--- a/src/HOL/Induct/LFilter.ML Mon Nov 03 12:13:18 1997 +0100
+++ b/src/HOL/Induct/LFilter.ML Mon Nov 03 12:22:43 1997 +0100
@@ -31,7 +31,7 @@
qed_spec_mp "findRel_imp_LCons";
goal thy "!!p. (LNil,l): findRel p ==> R";
-by (blast_tac (!claset addEs [findRel.elim]) 1);
+by (blast_tac (claset() addEs [findRel.elim]) 1);
qed "findRel_LNil";
AddSEs [findRel_LNil];
@@ -41,7 +41,7 @@
goal thy "!!p. LCons x l : Domain(findRel p) = (p x | l : Domain(findRel p))";
by (case_tac "p x" 1);
-by (ALLGOALS (blast_tac (!claset addIs findRel.intrs)));
+by (ALLGOALS (blast_tac (claset() addIs findRel.intrs)));
qed "LCons_Domain_findRel";
Addsimps [LCons_Domain_findRel];
@@ -61,27 +61,27 @@
"[| !!x. p x ==> q x |] ==> Domain (findRel p) <= Domain (findRel q)";
by (Clarify_tac 1);
by (etac findRel.induct 1);
-by (blast_tac (!claset addIs (findRel.intrs@prems)) 1);
-by (blast_tac (!claset addIs findRel.intrs) 1);
+by (blast_tac (claset() addIs (findRel.intrs@prems)) 1);
+by (blast_tac (claset() addIs findRel.intrs) 1);
qed "Domain_findRel_mono";
(*** find: basic equations ***)
goalw thy [find_def] "find p LNil = LNil";
-by (blast_tac (!claset addIs [select_equality]) 1);
+by (blast_tac (claset() addIs [select_equality]) 1);
qed "find_LNil";
goalw thy [find_def] "!!p. (l,l') : findRel p ==> find p l = l'";
-by (blast_tac (!claset addIs [select_equality] addDs [findRel_functional]) 1);
+by (blast_tac (claset() addIs [select_equality] addDs [findRel_functional]) 1);
qed "findRel_imp_find";
goal thy "!!p. p x ==> find p (LCons x l) = LCons x l";
-by (blast_tac (!claset addIs (findRel_imp_find::findRel.intrs)) 1);
+by (blast_tac (claset() addIs (findRel_imp_find::findRel.intrs)) 1);
qed "find_LCons_found";
goalw thy [find_def] "!!p. l ~: Domain(findRel p) ==> find p l = LNil";
-by (blast_tac (!claset addIs [select_equality]) 1);
+by (blast_tac (claset() addIs [select_equality]) 1);
qed "diverge_find_LNil";
Addsimps [diverge_find_LNil];
@@ -90,12 +90,12 @@
by (case_tac "LCons x l : Domain(findRel p)" 1);
by (Asm_full_simp_tac 2);
by (Clarify_tac 1);
-by (asm_simp_tac (!simpset addsimps [findRel_imp_find]) 1);
-by (blast_tac (!claset addIs (findRel_imp_find::findRel.intrs)) 1);
+by (asm_simp_tac (simpset() addsimps [findRel_imp_find]) 1);
+by (blast_tac (claset() addIs (findRel_imp_find::findRel.intrs)) 1);
qed "find_LCons_seek";
goal thy "find p (LCons x l) = (if p x then LCons x l else find p l)";
-by (asm_simp_tac (!simpset addsimps [find_LCons_found, find_LCons_seek]
+by (asm_simp_tac (simpset() addsimps [find_LCons_found, find_LCons_seek]
addsplits [expand_if]) 1);
qed "find_LCons";
@@ -105,7 +105,7 @@
goal thy "lfilter p LNil = LNil";
by (rtac (lfilter_def RS def_llist_corec RS trans) 1);
-by (simp_tac (!simpset addsimps [find_LNil]) 1);
+by (simp_tac (simpset() addsimps [find_LNil]) 1);
qed "lfilter_LNil";
goal thy "!!p. l ~: Domain(findRel p) ==> lfilter p l = LNil";
