--- a/QuotMain.thy Mon Nov 09 13:47:46 2009 +0100
+++ b/QuotMain.thy Mon Nov 09 15:23:33 2009 +0100
@@ -160,16 +160,6 @@
(* lifting of constants *)
use "quotient_def.ML"
-
-text {* FIXME: auxiliary function *}
-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);
-*}
-
section {* ATOMIZE *}
lemma atomize_eqv[atomize]:
@@ -340,6 +330,8 @@
| _ => trm
*}
+(* For polymorphic types we need to find the type of the Relation term. *)
+(* TODO: we assume that the relation is a Constant. Is this always true? *)
ML {*
fun my_reg_inst lthy rel rty trm =
case rel of
@@ -349,7 +341,7 @@
(*
ML {*
- text {*val r = term_of @{cpat "R::?'a list \<Rightarrow> ?'a list \<Rightarrow>bool"};*}
+ text {*val r = term_of @{cpat "R::?'a list \<Rightarrow> ?'a list \<Rightarrow> bool"};*}
val r = Free ("R", dummyT);
val t = (my_reg @{context} r @{typ "'a list"} @{term "\<forall>(x::'b list). P x"});
val t2 = Syntax.check_term @{context} t;
@@ -372,7 +364,8 @@
"(c \<longrightarrow> a) \<Longrightarrow> (a \<Longrightarrow> b \<longrightarrow> d) \<Longrightarrow> (a \<longrightarrow> b) \<longrightarrow> (c \<longrightarrow> d)"
by auto
-(*lemma equality_twice: "a = c \<Longrightarrow> b = d \<Longrightarrow> (a = b \<longrightarrow> c = d)"
+(*lemma equality_twice:
+ "a = c \<Longrightarrow> b = d \<Longrightarrow> (a = b \<longrightarrow> c = d)"
by auto*)
ML {*
@@ -381,27 +374,72 @@
val goal = build_regularize_goal thm rty rel lthy;
fun tac ctxt =
(ObjectLogic.full_atomize_tac) THEN'
- REPEAT_ALL_NEW (FIRST' [
- rtac rel_refl,
- atac,
- rtac @{thm universal_twice},
- (rtac @{thm impI} THEN' atac),
- rtac @{thm implication_twice},
- (*rtac @{thm equality_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 HOL_ss) THEN' rtac rel_refl),
- (rtac @{thm RIGHT_RES_FORALL_REGULAR})
- ]);
- val cthm = Goal.prove lthy [] [] goal
- (fn {context,...} => tac context 1);
+ REPEAT_ALL_NEW (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 HOL_ss) THEN' rtac rel_refl),
+ (rtac @{thm RIGHT_RES_FORALL_REGULAR})
+ ]);
+ val cthm = Goal.prove lthy [] [] goal
+ (fn {context, ...} => tac context 1);
in
cthm OF [thm]
end
*}
section {* RepAbs injection *}
+(*
+
+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.
+ 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.
+
+The injection is done in the following phases:
+ 1) build_repabs_term inserts rep-abs pairs in the term
+ 2) we prove the equality between the original theorem and this one
+ 3) we use Pure.equal_elim_rule1 to get the new theorem.
+
+To prove that the old theorem implies the new one, we first
+atomize it and then try:
+
+ 1) theorems 'trans2' from the QUOT_TYPE
+ 2) remove lambdas from both sides (LAMBDA_RES_TAC)
+ 3) remove Ball/Bex
+ 4) use RSP theorems
+ 5) remove rep_abs from right side
+ 6) reflexivity
+ 7) split applications of lifted type (apply_rsp)
+ 8) split applications of non-lifted type (cong_tac)
+ 9) apply extentionality
+10) relation reflexive
+11) assumption
+12) proving obvious higher order equalities by simplifying fun_rel
+ (not sure if still needed?)
