--- a/src/HOL/MetisExamples/Abstraction.thy Fri Oct 03 19:35:18 2008 +0200
+++ b/src/HOL/MetisExamples/Abstraction.thy Fri Oct 03 20:10:43 2008 +0200
@@ -22,7 +22,7 @@
pset :: "'a set => 'a set"
order :: "'a set => ('a * 'a) set"
-ML{*ResAtp.problem_name := "Abstraction__Collect_triv"*}
+ML{*AtpThread.problem_name := "Abstraction__Collect_triv"*}
lemma (*Collect_triv:*) "a \<in> {x. P x} ==> P a"
proof (neg_clausify)
assume 0: "(a\<Colon>'a\<Colon>type) \<in> Collect (P\<Colon>'a\<Colon>type \<Rightarrow> bool)"
@@ -37,12 +37,12 @@
by (metis mem_Collect_eq)
-ML{*ResAtp.problem_name := "Abstraction__Collect_mp"*}
+ML{*AtpThread.problem_name := "Abstraction__Collect_mp"*}
lemma "a \<in> {x. P x --> Q x} ==> a \<in> {x. P x} ==> a \<in> {x. Q x}"
by (metis CollectI Collect_imp_eq ComplD UnE mem_Collect_eq);
--{*34 secs*}
-ML{*ResAtp.problem_name := "Abstraction__Sigma_triv"*}
+ML{*AtpThread.problem_name := "Abstraction__Sigma_triv"*}
lemma "(a,b) \<in> Sigma A B ==> a \<in> A & b \<in> B a"
proof (neg_clausify)
assume 0: "(a\<Colon>'a\<Colon>type, b\<Colon>'b\<Colon>type) \<in> Sigma (A\<Colon>'a\<Colon>type set) (B\<Colon>'a\<Colon>type \<Rightarrow> 'b\<Colon>type set)"
@@ -60,7 +60,7 @@
lemma Sigma_triv: "(a,b) \<in> Sigma A B ==> a \<in> A & b \<in> B a"
by (metis SigmaD1 SigmaD2)
-ML{*ResAtp.problem_name := "Abstraction__Sigma_Collect"*}
+ML{*AtpThread.problem_name := "Abstraction__Sigma_Collect"*}
lemma "(a,b) \<in> (SIGMA x: A. {y. x = f y}) ==> a \<in> A & a = f b"
(*???metis cannot prove this
by (metis CollectD SigmaD1 SigmaD2 UN_eq)
@@ -112,7 +112,7 @@
qed
-ML{*ResAtp.problem_name := "Abstraction__CLF_eq_in_pp"*}
+ML{*AtpThread.problem_name := "Abstraction__CLF_eq_in_pp"*}
lemma "(cl,f) \<in> CLF ==> CLF = (SIGMA cl: CL.{f. f \<in> pset cl}) ==> f \<in> pset cl"
by (metis Collect_mem_eq SigmaD2)
@@ -131,7 +131,7 @@
by (metis 5 0)
qed
-ML{*ResAtp.problem_name := "Abstraction__Sigma_Collect_Pi"*}
+ML{*AtpThread.problem_name := "Abstraction__Sigma_Collect_Pi"*}
lemma
"(cl,f) \<in> (SIGMA cl: CL. {f. f \<in> pset cl \<rightarrow> pset cl}) ==>
f \<in> pset cl \<rightarrow> pset cl"
@@ -147,7 +147,7 @@
qed
-ML{*ResAtp.problem_name := "Abstraction__Sigma_Collect_Int"*}
+ML{*AtpThread.problem_name := "Abstraction__Sigma_Collect_Int"*}
lemma
"(cl,f) \<in> (SIGMA cl: CL. {f. f \<in> pset cl \<inter> cl}) ==>
f \<in> pset cl \<inter> cl"
@@ -170,13 +170,13 @@
qed
-ML{*ResAtp.problem_name := "Abstraction__Sigma_Collect_Pi_mono"*}
+ML{*AtpThread.problem_name := "Abstraction__Sigma_Collect_Pi_mono"*}
lemma
"(cl,f) \<in> (SIGMA cl: CL. {f. f \<in> pset cl \<rightarrow> pset cl & monotone f (pset cl) (order cl)}) ==>
(f \<in> pset cl \<rightarrow> pset cl) & (monotone f (pset cl) (order cl))"
by auto
-ML{*ResAtp.problem_name := "Abstraction__CLF_subset_Collect_Int"*}
+ML{*AtpThread.problem_name := "Abstraction__CLF_subset_Collect_Int"*}
lemma "(cl,f) \<in> CLF ==>
CLF \<subseteq> (SIGMA cl: CL. {f. f \<in> pset cl \<inter> cl}) ==>
f \<in> pset cl \<inter> cl"
@@ -187,7 +187,7 @@
--{*@{text Int_def} is redundant*}
*)
-ML{*ResAtp.problem_name := "Abstraction__CLF_eq_Collect_Int"*}
+ML{*AtpThread.problem_name := "Abstraction__CLF_eq_Collect_Int"*}
lemma "(cl,f) \<in> CLF ==>
CLF = (SIGMA cl: CL. {f. f \<in> pset cl \<inter> cl}) ==>
f \<in> pset cl \<inter> cl"
@@ -196,7 +196,7 @@
by (metis Collect_mem_eq Int_commute SigmaD2)
*)
-ML{*ResAtp.problem_name := "Abstraction__CLF_subset_Collect_Pi"*}
+ML{*AtpThread.problem_name := "Abstraction__CLF_subset_Collect_Pi"*}
lemma
"(cl,f) \<in> CLF ==>
CLF \<subseteq> (SIGMA cl': CL. {f. f \<in> pset cl' \<rightarrow> pset cl'}) ==>
@@ -206,7 +206,7 @@
by (metis Collect_mem_eq SigmaD2 subsetD)
*)
-ML{*ResAtp.problem_name := "Abstraction__CLF_eq_Collect_Pi"*}
+ML{*AtpThread.problem_name := "Abstraction__CLF_eq_Collect_Pi"*}
lemma
"(cl,f) \<in> CLF ==>
CLF = (SIGMA cl: CL. {f. f \<in> pset cl \<rightarrow> pset cl}) ==>
