
diff -r 6088fea1c8b1 -r 8a1c8dc72b5c QuotMain.thy
--- a/QuotMain.thy	Mon Dec 07 14:00:36 2009 +0100
+++ /dev/null	Thu Jan 01 00:00:00 1970 +0000
@@ -1,1191 +0,0 @@
-theory QuotMain
-imports QuotScript QuotList QuotProd Prove
-uses ("quotient_info.ML")
-     ("quotient.ML")
-     ("quotient_def.ML")
-begin
-
-
-locale QUOT_TYPE =
-  fixes R :: "'a \<Rightarrow> 'a \<Rightarrow> bool"
-  and   Abs :: "('a \<Rightarrow> bool) \<Rightarrow> 'b"
-  and   Rep :: "'b \<Rightarrow> ('a \<Rightarrow> bool)"
-  assumes equivp: "equivp R"
-  and     rep_prop: "\<And>y. \<exists>x. Rep y = R x"
-  and     rep_inverse: "\<And>x. Abs (Rep x) = x"
-  and     abs_inverse: "\<And>x. (Rep (Abs (R x))) = (R x)"
-  and     rep_inject: "\<And>x y. (Rep x = Rep y) = (x = y)"
-begin
-
-definition
-  ABS::"'a \<Rightarrow> 'b"
-where
-  "ABS x \<equiv> Abs (R x)"
-
-definition
-  REP::"'b \<Rightarrow> 'a"
-where
-  "REP a = Eps (Rep a)"
-
-lemma lem9:
-  shows "R (Eps (R x)) = R x"
-proof -
-  have a: "R x x" using equivp by (simp add: equivp_reflp_symp_transp reflp_def)
-  then have "R x (Eps (R x))" by (rule someI)
-  then show "R (Eps (R x)) = R x"
-    using equivp unfolding equivp_def by simp
-qed
-
-theorem thm10:
-  shows "ABS (REP a) \<equiv> a"
-  apply  (rule eq_reflection)
-  unfolding ABS_def REP_def
-proof -
-  from rep_prop
-  obtain x where eq: "Rep a = R x" by auto
-  have "Abs (R (Eps (Rep a))) = Abs (R (Eps (R x)))" using eq by simp
-  also have "\<dots> = Abs (R x)" using lem9 by simp
-  also have "\<dots> = Abs (Rep a)" using eq by simp
-  also have "\<dots> = a" using rep_inverse by simp
-  finally
-  show "Abs (R (Eps (Rep a))) = a" by simp
-qed
-
-lemma REP_refl:
-  shows "R (REP a) (REP a)"
-unfolding REP_def
-by (simp add: equivp[simplified equivp_def])
-
-lemma lem7:
-  shows "(R x = R y) = (Abs (R x) = Abs (R y))"
-apply(rule iffI)
-apply(simp)
-apply(drule rep_inject[THEN iffD2])
-apply(simp add: abs_inverse)
-done
-
-theorem thm11:
-  shows "R r r' = (ABS r = ABS r')"
-unfolding ABS_def
-by (simp only: equivp[simplified equivp_def] lem7)
-
-
-lemma REP_ABS_rsp:
-  shows "R f (REP (ABS g)) = R f g"
-  and   "R (REP (ABS g)) f = R g f"
-by (simp_all add: thm10 thm11)
-
-lemma Quotient:
-  "Quotient R ABS REP"
-apply(unfold Quotient_def)
-apply(simp add: thm10)
-apply(simp add: REP_refl)
-apply(subst thm11[symmetric])
-apply(simp add: equivp[simplified equivp_def])
-done
-
-lemma R_trans:
-  assumes ab: "R a b"
-  and     bc: "R b c"
-  shows "R a c"
-proof -
-  have tr: "transp R" using equivp equivp_reflp_symp_transp[of R] by simp
-  moreover have ab: "R a b" by fact
-  moreover have bc: "R b c" by fact
-  ultimately show "R a c" unfolding transp_def by blast
-qed
-
-lemma R_sym:
-  assumes ab: "R a b"
-  shows "R b a"
-proof -
-  have re: "symp R" using equivp equivp_reflp_symp_transp[of R] by simp
-  then show "R b a" using ab unfolding symp_def by blast
-qed
-
-lemma R_trans2:
-  assumes ac: "R a c"
-  and     bd: "R b d"
-  shows "R a b = R c d"
-using ac bd
-by (blast intro: R_trans R_sym)
-
-lemma REPS_same:
-  shows "R (REP a) (REP b) \<equiv> (a = b)"
-proof -
-  have "R (REP a) (REP b) = (a = b)"
-  proof
-    assume as: "R (REP a) (REP b)"
-    from rep_prop
-    obtain x y
-      where eqs: "Rep a = R x" "Rep b = R y" by blast
-    from eqs have "R (Eps (R x)) (Eps (R y))" using as unfolding REP_def by simp
-    then have "R x (Eps (R y))" using lem9 by simp
-    then have "R (Eps (R y)) x" using R_sym by blast
-    then have "R y x" using lem9 by simp
-    then have "R x y" using R_sym by blast
-    then have "ABS x = ABS y" using thm11 by simp
-    then have "Abs (Rep a) = Abs (Rep b)" using eqs unfolding ABS_def by simp
-    then show "a = b" using rep_inverse by simp
-  next
-    assume ab: "a = b"
-    have "reflp R" using equivp equivp_reflp_symp_transp[of R] by simp
-    then show "R (REP a) (REP b)" unfolding reflp_def using ab by auto
-  qed
-  then show "R (REP a) (REP b) \<equiv> (a = b)" by simp
-qed
-
-end
-
-section {* type definition for the quotient type *}
-
-(* the auxiliary data for the quotient types *)
-use "quotient_info.ML"
-
-declare [[map list = (map, list_rel)]]
-declare [[map * = (prod_fun, prod_rel)]]
-declare [[map "fun" = (fun_map, fun_rel)]]
-
-(* identity quotient is not here as it has to be applied first *)
-lemmas [quotient_thm] =
-  fun_quotient list_quotient prod_quotient
-
-lemmas [quotient_rsp] =
-  quot_rel_rsp nil_rsp cons_rsp foldl_rsp pair_rsp
-
-(* fun_map is not here since equivp is not true *)
-(* TODO: option, ... *)
-lemmas [quotient_equiv] =
-  identity_equivp list_equivp prod_equivp
-
-
-ML {* maps_lookup @{theory} "List.list" *}
-ML {* maps_lookup @{theory} "*" *}