+13) unfolding lambda on one side
+14) simplifying (= ===> =) for simpler respectfullness
+
+*)
+
(* Needed to have a meta-equality *)
lemma id_def_sym: "(\<lambda>x. x) \<equiv> id"
@@ -489,9 +527,10 @@
then (get_const flag (ty, (exchange_ty lthy rty qty ty)))
else (case ty of
TFree _ => (mk_identity ty, (ty, ty))
- | Type (_, []) => (mk_identity ty, (ty, ty))
- | Type ("fun" , [ty1, ty2]) =>
- get_fun_fun [get_fun_noexchange (negF flag) (rty,qty) lthy ty1, get_fun_noexchange flag (rty,qty) lthy ty2]
+ | Type (_, []) => (mk_identity ty, (ty, ty))
+ | Type ("fun" , [ty1, ty2]) =>
+ get_fun_fun [get_fun_noexchange (negF flag) (rty, qty) lthy ty1,
+ get_fun_noexchange flag (rty, qty) lthy ty2]
| Type (s, tys) => get_fun_aux s (map (get_fun_noexchange flag (rty, qty) lthy) tys)
| _ => raise ERROR ("no type variables"))
end
@@ -582,7 +621,7 @@
val cgoal = cterm_of (ProofContext.theory_of ctxt) (Logic.mk_equals (term_of (Thm.cprop_of thm), term_of a'))
val rt = Toplevel.program (fn () => Goal.prove_internal [] cgoal (fn _ => tac));
in
- @{thm Pure.equal_elim_rule1} OF [rt,thm]
+ @{thm Pure.equal_elim_rule1} OF [rt, thm]
end
*}
@@ -593,7 +632,7 @@
*}
ML {*
-fun build_repabs_term lthy thm constructors rty qty =
+fun build_repabs_term lthy thm consts rty qty =
let
val rty = Logic.varifyT rty;
val qty = Logic.varifyT qty;
@@ -607,44 +646,44 @@
val ty = fastype_of tm
in Syntax.check_term lthy ((get_fun_new repF (rty, qty) lthy ty) $ (mk_abs tm)) end
- fun is_constructor (Const (x, _)) = member (op =) constructors x
- | is_constructor _ = false;
+ fun is_lifted_const (Const (x, _)) = member (op =) consts x
+ | is_lifted_const _ = false;
fun build_aux lthy tm =
case tm of
- Abs (a as (_, vty, _)) =>
- let
- val (vs, t) = Term.dest_abs a;
- val v = Free(vs, vty);
- val t' = lambda v (build_aux lthy t)
- in
- if (not (needs_lift rty (fastype_of tm))) then t'
- else mk_repabs (
- if not (needs_lift rty vty) then t'
- else
+ Abs (a as (_, vty, _)) =>
let
- val v' = mk_repabs v;
- val t1 = Envir.beta_norm (t' $ v')
+ val (vs, t) = Term.dest_abs a;
+ val v = Free(vs, vty);
+ val t' = lambda v (build_aux lthy t)
in
- lambda v t1
+ if (not (needs_lift rty (fastype_of tm))) then t'
+ else mk_repabs (
+ if not (needs_lift rty vty) then t'
+ else
+ let
+ val v' = mk_repabs v;
+ (* TODO: I believe this is not needed any more *)
+ val t1 = Envir.beta_norm (t' $ v')
+ in
+ lambda v t1
+ end)
end
- )
- end
- | x =>
- let
- val (opp, tms0) = Term.strip_comb tm
- val tms = map (build_aux lthy) tms0
- val ty = fastype_of tm
- in
- if (((fst (Term.dest_Const opp)) = @{const_name Respects}) handle _ => false)
- then (list_comb (opp, (hd tms0) :: (tl tms)))
- else if (is_constructor opp andalso needs_lift rty ty) then
- mk_repabs (list_comb (opp,tms))