@@ -216,21 +216,21 @@
by (metis Collect_mem_eq SigmaD2 contra_subsetD equalityE)
*)
-ML{*ResAtp.problem_name := "Abstraction__CLF_eq_Collect_Pi_mono"*}
+ML{*AtpThread.problem_name := "Abstraction__CLF_eq_Collect_Pi_mono"*}
lemma
"(cl,f) \<in> CLF ==>
CLF = (SIGMA cl: CL. {f. f \<in> pset cl \<rightarrow> pset cl & monotone f (pset cl) (order cl)}) ==>
(f \<in> pset cl \<rightarrow> pset cl) & (monotone f (pset cl) (order cl))"
by auto
-ML{*ResAtp.problem_name := "Abstraction__map_eq_zipA"*}
+ML{*AtpThread.problem_name := "Abstraction__map_eq_zipA"*}
lemma "map (%x. (f x, g x)) xs = zip (map f xs) (map g xs)"
apply (induct xs)
(*sledgehammer*)
apply auto
done
-ML{*ResAtp.problem_name := "Abstraction__map_eq_zipB"*}
+ML{*AtpThread.problem_name := "Abstraction__map_eq_zipB"*}
lemma "map (%w. (w -> w, w \<times> w)) xs =
zip (map (%w. w -> w) xs) (map (%w. w \<times> w) xs)"
apply (induct xs)
@@ -238,28 +238,28 @@
apply auto
done
-ML{*ResAtp.problem_name := "Abstraction__image_evenA"*}
+ML{*AtpThread.problem_name := "Abstraction__image_evenA"*}
lemma "(%x. Suc(f x)) ` {x. even x} <= A ==> (\<forall>x. even x --> Suc(f x) \<in> A)";
(*sledgehammer*)
by auto
-ML{*ResAtp.problem_name := "Abstraction__image_evenB"*}
+ML{*AtpThread.problem_name := "Abstraction__image_evenB"*}
lemma "(%x. f (f x)) ` ((%x. Suc(f x)) ` {x. even x}) <= A
==> (\<forall>x. even x --> f (f (Suc(f x))) \<in> A)";
(*sledgehammer*)
by auto
-ML{*ResAtp.problem_name := "Abstraction__image_curry"*}
+ML{*AtpThread.problem_name := "Abstraction__image_curry"*}
lemma "f \<in> (%u v. b \<times> u \<times> v) ` A ==> \<forall>u v. P (b \<times> u \<times> v) ==> P(f y)"
(*sledgehammer*)
by auto
-ML{*ResAtp.problem_name := "Abstraction__image_TimesA"*}
+ML{*AtpThread.problem_name := "Abstraction__image_TimesA"*}
lemma image_TimesA: "(%(x,y). (f x, g y)) ` (A \<times> B) = (f`A) \<times> (g`B)"
(*sledgehammer*)
apply (rule equalityI)
(***Even the two inclusions are far too difficult
-ML{*ResAtp.problem_name := "Abstraction__image_TimesA_simpler"*}
+ML{*AtpThread.problem_name := "Abstraction__image_TimesA_simpler"*}
***)
apply (rule subsetI)
apply (erule imageE)
@@ -282,13 +282,13 @@
(*Given the difficulty of the previous problem, these two are probably
impossible*)
-ML{*ResAtp.problem_name := "Abstraction__image_TimesB"*}
+ML{*AtpThread.problem_name := "Abstraction__image_TimesB"*}
lemma image_TimesB:
"(%(x,y,z). (f x, g y, h z)) ` (A \<times> B \<times> C) = (f`A) \<times> (g`B) \<times> (h`C)"
(*sledgehammer*)
by force
-ML{*ResAtp.problem_name := "Abstraction__image_TimesC"*}
+ML{*AtpThread.problem_name := "Abstraction__image_TimesC"*}
lemma image_TimesC:
"(%(x,y). (x \<rightarrow> x, y \<times> y)) ` (A \<times> B) =
((%x. x \<rightarrow> x) ` A) \<times> ((%y. y \<times> y) ` B)"
--- a/src/HOL/MetisExamples/BT.thy Fri Oct 03 19:35:18 2008 +0200
+++ b/src/HOL/MetisExamples/BT.thy Fri Oct 03 20:10:43 2008 +0200
@@ -66,21 +66,21 @@
text {* \medskip BT simplification *}
-ML {*ResAtp.problem_name := "BT__n_leaves_reflect"*}
+ML {*AtpThread.problem_name := "BT__n_leaves_reflect"*}
lemma n_leaves_reflect: "n_leaves (reflect t) = n_leaves t"
apply (induct t)
apply (metis add_right_cancel n_leaves.simps(1) reflect.simps(1))
apply (metis add_commute n_leaves.simps(2) reflect.simps(2))
done
-ML {*ResAtp.problem_name := "BT__n_nodes_reflect"*}
+ML {*AtpThread.problem_name := "BT__n_nodes_reflect"*}
lemma n_nodes_reflect: "n_nodes (reflect t) = n_nodes t"
apply (induct t)
apply (metis reflect.simps(1))
apply (metis n_nodes.simps(2) nat_add_commute reflect.simps(2))
done
-ML {*ResAtp.problem_name := "BT__depth_reflect"*}
+ML {*AtpThread.problem_name := "BT__depth_reflect"*}
lemma depth_reflect: "depth (reflect t) = depth t"
apply (induct t)
apply (metis depth.simps(1) reflect.simps(1))
@@ -91,21 +91,21 @@
The famous relationship between the numbers of leaves and nodes.
