
apply (simp only: id_def[symmetric])
(* APPLY_RSP_TAC *)
-apply (tactic {* instantiate_tac @{thm APPLY_RSP} @{context} 1 *})
-apply (rule FUN_QUOTIENT)
-apply (rule FUN_QUOTIENT)
-apply (rule QUOTIENT_fset)
-apply (rule IDENTITY_QUOTIENT)
-apply (rule IDENTITY_QUOTIENT)
-apply (rule IDENTITY_QUOTIENT)
+apply (tactic {* r_mk_comb_tac_fset @{context} 1 *})
+apply (tactic {* REPEAT_ALL_NEW (r_mk_comb_tac_fset @{context}) 1 *})
+apply (tactic {* r_mk_comb_tac_fset @{context} 1 *})
prefer 2
-(* ABS_REP_RSP_TAC *)
-apply (tactic {* instantiate_tac @{thm REP_ABS_RSP(1)} @{context} 1 *})
-apply (rule FUN_QUOTIENT)
-apply (rule FUN_QUOTIENT)
-apply (rule QUOTIENT_fset)
-apply (rule IDENTITY_QUOTIENT)
-apply (rule IDENTITY_QUOTIENT)
+apply (tactic {* r_mk_comb_tac_fset @{context} 1 *})
+apply (tactic {* REPEAT_ALL_NEW (r_mk_comb_tac_fset @{context}) 1 *})
(* LAMBDA_RES_TAC *)
apply (simp only: FUN_REL.simps)
apply (rule allI)
@@ -1064,30 +1078,19 @@
(* REFL_TAC *)
apply (simp)
(* APPLY_RSP_TAC *)
-apply (tactic {* instantiate_tac @{thm APPLY_RSP} @{context} 1 *})
-apply (rule QUOTIENT_fset)
-apply (rule IDENTITY_QUOTIENT)
-apply (tactic {* instantiate_tac @{thm REP_ABS_RSP(1)} @{context} 1 *})
-apply (rule FUN_QUOTIENT)
-apply (rule QUOTIENT_fset)
-apply (rule IDENTITY_QUOTIENT)
+apply (tactic {* r_mk_comb_tac_fset @{context} 1 *})
+apply (tactic {* REPEAT_ALL_NEW (r_mk_comb_tac_fset @{context}) 1 *})
+apply (tactic {* r_mk_comb_tac_fset @{context} 1 *})
+apply (tactic {* REPEAT_ALL_NEW (r_mk_comb_tac_fset @{context}) 1 *})
apply (simp only: FUN_REL.simps)
-apply (tactic {* instantiate_tac @{thm REP_ABS_RSP(1)} @{context} 1 *})
-apply (rule QUOTIENT_fset)
-(* MINE *)
-apply (rule list_eq_refl )
-apply (tactic {* instantiate_tac @{thm APPLY_RSP} @{context} 1 *})
-apply (rule FUN_QUOTIENT)
-apply (rule QUOTIENT_fset)
-apply (rule IDENTITY_QUOTIENT)
-apply (rule IDENTITY_QUOTIENT)
+apply (tactic {* REPEAT_ALL_NEW (r_mk_comb_tac_fset @{context}) 1 *})
+apply (tactic {* r_mk_comb_tac_fset @{context} 1 *})
+apply (tactic {* REPEAT_ALL_NEW (r_mk_comb_tac_fset @{context}) 1 *})
+apply (tactic {* r_mk_comb_tac_fset @{context} 1 *})
(* TODO don't know how to handle ho_respects *)
prefer 2
(* ABS_REP_RSP *)
-apply (tactic {* instantiate_tac @{thm REP_ABS_RSP(1)} @{context} 1 *})
-apply (rule FUN_QUOTIENT)
-apply (rule QUOTIENT_fset)
-apply (rule IDENTITY_QUOTIENT)
+apply (tactic {* REPEAT_ALL_NEW (r_mk_comb_tac_fset @{context}) 1 *})
(* LAMBDA_RSP *)
apply (simp only: FUN_REL.simps)
apply (rule allI)
@@ -1100,45 +1103,32 @@
(* REFL_TAC *)
apply (simp)
(* APPLY_RSP *)
-apply (tactic {* instantiate_tac @{thm APPLY_RSP} @{context} 1 *})
-apply (rule QUOTIENT_fset)
-apply (rule IDENTITY_QUOTIENT)
-apply (tactic {* instantiate_tac @{thm REP_ABS_RSP(1)} @{context} 1 *})
-apply (rule FUN_QUOTIENT)
-apply (rule QUOTIENT_fset)
-apply (rule IDENTITY_QUOTIENT)
+apply (tactic {* r_mk_comb_tac_fset @{context} 1 *})
+apply (tactic {* REPEAT_ALL_NEW (r_mk_comb_tac_fset @{context}) 1 *})
+apply (tactic {* r_mk_comb_tac_fset @{context} 1 *})
+apply (tactic {* REPEAT_ALL_NEW (r_mk_comb_tac_fset @{context}) 1 *})
(* MINE *)
apply (simp only: FUN_REL.simps)
-apply (tactic {* instantiate_tac @{thm REP_ABS_RSP(1)} @{context} 1 *})
-apply (rule QUOTIENT_fset)
-(* FIRST_ASSUM MATCH_ACCEPT_TAC *)
-apply (assumption)
+apply (tactic {* REPEAT_ALL_NEW (r_mk_comb_tac_fset @{context}) 1 *})
(* MK_COMB_TAC *)
apply (tactic {* Cong_Tac.cong_tac @{thm cong} 1 *})