-ML {* maps_lookup @{theory} "fun" *}
-
-
-(* definition of the quotient types *)
-(* FIXME: should be called quotient_typ.ML *)
-use "quotient.ML"
-
-
-(* lifting of constants *)
-use "quotient_def.ML"
-
-section {* Simset setup *}
-
-(* since HOL_basic_ss is too "big", we need to set up *)
-(* our own minimal simpset                            *)
-ML {*
-fun  mk_minimal_ss ctxt =
-  Simplifier.context ctxt empty_ss
-    setsubgoaler asm_simp_tac
-    setmksimps (mksimps [])
-*}
-
-section {* atomize *}
-
-lemma atomize_eqv[atomize]:
-  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 atomize_thm thm =
-let
-  val thm' = Thm.freezeT (forall_intr_vars thm)
-  val thm'' = ObjectLogic.atomize (cprop_of thm')
-in
-  @{thm equal_elim_rule1} OF [thm'', thm']
-end
-*}
-
-section {* infrastructure about id *}
-
-lemma prod_fun_id: "prod_fun id id \<equiv> id"
-  by (rule eq_reflection) (simp add: prod_fun_def)
-
-lemma map_id: "map id \<equiv> id"
-  apply (rule eq_reflection)
-  apply (rule ext)
-  apply (rule_tac list="x" in list.induct)
-  apply (simp_all)
-  done
-
-lemmas id_simps =
-  fun_map_id[THEN eq_reflection]
-  id_apply[THEN eq_reflection]
-  id_def[THEN eq_reflection,symmetric]
-  prod_fun_id map_id
-
-ML {*
-fun simp_ids thm =
-  MetaSimplifier.rewrite_rule @{thms id_simps} thm
-*}
-
-section {* Debugging infrastructure for testing tactics *}
-
-ML {*
-fun my_print_tac ctxt s i thm =
-let
-  val prem_str = nth (prems_of thm) (i - 1)
-                 |> Syntax.string_of_term ctxt
-                 handle Subscript => "no subgoal"
-  val _ = tracing (s ^ "\n" ^ prem_str)
-in
-  Seq.single thm
-end *}
-
-ML {*
-fun DT ctxt s tac i thm =
-let
-  val before_goal = nth (prems_of thm) (i - 1)
-                    |> Syntax.string_of_term ctxt
-  val before_msg = ["before: " ^ s, before_goal, "after: " ^ s]
-                   |> cat_lines
-in 
-  EVERY [tac i, my_print_tac ctxt before_msg i] thm
-end
-
-fun NDT ctxt s tac thm = tac thm  
-*}
-
-section {* Matching of terms and types *}
-
-ML {*
-fun matches_typ (ty, ty') =
-  case (ty, ty') of
-    (_, TVar _) => true
-  | (TFree x, TFree x') => x = x'
-  | (Type (s, tys), Type (s', tys')) => 
-       s = s' andalso 
-       if (length tys = length tys') 
-       then (List.all matches_typ (tys ~~ tys')) 
-       else false
-  | _ => false
-*}
-
-ML {*
-fun matches_term (trm, trm') = 
-   case (trm, trm') of 
-     (_, Var _) => true
-   | (Const (s, ty), Const (s', ty')) => s = s' andalso matches_typ (ty, ty')
-   | (Free (x, ty), Free (x', ty')) => x = x' andalso matches_typ (ty, ty')
-   | (Bound i, Bound j) => i = j
-   | (Abs (_, T, t), Abs (_, T', t')) => matches_typ (T, T') andalso matches_term (t, t')
-   | (t $ s, t' $ s') => matches_term (t, t') andalso matches_term (s, s') 
-   | _ => false
-*}
-
-section {* Infrastructure for collecting theorems for starting the lifting *}
-
-ML {*
-fun lookup_quot_data lthy qty =
-  let
-    val qty_name = fst (dest_Type qty)
-    val SOME quotdata = quotdata_lookup lthy qty_name
-    (* TODO: Should no longer be needed *)
-    val rty = Logic.unvarifyT (#rtyp quotdata)
-    val rel = #rel quotdata
-    val rel_eqv = #equiv_thm quotdata
-    val rel_refl = @{thm equivp_reflp} OF [rel_eqv]
-  in
-    (rty, rel, rel_refl, rel_eqv)
-  end
-*}
-
-ML {*
-fun lookup_quot_thms lthy qty_name =
-  let
-    val thy = ProofContext.theory_of lthy;
-    val trans2 = PureThy.get_thm thy ("QUOT_TYPE_I_" ^ qty_name ^ ".R_trans2")
-    val reps_same = PureThy.get_thm thy ("QUOT_TYPE_I_" ^ qty_name ^ ".REPS_same")
-    val absrep = PureThy.get_thm thy ("QUOT_TYPE_I_" ^ qty_name ^ ".thm10")
-    val quot = PureThy.get_thm thy ("Quotient_" ^ qty_name)
-  in
-    (trans2, reps_same, absrep, quot)
-  end
-*}
-
-section {* Regularization *} 
-
-(*
-Regularizing an rtrm means:
- - quantifiers over a type that needs lifting are replaced by
-   bounded quantifiers, for example:
-      \<forall>x. P     \<Longrightarrow>     \<forall>x \<in> (Respects R). P  /  All (Respects R) P
-
-   the relation R is given by the rty and qty;
- 
- - abstractions over a type that needs lifting are replaced
-   by bounded abstractions:
-      \<lambda>x. P     \<Longrightarrow>     Ball (Respects R) (\<lambda>x. P)
-
- - equalities over the type being lifted are replaced by
-   corresponding relations:
-      A = B     \<Longrightarrow>     A \<approx> B
-
-   example with more complicated types of A, B:
-      A = B     \<Longrightarrow>     (op = \<Longrightarrow> op \<approx>) A B
-*)
-
-ML {*
-(* builds the relation that is the argument of respects *)
-fun mk_resp_arg lthy (rty, qty) =
-let
-  val thy = ProofContext.theory_of lthy
-in  
-  if rty = qty