*}
-ML {*ResAtp.problem_name := "BT__n_leaves_nodes"*}
+ML {*AtpThread.problem_name := "BT__n_leaves_nodes"*}
lemma n_leaves_nodes: "n_leaves t = Suc (n_nodes t)"
apply (induct t)
apply (metis n_leaves.simps(1) n_nodes.simps(1))
apply auto
done
-ML {*ResAtp.problem_name := "BT__reflect_reflect_ident"*}
+ML {*AtpThread.problem_name := "BT__reflect_reflect_ident"*}
lemma reflect_reflect_ident: "reflect (reflect t) = t"
apply (induct t)
apply (metis add_right_cancel reflect.simps(1));
apply (metis reflect.simps(2))
done
-ML {*ResAtp.problem_name := "BT__bt_map_ident"*}
+ML {*AtpThread.problem_name := "BT__bt_map_ident"*}
lemma bt_map_ident: "bt_map (%x. x) = (%y. y)"
apply (rule ext)
apply (induct_tac y)
@@ -116,7 +116,7 @@
done
-ML {*ResAtp.problem_name := "BT__bt_map_appnd"*}
+ML {*AtpThread.problem_name := "BT__bt_map_appnd"*}
lemma bt_map_appnd: "bt_map f (appnd t u) = appnd (bt_map f t) (bt_map f u)"
apply (induct t)
apply (metis appnd.simps(1) bt_map.simps(1))
@@ -124,7 +124,7 @@
done
-ML {*ResAtp.problem_name := "BT__bt_map_compose"*}
+ML {*AtpThread.problem_name := "BT__bt_map_compose"*}
lemma bt_map_compose: "bt_map (f o g) t = bt_map f (bt_map g t)"
apply (induct t)
apply (metis bt_map.simps(1))
@@ -134,42 +134,42 @@
done
-ML {*ResAtp.problem_name := "BT__bt_map_reflect"*}
+ML {*AtpThread.problem_name := "BT__bt_map_reflect"*}
lemma bt_map_reflect: "bt_map f (reflect t) = reflect (bt_map f t)"
apply (induct t)
apply (metis add_right_cancel bt_map.simps(1) reflect.simps(1))
apply (metis add_right_cancel bt_map.simps(2) reflect.simps(2))
done
-ML {*ResAtp.problem_name := "BT__preorder_bt_map"*}
+ML {*AtpThread.problem_name := "BT__preorder_bt_map"*}
lemma preorder_bt_map: "preorder (bt_map f t) = map f (preorder t)"
apply (induct t)
apply (metis bt_map.simps(1) map.simps(1) preorder.simps(1))
apply simp
done
-ML {*ResAtp.problem_name := "BT__inorder_bt_map"*}
+ML {*AtpThread.problem_name := "BT__inorder_bt_map"*}
lemma inorder_bt_map: "inorder (bt_map f t) = map f (inorder t)"
apply (induct t)
apply (metis bt_map.simps(1) inorder.simps(1) map.simps(1))
apply simp
done
-ML {*ResAtp.problem_name := "BT__postorder_bt_map"*}
+ML {*AtpThread.problem_name := "BT__postorder_bt_map"*}
lemma postorder_bt_map: "postorder (bt_map f t) = map f (postorder t)"
apply (induct t)
apply (metis bt_map.simps(1) map.simps(1) postorder.simps(1))
apply simp
done
-ML {*ResAtp.problem_name := "BT__depth_bt_map"*}
+ML {*AtpThread.problem_name := "BT__depth_bt_map"*}
lemma depth_bt_map [simp]: "depth (bt_map f t) = depth t"
apply (induct t)
apply (metis bt_map.simps(1) depth.simps(1))
apply simp
done
-ML {*ResAtp.problem_name := "BT__n_leaves_bt_map"*}
+ML {*AtpThread.problem_name := "BT__n_leaves_bt_map"*}
lemma n_leaves_bt_map [simp]: "n_leaves (bt_map f t) = n_leaves t"
apply (induct t)
apply (metis One_nat_def Suc_eq_add_numeral_1 bt_map.simps(1) less_add_one less_antisym linorder_neq_iff n_leaves.simps(1))
@@ -177,21 +177,21 @@
done
-ML {*ResAtp.problem_name := "BT__preorder_reflect"*}
+ML {*AtpThread.problem_name := "BT__preorder_reflect"*}
lemma preorder_reflect: "preorder (reflect t) = rev (postorder t)"
apply (induct t)
apply (metis postorder.simps(1) preorder.simps(1) reflect.simps(1) rev_is_Nil_conv)
apply (metis Cons_eq_append_conv monoid_append.add_0_left postorder.simps(2) preorder.simps(2) reflect.simps(2) rev.simps(2) rev_append rev_rev_ident)
done
-ML {*ResAtp.problem_name := "BT__inorder_reflect"*}
+ML {*AtpThread.problem_name := "BT__inorder_reflect"*}
lemma inorder_reflect: "inorder (reflect t) = rev (inorder t)"
apply (induct t)
apply (metis inorder.simps(1) reflect.simps(1) rev.simps(1))
apply simp
done
-ML {*ResAtp.problem_name := "BT__postorder_reflect"*}
+ML {*AtpThread.problem_name := "BT__postorder_reflect"*}
lemma postorder_reflect: "postorder (reflect t) = rev (preorder t)"
apply (induct t)
apply (metis postorder.simps(1) preorder.simps(1) reflect.simps(1) rev.simps(1))
@@ -202,7 +202,7 @@
Analogues of the standard properties of the append function for lists.