@@ -116,31 +116,31 @@
goal thy "!!p. p x ==> lfilter p (LCons x l) = LCons x (lfilter p l)";
by (rtac (lfilter_def RS def_llist_corec RS trans) 1);
-by (asm_simp_tac (!simpset addsimps [find_LCons_found]) 1);
+by (asm_simp_tac (simpset() addsimps [find_LCons_found]) 1);
qed "lfilter_LCons_found";
goal thy "!!p. (l, LCons x l') : findRel p \
\ ==> lfilter p l = LCons x (lfilter p l')";
by (rtac (lfilter_def RS def_llist_corec RS trans) 1);
-by (asm_simp_tac (!simpset addsimps [findRel_imp_find]) 1);
+by (asm_simp_tac (simpset() addsimps [findRel_imp_find]) 1);
qed "findRel_imp_lfilter";
goal thy "!!p. ~ (p x) ==> lfilter p (LCons x l) = lfilter p l";
by (rtac (lfilter_def RS def_llist_corec RS trans) 1);
by (case_tac "LCons x l : Domain(findRel p)" 1);
-by (asm_full_simp_tac (!simpset addsimps [diverge_lfilter_LNil]) 2);
+by (asm_full_simp_tac (simpset() addsimps [diverge_lfilter_LNil]) 2);
by (etac Domain_findRelE 1);
-by (safe_tac (!claset delrules [conjI]));
+by (safe_tac (claset() delrules [conjI]));
by (asm_full_simp_tac
- (!simpset addsimps [findRel_imp_lfilter, findRel_imp_find,
+ (simpset() addsimps [findRel_imp_lfilter, findRel_imp_find,
find_LCons_seek]) 1);
qed "lfilter_LCons_seek";
goal thy "lfilter p (LCons x l) = \
\ (if p x then LCons x (lfilter p l) else lfilter p l)";
-by (asm_simp_tac (!simpset addsimps [lfilter_LCons_found, lfilter_LCons_seek]
+by (asm_simp_tac (simpset() addsimps [lfilter_LCons_found, lfilter_LCons_seek]
addsplits [expand_if]) 1);
qed "lfilter_LCons";
@@ -152,7 +152,7 @@
by (rtac notI 1);
by (etac Domain_findRelE 1);
by (etac rev_mp 1);
-by (asm_simp_tac (!simpset addsimps [findRel_imp_lfilter]) 1);
+by (asm_simp_tac (simpset() addsimps [findRel_imp_lfilter]) 1);
qed "lfilter_eq_LNil";
@@ -162,7 +162,7 @@
by (case_tac "l : Domain(findRel p)" 1);
by (etac Domain_findRelE 1);
by (Asm_simp_tac 2);
-by (asm_simp_tac (!simpset addsimps [findRel_imp_find]) 1);
+by (asm_simp_tac (simpset() addsimps [findRel_imp_find]) 1);
by (Blast_tac 1);
qed_spec_mp "lfilter_eq_LCons";
@@ -170,8 +170,8 @@
goal thy "lfilter p l = LNil | \
\ (EX y l'. lfilter p l = LCons y (lfilter p l') & p y)";
by (case_tac "l : Domain(findRel p)" 1);
-by (asm_simp_tac (!simpset addsimps [diverge_lfilter_LNil]) 2);
-by (blast_tac (!claset addSEs [Domain_findRelE]
+by (asm_simp_tac (simpset() addsimps [diverge_lfilter_LNil]) 2);
+by (blast_tac (claset() addSEs [Domain_findRelE]
addIs [findRel_imp_lfilter]) 1);
qed "lfilter_cases";
@@ -181,15 +181,13 @@
goal thy "lfilter (%x. True) l = l";
by (res_inst_tac [("l","l")] llist_fun_equalityI 1);
by (ALLGOALS Simp_tac);
-by (Blast_tac 1);
qed "lfilter_K_True";
goal thy "lfilter p (lfilter p l) = lfilter p l";
by (res_inst_tac [("l","l")] llist_fun_equalityI 1);
-by (ALLGOALS (simp_tac (!simpset addsplits [expand_if])));
+by (ALLGOALS (simp_tac (simpset() addsplits [expand_if])));
by Safe_tac;