-  then HOLogic.eq_const rty
-  else
-    case (rty, qty) of
-      (Type (s, tys), Type (s', tys')) =>
-       if s = s' 
-       then let
-              val SOME map_info = maps_lookup thy s
-              val args = map (mk_resp_arg lthy) (tys ~~ tys')
-            in
-              list_comb (Const (#relfun map_info, dummyT), args) 
-            end  
-       else let  
-              val SOME qinfo = quotdata_lookup_thy thy s'
-              (* FIXME: check in this case that the rty and qty *)
-              (* FIXME: correspond to each other *)
-              val (s, _) = dest_Const (#rel qinfo)
-              (* FIXME: the relation should only be the string        *)
-              (* FIXME: and the type needs to be calculated as below; *)
-              (* FIXME: maybe one should actually have a term         *)
-              (* FIXME: and one needs to force it to have this type   *)
-            in
-              Const (s, rty --> rty --> @{typ bool})
-            end
-      | _ => HOLogic.eq_const dummyT 
-             (* FIXME: check that the types correspond to each other? *)
-end
-*}
-
-ML {*
-val mk_babs = Const (@{const_name Babs}, dummyT)
-val mk_ball = Const (@{const_name Ball}, dummyT)
-val mk_bex  = Const (@{const_name Bex}, dummyT)
-val mk_resp = Const (@{const_name Respects}, dummyT)
-*}
-
-ML {*
-(* - applies f to the subterm of an abstraction,   *)
-(*   otherwise to the given term,                  *)
-(* - used by regularize, therefore abstracted      *)
-(*   variables do not have to be treated specially *)
-
-fun apply_subt f trm1 trm2 =
-  case (trm1, trm2) of
-    (Abs (x, T, t), Abs (x', T', t')) => Abs (x, T, f t t')
-  | _ => f trm1 trm2
-
-(* the major type of All and Ex quantifiers *)
-fun qnt_typ ty = domain_type (domain_type ty)  
-*}
-
-ML {*
-(* produces a regularized version of rtm      *)
-(* - the result is still not completely typed *)
-(* - does not need any special treatment of   *)
-(*   bound variables                          *)
-
-fun regularize_trm lthy rtrm qtrm =
-  case (rtrm, qtrm) of
-    (Abs (x, ty, t), Abs (x', ty', t')) =>
-       let
-         val subtrm = Abs(x, ty, regularize_trm lthy t t')
-       in
-         if ty = ty'
-         then subtrm
-         else mk_babs $ (mk_resp $ mk_resp_arg lthy (ty, ty')) $ subtrm
-       end
-
-  | (Const (@{const_name "All"}, ty) $ t, Const (@{const_name "All"}, ty') $ t') =>
-       let
-         val subtrm = apply_subt (regularize_trm lthy) t t'
-       in
-         if ty = ty'
-         then Const (@{const_name "All"}, ty) $ subtrm
-         else mk_ball $ (mk_resp $ mk_resp_arg lthy (qnt_typ ty, qnt_typ ty')) $ subtrm
-       end
-
-  | (Const (@{const_name "Ex"}, ty) $ t, Const (@{const_name "Ex"}, ty') $ t') =>
-       let
-         val subtrm = apply_subt (regularize_trm lthy) t t'
-       in
-         if ty = ty'
-         then Const (@{const_name "Ex"}, ty) $ subtrm
-         else mk_bex $ (mk_resp $ mk_resp_arg lthy (qnt_typ ty, qnt_typ ty')) $ subtrm
-       end
-
-  | (* equalities need to be replaced by appropriate equivalence relations *) 
-    (Const (@{const_name "op ="}, ty), Const (@{const_name "op ="}, ty')) =>
-         if ty = ty'
-         then rtrm
-         else mk_resp_arg lthy (domain_type ty, domain_type ty') 
-
-  | (* in this case we check whether the given equivalence relation is correct *) 
-    (rel, Const (@{const_name "op ="}, ty')) =>
-       let 
-         val exc = LIFT_MATCH "regularise (relation mismatch)"
-         val rel_ty = (fastype_of rel) handle TERM _ => raise exc 
-         val rel' = mk_resp_arg lthy (domain_type rel_ty, domain_type ty') 
-       in 
-         if rel' = rel
-         then rtrm
-         else raise exc
-       end  
-  | (_, Const (s, _)) =>
-       let 
-         fun same_name (Const (s, _)) (Const (s', _)) = (s = s')
-           | same_name _ _ = false
-       in
-         if same_name rtrm qtrm 
-         then rtrm 
-         else 
-           let 
-             fun exc1 s = LIFT_MATCH ("regularize (constant " ^ s ^ " not found)")
-             val exc2   = LIFT_MATCH ("regularize (constant mismatch)")
-             val thy = ProofContext.theory_of lthy
-             val rtrm' = (#rconst (qconsts_lookup thy s)) handle NotFound => raise (exc1 s) 
-           in 
-             if matches_term (rtrm, rtrm')
-             then rtrm
-             else raise exc2
-           end
-       end 
-
-  | (t1 $ t2, t1' $ t2') =>
-       (regularize_trm lthy t1 t1') $ (regularize_trm lthy t2 t2')
-
-  | (Free (x, ty), Free (x', ty')) => 
-       (* this case cannot arrise as we start with two fully atomized terms *)
-       raise (LIFT_MATCH "regularize (frees)")
-
-  | (Bound i, Bound i') =>