- else if ((Term.is_Free opp) andalso (length tms > 0) andalso (needs_lift rty ty)) then
- mk_repabs(list_comb(opp,tms))
- else if tms = [] then opp
- else list_comb(opp, tms)
- end
+ | x =>
+ case Term.strip_comb tm of
+ (Const(@{const_name Respects}, _), _) => tm
+ | (opp, tms0) =>
+ let
+ val tms = map (build_aux lthy) tms0
+ val ty = fastype_of tm
+ in
+ if (is_lifted_const opp andalso needs_lift rty ty) then
+ mk_repabs (list_comb (opp, tms))
+ else if ((Term.is_Free opp) andalso (length tms > 0) andalso (needs_lift rty ty)) then
+ mk_repabs (list_comb (opp, tms))
+ else if tms = [] then opp
+ else list_comb(opp, tms)
+ end
in
repeat_eqsubst_prop lthy @{thms id_def_sym}
(build_aux lthy (Thm.prop_of thm))
@@ -675,14 +714,17 @@
rtac @{thm FUN_QUOTIENT},
rtac quot_thm,
rtac @{thm IDENTITY_QUOTIENT},
- (fn i => CHANGED (simp_tac (HOL_ss addsimps @{thms FUN_MAP_I}) i) THEN rtac @{thm IDENTITY_QUOTIENT} i)
+ (
+ fn i => CHANGED (simp_tac (HOL_ss addsimps @{thms FUN_MAP_I}) i) THEN
+ rtac @{thm IDENTITY_QUOTIENT} i
+ )
])
*}
ML {*
fun LAMBDA_RES_TAC ctxt i st =
(case (term_of o #concl o fst) (Subgoal.focus ctxt i st) of
- (_ $ (_ $ (Abs(_,_,_))$(Abs(_,_,_)))) =>
+ (_ $ (_ $ (Abs(_, _, _))$(Abs(_, _, _)))) =>
(EqSubst.eqsubst_tac ctxt [0] @{thms FUN_REL.simps}) THEN'
(rtac @{thm allI}) THEN' (rtac @{thm allI}) THEN' (rtac @{thm impI})
| _ => fn _ => no_tac) i st
@@ -691,10 +733,10 @@
ML {*
fun WEAK_LAMBDA_RES_TAC ctxt i st =
(case (term_of o #concl o fst) (Subgoal.focus ctxt i st) of
- (_ $ (_ $ _$(Abs(_,_,_)))) =>
+ (_ $ (_ $ _ $ (Abs(_, _, _)))) =>
(EqSubst.eqsubst_tac ctxt [0] @{thms FUN_REL.simps}) THEN'
(rtac @{thm allI}) THEN' (rtac @{thm allI}) THEN' (rtac @{thm impI})
- | (_ $ (_ $ (Abs(_,_,_))$_)) =>
+ | (_ $ (_ $ (Abs(_, _, _)) $ _)) =>
(EqSubst.eqsubst_tac ctxt [0] @{thms FUN_REL.simps}) THEN'
(rtac @{thm allI}) THEN' (rtac @{thm allI}) THEN' (rtac @{thm impI})
| _ => fn _ => no_tac) i st
@@ -715,9 +757,10 @@
*}
ML {*
-val res_forall_rsp_tac = Subgoal.FOCUS (fn {concl, context = ctxt, ...} =>
+val ball_rsp_tac = Subgoal.FOCUS (fn {concl, context = ctxt, ...} =>
let
- val _ $ (_ $ (Const (@{const_name Ball}, _) $ _) $ (Const (@{const_name Ball}, _) $ _)) = term_of concl
+ val _ $ (_ $ (Const (@{const_name Ball}, _) $ _) $
+ (Const (@{const_name Ball}, _) $ _)) = term_of concl
in
((simp_tac ((Simplifier.context ctxt HOL_ss) addsimps @{thms FUN_REL.simps}))
THEN' rtac @{thm allI} THEN' rtac @{thm allI} THEN' rtac @{thm impI}
@@ -729,9 +772,10 @@
*}
ML {*
-val res_exists_rsp_tac = Subgoal.FOCUS (fn {concl, context = ctxt, ...} =>
+val bex_rsp_tac = Subgoal.FOCUS (fn {concl, context = ctxt, ...} =>
let
- val _ $ (_ $ (Const (@{const_name Bex}, _) $ _) $ (Const (@{const_name Bex}, _) $ _)) = term_of concl
