--- a/src/HOL/ex/LList.ML Wed Oct 04 13:11:57 1995 +0100
+++ b/src/HOL/ex/LList.ML Wed Oct 04 13:12:14 1995 +0100
@@ -10,8 +10,7 @@
(** Simplification **)
-val llist_ss = univ_ss addcongs [split_weak_cong, sum_case_weak_cong]
- setloop split_tac [expand_split, expand_sum_case];
+simpset := !simpset setloop split_tac [expand_split, expand_sum_case];
(*For adding _eqI rules to a simpset; we must remove Pair_eq because
it may turn an instance of reflexivity into a conjunction!*)
@@ -64,16 +63,16 @@
(*A continuity result?*)
goalw LList.thy [CONS_def] "CONS M (UN x.f(x)) = (UN x. CONS M (f x))";
-by (simp_tac (univ_ss addsimps [In1_UN1, Scons_UN1_y]) 1);
+by (simp_tac (!simpset addsimps [In1_UN1, Scons_UN1_y]) 1);
qed "CONS_UN1";
(*UNUSED; obsolete?
goal Prod.thy "split p (%x y.UN z.f x y z) = (UN z. split p (%x y.f x y z))";
-by (simp_tac (prod_ss setloop (split_tac [expand_split])) 1);
+by (simp_tac (!simpset setloop (split_tac [expand_split])) 1);
qed "split_UN1";
goal Sum.thy "sum_case s f (%y.UN z.g y z) = (UN z.sum_case s f (%y.g y z))";
-by (simp_tac (sum_ss setloop (split_tac [expand_sum_case])) 1);
+by (simp_tac (!simpset setloop (split_tac [expand_sum_case])) 1);
qed "sum_case2_UN1";
*)
@@ -82,9 +81,8 @@
by (REPEAT (resolve_tac ([In1_mono,Scons_mono]@prems) 1));
qed "CONS_mono";
-val corec_fun_simps = [LList_corec_fun_def RS def_nat_rec_0,
- LList_corec_fun_def RS def_nat_rec_Suc];
-val corec_fun_ss = llist_ss addsimps corec_fun_simps;
+Addsimps [LList_corec_fun_def RS def_nat_rec_0,
+ LList_corec_fun_def RS def_nat_rec_Suc];
(** The directions of the equality are proved separately **)
@@ -93,17 +91,16 @@
\ (split(%z w. CONS z (LList_corec w f))) (f a)";
by (rtac UN1_least 1);
by (res_inst_tac [("n","k")] natE 1);
-by (ALLGOALS (asm_simp_tac corec_fun_ss));
+by (ALLGOALS (Asm_simp_tac));
by (REPEAT (resolve_tac [allI, impI, subset_refl RS CONS_mono, UN1_upper] 1));
qed "LList_corec_subset1";
goalw LList.thy [LList_corec_def]
"sum_case (%u.NIL) (split(%z w. CONS z (LList_corec w f))) (f a) <= \
\ LList_corec a f";
-by (simp_tac (corec_fun_ss addsimps [CONS_UN1]) 1);
+by (simp_tac (!simpset addsimps [CONS_UN1]) 1);
by (safe_tac set_cs);
-by (ALLGOALS (res_inst_tac [("x","Suc(?k)")] UN1_I THEN'
- asm_simp_tac corec_fun_ss));
+by (ALLGOALS (res_inst_tac [("x","Suc(?k)")] UN1_I THEN' Asm_simp_tac));
qed "LList_corec_subset2";
(*the recursion equation for LList_corec -- NOT SUITABLE FOR REWRITING!*)
@@ -129,7 +126,7 @@
by (rtac rangeI 1);
by (safe_tac set_cs);
by (stac LList_corec 1);
-by (simp_tac (llist_ss addsimps [list_Fun_NIL_I, list_Fun_CONS_I, CollectI]