-       if i = i' 
-       then rtrm 
-       else raise (LIFT_MATCH "regularize (bounds mismatch)")
-
-  | (rt, qt) =>
-       raise (LIFT_MATCH "regularize (default)")
-*}
-
-ML {*
-fun equiv_tac ctxt =
-  REPEAT_ALL_NEW (FIRST' 
-    [resolve_tac (equiv_rules_get ctxt)])
-*}
-
-ML {*
-fun equiv_solver_tac ss = equiv_tac (Simplifier.the_context ss)
-val equiv_solver = Simplifier.mk_solver' "Equivalence goal solver" equiv_solver_tac
-*}
-
-ML {*
-fun prep_trm thy (x, (T, t)) =
-  (cterm_of thy (Var (x, T)), cterm_of thy t)
-
-fun prep_ty thy (x, (S, ty)) =
-  (ctyp_of thy (TVar (x, S)), ctyp_of thy ty)
-*}
-
-ML {*
-fun matching_prs thy pat trm =
-let
-  val univ = Unify.matchers thy [(pat, trm)]
-  val SOME (env, _) = Seq.pull univ
-  val tenv = Vartab.dest (Envir.term_env env)
-  val tyenv = Vartab.dest (Envir.type_env env)
-in
-  (map (prep_ty thy) tyenv, map (prep_trm thy) tenv)
-end
-*}
-
-ML {*
-fun calculate_instance ctxt thm redex R1 R2 =
-let
-  val thy = ProofContext.theory_of ctxt
-  val goal = Const (@{const_name "equivp"}, dummyT) $ R2  
-             |> Syntax.check_term ctxt
-             |> HOLogic.mk_Trueprop 
-  val eqv_prem = Goal.prove ctxt [] [] goal (fn {context,...} => equiv_tac context 1)
-  val thm = (@{thm eq_reflection} OF [thm OF [eqv_prem]])
-  val R1c = cterm_of thy R1
-  val thmi = Drule.instantiate' [] [SOME R1c] thm
-  val inst = matching_prs thy (term_of (Thm.lhs_of thmi)) redex
-  val thm2 = Drule.eta_contraction_rule (Drule.instantiate inst thmi)
-in
-  SOME thm2
-end
-handle _ => NONE
-(* FIXME/TODO: what is the place where the exception can be raised: matching_prs? *)
-*}
-
-ML {*
-fun ball_bex_range_simproc ss redex =
-let
-  val ctxt = Simplifier.the_context ss
-in 
- case redex of
-    (Const (@{const_name "Ball"}, _) $ (Const (@{const_name "Respects"}, _) $ 
-      (Const (@{const_name "fun_rel"}, _) $ R1 $ R2)) $ _) =>
-        calculate_instance ctxt @{thm ball_reg_eqv_range} redex R1 R2
-  | (Const (@{const_name "Bex"}, _) $ (Const (@{const_name "Respects"}, _) $ 
-      (Const (@{const_name "fun_rel"}, _) $ R1 $ R2)) $ _) =>  
-        calculate_instance ctxt @{thm bex_reg_eqv_range} redex R1 R2
-  | _ => NONE
-end
-*}
-
-lemma eq_imp_rel: 
-  shows "equivp R \<Longrightarrow> a = b \<longrightarrow> R a b"
-by (simp add: equivp_reflp)
-
-(* FIXME/TODO: How does regularizing work? *)
-(* FIXME/TODO: needs to be adapted
-
-To prove that the raw theorem implies the regularised one, 
-we try in order:
-
- - Reflexivity of the relation
- - Assumption
- - Elimnating quantifiers on both sides of toplevel implication
- - Simplifying implications on both sides of toplevel implication
- - Ball (Respects ?E) ?P = All ?P
- - (\<And>x. ?R x \<Longrightarrow> ?P x \<longrightarrow> ?Q x) \<Longrightarrow> All ?P \<longrightarrow> Ball ?R ?Q
-
-*)
-ML {*
-fun regularize_tac ctxt =
-let
-  val thy = ProofContext.theory_of ctxt
-  val pat_ball = @{term "Ball (Respects (R1 ===> R2)) P"}
-  val pat_bex  = @{term "Bex (Respects (R1 ===> R2)) P"}
-  val simproc = Simplifier.simproc_i thy "" [pat_ball, pat_bex] (K (ball_bex_range_simproc))
-  val simpset = (mk_minimal_ss ctxt) 
-                       addsimps @{thms ball_reg_eqv bex_reg_eqv}
-                       addsimprocs [simproc] addSolver equiv_solver
-  (* TODO: Make sure that there are no list_rel, pair_rel etc involved *)
-  val eq_eqvs = map (fn x => @{thm eq_imp_rel} OF [x]) (equiv_rules_get ctxt)
-in
-  ObjectLogic.full_atomize_tac THEN'
-  simp_tac simpset THEN'
-  REPEAT_ALL_NEW (FIRST' [
-    rtac @{thm ball_reg_right},
-    rtac @{thm bex_reg_left},
-    resolve_tac (Inductive.get_monos ctxt),
-    rtac @{thm ball_all_comm},
-    rtac @{thm bex_ex_comm},
-    resolve_tac eq_eqvs,
-    simp_tac simpset])
-end
-*}
-
-section {* Injections of rep and abses *}
-
-(*
-Injecting repabs means:
-
-  For abstractions:
-  * If the type of the abstraction doesn't need lifting we recurse.
-  * If it does we add RepAbs around the whole term and check if the
-    variable needs lifting.
-    * If it doesn't then we recurse
-    * If it does we recurse and put 'RepAbs' around all occurences
-      of the variable in the obtained subterm. This in combination
-      with the RepAbs above will let us change the type of the
-      abstraction with rewriting.
-  For applications:
-  * If the term is 'Respects' applied to anything we leave it unchanged
-  * If the term needs lifting and the head is a constant that we know
-    how to lift, we put a RepAbs and recurse
-  * If the term needs lifting and the head is a free applied to subterms
-    (if it is not applied we treated it in Abs branch) then we
-    put RepAbs and recurse
-  * Otherwise just recurse.