+ val _ $ (_ $ (Const (@{const_name Bex}, _) $ _) $
+ (Const (@{const_name Bex}, _) $ _)) = term_of concl
in
((simp_tac ((Simplifier.context ctxt HOL_ss) addsimps @{thms FUN_REL.simps}))
THEN' rtac @{thm allI} THEN' rtac @{thm allI} THEN' rtac @{thm impI}
@@ -745,13 +789,10 @@
ML {*
fun r_mk_comb_tac ctxt rty quot_thm reflex_thm trans_thm rsp_thms =
(FIRST' [
-(* rtac @{thm FUN_QUOTIENT},
- rtac quot_thm,
- rtac @{thm IDENTITY_QUOTIENT},*)
rtac trans_thm,
LAMBDA_RES_TAC ctxt,
- res_forall_rsp_tac ctxt,
- res_exists_rsp_tac ctxt,
+ ball_rsp_tac ctxt,
+ bex_rsp_tac ctxt,
FIRST' (map rtac rsp_thms),
(instantiate_tac @{thm REP_ABS_RSP(1)} ctxt THEN' (RANGE [quotient_tac quot_thm])),
rtac refl,
@@ -771,9 +812,9 @@
*}
ML {*
-fun repabs lthy thm constructors rty qty quot_thm reflex_thm trans_thm rsp_thms =
+fun repabs lthy thm consts rty qty quot_thm reflex_thm trans_thm rsp_thms =
let
- val rt = build_repabs_term lthy thm constructors rty qty;
+ val rt = build_repabs_term lthy thm consts rty qty;
val rg = Logic.mk_equals ((Thm.prop_of thm), rt);
fun tac ctxt = (ObjectLogic.full_atomize_tac) THEN'
(REPEAT_ALL_NEW (r_mk_comb_tac ctxt rty quot_thm reflex_thm trans_thm rsp_thms));
@@ -802,15 +843,15 @@
text {* expects atomized definition *}
ML {*
- fun add_lower_defs_aux lthy thm =
- let
- val e1 = @{thm fun_cong} OF [thm];
- val f = eqsubst_thm lthy @{thms fun_map.simps} e1;
- val g = simp_ids lthy f
- in
- (simp_ids lthy thm) :: (add_lower_defs_aux lthy g)
- end
- handle _ => [simp_ids lthy thm]
+fun add_lower_defs_aux lthy thm =
+ let
+ val e1 = @{thm fun_cong} OF [thm];
+ val f = eqsubst_thm lthy @{thms fun_map.simps} e1;
+ val g = simp_ids lthy f
+ in
+ (simp_ids lthy thm) :: (add_lower_defs_aux lthy g)
+ end
+ handle _ => [simp_ids lthy thm]
*}
ML {*
@@ -825,30 +866,31 @@
*}
ML {*
- fun findabs_all rty tm =
- case tm of
- Abs(_, T, b) =>
- let
- val b' = subst_bound ((Free ("x", T)), b);
- val tys = findabs_all rty b'
- val ty = fastype_of tm
- in if needs_lift rty ty then (ty :: tys) else tys
- end
- | f $ a => (findabs_all rty f) @ (findabs_all rty a)
- | _ => [];
- fun findabs rty tm = distinct (op =) (findabs_all rty tm)
+fun findabs_all rty tm =
+ case tm of
+ Abs(_, T, b) =>
+ let
+ val b' = subst_bound ((Free ("x", T)), b);
+ val tys = findabs_all rty b'
+ val ty = fastype_of tm
+ in if needs_lift rty ty then (ty :: tys) else tys
+ end
+ | f $ a => (findabs_all rty f) @ (findabs_all rty a)
+ | _ => [];
+fun findabs rty tm = distinct (op =) (findabs_all rty tm)
*}
ML {*
- fun findaps_all rty tm =
- case tm of
- Abs(_, T, b) =>
- findaps_all rty (subst_bound ((Free ("x", T)), b))
- | (f $ a) => (findaps_all rty f @ findaps_all rty a)
- | Free (_, (T as (Type ("fun", (_ :: _))))) => (if needs_lift rty T then [T] else [])
- | _ => [];