*}
-ML {*ResAtp.problem_name := "BT__appnd_assoc"*}
+ML {*AtpThread.problem_name := "BT__appnd_assoc"*}
lemma appnd_assoc [simp]:
"appnd (appnd t1 t2) t3 = appnd t1 (appnd t2 t3)"
apply (induct t1)
@@ -210,14 +210,14 @@
apply (metis appnd.simps(2))
done
-ML {*ResAtp.problem_name := "BT__appnd_Lf2"*}
+ML {*AtpThread.problem_name := "BT__appnd_Lf2"*}
lemma appnd_Lf2 [simp]: "appnd t Lf = t"
apply (induct t)
apply (metis appnd.simps(1))
apply (metis appnd.simps(2))
done
-ML {*ResAtp.problem_name := "BT__depth_appnd"*}
+ML {*AtpThread.problem_name := "BT__depth_appnd"*}
declare max_add_distrib_left [simp]
lemma depth_appnd [simp]: "depth (appnd t1 t2) = depth t1 + depth t2"
apply (induct t1)
@@ -225,7 +225,7 @@
apply (simp add: );
done
-ML {*ResAtp.problem_name := "BT__n_leaves_appnd"*}
+ML {*AtpThread.problem_name := "BT__n_leaves_appnd"*}
lemma n_leaves_appnd [simp]:
"n_leaves (appnd t1 t2) = n_leaves t1 * n_leaves t2"
apply (induct t1)
@@ -233,7 +233,7 @@
apply (simp add: left_distrib)
done
-ML {*ResAtp.problem_name := "BT__bt_map_appnd"*}
+ML {*AtpThread.problem_name := "BT__bt_map_appnd"*}
lemma (*bt_map_appnd:*)
"bt_map f (appnd t1 t2) = appnd (bt_map f t1) (bt_map f t2)"
apply (induct t1)
--- a/src/HOL/MetisExamples/BigO.thy Fri Oct 03 19:35:18 2008 +0200
+++ b/src/HOL/MetisExamples/BigO.thy Fri Oct 03 20:10:43 2008 +0200
@@ -18,7 +18,7 @@
bigo :: "('a => 'b::ordered_idom) => ('a => 'b) set" ("(1O'(_'))")
"O(f::('a => 'b)) == {h. EX c. ALL x. abs (h x) <= c * abs (f x)}"
-ML_command{*ResAtp.problem_name := "BigO__bigo_pos_const"*}
+ML_command{*AtpThread.problem_name := "BigO__bigo_pos_const"*}
lemma bigo_pos_const: "(EX (c::'a::ordered_idom).
ALL x. (abs (h x)) <= (c * (abs (f x))))
= (EX c. 0 < c & (ALL x. (abs(h x)) <= (c * (abs (f x)))))"
@@ -215,7 +215,7 @@
{h. EX c. (0 < c & (ALL x. abs (h x) <= c * abs (f x)))}"
by (auto simp add: bigo_def bigo_pos_const)
-ML_command{*ResAtp.problem_name := "BigO__bigo_elt_subset"*}
+ML_command{*AtpThread.problem_name := "BigO__bigo_elt_subset"*}
lemma bigo_elt_subset [intro]: "f : O(g) ==> O(f) <= O(g)"
apply (auto simp add: bigo_alt_def)
apply (rule_tac x = "ca * c" in exI)
@@ -233,7 +233,7 @@
done
-ML_command{*ResAtp.problem_name := "BigO__bigo_refl"*}
+ML_command{*AtpThread.problem_name := "BigO__bigo_refl"*}
lemma bigo_refl [intro]: "f : O(f)"
apply(auto simp add: bigo_def)
proof (neg_clausify)
@@ -247,7 +247,7 @@
by (metis 0 2)
qed
-ML_command{*ResAtp.problem_name := "BigO__bigo_zero"*}
+ML_command{*AtpThread.problem_name := "BigO__bigo_zero"*}
lemma bigo_zero: "0 : O(g)"
apply (auto simp add: bigo_def func_zero)
proof (neg_clausify)
@@ -337,7 +337,7 @@
apply (auto del: subsetI simp del: bigo_plus_idemp)
done
-ML_command{*ResAtp.problem_name := "BigO__bigo_plus_eq"*}
+ML_command{*AtpThread.problem_name := "BigO__bigo_plus_eq"*}
lemma bigo_plus_eq: "ALL x. 0 <= f x ==> ALL x. 0 <= g x ==>
O(f + g) = O(f) \<oplus> O(g)"
apply (rule equalityI)
@@ -360,13 +360,13 @@
apply (rule abs_triangle_ineq)
apply (metis add_nonneg_nonneg)
apply (rule add_mono)
-ML_command{*ResAtp.problem_name := "BigO__bigo_plus_eq_simpler"*}
+ML_command{*AtpThread.problem_name := "BigO__bigo_plus_eq_simpler"*}
(*Found by SPASS; SLOW*)
apply (metis le_maxI2 linorder_linear linorder_not_le min_max.less_eq_less_sup.sup_absorb1 mult_le_cancel_right order_trans)
apply (metis le_maxI2 linorder_not_le mult_le_cancel_right order_trans)
done
-ML_command{*ResAtp.problem_name := "BigO__bigo_bounded_alt"*}
+ML_command{*AtpThread.problem_name := "BigO__bigo_bounded_alt"*}
lemma bigo_bounded_alt: "ALL x. 0 <= f x ==> ALL x. f x <= c * g x ==>
f : O(g)"
apply (auto simp add: bigo_def)
@@ -426,7 +426,7 @@
text{*So here is the easier (and more natural) problem using transitivity*}
-ML_command{*ResAtp.problem_name := "BigO__bigo_bounded_alt_trans"*}