+by (simp_tac (!simpset addsimps [list_Fun_NIL_I, list_Fun_CONS_I, CollectI]
|> add_eqI) 1);
qed "LList_corec_type";
@@ -141,7 +138,7 @@
by (rtac rangeI 1);
by (safe_tac set_cs);
by (stac LList_corec 1);
-by (asm_simp_tac (llist_ss addsimps [list_Fun_NIL_I]) 1);
+by (asm_simp_tac (!simpset addsimps [list_Fun_NIL_I]) 1);
by (fast_tac (set_cs addSIs [list_Fun_CONS_I]) 1);
qed "LList_corec_type2";
@@ -162,11 +159,11 @@
by (etac LListD.elim 1);
by (safe_tac (prod_cs addSEs [diagE]));
by (res_inst_tac [("n", "n")] natE 1);
-by (asm_simp_tac (univ_ss addsimps [ntrunc_0]) 1);
+by (asm_simp_tac (!simpset addsimps [ntrunc_0]) 1);
by (rename_tac "n'" 1);
by (res_inst_tac [("n", "n'")] natE 1);
-by (asm_simp_tac (univ_ss addsimps [CONS_def, ntrunc_one_In1]) 1);
-by (asm_simp_tac (univ_ss addsimps [CONS_def, ntrunc_In1, ntrunc_Scons]) 1);
+by (asm_simp_tac (!simpset addsimps [CONS_def, ntrunc_one_In1]) 1);
+by (asm_simp_tac (!simpset addsimps [CONS_def, ntrunc_In1, ntrunc_Scons]) 1);
qed "LListD_implies_ntrunc_equality";
(*The domain of the LListD relation*)
@@ -175,7 +172,7 @@
by (rtac gfp_upperbound 1);
(*avoids unfolding LListD on the rhs*)
by (res_inst_tac [("P", "%x. fst``x <= ?B")] (LListD_unfold RS ssubst) 1);
-by (simp_tac fst_image_ss 1);
+by (Simp_tac 1);
by (fast_tac univ_cs 1);
qed "fst_image_LListD";
@@ -227,7 +224,7 @@
by (etac ssubst 1);
by (eresolve_tac [llist.elim] 1);
by (ALLGOALS
- (asm_simp_tac (llist_ss addsimps [diagI, LListD_Fun_NIL_I,
+ (asm_simp_tac (!simpset addsimps [diagI, LListD_Fun_NIL_I,
LListD_Fun_CONS_I])));
qed "diag_subset_LListD";
@@ -240,7 +237,7 @@
"!!M N. M: llist(A) ==> (M,M) : LListD_Fun (diag A) (X Un diag(llist(A)))";
by (rtac (LListD_eq_diag RS subst) 1);
by (rtac LListD_Fun_LListD_I 1);
-by (asm_simp_tac (HOL_ss addsimps [LListD_eq_diag, diagI]) 1);
+by (asm_simp_tac (!simpset addsimps [LListD_eq_diag, diagI]) 1);
qed "LListD_Fun_diag_I";
@@ -252,7 +249,7 @@
\ |] ==> M=N";
by (rtac (LListD_subset_diag RS subsetD RS diagE) 1);
by (etac LListD_coinduct 1);
-by (asm_simp_tac (HOL_ss addsimps [LListD_eq_diag]) 1);
+by (asm_simp_tac (!simpset addsimps [LListD_eq_diag]) 1);
by (safe_tac prod_cs);
qed "LList_equalityI";
@@ -272,7 +269,7 @@
by (safe_tac set_cs);
by (stac prem1 1);
by (stac prem2 1);
-by (simp_tac (llist_ss addsimps [LListD_Fun_NIL_I,
+by (simp_tac (!simpset addsimps [LListD_Fun_NIL_I,
CollectI RS LListD_Fun_CONS_I]
|> add_eqI) 1);
qed "LList_corec_unique";
@@ -292,7 +289,7 @@
goalw LList.thy [CONS_def]
"ntrunc (Suc(Suc(k))) (CONS M N) = CONS (ntrunc k M) (ntrunc k N)";