- fun findaps rty tm = distinct (op =) (findaps_all rty tm)
+fun findaps_all rty tm =
+ case tm of
+ Abs(_, T, b) =>
+ findaps_all rty (subst_bound ((Free ("x", T)), b))
+ | (f $ a) => (findaps_all rty f @ findaps_all rty a)
+ | Free (_, (T as (Type ("fun", (_ :: _))))) =>
+ (if needs_lift rty T then [T] else [])
+ | _ => [];
+fun findaps rty tm = distinct (op =) (findaps_all rty tm)
*}
ML {*
@@ -870,39 +912,39 @@
*}
ML {*
- fun findallex_all rty qty tm =
- case tm of
- Const (@{const_name All}, T) $ (s as (Abs(_, _, b))) =>
- let
- val (tya, tye) = findallex_all rty qty s
- in if needs_lift rty T then
- ((T :: tya), tye)
- else (tya, tye) end
- | Const (@{const_name Ex}, T) $ (s as (Abs(_, _, b))) =>
- let
- val (tya, tye) = findallex_all rty qty s
- in if needs_lift rty T then
- (tya, (T :: tye))
- else (tya, tye) end
- | Abs(_, T, b) =>
- findallex_all rty qty (subst_bound ((Free ("x", T)), b))
- | f $ a =>
- let
- val (a1, e1) = findallex_all rty qty f;
- val (a2, e2) = findallex_all rty qty a;
- in (a1 @ a2, e1 @ e2) end
- | _ => ([], []);
+fun findallex_all rty qty tm =
+ case tm of
+ Const (@{const_name All}, T) $ (s as (Abs(_, _, b))) =>
+ let
+ val (tya, tye) = findallex_all rty qty s
+ in if needs_lift rty T then
+ ((T :: tya), tye)
+ else (tya, tye) end
+ | Const (@{const_name Ex}, T) $ (s as (Abs(_, _, b))) =>
+ let
+ val (tya, tye) = findallex_all rty qty s
+ in if needs_lift rty T then
+ (tya, (T :: tye))
+ else (tya, tye) end
+ | Abs(_, T, b) =>
+ findallex_all rty qty (subst_bound ((Free ("x", T)), b))
+ | f $ a =>
+ let
+ val (a1, e1) = findallex_all rty qty f;
+ val (a2, e2) = findallex_all rty qty a;
+ in (a1 @ a2, e1 @ e2) end
+ | _ => ([], []);
*}
ML {*
- fun findallex lthy rty qty tm =
- let
- val (a, e) = findallex_all rty qty tm;
- val (ad, ed) = (map domain_type a, map domain_type e);
- val (au, eu) = (distinct (op =) ad, distinct (op =) ed);
- val (rty, qty) = (Logic.varifyT rty, Logic.varifyT qty)
- in
- (map (exchange_ty lthy rty qty) au, map (exchange_ty lthy rty qty) eu)
- end
+fun findallex lthy rty qty tm =
+ let
+ val (a, e) = findallex_all rty qty tm;
+ val (ad, ed) = (map domain_type a, map domain_type e);
+ val (au, eu) = (distinct (op =) ad, distinct (op =) ed);
+ val (rty, qty) = (Logic.varifyT rty, Logic.varifyT qty)
+ in
+ (map (exchange_ty lthy rty qty) au, map (exchange_ty lthy rty qty) eu)
+ end
*}
ML {*
@@ -918,7 +960,8 @@
(quotient_tac quot_thm);
val gc = Drule.strip_imp_concl (cprop_of lpi);
val t = Goal.prove_internal [] gc (fn _ => tac 1)
- val t_noid = MetaSimplifier.rewrite_rule [@{thm eq_reflection} OF @{thms id_apply}] t;
+ val t_noid = MetaSimplifier.rewrite_rule
+ [@{thm eq_reflection} OF @{thms id_apply}] t;
val t_sym = @{thm "HOL.sym"} OF [t_noid];