(* REFL_TAC *)
apply (simp)
(* W(C (curry op THEN) (G... *)
-apply (rule ext)
-(* APPLY_RSP *)
-apply (tactic {* instantiate_tac @{thm APPLY_RSP} @{context} 1 *})
-apply (rule QUOTIENT_fset)
-apply (rule IDENTITY_QUOTIENT)
-apply (tactic {* instantiate_tac @{thm REP_ABS_RSP(1)} @{context} 1 *})
-apply (rule FUN_QUOTIENT)
-apply (rule QUOTIENT_fset)
-apply (rule IDENTITY_QUOTIENT)
+apply (tactic {* r_mk_comb_tac_fset @{context} 1 *})
+apply (tactic {* r_mk_comb_tac_fset @{context} 1 *})
+apply (tactic {* REPEAT_ALL_NEW (r_mk_comb_tac_fset @{context}) 1 *})
+apply (tactic {* r_mk_comb_tac_fset @{context} 1 *})
+apply (tactic {* REPEAT_ALL_NEW (r_mk_comb_tac_fset @{context}) 1 *})
apply (simp only: FUN_REL.simps)
-apply (tactic {* instantiate_tac @{thm REP_ABS_RSP(1)} @{context} 1 *})
-apply (rule QUOTIENT_fset)
-(* APPLY_RSP *)
-apply (tactic {* instantiate_tac @{thm APPLY_RSP} @{context} 1 *})
-apply (rule QUOTIENT_fset)
-apply (rule QUOTIENT_fset)
-apply (tactic {* instantiate_tac @{thm APPLY_RSP} @{context} 1 *})
-apply (rule IDENTITY_QUOTIENT)
-apply (rule FUN_QUOTIENT)
-apply (rule QUOTIENT_fset)
-apply (rule QUOTIENT_fset)
+apply (tactic {* r_mk_comb_tac_fset @{context} 1 *})
+apply (tactic {* r_mk_comb_tac_fset @{context} 1 *})
+apply (tactic {* r_mk_comb_tac_fset @{context} 1 *})
+apply (tactic {* r_mk_comb_tac_fset @{context} 1 *})
+apply (tactic {* r_mk_comb_tac_fset @{context} 1 *})
+apply (tactic {* r_mk_comb_tac_fset @{context} 1 *})
+apply (tactic {* REPEAT_ALL_NEW (r_mk_comb_tac_fset @{context}) 1 *})
+apply (tactic {* REPEAT_ALL_NEW (r_mk_comb_tac_fset @{context}) 1 *})
(* CONS respects *)
apply (simp add: FUN_REL.simps)
apply (rule allI)
@@ -1148,35 +1138,23 @@
apply (rule cons_preserves)
apply (assumption)
apply (simp)
-apply (tactic {* instantiate_tac @{thm REP_ABS_RSP(1)} @{context} 1 *})
-apply (rule QUOTIENT_fset)
-apply (assumption)
+apply (tactic {* REPEAT_ALL_NEW (r_mk_comb_tac_fset @{context}) 1 *})
prefer 2
-apply (tactic {* instantiate_tac @{thm APPLY_RSP} @{context} 1 *})
-apply (rule FUN_QUOTIENT)
-apply (rule QUOTIENT_fset)
-apply (rule IDENTITY_QUOTIENT)
-apply (rule IDENTITY_QUOTIENT)
+apply (tactic {* r_mk_comb_tac_fset @{context} 1 *})
+apply (tactic {* REPEAT_ALL_NEW (r_mk_comb_tac_fset @{context}) 1 *})
+apply (tactic {* r_mk_comb_tac_fset @{context} 1 *})
prefer 2
-apply (tactic {* instantiate_tac @{thm REP_ABS_RSP(1)} @{context} 1 *})
-apply (rule FUN_QUOTIENT)
-apply (rule QUOTIENT_fset)
-apply (rule IDENTITY_QUOTIENT)
+apply (tactic {* REPEAT_ALL_NEW (r_mk_comb_tac_fset @{context}) 1 *})
apply (simp only: FUN_REL.simps)
apply (rule allI)
apply (rule allI)
apply (rule impI)
-apply (tactic {* instantiate_tac @{thm APPLY_RSP} @{context} 1 *})
-apply (rule QUOTIENT_fset)
-apply (rule IDENTITY_QUOTIENT)
-apply (tactic {* instantiate_tac @{thm REP_ABS_RSP(1)} @{context} 1 *})
-apply (rule FUN_QUOTIENT)
-apply (rule QUOTIENT_fset)
-apply (rule IDENTITY_QUOTIENT)
+apply (tactic {* r_mk_comb_tac_fset @{context} 1 *})
+apply (tactic {* REPEAT_ALL_NEW (r_mk_comb_tac_fset @{context}) 1 *})
+apply (tactic {* r_mk_comb_tac_fset @{context} 1 *})
+apply (tactic {* REPEAT_ALL_NEW (r_mk_comb_tac_fset @{context}) 1 *})
apply (simp add: FUN_REL.simps)
-apply (tactic {* instantiate_tac @{thm REP_ABS_RSP(1)} @{context} 1 *})
-apply (rule QUOTIENT_fset)
-apply (assumption)
+apply (tactic {* REPEAT_ALL_NEW (r_mk_comb_tac_fset @{context}) 1 *})
sorry
prove list_induct_t: trm