+ML_command{*AtpThread.problem_name := "BigO__bigo_bounded_alt_trans"*}
lemma "ALL x. 0 <= f x ==> ALL x. f x <= c * g x ==> f : O(g)"
apply (auto simp add: bigo_def)
(*Version 1: one-shot proof*)
@@ -434,7 +434,7 @@
done
text{*So here is the easier (and more natural) problem using transitivity*}
-ML_command{*ResAtp.problem_name := "BigO__bigo_bounded_alt_trans"*}
+ML_command{*AtpThread.problem_name := "BigO__bigo_bounded_alt_trans"*}
lemma "ALL x. 0 <= f x ==> ALL x. f x <= c * g x ==> f : O(g)"
apply (auto simp add: bigo_def)
(*Version 2: single-step proof*)
@@ -473,7 +473,7 @@
apply simp
done
-ML_command{*ResAtp.problem_name := "BigO__bigo_bounded2"*}
+ML_command{*AtpThread.problem_name := "BigO__bigo_bounded2"*}
lemma bigo_bounded2: "ALL x. lb x <= f x ==> ALL x. f x <= lb x + g x ==>
f : lb +o O(g)"
apply (rule set_minus_imp_plus)
@@ -496,7 +496,7 @@
by (metis 4 2 0)
qed
-ML_command{*ResAtp.problem_name := "BigO__bigo_abs"*}
+ML_command{*AtpThread.problem_name := "BigO__bigo_abs"*}
lemma bigo_abs: "(%x. abs(f x)) =o O(f)"
apply (unfold bigo_def)
apply auto
@@ -511,7 +511,7 @@
by (metis 0 2)
qed
-ML_command{*ResAtp.problem_name := "BigO__bigo_abs2"*}
+ML_command{*AtpThread.problem_name := "BigO__bigo_abs2"*}
lemma bigo_abs2: "f =o O(%x. abs(f x))"
apply (unfold bigo_def)
apply auto
@@ -583,7 +583,7 @@
by (simp add: bigo_abs3 [symmetric])
qed
-ML_command{*ResAtp.problem_name := "BigO__bigo_mult"*}
+ML_command{*AtpThread.problem_name := "BigO__bigo_mult"*}
lemma bigo_mult [intro]: "O(f)\<otimes>O(g) <= O(f * g)"
apply (rule subsetI)
apply (subst bigo_def)
@@ -595,7 +595,7 @@
apply(erule_tac x = x in allE)+
apply(subgoal_tac "c * ca * abs(f x * g x) =
(c * abs(f x)) * (ca * abs(g x))")
-ML_command{*ResAtp.problem_name := "BigO__bigo_mult_simpler"*}
+ML_command{*AtpThread.problem_name := "BigO__bigo_mult_simpler"*}
prefer 2
apply (metis mult_assoc mult_left_commute
OrderedGroup.abs_of_pos OrderedGroup.mult_left_commute
@@ -660,14 +660,14 @@
qed
-ML_command{*ResAtp.problem_name := "BigO__bigo_mult2"*}
+ML_command{*AtpThread.problem_name := "BigO__bigo_mult2"*}
lemma bigo_mult2 [intro]: "f *o O(g) <= O(f * g)"
apply (auto simp add: bigo_def elt_set_times_def func_times abs_mult)
(*sledgehammer*);
apply (rule_tac x = c in exI)
apply clarify
apply (drule_tac x = x in spec)
-ML_command{*ResAtp.problem_name := "BigO__bigo_mult2_simpler"*}
+ML_command{*AtpThread.problem_name := "BigO__bigo_mult2_simpler"*}
(*sledgehammer [no luck]*);
apply (subgoal_tac "abs(f x) * abs(b x) <= abs(f x) * (c * abs(g x))")
apply (simp add: mult_ac)
@@ -675,11 +675,11 @@
apply (rule abs_ge_zero)
done
-ML_command{*ResAtp.problem_name:="BigO__bigo_mult3"*}
+ML_command{*AtpThread.problem_name:="BigO__bigo_mult3"*}
lemma bigo_mult3: "f : O(h) ==> g : O(j) ==> f * g : O(h * j)"
by (metis bigo_mult set_times_intro subset_iff)
-ML_command{*ResAtp.problem_name:="BigO__bigo_mult4"*}
+ML_command{*AtpThread.problem_name:="BigO__bigo_mult4"*}
lemma bigo_mult4 [intro]:"f : k +o O(h) ==> g * f : (g * k) +o O(g * h)"
by (metis bigo_mult2 set_plus_mono_b set_times_intro2 set_times_plus_distrib)
@@ -713,13 +713,13 @@
qed
qed
-ML_command{*ResAtp.problem_name := "BigO__bigo_mult6"*}
+ML_command{*AtpThread.problem_name := "BigO__bigo_mult6"*}
lemma bigo_mult6: "ALL x. f x ~= 0 ==>
O(f * g) = (f::'a => ('b::ordered_field)) *o O(g)"
by (metis bigo_mult2 bigo_mult5 order_antisym)
(*proof requires relaxing relevance: 2007-01-25*)
-ML_command{*ResAtp.problem_name := "BigO__bigo_mult7"*}
+ML_command{*AtpThread.problem_name := "BigO__bigo_mult7"*}
declare bigo_mult6 [simp]
lemma bigo_mult7: "ALL x. f x ~= 0 ==>
O(f * g) <= O(f::'a => ('b::ordered_field)) \<otimes> O(g)"
@@ -731,7 +731,7 @@
done
declare bigo_mult6 [simp del]
-ML_command{*ResAtp.problem_name := "BigO__bigo_mult8"*}
+ML_command{*AtpThread.problem_name := "BigO__bigo_mult8"*}
declare bigo_mult7[intro!]