-by (simp_tac (HOL_ss addsimps [ntrunc_Scons,ntrunc_In1]) 1);
+by (simp_tac (!simpset addsimps [ntrunc_Scons,ntrunc_In1]) 1);
qed "ntrunc_CONS";
val [prem1,prem2] = goal LList.thy
@@ -305,11 +302,11 @@
by (rtac allI 1);
by (stac prem1 1);
by (stac prem2 1);
-by (simp_tac (sum_ss setloop (split_tac [expand_split,expand_sum_case])) 1);
+by (simp_tac (!simpset setloop (split_tac [expand_split,expand_sum_case])) 1);
by (strip_tac 1);
by (res_inst_tac [("n", "n")] natE 1);
by (res_inst_tac [("n", "xc")] natE 2);
-by (ALLGOALS(asm_simp_tac(nat_ss addsimps
+by (ALLGOALS(asm_simp_tac(!simpset addsimps
[ntrunc_0,ntrunc_one_CONS,ntrunc_CONS])));
result();
@@ -334,14 +331,14 @@
goal LList.thy "Lconst(M) = LList_corec M (%x.Inr((x,x)))";
by (rtac (equals_LList_corec RS fun_cong) 1);
-by (simp_tac sum_ss 1);
+by (Simp_tac 1);
by (rtac Lconst 1);
qed "Lconst_eq_LList_corec";
(*Thus we could have used gfp in the definition of Lconst*)
goal LList.thy "gfp(%N. CONS M N) = LList_corec M (%x.Inr((x,x)))";
by (rtac (equals_LList_corec RS fun_cong) 1);
-by (simp_tac sum_ss 1);
+by (Simp_tac 1);
by (rtac (Lconst_fun_mono RS gfp_Tarski) 1);
qed "gfp_Lconst_eq_LList_corec";
@@ -387,7 +384,7 @@
goalw LList.thy [CONS_def] "(CONS M N=CONS M' N') = (M=M' & N=N')";
by (fast_tac (HOL_cs addSEs [Scons_inject, make_elim In1_inject]) 1);
-qed "CONS_CONS_eq";
+qed "CONS_CONS_eq2";
bind_thm ("CONS_inject", (CONS_CONS_eq RS iffD1 RS conjE));
@@ -407,13 +404,12 @@
by (rtac (major RS llist.elim) 1);
by (etac CONS_neq_NIL 1);
by (fast_tac llist_cs 1);
-qed "CONS_D";
+qed "CONS_D2";
(****** Reasoning about llist(A) ******)
-(*Don't use llist_ss, as it does case splits!*)
-val List_case_ss = univ_ss addsimps [List_case_NIL, List_case_CONS];
+Addsimps [List_case_NIL, List_case_CONS];
(*A special case of list_equality for functions over lazy lists*)
val [Mlist,gMlist,NILcase,CONScase] = goal LList.thy
@@ -442,12 +438,12 @@
goal LList.thy "Lmap f NIL = NIL";
by (rtac (Lmap_def RS def_LList_corec RS trans) 1);
-by (simp_tac List_case_ss 1);
+by (Simp_tac 1);
qed "Lmap_NIL";
goal LList.thy "Lmap f (CONS M N) = CONS (f M) (Lmap f N)";
by (rtac (Lmap_def RS def_LList_corec RS trans) 1);
-by (simp_tac List_case_ss 1);
+by (Simp_tac 1);
qed "Lmap_CONS";
(*Another type-checking proof by coinduction*)
@@ -456,7 +452,7 @@
by (rtac (major RS imageI RS llist_coinduct) 1);
by (safe_tac set_cs);
by (etac llist.elim 1);
-by (ALLGOALS (asm_simp_tac (HOL_ss addsimps [Lmap_NIL,Lmap_CONS])));
+by (ALLGOALS (asm_simp_tac (!simpset addsimps [Lmap_NIL,Lmap_CONS])));