val t_eq = @{thm "eq_reflection"} OF [t_sym]
in
@@ -928,36 +971,36 @@
ML {*
fun applic_prs lthy rty qty absrep ty =
- let
+ let
val rty = Logic.varifyT rty;
val qty = Logic.varifyT qty;
- fun absty ty =
- exchange_ty lthy rty qty ty
- fun mk_rep tm =
- let
- val ty = exchange_ty lthy qty rty (fastype_of tm)
- in Syntax.check_term lthy ((get_fun_new repF (rty, qty) lthy ty) $ tm) end;
- fun mk_abs tm =
- let
- val ty = fastype_of tm
- in Syntax.check_term lthy ((get_fun_new absF (rty, qty) lthy ty) $ tm) end
- val (l, ltl) = Term.strip_type ty;
- val nl = map absty l;
- val vs = map (fn _ => "x") l;
- val ((fname :: vfs), lthy') = Variable.variant_fixes ("f" :: vs) lthy;
- val args = map Free (vfs ~~ nl);
- val lhs = list_comb((Free (fname, nl ---> ltl)), args);
- val rargs = map mk_rep args;
- val f = Free (fname, nl ---> ltl);
- val rhs = mk_abs (list_comb((mk_rep f), rargs));
- val eq = Logic.mk_equals (rhs, lhs);
- val ceq = cterm_of (ProofContext.theory_of lthy') eq;
- val sctxt = (Simplifier.context lthy' HOL_ss) addsimps (absrep :: @{thms fun_map.simps});
- val t = Goal.prove_internal [] ceq (fn _ => simp_tac sctxt 1)
- val t_id = MetaSimplifier.rewrite_rule @{thms id_def_sym} t;
- in
- singleton (ProofContext.export lthy' lthy) t_id
- end
+ fun absty ty =
+ exchange_ty lthy rty qty ty
+ fun mk_rep tm =
+ let
+ val ty = exchange_ty lthy qty rty (fastype_of tm)
+ in Syntax.check_term lthy ((get_fun_new repF (rty, qty) lthy ty) $ tm) end;
+ fun mk_abs tm =
+ let
+ val ty = fastype_of tm
+ in Syntax.check_term lthy ((get_fun_new absF (rty, qty) lthy ty) $ tm) end
+ val (l, ltl) = Term.strip_type ty;
+ val nl = map absty l;
+ val vs = map (fn _ => "x") l;
+ val ((fname :: vfs), lthy') = Variable.variant_fixes ("f" :: vs) lthy;
+ val args = map Free (vfs ~~ nl);
+ val lhs = list_comb((Free (fname, nl ---> ltl)), args);
+ val rargs = map mk_rep args;
+ val f = Free (fname, nl ---> ltl);
+ val rhs = mk_abs (list_comb((mk_rep f), rargs));
+ val eq = Logic.mk_equals (rhs, lhs);
+ val ceq = cterm_of (ProofContext.theory_of lthy') eq;
+ val sctxt = (Simplifier.context lthy' HOL_ss) addsimps (absrep :: @{thms fun_map.simps});
+ val t = Goal.prove_internal [] ceq (fn _ => simp_tac sctxt 1)
+ val t_id = MetaSimplifier.rewrite_rule @{thms id_def_sym} t;
+ in
+ singleton (ProofContext.export lthy' lthy) t_id
+ end
*}
ML {*
@@ -1032,13 +1075,13 @@
ML {*
- fun lift_thm_note qty qty_name rsp_thms defs thm name lthy =
- let
- val lifted_thm = lift_thm lthy qty qty_name rsp_thms defs thm;
- val (_, lthy2) = note (name, lifted_thm) lthy;
- in
- lthy2
- end;
+fun lift_thm_note qty qty_name rsp_thms defs thm name lthy =
+ let
+ val lifted_thm = lift_thm lthy qty qty_name rsp_thms defs thm;
+ val (_, lthy2) = note (name, lifted_thm) lthy;
+ in
+ lthy2
+ end
*}