lemma bigo_mult8: "ALL x. f x ~= 0 ==>
O(f * g) = O(f::'a => ('b::ordered_field)) \<otimes> O(g)"
@@ -782,7 +782,7 @@
qed
qed
-ML_command{*ResAtp.problem_name:="BigO__bigo_plus_absorb"*}
+ML_command{*AtpThread.problem_name:="BigO__bigo_plus_absorb"*}
lemma bigo_plus_absorb [simp]: "f : O(g) ==> f +o O(g) = O(g)"
by (metis bigo_plus_absorb_lemma1 bigo_plus_absorb_lemma2 order_eq_iff);
@@ -809,7 +809,7 @@
lemma bigo_const1: "(%x. c) : O(%x. 1)"
by (auto simp add: bigo_def mult_ac)
-ML_command{*ResAtp.problem_name:="BigO__bigo_const2"*}
+ML_command{*AtpThread.problem_name:="BigO__bigo_const2"*}
lemma (*bigo_const2 [intro]:*) "O(%x. c) <= O(%x. 1)"
by (metis bigo_const1 bigo_elt_subset);
@@ -832,7 +832,7 @@
apply (rule bigo_const1)
done
-ML_command{*ResAtp.problem_name := "BigO__bigo_const3"*}
+ML_command{*AtpThread.problem_name := "BigO__bigo_const3"*}
lemma bigo_const3: "(c::'a::ordered_field) ~= 0 ==> (%x. 1) : O(%x. c)"
apply (simp add: bigo_def)
proof (neg_clausify)
@@ -856,7 +856,7 @@
O(%x. c) = O(%x. 1)"
by (rule equalityI, rule bigo_const2, rule bigo_const4, assumption)
-ML_command{*ResAtp.problem_name := "BigO__bigo_const_mult1"*}
+ML_command{*AtpThread.problem_name := "BigO__bigo_const_mult1"*}
lemma bigo_const_mult1: "(%x. c * f x) : O(f)"
apply (simp add: bigo_def abs_mult)
proof (neg_clausify)
@@ -872,7 +872,7 @@
lemma bigo_const_mult2: "O(%x. c * f x) <= O(f)"
by (rule bigo_elt_subset, rule bigo_const_mult1)
-ML_command{*ResAtp.problem_name := "BigO__bigo_const_mult3"*}
+ML_command{*AtpThread.problem_name := "BigO__bigo_const_mult3"*}
lemma bigo_const_mult3: "(c::'a::ordered_field) ~= 0 ==> f : O(%x. c * f x)"
apply (simp add: bigo_def)
(*sledgehammer [no luck]*);
@@ -890,7 +890,7 @@
O(%x. c * f x) = O(f)"
by (rule equalityI, rule bigo_const_mult2, erule bigo_const_mult4)
-ML_command{*ResAtp.problem_name := "BigO__bigo_const_mult5"*}
+ML_command{*AtpThread.problem_name := "BigO__bigo_const_mult5"*}
lemma bigo_const_mult5 [simp]: "(c::'a::ordered_field) ~= 0 ==>
(%x. c) *o O(f) = O(f)"
apply (auto del: subsetI)
@@ -910,7 +910,7 @@
done
-ML_command{*ResAtp.problem_name := "BigO__bigo_const_mult6"*}
+ML_command{*AtpThread.problem_name := "BigO__bigo_const_mult6"*}
lemma bigo_const_mult6 [intro]: "(%x. c) *o O(f) <= O(f)"
apply (auto intro!: subsetI
simp add: bigo_def elt_set_times_def func_times
@@ -967,7 +967,7 @@
apply (blast intro: order_trans mult_right_mono abs_ge_self)
done
-ML_command{*ResAtp.problem_name := "BigO__bigo_setsum1"*}
+ML_command{*AtpThread.problem_name := "BigO__bigo_setsum1"*}
lemma bigo_setsum1: "ALL x y. 0 <= h x y ==>
EX c. ALL x y. abs(f x y) <= c * (h x y) ==>
(%x. SUM y : A x. f x y) =o O(%x. SUM y : A x. h x y)"
@@ -984,7 +984,7 @@
(%x. SUM y : A x. f y) =o O(%x. SUM y : A x. h y)"
by (rule bigo_setsum1, auto)
-ML_command{*ResAtp.problem_name := "BigO__bigo_setsum3"*}
+ML_command{*AtpThread.problem_name := "BigO__bigo_setsum3"*}
lemma bigo_setsum3: "f =o O(h) ==>
(%x. SUM y : A x. (l x y) * f(k x y)) =o
O(%x. SUM y : A x. abs(l x y * h(k x y)))"
@@ -1015,7 +1015,7 @@
apply (erule set_plus_imp_minus)
done
-ML_command{*ResAtp.problem_name := "BigO__bigo_setsum5"*}
+ML_command{*AtpThread.problem_name := "BigO__bigo_setsum5"*}
lemma bigo_setsum5: "f =o O(h) ==> ALL x y. 0 <= l x y ==>
ALL x. 0 <= h x ==>
(%x. SUM y : A x. (l x y) * f(k x y)) =o
@@ -1072,7 +1072,7 @@
apply (simp add: func_times)
done
-ML_command{*ResAtp.problem_name := "BigO__bigo_fix"*}
+ML_command{*AtpThread.problem_name := "BigO__bigo_fix"*}
lemma bigo_fix: "(%x. f ((x::nat) + 1)) =o O(%x. h(x + 1)) ==> f 0 = 0 ==>
f =o O(h)"
apply (simp add: bigo_alt_def)
@@ -1137,7 +1137,7 @@
apply (erule spec)+
done
-ML_command{*ResAtp.problem_name:="BigO__bigo_lesso1"*}