-*)
-
-ML {*
-fun mk_repabs lthy (T, T') trm = 
-  Quotient_Def.get_fun repF lthy (T, T') 
-    $ (Quotient_Def.get_fun absF lthy (T, T') $ trm)
-*}
-
-ML {*
-(* bound variables need to be treated properly,    *)
-(* as the type of subterms need to be calculated   *)
-(* in the abstraction case                         *)
-
-fun inj_repabs_trm lthy (rtrm, qtrm) =
- case (rtrm, qtrm) of
-    (Const (@{const_name "Ball"}, T) $ r $ t, Const (@{const_name "All"}, _) $ t') =>
-       Const (@{const_name "Ball"}, T) $ r $ (inj_repabs_trm lthy (t, t'))
-
-  | (Const (@{const_name "Bex"}, T) $ r $ t, Const (@{const_name "Ex"}, _) $ t') =>
-       Const (@{const_name "Bex"}, T) $ r $ (inj_repabs_trm lthy (t, t'))
-
-  | (Const (@{const_name "Babs"}, T) $ r $ t, t' as (Abs _)) =>
-       Const (@{const_name "Babs"}, T) $ r $ (inj_repabs_trm lthy (t, t'))
-
-  | (Abs (x, T, t), Abs (x', T', t')) =>
-      let
-        val rty = fastype_of rtrm
-        val qty = fastype_of qtrm
-        val (y, s) = Term.dest_abs (x, T, t)
-        val (_, s') = Term.dest_abs (x', T', t')
-        val yvar = Free (y, T)
-        val result = Term.lambda_name (y, yvar) (inj_repabs_trm lthy (s, s'))
-      in
-        if rty = qty 
-        then result
-        else mk_repabs lthy (rty, qty) result
-      end
-
-  | (t $ s, t' $ s') =>  
-       (inj_repabs_trm lthy (t, t')) $ (inj_repabs_trm lthy (s, s'))
-
-  | (Free (_, T), Free (_, T')) => 
-        if T = T' 
-        then rtrm 
-        else mk_repabs lthy (T, T') rtrm
-
-  | (_, Const (@{const_name "op ="}, _)) => rtrm
-
-    (* FIXME: check here that rtrm is the corresponding definition for the const *)
-  | (_, Const (_, T')) =>
-      let
-        val rty = fastype_of rtrm
-      in 
-        if rty = T'                    
-        then rtrm
-        else mk_repabs lthy (rty, T') rtrm
-      end   
-  
-  | _ => raise (LIFT_MATCH "injection")
-*}
-
-section {* RepAbs Injection Tactic *}
-
-ML {*
-fun quotient_tac ctxt =
-  REPEAT_ALL_NEW (FIRST'
-    [rtac @{thm identity_quotient},
-     resolve_tac (quotient_rules_get ctxt)])
-*}
-
-(* solver for the simplifier *)
-ML {*
-fun quotient_solver_tac ss = quotient_tac (Simplifier.the_context ss)
-val quotient_solver = Simplifier.mk_solver' "Quotient goal solver" quotient_solver_tac
-*}
-
-ML {*
-fun solve_quotient_assums ctxt thm =
-  let val gl = hd (Drule.strip_imp_prems (cprop_of thm)) in
-  thm OF [Goal.prove_internal [] gl (fn _ => quotient_tac ctxt 1)]
-  end
-  handle _ => error "solve_quotient_assums failed. Maybe a quotient_thm is missing"
-*}
-
-(* Not used *)
-(* It proves the Quotient assumptions by calling quotient_tac *)
-ML {*
-fun solve_quotient_assum i ctxt thm =
-  let
-    val tac =
-      (compose_tac (false, thm, i)) THEN_ALL_NEW
-      (quotient_tac ctxt);
-    val gc = Drule.strip_imp_concl (cprop_of thm);
-  in
-    Goal.prove_internal [] gc (fn _ => tac 1)
-  end
-  handle _ => error "solve_quotient_assum"
-*}
-
-definition
-  "QUOT_TRUE x \<equiv> True"
-
-ML {*
-fun find_qt_asm asms =
-  let
-    fun find_fun trm =
-      case trm of
-        (Const(@{const_name Trueprop}, _) $ (Const (@{const_name QUOT_TRUE}, _) $ _)) => true
-      | _ => false
-  in
-    case find_first find_fun asms of
-      SOME (_ $ (_ $ (f $ a))) => (f, a)
-    | SOME _ => error "find_qt_asm: no pair"
-    | NONE => error "find_qt_asm: no assumption"
-  end
-*}
-
-(*
-To prove that the regularised theorem implies the abs/rep injected, 
-we try:
-
- 1) theorems 'trans2' from the appropriate QUOT_TYPE
- 2) remove lambdas from both sides: lambda_rsp_tac
- 3) remove Ball/Bex from the right hand side
- 4) use user-supplied RSP theorems
- 5) remove rep_abs from the right side
- 6) reflexivity of equality
- 7) split applications of lifted type (apply_rsp)
- 8) split applications of non-lifted type (cong_tac)
- 9) apply extentionality
- A) reflexivity of the relation
- B) assumption
-    (Lambdas under respects may have left us some assumptions)
- C) proving obvious higher order equalities by simplifying fun_rel
-    (not sure if it is still needed?)
- D) unfolding lambda on one side
- E) simplifying (= ===> =) for simpler respectfulness
-
-*)
-
-lemma quot_true_dests:
-  shows QT_all: "QUOT_TRUE (All P) \<Longrightarrow> QUOT_TRUE P"
-  and   QT_ex:  "QUOT_TRUE (Ex P) \<Longrightarrow> QUOT_TRUE P"
-  and   QT_lam: "QUOT_TRUE (\<lambda>x. P x) \<Longrightarrow> (\<And>x. QUOT_TRUE  (P x))"
-  and   QT_ext: "(\<And>x. QUOT_TRUE (a x) \<Longrightarrow> f x = g x) \<Longrightarrow> (QUOT_TRUE a \<Longrightarrow> f = g)"
-apply(simp_all add: QUOT_TRUE_def ext)
-done
-
-lemma QUOT_TRUE_i: "(QUOT_TRUE (a :: bool) \<Longrightarrow> P) \<Longrightarrow> P"
-by (simp add: QUOT_TRUE_def)
-
-lemma QUOT_TRUE_imp: "QUOT_TRUE a \<equiv> QUOT_TRUE b"
-by (simp add: QUOT_TRUE_def)
-
-ML {*
-fun quot_true_conv1 ctxt fnctn ctrm =
-  case (term_of ctrm) of
-    (Const (@{const_name QUOT_TRUE}, _) $ x) =>
-    let
-      val fx = fnctn x;