by (REPEAT (ares_tac [list_Fun_NIL_I, list_Fun_CONS_I,
minor, imageI, UnI1] 1));
qed "Lmap_type";
@@ -474,7 +470,7 @@
by (rtac (prem RS imageI RS LList_equalityI) 1);
by (safe_tac set_cs);
by (etac llist.elim 1);
-by (ALLGOALS (asm_simp_tac (HOL_ss addsimps [Lmap_NIL,Lmap_CONS])));
+by (ALLGOALS (asm_simp_tac (!simpset addsimps [Lmap_NIL,Lmap_CONS])));
by (REPEAT (ares_tac [LListD_Fun_NIL_I, imageI, UnI1,
rangeI RS LListD_Fun_CONS_I] 1));
qed "Lmap_compose";
@@ -483,7 +479,7 @@
by (rtac (prem RS imageI RS LList_equalityI) 1);
by (safe_tac set_cs);
by (etac llist.elim 1);
-by (ALLGOALS (asm_simp_tac (HOL_ss addsimps [Lmap_NIL,Lmap_CONS])));
+by (ALLGOALS (asm_simp_tac (!simpset addsimps [Lmap_NIL,Lmap_CONS])));
by (REPEAT (ares_tac [LListD_Fun_NIL_I, imageI RS UnI1,
rangeI RS LListD_Fun_CONS_I] 1));
qed "Lmap_ident";
@@ -493,34 +489,33 @@
goalw LList.thy [Lappend_def] "Lappend NIL NIL = NIL";
by (rtac (LList_corec RS trans) 1);
-by (simp_tac List_case_ss 1);
+by (Simp_tac 1);
qed "Lappend_NIL_NIL";
goalw LList.thy [Lappend_def]
"Lappend NIL (CONS N N') = CONS N (Lappend NIL N')";
by (rtac (LList_corec RS trans) 1);
-by (simp_tac List_case_ss 1);
+by (Simp_tac 1);
qed "Lappend_NIL_CONS";
goalw LList.thy [Lappend_def]
"Lappend (CONS M M') N = CONS M (Lappend M' N)";
by (rtac (LList_corec RS trans) 1);
-by (simp_tac List_case_ss 1);
+by (Simp_tac 1);
qed "Lappend_CONS";
-val Lappend_ss =
- List_case_ss addsimps [llist.NIL_I, Lappend_NIL_NIL, Lappend_NIL_CONS,
- Lappend_CONS, LListD_Fun_CONS_I]
- |> add_eqI;
+Addsimps [llist.NIL_I, Lappend_NIL_NIL, Lappend_NIL_CONS,
+ Lappend_CONS, LListD_Fun_CONS_I, range_eqI, image_eqI];
+Delsimps [Pair_eq];
goal LList.thy "!!M. M: llist(A) ==> Lappend NIL M = M";
by (etac LList_fun_equalityI 1);
-by (ALLGOALS (asm_simp_tac Lappend_ss));
+by (ALLGOALS Asm_simp_tac);
qed "Lappend_NIL";
goal LList.thy "!!M. M: llist(A) ==> Lappend M NIL = M";
by (etac LList_fun_equalityI 1);
-by (ALLGOALS (asm_simp_tac Lappend_ss));
+by (ALLGOALS Asm_simp_tac);
qed "Lappend_NIL2";
(** Alternative type-checking proofs for Lappend **)
@@ -535,7 +530,7 @@
by (eres_inst_tac [("a", "u")] llist.elim 1);
by (eres_inst_tac [("a", "v")] llist.elim 1);
by (ALLGOALS
- (asm_simp_tac Lappend_ss THEN'
+ (Asm_simp_tac THEN'
fast_tac (set_cs addSIs [llist.NIL_I, list_Fun_NIL_I, list_Fun_CONS_I])));
qed "Lappend_type";
@@ -547,8 +542,8 @@
by (rtac subsetI 1);
by (etac imageE 1);
by (eres_inst_tac [("a", "u")] llist.elim 1);
-by (asm_simp_tac (Lappend_ss addsimps [Lappend_NIL, list_Fun_llist_I]) 1);
-by (asm_simp_tac Lappend_ss 1);