+ML_command{*AtpThread.problem_name:="BigO__bigo_lesso1"*}
lemma bigo_lesso1: "ALL x. f x <= g x ==> f <o g =o O(h)"
apply (unfold lesso_def)
apply (subgoal_tac "(%x. max (f x - g x) 0) = 0")
@@ -1149,7 +1149,7 @@
done
-ML_command{*ResAtp.problem_name := "BigO__bigo_lesso2"*}
+ML_command{*AtpThread.problem_name := "BigO__bigo_lesso2"*}
lemma bigo_lesso2: "f =o g +o O(h) ==>
ALL x. 0 <= k x ==> ALL x. k x <= f x ==>
k <o g =o O(h)"
@@ -1186,7 +1186,7 @@
by (metis min_max.less_eq_less_sup.sup_commute min_max.less_eq_less_inf.inf_commute min_max.less_eq_less_inf_sup.sup_inf_absorb min_max.less_eq_less_inf.le_iff_inf 0 max_diff_distrib_left 1 linorder_not_le 8)
qed
-ML_command{*ResAtp.problem_name := "BigO__bigo_lesso3"*}
+ML_command{*AtpThread.problem_name := "BigO__bigo_lesso3"*}
lemma bigo_lesso3: "f =o g +o O(h) ==>
ALL x. 0 <= k x ==> ALL x. g x <= k x ==>
f <o k =o O(h)"
@@ -1203,7 +1203,7 @@
apply (simp del: compare_rls diff_minus);
apply (subst abs_of_nonneg)
apply (drule_tac x = x in spec) back
-ML_command{*ResAtp.problem_name := "BigO__bigo_lesso3_simpler"*}
+ML_command{*AtpThread.problem_name := "BigO__bigo_lesso3_simpler"*}
apply (metis diff_less_0_iff_less linorder_not_le not_leE uminus_add_conv_diff xt1(12) xt1(6))
apply (metis add_minus_cancel diff_le_eq le_diff_eq uminus_add_conv_diff)
apply (metis abs_ge_zero linorder_linear min_max.less_eq_less_sup.sup_absorb1 min_max.less_eq_less_sup.sup_commute)
@@ -1223,7 +1223,7 @@
split: split_max abs_split)
done
-ML_command{*ResAtp.problem_name := "BigO__bigo_lesso5"*}
+ML_command{*AtpThread.problem_name := "BigO__bigo_lesso5"*}
lemma bigo_lesso5: "f <o g =o O(h) ==>
EX C. ALL x. f x <= g x + C * abs(h x)"
apply (simp only: lesso_def bigo_alt_def)
--- a/src/HOL/MetisExamples/Message.thy Fri Oct 03 19:35:18 2008 +0200
+++ b/src/HOL/MetisExamples/Message.thy Fri Oct 03 20:10:43 2008 +0200
@@ -78,7 +78,7 @@
| Body: "Crypt K X \<in> parts H ==> X \<in> parts H"
-ML{*ResAtp.problem_name := "Message__parts_mono"*}
+ML{*AtpThread.problem_name := "Message__parts_mono"*}
lemma parts_mono: "G \<subseteq> H ==> parts(G) \<subseteq> parts(H)"
apply auto
apply (erule parts.induct)
@@ -102,7 +102,7 @@
subsubsection{*Inverse of keys *}
-ML{*ResAtp.problem_name := "Message__invKey_eq"*}
+ML{*AtpThread.problem_name := "Message__invKey_eq"*}
lemma invKey_eq [simp]: "(invKey K = invKey K') = (K=K')"
by (metis invKey)
@@ -203,7 +203,7 @@
apply (simp only: parts_Un)
done
-ML{*ResAtp.problem_name := "Message__parts_insert_two"*}
+ML{*AtpThread.problem_name := "Message__parts_insert_two"*}
lemma parts_insert2:
"parts (insert X (insert Y H)) = parts {X} \<union> parts {Y} \<union> parts H"
by (metis Un_commute Un_empty_left Un_empty_right Un_insert_left Un_insert_right parts_Un)
@@ -240,7 +240,7 @@
lemma parts_idem [simp]: "parts (parts H) = parts H"
by blast
-ML{*ResAtp.problem_name := "Message__parts_subset_iff"*}
+ML{*AtpThread.problem_name := "Message__parts_subset_iff"*}
lemma parts_subset_iff [simp]: "(parts G \<subseteq> parts H) = (G \<subseteq> parts H)"
apply (rule iffI)
apply (metis Un_absorb1 Un_subset_iff parts_Un parts_increasing)
@@ -251,7 +251,7 @@
by (blast dest: parts_mono);
-ML{*ResAtp.problem_name := "Message__parts_cut"*}
+ML{*AtpThread.problem_name := "Message__parts_cut"*}
lemma parts_cut: "[|Y\<in> parts(insert X G); X\<in> parts H|] ==> Y\<in> parts(G \<union> H)"
by (metis Un_subset_iff insert_subset parts_increasing parts_trans)
@@ -316,7 +316,7 @@
done
-ML{*ResAtp.problem_name := "Message__msg_Nonce_supply"*}
+ML{*AtpThread.problem_name := "Message__msg_Nonce_supply"*}
lemma msg_Nonce_supply: "\<exists>N. \<forall>n. N\<le>n --> Nonce n \<notin> parts {msg}"
apply (induct_tac "msg")