-      val thy = ProofContext.theory_of ctxt;
-      val cx = cterm_of thy x;
-      val cfx = cterm_of thy fx;
-      val cxt = ctyp_of thy (fastype_of x);
-      val cfxt = ctyp_of thy (fastype_of fx);
-      val thm = Drule.instantiate' [SOME cxt, SOME cfxt] [SOME cx, SOME cfx] @{thm QUOT_TRUE_imp}
-    in
-      Conv.rewr_conv thm ctrm
-    end
-*}
-
-ML {*
-fun quot_true_conv ctxt fnctn ctrm =
-  case (term_of ctrm) of
-    (Const (@{const_name QUOT_TRUE}, _) $ _) =>
-      quot_true_conv1 ctxt fnctn ctrm
-  | _ $ _ => Conv.comb_conv (quot_true_conv ctxt fnctn) ctrm
-  | Abs _ => Conv.abs_conv (fn (_, ctxt) => quot_true_conv ctxt fnctn) ctxt ctrm
-  | _ => Conv.all_conv ctrm
-*}
-
-ML {*
-fun quot_true_tac ctxt fnctn = CONVERSION
-    ((Conv.params_conv ~1 (fn ctxt =>
-       (Conv.prems_conv ~1 (quot_true_conv ctxt fnctn)))) ctxt)
-*}
-
-ML {* fun dest_comb (f $ a) = (f, a) *}
-ML {* fun dest_bcomb ((_ $ l) $ r) = (l, r) *}
-(* TODO: Can this be done easier? *)
-ML {*
-fun unlam t =
-  case t of
-    (Abs a) => snd (Term.dest_abs a)
-  | _ => unlam (Abs("", domain_type (fastype_of t), (incr_boundvars 1 t) $ (Bound 0)))
-*}
-
-ML {*
-fun dest_fun_type (Type("fun", [T, S])) = (T, S)
-  | dest_fun_type _ = error "dest_fun_type"
-*}
-
-ML {*
-val bare_concl = HOLogic.dest_Trueprop o Logic.strip_assums_concl
-*}
-
-ML {*
-val apply_rsp_tac =
-  Subgoal.FOCUS (fn {concl, asms, context,...} =>
-    case ((HOLogic.dest_Trueprop (term_of concl))) of
-      ((R2 $ (f $ x) $ (g $ y))) =>
-        (let
-          val (asmf, asma) = find_qt_asm (map term_of asms);
-        in
-          if (fastype_of asmf) = (fastype_of f) then no_tac else let
-            val ty_a = fastype_of x;
-            val ty_b = fastype_of asma;
-            val ty_c = range_type (type_of f);
-            val thy = ProofContext.theory_of context;
-            val ty_inst = map (SOME o (ctyp_of thy)) [ty_a, ty_b, ty_c];
-            val thm = Drule.instantiate' ty_inst [] @{thm apply_rsp}
-            val te = solve_quotient_assums context thm
-            val t_inst = map (SOME o (cterm_of thy)) [R2, f, g, x, y];
-            val thm = Drule.instantiate' [] t_inst te
-          in
-            compose_tac (false, thm, 2) 1
-          end
-        end
-        handle ERROR "find_qt_asm: no pair" => no_tac)
-    | _ => no_tac)
-*}
-ML {*
-fun SOLVES' tac = tac THEN_ALL_NEW (fn _ => no_tac)
-*}
-
-ML {*
-fun rep_abs_rsp_tac ctxt =
-  SUBGOAL (fn (goal, i) =>
-    case (bare_concl goal) of 
-      (rel $ _ $ (rep $ (abs $ _))) =>
-        (let
-           val thy = ProofContext.theory_of ctxt;
-           val (ty_a, ty_b) = dest_fun_type (fastype_of abs);
-           val ty_inst = map (SOME o (ctyp_of thy)) [ty_a, ty_b];
-           val t_inst = map (SOME o (cterm_of thy)) [rel, abs, rep];
-           val thm = Drule.instantiate' ty_inst t_inst @{thm rep_abs_rsp}
-           val te = solve_quotient_assums ctxt thm
-         in
-           rtac te i
-         end
-         handle _ => no_tac)
-    | _ => no_tac)
-*}
-
-ML {*
-fun inj_repabs_tac_match ctxt trans2 = SUBGOAL (fn (goal, i) =>
-(case (bare_concl goal) of
-    (* (R1 ===> R2) (\<lambda>x\<dots>) (\<lambda>y\<dots>) ----> \<lbrakk>R1 x y\<rbrakk> \<Longrightarrow> R2 (\<dots>x) (\<dots>y) *)
-  ((Const (@{const_name fun_rel}, _) $ _ $ _) $ (Abs _) $ (Abs _))
-      => rtac @{thm fun_rel_id} THEN' quot_true_tac ctxt unlam
-
-    (* (op =) (Ball\<dots>) (Ball\<dots>) ----> (op =) (\<dots>) (\<dots>) *)
-| (Const (@{const_name "op ="},_) $
-    (Const(@{const_name Ball},_) $ (Const (@{const_name Respects}, _) $ _) $ _) $
-    (Const(@{const_name Ball},_) $ (Const (@{const_name Respects}, _) $ _) $ _))
-      => rtac @{thm ball_rsp} THEN' dtac @{thm QT_all}
-
-    (* (R1 ===> op =) (Ball\<dots>) (Ball\<dots>) ----> \<lbrakk>R1 x y\<rbrakk> \<Longrightarrow> (Ball\<dots>x) = (Ball\<dots>y) *)
-| (Const (@{const_name fun_rel}, _) $ _ $ _) $
-    (Const(@{const_name Ball},_) $ (Const (@{const_name Respects}, _) $ _) $ _) $
-    (Const(@{const_name Ball},_) $ (Const (@{const_name Respects}, _) $ _) $ _)
-      => rtac @{thm fun_rel_id} THEN' quot_true_tac ctxt unlam
-
-    (* (op =) (Bex\<dots>) (Bex\<dots>) ----> (op =) (\<dots>) (\<dots>) *)
-| Const (@{const_name "op ="},_) $
-    (Const(@{const_name Bex},_) $ (Const (@{const_name Respects}, _) $ _) $ _) $
-    (Const(@{const_name Bex},_) $ (Const (@{const_name Respects}, _) $ _) $ _)
-      => rtac @{thm bex_rsp} THEN' dtac @{thm QT_ex}
-
-    (* (R1 ===> op =) (Bex\<dots>) (Bex\<dots>) ----> \<lbrakk>R1 x y\<rbrakk> \<Longrightarrow> (Bex\<dots>x) = (Bex\<dots>y) *)
-| (Const (@{const_name fun_rel}, _) $ _ $ _) $
-    (Const(@{const_name Bex},_) $ (Const (@{const_name Respects}, _) $ _) $ _) $
-    (Const(@{const_name Bex},_) $ (Const (@{const_name Respects}, _) $ _) $ _)
-      => rtac @{thm fun_rel_id} THEN' quot_true_tac ctxt unlam
-
-| (_ $
-    (Const(@{const_name Babs},_) $ (Const (@{const_name Respects}, _) $ _) $ _) $