+by (asm_simp_tac (!simpset addsimps [Lappend_NIL, list_Fun_llist_I]) 1);
+by (Asm_simp_tac 1);
by (fast_tac (set_cs addSIs [list_Fun_CONS_I]) 1);
qed "Lappend_type";
@@ -556,20 +551,16 @@
(** llist_case: case analysis for 'a llist **)
-val Rep_llist_simps =
- [List_case_NIL, List_case_CONS,
- Abs_llist_inverse, Rep_llist_inverse,
- Rep_llist, rangeI, inj_Leaf, Inv_f_f]
- @ llist.intrs;
-val Rep_llist_ss = llist_ss addsimps Rep_llist_simps;
+Addsimps ([Abs_llist_inverse, Rep_llist_inverse,
+ Rep_llist, rangeI, inj_Leaf, Inv_f_f] @ llist.intrs);
goalw LList.thy [llist_case_def,LNil_def] "llist_case c d LNil = c";
-by (simp_tac Rep_llist_ss 1);
+by (Simp_tac 1);
qed "llist_case_LNil";
goalw LList.thy [llist_case_def,LCons_def]
"llist_case c d (LCons M N) = d M N";
-by (simp_tac Rep_llist_ss 1);
+by (Simp_tac 1);
qed "llist_case_LCons";
(*Elimination is case analysis, not induction.*)
@@ -582,7 +573,7 @@
by (assume_tac 1);
by (etac rangeE 1);
by (rtac (inj_Rep_llist RS injD RS prem2) 1);
-by (asm_simp_tac (HOL_ss addsimps [Rep_llist_LCons]) 1);
+by (asm_simp_tac (!simpset delsimps [CONS_CONS_eq] addsimps [Rep_llist_LCons]) 1);
by (etac (Abs_llist_inverse RS ssubst) 1);
by (rtac refl 1);
qed "llistE";
@@ -594,11 +585,11 @@
\ (split(%z w. LCons z (llist_corec w f))) (f a)";
by (stac LList_corec 1);
by (res_inst_tac [("s","f(a)")] sumE 1);
-by (asm_simp_tac (llist_ss addsimps [LList_corec_type2,Abs_llist_inverse]) 1);
+by (asm_simp_tac (!simpset addsimps [LList_corec_type2]) 1);
by (res_inst_tac [("p","y")] PairE 1);
-by (asm_simp_tac (llist_ss addsimps [LList_corec_type2,Abs_llist_inverse]) 1);
+by (asm_simp_tac (!simpset addsimps [LList_corec_type2]) 1);
(*FIXME: correct case splits usd to be found automatically:
-by (ASM_SIMP_TAC(llist_ss addsimps [LList_corec_type2,Abs_llist_inverse]) 1);*)
+by (ASM_SIMP_TAC(!simpset addsimps [LList_corec_type2]) 1);*)
qed "llist_corec";
(*definitional version of same*)
@@ -617,7 +608,7 @@
"!!r A. r <= Sigma (llist A) (%x.llist(A)) ==> \
\ LListD_Fun (diag A) r <= Sigma (llist A) (%x.llist(A))";
by (stac llist_unfold 1);
-by (simp_tac (HOL_ss addsimps [NIL_def, CONS_def]) 1);
+by (simp_tac (!simpset addsimps [NIL_def, CONS_def]) 1);
by (fast_tac univ_cs 1);
qed "LListD_Fun_subset_Sigma_llist";
@@ -633,7 +624,7 @@
by (safe_tac prod_cs);
by (rtac (prem RS subsetD RS SigmaE2) 1);
by (assume_tac 1);
-by (asm_simp_tac (HOL_ss addsimps [o_def,prod_fun,Abs_llist_inverse]) 1);
+by (asm_simp_tac (!simpset addsimps [o_def,prod_fun,Abs_llist_inverse]) 1);
qed "prod_fun_lemma";
goal LList.thy
@@ -704,22 +695,20 @@