(*Cases: p x is true or false*)
-by (Blast_tac 1);
by (rtac (lfilter_cases RS disjE) 1);
by (etac ssubst 1);
by (Auto_tac());
@@ -203,8 +201,8 @@
goal thy "!!p. (l,l') : findRel q \
\ ==> l' = LCons x l'' --> p x --> (l,l') : findRel (%x. p x & q x)";
by (etac findRel.induct 1);
-by (blast_tac (!claset addIs findRel.intrs) 1);
-by (blast_tac (!claset addIs findRel.intrs) 1);
+by (blast_tac (claset() addIs findRel.intrs) 1);
+by (blast_tac (claset() addIs findRel.intrs) 1);
qed_spec_mp "findRel_conj_lemma";
val findRel_conj = refl RSN (2, findRel_conj_lemma);
@@ -221,7 +219,7 @@
\ lxx = LCons x lx --> (lx,lz) : findRel(%x. p x & q x) --> ~ p x \
\ --> (l,lz) : findRel (%x. p x & q x)";
by (etac findRel.induct 1);
-by (ALLGOALS (blast_tac (!claset addIs findRel.intrs)));
+by (ALLGOALS (blast_tac (claset() addIs findRel.intrs)));
qed_spec_mp "findRel_conj2";
@@ -229,14 +227,14 @@
\ ==> ALL l. lx = lfilter q l \
\ --> l : Domain (findRel(%x. p x & q x))";
by (etac findRel.induct 1);
-by (blast_tac (!claset addSDs [sym RS lfilter_eq_LCons]
+by (blast_tac (claset() addSDs [sym RS lfilter_eq_LCons]
addIs [findRel_conj]) 1);
by (Auto_tac());
by (dtac (sym RS lfilter_eq_LCons) 1);
by (Auto_tac());
by (dtac spec 1);
by (dtac (refl RS rev_mp) 1);
-by (blast_tac (!claset addIs [findRel_conj2]) 1);
+by (blast_tac (claset() addIs [findRel_conj2]) 1);
qed_spec_mp "findRel_lfilter_Domain_conj";
@@ -244,8 +242,8 @@
\ ==> l'' = LCons y l' --> \
\ (lfilter q l, LCons y (lfilter q l')) : findRel p";
by (etac findRel.induct 1);
-by (ALLGOALS (asm_simp_tac (!simpset addsplits [expand_if])));
-by (ALLGOALS (blast_tac (!claset addIs findRel.intrs)));
+by (ALLGOALS (asm_simp_tac (simpset() addsplits [expand_if])));
+by (ALLGOALS (blast_tac (claset() addIs findRel.intrs)));
qed_spec_mp "findRel_conj_lfilter";
@@ -256,40 +254,38 @@
\ lfilter (%x. p x & q x) u)))";
by (case_tac "l : Domain(findRel q)" 1);
by (subgoal_tac "l ~: Domain (findRel (%x. p x & q x))" 2);
-by (blast_tac (!claset addIs [impOfSubs Domain_findRel_mono]) 3);
+by (blast_tac (claset() addIs [impOfSubs Domain_findRel_mono]) 3);
(*There are no qs in l: both lists are LNil*)
-by (asm_simp_tac (!simpset addsimps [diverge_lfilter_LNil]) 2);
+by (asm_simp_tac (simpset() addsimps [diverge_lfilter_LNil]) 2);
by (etac Domain_findRelE 1);
(*case q x*)
by (case_tac "p x" 1);
-by (asm_simp_tac (!simpset addsimps [findRel_imp_lfilter,
+by (asm_simp_tac (simpset() addsimps [findRel_imp_lfilter,
findRel_conj RS findRel_imp_lfilter]) 1);
-by (Blast_tac 1);
(*case q x and ~(p x) *)
-by (asm_simp_tac (!simpset addsimps [findRel_imp_lfilter]) 1);
+by (asm_simp_tac (simpset() addsimps [findRel_imp_lfilter]) 1);
by (case_tac "l' : Domain (findRel (%x. p x & q x))" 1);
(*subcase: there is no p&q in l' and therefore none in l*)
by (subgoal_tac "l ~: Domain (findRel (%x. p x & q x))" 2);
-by (blast_tac (!claset addIs [findRel_not_conj_Domain]) 3);