-    (Const(@{const_name Babs},_) $ (Const (@{const_name Respects}, _) $ _) $ _))
-      => rtac @{thm babs_rsp} THEN' RANGE [quotient_tac ctxt]
-
-    (* reflexivity of operators arising from Cong_tac *)
-| Const (@{const_name "op ="},_) $ _ $ _ 
-      => rtac @{thm refl} ORELSE'
-          (resolve_tac trans2 THEN' RANGE [
-            quot_true_tac ctxt (fst o dest_bcomb), quot_true_tac ctxt (snd o dest_bcomb)])
-
-(* TODO: These patterns should should be somehow combined and generalized... *)
-| (Const (@{const_name fun_rel}, _) $ _ $ _) $
-    (Const (@{const_name fun_rel}, _) $ _ $ _) $
-    (Const (@{const_name fun_rel}, _) $ _ $ _)
-    => rtac @{thm quot_rel_rsp} THEN_ALL_NEW quotient_tac ctxt
-
-| (Const (@{const_name fun_rel}, _) $ _ $ _) $
-    (Const (@{const_name prod_rel}, _) $ _ $ _) $
-    (Const (@{const_name prod_rel}, _) $ _ $ _)
-    => rtac @{thm quot_rel_rsp} THEN_ALL_NEW quotient_tac ctxt
-
-   (* respectfulness of constants; in particular of a simple relation *)
-| _ $ (Const _) $ (Const _)  (* fun_rel, list_rel, etc but not equality *)
-    => resolve_tac (rsp_rules_get ctxt) THEN_ALL_NEW quotient_tac ctxt
-
-    (* R (\<dots>) (Rep (Abs \<dots>)) ----> R (\<dots>) (\<dots>) *)
-    (* observe ---> *)
-| _ $ _ $ _ 
-    => rep_abs_rsp_tac ctxt
-
-| _ => error "inj_repabs_tac not a relation"
-) i)
-*}
-
-ML {*
-fun inj_repabs_tac ctxt rel_refl trans2 =
-  (FIRST' [
-    inj_repabs_tac_match ctxt trans2,
-    (* R (t $ \<dots>) (t' $ \<dots>) ----> apply_rsp   provided type of t needs lifting *)
-    NDT ctxt "A" (apply_rsp_tac ctxt THEN'
-                (RANGE [quot_true_tac ctxt (fst o dest_comb), quot_true_tac ctxt (snd o dest_comb)])),
-    (* (op =) (t $ \<dots>) (t' $ \<dots>) ----> Cong   provided type of t does not need lifting *)
-    (* merge with previous tactic *)
-    NDT ctxt "B" (Cong_Tac.cong_tac @{thm cong} THEN'
-                (RANGE [quot_true_tac ctxt (fst o dest_comb), quot_true_tac ctxt (snd o dest_comb)])),
-    (* (op =) (\<lambda>x\<dots>) (\<lambda>x\<dots>) ----> (op =) (\<dots>) (\<dots>) *)
-    NDT ctxt "C" (rtac @{thm ext} THEN' quot_true_tac ctxt unlam),
-    (* resolving with R x y assumptions *)
-    NDT ctxt "E" (atac),
-    (* reflexivity of the basic relations *)
-    (* R \<dots> \<dots> *)
-    NDT ctxt "D" (resolve_tac rel_refl)
-    ])
-*}
-
-ML {*
-fun all_inj_repabs_tac ctxt rel_refl trans2 =
-  REPEAT_ALL_NEW (inj_repabs_tac ctxt rel_refl trans2)
-*}
-
-section {* Cleaning of the theorem *}
-
-ML {*
-fun make_inst lhs t =
-  let
-    val _ $ (Abs (_, _, (f as Var (_, Type ("fun", [T, _]))) $ u)) = lhs;
-    val _ $ (Abs (_, _, g)) = t;
-    fun mk_abs i t =
-      if incr_boundvars i u aconv t then Bound i
-      else (case t of
-        t1 $ t2 => mk_abs i t1 $ mk_abs i t2
-      | Abs (s, T, t') => Abs (s, T, mk_abs (i + 1) t')
-      | Bound j => if i = j then error "make_inst" else t
-      | _ => t);
-  in (f, Abs ("x", T, mk_abs 0 g)) end;
-*}
-
-ML {*
-fun lambda_prs_simple_conv ctxt ctrm =
-  case (term_of ctrm) of
-   ((Const (@{const_name fun_map}, _) $ r1 $ (a2 as (Const (s,_)))) $ (Abs _)) =>
-     let
-       val thy = ProofContext.theory_of ctxt
-       val (ty_b, ty_a) = dest_fun_type (fastype_of r1)
-       val (ty_c, ty_d) = dest_fun_type (fastype_of a2)
-       val tyinst = map (SOME o (ctyp_of thy)) [ty_a, ty_b, ty_c, ty_d]
-       val tinst = [NONE, NONE, SOME (cterm_of thy r1), NONE, SOME (cterm_of thy a2)]
-       val lpi = Drule.instantiate' tyinst tinst @{thm lambda_prs}
-       val te = @{thm eq_reflection} OF [solve_quotient_assums ctxt (solve_quotient_assums ctxt lpi)]
-       val ts = MetaSimplifier.rewrite_rule @{thms id_simps} te
-       val _ = tracing ("te rule:\n" ^ (Syntax.string_of_term ctxt (prop_of te)));
-       val tl = Thm.lhs_of ts
-       val (insp, inst) = make_inst (term_of tl) (term_of ctrm)
-       val ti = Drule.instantiate ([], [(cterm_of thy insp, cterm_of thy inst)]) ts
-       val _ = if not (s = @{const_name "id"}) then
-                  (tracing "lambda_prs";
-                   tracing ("redex:\n" ^ (Syntax.string_of_term ctxt (term_of ctrm)));
-                   tracing ("lpi rule:\n" ^ (Syntax.string_of_term ctxt (prop_of lpi)));
-                   tracing ("te rule:\n" ^ (Syntax.string_of_term ctxt (prop_of te)));
-                   tracing ("ts rule:\n" ^ (Syntax.string_of_term ctxt (prop_of ts)));
-                   tracing ("instantiated rule:\n" ^ (Syntax.string_of_term ctxt (prop_of ti))))
-               else ()
-     in
-       Conv.rewr_conv ti ctrm
-     end
-  | _ => Conv.all_conv ctrm
-*}
-
-ML {*
-val lambda_prs_conv =
-  More_Conv.top_conv lambda_prs_simple_conv
-
-fun lambda_prs_tac ctxt = CONVERSION (lambda_prs_conv ctxt)
-*}
-
-(*
- Cleaning the theorem consists of three rewriting steps.
- The first two need to be done before fun_map is unfolded
-
- 1) lambda_prs:
-     (Rep1 ---> Abs2) (\<lambda>x. Rep2 (f (Abs1 x)))  ---->  f
-
-    Implemented as conversion since it is not a pattern.