qed "llist_fun_equalityI";
(*simpset for llist bisimulations*)
-val llistD_simps = [llist_case_LNil, llist_case_LCons,
- llistD_Fun_LNil_I, llistD_Fun_LCons_I];
-(*Don't use llist_ss, as it does case splits!*)
-val llistD_ss = univ_ss addsimps llistD_simps |> add_eqI;
+Addsimps [llist_case_LNil, llist_case_LCons,
+ llistD_Fun_LNil_I, llistD_Fun_LCons_I];
(*** The functional "lmap" ***)
goal LList.thy "lmap f LNil = LNil";
by (rtac (lmap_def RS def_llist_corec RS trans) 1);
-by (simp_tac llistD_ss 1);
+by (Simp_tac 1);
qed "lmap_LNil";
goal LList.thy "lmap f (LCons M N) = LCons (f M) (lmap f N)";
by (rtac (lmap_def RS def_llist_corec RS trans) 1);
-by (simp_tac llistD_ss 1);
+by (Simp_tac 1);
qed "lmap_LCons";
@@ -727,12 +716,12 @@
goal LList.thy "lmap (f o g) l = lmap f (lmap g l)";
by (res_inst_tac [("l","l")] llist_fun_equalityI 1);
-by (ALLGOALS (simp_tac (llistD_ss addsimps [lmap_LNil, lmap_LCons])));
+by (ALLGOALS (simp_tac (!simpset addsimps [lmap_LNil, lmap_LCons])));
qed "lmap_compose";
goal LList.thy "lmap (%x.x) l = l";
by (res_inst_tac [("l","l")] llist_fun_equalityI 1);
-by (ALLGOALS (simp_tac (llistD_ss addsimps [lmap_LNil, lmap_LCons])));
+by (ALLGOALS (simp_tac (!simpset addsimps [lmap_LNil, lmap_LCons])));
qed "lmap_ident";
@@ -740,7 +729,7 @@
goal LList.thy "iterates f x = LCons x (iterates f (f x))";
by (rtac (iterates_def RS def_llist_corec RS trans) 1);
-by (simp_tac sum_ss 1);
+by (Simp_tac 1);
qed "iterates";
goal LList.thy "lmap f (iterates f x) = iterates f (f x)";
@@ -750,7 +739,7 @@
by (safe_tac set_cs);
by (res_inst_tac [("x1", "f(u)")] (iterates RS ssubst) 1);
by (res_inst_tac [("x1", "u")] (iterates RS ssubst) 1);
-by (simp_tac (llistD_ss addsimps [lmap_LCons]) 1);
+by (simp_tac (!simpset addsimps [lmap_LCons]) 1);
qed "lmap_iterates";
goal LList.thy "iterates f x = LCons x (lmap f (iterates f x))";
@@ -766,12 +755,12 @@
"nat_rec n (LCons b l) (%m. lmap(f)) = \
\ LCons (nat_rec n b (%m. f)) (nat_rec n l (%m. lmap(f)))";
by (nat_ind_tac "n" 1);
-by (ALLGOALS (asm_simp_tac (nat_ss addsimps [lmap_LCons])));
+by (ALLGOALS (asm_simp_tac (!simpset addsimps [lmap_LCons])));
qed "fun_power_lmap";
goal Nat.thy "nat_rec n (g x) (%m. g) = nat_rec (Suc n) x (%m. g)";
by (nat_ind_tac "n" 1);
-by (ALLGOALS (asm_simp_tac nat_ss));
+by (ALLGOALS Asm_simp_tac);
qed "fun_power_Suc";
val Pair_cong = read_instantiate_sg (sign_of Prod.thy)
@@ -805,31 +794,31 @@
goalw LList.thy [lappend_def] "lappend LNil LNil = LNil";
by (rtac (llist_corec RS trans) 1);
-by (simp_tac llistD_ss 1);
+by (Simp_tac 1);