+by (blast_tac (claset() addIs [findRel_not_conj_Domain]) 3);
by (subgoal_tac "lfilter q l' ~: Domain(findRel p)" 2);
-by (blast_tac (!claset addIs [findRel_lfilter_Domain_conj]) 3);
+by (blast_tac (claset() addIs [findRel_lfilter_Domain_conj]) 3);
(* ...and therefore too, no p in lfilter q l'. Both results are Lnil*)
-by (asm_simp_tac (!simpset addsimps [diverge_lfilter_LNil]) 2);
+by (asm_simp_tac (simpset() addsimps [diverge_lfilter_LNil]) 2);
(*subcase: there is a p&q in l' and therefore also one in l*)
by (etac Domain_findRelE 1);
by (subgoal_tac "(l, LCons xa l'a) : findRel(%x. p x & q x)" 1);
-by (blast_tac (!claset addIs [findRel_conj2]) 2);
+by (blast_tac (claset() addIs [findRel_conj2]) 2);
by (subgoal_tac "(lfilter q l', LCons xa (lfilter q l'a)) : findRel p" 1);
-by (blast_tac (!claset addIs [findRel_conj_lfilter]) 2);
-by (asm_simp_tac (!simpset addsimps [findRel_imp_lfilter]) 1);
-by (Blast_tac 1);
+by (blast_tac (claset() addIs [findRel_conj_lfilter]) 2);
+by (asm_simp_tac (simpset() addsimps [findRel_imp_lfilter]) 1);
val lemma = result();
goal thy "lfilter p (lfilter q l) = lfilter (%x. p x & q x) l";
by (res_inst_tac [("l","l")] llist_fun_equalityI 1);
-by (ALLGOALS (simp_tac (!simpset addsplits [expand_if])));
-by (blast_tac (!claset addIs [lemma, impOfSubs llistD_Fun_mono]) 1);
+by (ALLGOALS (simp_tac (simpset() addsplits [expand_if])));
+by (blast_tac (claset() addIs [lemma, impOfSubs llistD_Fun_mono]) 1);
qed "lfilter_conj";
@@ -317,25 +313,23 @@
\ (l, LCons y l'') : findRel(%x. p(f x)))";
by (etac findRel.induct 1);
by (ALLGOALS Asm_simp_tac);
-by (safe_tac (!claset addSDs [lmap_eq_LCons]));
-by (blast_tac (!claset addIs findRel.intrs) 1);
-by (blast_tac (!claset addIs findRel.intrs) 1);
+by (safe_tac (claset() addSDs [lmap_eq_LCons]));
+by (blast_tac (claset() addIs findRel.intrs) 1);
+by (blast_tac (claset() addIs findRel.intrs) 1);
qed_spec_mp "lmap_LCons_findRel_lemma";
val lmap_LCons_findRel = refl RSN (2, refl RSN (2, lmap_LCons_findRel_lemma));
goal thy "lfilter p (lmap f l) = lmap f (lfilter (p o f) l)";
by (res_inst_tac [("l","l")] llist_fun_equalityI 1);
-by (ALLGOALS (simp_tac (!simpset addsplits [expand_if])));
+by (ALLGOALS (simp_tac (simpset() addsplits [expand_if])));
by Safe_tac;
-by (Blast_tac 1);
by (case_tac "lmap f l : Domain (findRel p)" 1);
by (subgoal_tac "l ~: Domain (findRel(%x. p (f x)))" 2);
-by (blast_tac (!claset addIs [findRel_lmap_Domain]) 3);
-by (asm_simp_tac (!simpset addsimps [diverge_lfilter_LNil]) 2);
+by (blast_tac (claset() addIs [findRel_lmap_Domain]) 3);
+by (asm_simp_tac (simpset() addsimps [diverge_lfilter_LNil]) 2);
by (etac Domain_findRelE 1);
by (forward_tac [lmap_LCons_findRel] 1);
by (Clarify_tac 1);
-by (asm_simp_tac (!simpset addsimps [findRel_imp_lfilter]) 1);
-by (Blast_tac 1);
+by (asm_simp_tac (simpset() addsimps [findRel_imp_lfilter]) 1);
qed "lfilter_lmap";