-
- 2) all_prs (the same for exists):
-     Ball (Respects R) ((abs ---> id) f)  ---->  All f
-
-    Rewriting with definitions from the argument defs
-     (rep ---> abs) oldConst ----> newconst
-
- 3) Quotient_rel_rep:
-      Rel (Rep x) (Rep y)  ---->  x = y
-
-    Quotient_abs_rep:
-      Abs (Rep x)  ---->  x
-
-    id_simps; fun_map.simps
-*)
-
-ML {*
-fun clean_tac lthy =
-  let
-    val thy = ProofContext.theory_of lthy;
-    val defs = map (Thm.varifyT o symmetric o #def) (qconsts_dest thy)
-      (* FIXME: shouldn't the definitions already be varified? *)
-    val thms1 = @{thms all_prs ex_prs} @ defs
-    val thms2 = @{thms eq_reflection[OF fun_map.simps]} 
-                @ @{thms id_simps Quotient_abs_rep Quotient_rel_rep} 
-    fun simps thms = (mk_minimal_ss lthy) addsimps thms addSolver quotient_solver
-  in
-    EVERY' [lambda_prs_tac lthy,
-            simp_tac (simps thms1),
-            simp_tac (simps thms2),
-            TRY o rtac refl]
-  end
-*}
-
-section {* Genralisation of free variables in a goal *}
-
-ML {*
-fun inst_spec ctrm =
-   Drule.instantiate' [SOME (ctyp_of_term ctrm)] [NONE, SOME ctrm] @{thm spec}
-
-fun inst_spec_tac ctrms =
-  EVERY' (map (dtac o inst_spec) ctrms)
-
-fun all_list xs trm = 
-  fold (fn (x, T) => fn t' => HOLogic.mk_all (x, T, t')) xs trm
-
-fun apply_under_Trueprop f = 
-  HOLogic.dest_Trueprop #> f #> HOLogic.mk_Trueprop
-
-fun gen_frees_tac ctxt =
- SUBGOAL (fn (concl, i) =>
-  let
-    val thy = ProofContext.theory_of ctxt
-    val vrs = Term.add_frees concl []
-    val cvrs = map (cterm_of thy o Free) vrs
-    val concl' = apply_under_Trueprop (all_list vrs) concl
-    val goal = Logic.mk_implies (concl', concl)
-    val rule = Goal.prove ctxt [] [] goal 
-      (K (EVERY1 [inst_spec_tac (rev cvrs), atac]))
-  in
-    rtac rule i
-  end)  
-*}
-
-section {* General outline of the lifting procedure *}
-
-(* - A is the original raw theorem          *)
-(* - B is the regularized theorem           *)
-(* - C is the rep/abs injected version of B *) 
-(* - D is the lifted theorem                *)
-(*                                          *)
-(* - b is the regularization step           *)
-(* - c is the rep/abs injection step        *)
-(* - d is the cleaning part                 *)
-
-lemma lifting_procedure:
-  assumes a: "A"
-  and     b: "A \<Longrightarrow> B"
-  and     c: "B = C"
-  and     d: "C = D"
-  shows   "D"
-  using a b c d
-  by simp
-
-ML {*
-fun lift_match_error ctxt fun_str rtrm qtrm =
-let
-  val rtrm_str = Syntax.string_of_term ctxt rtrm
-  val qtrm_str = Syntax.string_of_term ctxt qtrm
-  val msg = [enclose "[" "]" fun_str, "The quotient theorem\n", qtrm_str, 
-             "and the lifted theorem\n", rtrm_str, "do not match"]
-in
-  error (space_implode " " msg)
-end
-*}
-
-ML {* 
-fun procedure_inst ctxt rtrm qtrm =
-let
-  val thy = ProofContext.theory_of ctxt
-  val rtrm' = HOLogic.dest_Trueprop rtrm
-  val qtrm' = HOLogic.dest_Trueprop qtrm
-  val reg_goal = 
-        Syntax.check_term ctxt (regularize_trm ctxt rtrm' qtrm')
-        handle (LIFT_MATCH s) => lift_match_error ctxt s rtrm qtrm
-  val _ = warning "Regularization done."
-  val inj_goal = 
-        Syntax.check_term ctxt (inj_repabs_trm ctxt (reg_goal, qtrm'))
-        handle (LIFT_MATCH s) => lift_match_error ctxt s rtrm qtrm
-  val _ = warning "RepAbs Injection done."
-in
-  Drule.instantiate' []
-    [SOME (cterm_of thy rtrm'),
-     SOME (cterm_of thy reg_goal),
-     SOME (cterm_of thy inj_goal)] @{thm lifting_procedure}
-end
-*}
-
-(* Left for debugging *)
-ML {*
-fun procedure_tac ctxt rthm =
-  ObjectLogic.full_atomize_tac
-  THEN' gen_frees_tac ctxt
-  THEN' CSUBGOAL (fn (gl, i) =>
-    let
-      val rthm' = atomize_thm rthm
-      val rule = procedure_inst ctxt (prop_of rthm') (term_of gl)
-      val thm = Drule.instantiate' [] [SOME (snd (Thm.dest_comb gl))] @{thm QUOT_TRUE_i}
-    in
-      (rtac rule THEN' RANGE [rtac rthm', (fn _ => all_tac), rtac thm]) i
-    end)
-*}
-
-ML {*
-(* FIXME/TODO should only get as arguments the rthm like procedure_tac *)
-
-fun lift_tac ctxt rthm =
-  ObjectLogic.full_atomize_tac
-  THEN' gen_frees_tac ctxt
-  THEN' CSUBGOAL (fn (gl, i) =>
-    let
-      val rthm' = atomize_thm rthm
-      val rule = procedure_inst ctxt (prop_of rthm') (term_of gl)
-      val rel_refl = map (fn x => @{thm equivp_reflp} OF [x]) (equiv_rules_get ctxt)
-      val quotients = quotient_rules_get ctxt
-      val trans2 = map (fn x => @{thm equals_rsp} OF [x]) quotients
-      val thm = Drule.instantiate' [] [SOME (snd (Thm.dest_comb gl))] @{thm QUOT_TRUE_i}
-    in
-      (rtac rule THEN'
-       RANGE [rtac rthm',
-              regularize_tac ctxt,
-              rtac thm THEN' all_inj_repabs_tac ctxt rel_refl trans2,
-              clean_tac ctxt]) i
-    end)
-*}
-
-end
-