qed "lappend_LNil_LNil";
goalw LList.thy [lappend_def]
"lappend LNil (LCons l l') = LCons l (lappend LNil l')";
by (rtac (llist_corec RS trans) 1);
-by (simp_tac llistD_ss 1);
+by (Simp_tac 1);
qed "lappend_LNil_LCons";
goalw LList.thy [lappend_def]
"lappend (LCons l l') N = LCons l (lappend l' N)";
by (rtac (llist_corec RS trans) 1);
-by (simp_tac llistD_ss 1);
+by (Simp_tac 1);
qed "lappend_LCons";
goal LList.thy "lappend LNil l = l";
by (res_inst_tac [("l","l")] llist_fun_equalityI 1);
by (ALLGOALS
- (simp_tac (llistD_ss addsimps [lappend_LNil_LNil, lappend_LNil_LCons])));
+ (simp_tac (!simpset addsimps [lappend_LNil_LNil, lappend_LNil_LCons])));
qed "lappend_LNil";
goal LList.thy "lappend l LNil = l";
by (res_inst_tac [("l","l")] llist_fun_equalityI 1);
by (ALLGOALS
- (simp_tac (llistD_ss addsimps [lappend_LNil_LNil, lappend_LCons])));
+ (simp_tac (!simpset addsimps [lappend_LNil_LNil, lappend_LCons])));
qed "lappend_LNil2";
(*The infinite first argument blocks the second*)
@@ -839,7 +828,7 @@
by (rtac rangeI 1);
by (safe_tac set_cs);
by (stac iterates 1);
-by (simp_tac (llistD_ss addsimps [lappend_LCons]) 1);
+by (simp_tac (!simpset addsimps [lappend_LCons]) 1);
qed "lappend_iterates";
(** Two proofs that lmap distributes over lappend **)
@@ -855,7 +844,7 @@
by (safe_tac set_cs);
by (res_inst_tac [("l", "l")] llistE 1);
by (res_inst_tac [("l", "n")] llistE 1);
-by (ALLGOALS (asm_simp_tac (llistD_ss addsimps
+by (ALLGOALS (asm_simp_tac (!simpset addsimps
[lappend_LNil_LNil,lappend_LCons,lappend_LNil_LCons,
lmap_LNil,lmap_LCons])));
by (REPEAT_SOME (ares_tac [llistD_Fun_LCons_I, UN1_I RS UnI1, rangeI]));
@@ -868,13 +857,13 @@
(*Shorter proof of theorem above using llist_equalityI as strong coinduction*)
goal LList.thy "lmap f (lappend l n) = lappend (lmap f l) (lmap f n)";
by (res_inst_tac [("l","l")] llist_fun_equalityI 1);
-by (simp_tac (llistD_ss addsimps [lappend_LNil, lmap_LNil])1);
-by (simp_tac (llistD_ss addsimps [lappend_LCons, lmap_LCons]) 1);
+by (simp_tac (!simpset addsimps [lappend_LNil, lmap_LNil])1);
+by (simp_tac (!simpset addsimps [lappend_LCons, lmap_LCons]) 1);
qed "lmap_lappend_distrib";
(*Without strong coinduction, three case analyses might be needed*)
goal LList.thy "lappend (lappend l1 l2) l3 = lappend l1 (lappend l2 l3)";
by (res_inst_tac [("l","l1")] llist_fun_equalityI 1);
-by (simp_tac (llistD_ss addsimps [lappend_LNil])1);
-by (simp_tac (llistD_ss addsimps [lappend_LCons]) 1);
+by (simp_tac (!simpset addsimps [lappend_LNil])1);
+by (simp_tac (!simpset addsimps [lappend_LCons]) 1);
qed "lappend_assoc";