--- a/LamEx.thy	Fri Oct 30 19:03:53 2009 +0100
+++ b/LamEx.thy	Sat Oct 31 11:20:55 2009 +0100
@@ -196,6 +196,7 @@
 
 thm rlam.inject
 thm pi_var
+ 
 
 lemma var_inject:
   shows "(Var a = Var b) = (a = b)"
@@ -221,19 +222,54 @@
 
 
 
-ML {* val t_a = atomize_thm @{thm alpha.cases} *}
+ML {* val t_a = atomize_thm @{thm alpha.induct} *}
+(* prove {* build_regularize_goal t_a rty rel @{context}  *}
+ML_prf {*  fun tac ctxt =
+     (FIRST' [
+      rtac rel_refl,
+      atac,
+      rtac @{thm universal_twice},
+      (rtac @{thm impI} THEN' atac),
+      rtac @{thm implication_twice},
+      EqSubst.eqsubst_tac ctxt [0]
+        [(@{thm equiv_res_forall} OF [rel_eqv]),
+         (@{thm equiv_res_exists} OF [rel_eqv])],
+      (rtac @{thm impI} THEN' (asm_full_simp_tac (Simplifier.context ctxt HOL_ss)) THEN' rtac rel_refl),
+      (rtac @{thm RIGHT_RES_FORALL_REGULAR})
+     ]);
+ *}
+  apply (tactic {* tac @{context} 1 *}) *)
 ML {* val t_r = regularize t_a rty rel rel_eqv rel_refl @{context} *}
 ML {* val t_t = repabs @{context} t_r consts rty qty quot rel_refl trans2 rsp_thms *}
-ML {* val abs = findabs rty (prop_of t_a); *}
-ML {* val simp_lam_prs_thms = map (make_simp_lam_prs_thm @{context} quot) abs *}
-ML {* val t_l = repeat_eqsubst_thm @{context} simp_lam_prs_thms t_t *}
+
+ML {* val abs = findabs rty (prop_of (atomize_thm @{thm alpha.induct})) *}
+ML {* val aps = findaps rty (prop_of (atomize_thm @{thm alpha.induct})) *}
+ML {* val aps = @{typ "LamEx.rlam \<Rightarrow> bool"} :: aps; *}
+ML {* val simp_app_prs_thms = map (make_simp_prs_thm @{context} quot @{thm APP_PRS}) aps *}
+ML {* val simp_lam_prs_thms = map (make_simp_prs_thm @{context} quot @{thm LAMBDA_PRS}) abs *}
+ML {* val t_l = repeat_eqsubst_thm @{context} (simp_app_prs_thms @ simp_lam_prs_thms) t_t *}
 ML {* val t_a = simp_allex_prs @{context} quot t_l *}
+ML {* val thm = 
+  @{thm FORALL_PRS[OF FUN_QUOTIENT[OF QUOTIENT_lam FUN_QUOTIENT[OF QUOTIENT_lam IDENTITY_QUOTIENT]], symmetric]} *}
+ML {* val t_a1 = eqsubst_thm @{context} [thm] t_a *}
 ML {* val defs_sym = add_lower_defs @{context} defs; *}
-ML {* val t_d = repeat_eqsubst_thm @{context} defs_sym t_a *}
+ML {* val t_d = repeat_eqsubst_thm @{context} defs_sym t_a1 *}
 ML {* val t_r = MetaSimplifier.rewrite_rule [reps_same] t_d *}
-ML {* ObjectLogic.rulify t_r *}
+ML {* val t_r1 = repeat_eqsubst_thm @{context} @{thms fun_map.simps} t_r *}
+ML {* val t_r2 = repeat_eqsubst_thm @{context} @{thms QUOT_TYPE_I_lam.thm10} t_r1 *}
+ML {* val t_r3 = repeat_eqsubst_thm @{context} @{thms id_apply} t_r2 *}
+
+ML {* val alpha_induct = ObjectLogic.rulify t_r3 *}
 
+local_setup {*
+  Quotient.note (@{binding "alpha_induct"}, alpha_induct) #> snd
+*}
 
+lemma
+  assumes a: "(a::lam) = b"
+  shows "False"
+  using a
+  apply (rule alpha_induct)
 
 fun
   option_map::"('a \<Rightarrow> 'b) \<Rightarrow> ('a noption) \<Rightarrow> ('b noption)"