apply (simp_all add: parts_insert2)
@@ -368,7 +368,7 @@
lemmas not_parts_not_analz = analz_subset_parts [THEN contra_subsetD, standard]
-ML{*ResAtp.problem_name := "Message__parts_analz"*}
+ML{*AtpThread.problem_name := "Message__parts_analz"*}
lemma parts_analz [simp]: "parts (analz H) = parts H"
apply (rule equalityI)
apply (metis analz_subset_parts parts_subset_iff)
@@ -520,7 +520,7 @@
by (drule analz_mono, blast)
-ML{*ResAtp.problem_name := "Message__analz_cut"*}
+ML{*AtpThread.problem_name := "Message__analz_cut"*}
declare analz_trans[intro]
lemma analz_cut: "[| Y\<in> analz (insert X H); X\<in> analz H |] ==> Y\<in> analz H"
(*TOO SLOW
@@ -538,7 +538,7 @@
text{*A congruence rule for "analz" *}
-ML{*ResAtp.problem_name := "Message__analz_subset_cong"*}
+ML{*AtpThread.problem_name := "Message__analz_subset_cong"*}
lemma analz_subset_cong:
"[| analz G \<subseteq> analz G'; analz H \<subseteq> analz H' |]
==> analz (G \<union> H) \<subseteq> analz (G' \<union> H')"
@@ -616,7 +616,7 @@
by (intro Un_least synth_mono Un_upper1 Un_upper2)
-ML{*ResAtp.problem_name := "Message__synth_insert"*}
+ML{*AtpThread.problem_name := "Message__synth_insert"*}
lemma synth_insert: "insert X (synth H) \<subseteq> synth(insert X H)"
by (metis insert_iff insert_subset subset_insertI synth.Inj synth_mono)
@@ -638,7 +638,7 @@
lemma synth_trans: "[| X\<in> synth G; G \<subseteq> synth H |] ==> X\<in> synth H"
by (drule synth_mono, blast)
-ML{*ResAtp.problem_name := "Message__synth_cut"*}
+ML{*AtpThread.problem_name := "Message__synth_cut"*}
lemma synth_cut: "[| Y\<in> synth (insert X H); X\<in> synth H |] ==> Y\<in> synth H"
(*TOO SLOW
by (metis insert_absorb insert_mono insert_subset synth_idem synth_increasing synth_mono)
@@ -670,7 +670,7 @@
subsubsection{*Combinations of parts, analz and synth *}
-ML{*ResAtp.problem_name := "Message__parts_synth"*}
+ML{*AtpThread.problem_name := "Message__parts_synth"*}
lemma parts_synth [simp]: "parts (synth H) = parts H \<union> synth H"
apply (rule equalityI)
apply (rule subsetI)
@@ -685,14 +685,14 @@
-ML{*ResAtp.problem_name := "Message__analz_analz_Un"*}
+ML{*AtpThread.problem_name := "Message__analz_analz_Un"*}
lemma analz_analz_Un [simp]: "analz (analz G \<union> H) = analz (G \<union> H)"
apply (rule equalityI);
apply (metis analz_idem analz_subset_cong order_eq_refl)
apply (metis analz_increasing analz_subset_cong order_eq_refl)
done
-ML{*ResAtp.problem_name := "Message__analz_synth_Un"*}
+ML{*AtpThread.problem_name := "Message__analz_synth_Un"*}
declare analz_mono [intro] analz.Fst [intro] analz.Snd [intro] Un_least [intro]
lemma analz_synth_Un [simp]: "analz (synth G \<union> H) = analz (G \<union> H) \<union> synth G"
apply (rule equalityI)
@@ -706,7 +706,7 @@
done
-ML{*ResAtp.problem_name := "Message__analz_synth"*}
+ML{*AtpThread.problem_name := "Message__analz_synth"*}
lemma analz_synth [simp]: "analz (synth H) = analz H \<union> synth H"
proof (neg_clausify)
assume 0: "analz (synth H) \<noteq> analz H \<union> synth H"
@@ -729,7 +729,7 @@
subsubsection{*For reasoning about the Fake rule in traces *}
-ML{*ResAtp.problem_name := "Message__parts_insert_subset_Un"*}
+ML{*AtpThread.problem_name := "Message__parts_insert_subset_Un"*}
lemma parts_insert_subset_Un: "X\<in> G ==> parts(insert X H) \<subseteq> parts G \<union> parts H"
proof (neg_clausify)
assume 0: "X \<in> G"
@@ -748,7 +748,7 @@
by (metis 6 0)
qed
-ML{*ResAtp.problem_name := "Message__Fake_parts_insert"*}
+ML{*AtpThread.problem_name := "Message__Fake_parts_insert"*}
lemma Fake_parts_insert:
"X \<in> synth (analz H) ==>
parts (insert X H) \<subseteq> synth (analz H) \<union> parts H"
@@ -791,14 +791,14 @@
==> Z \<in> synth (analz H) \<union> parts H";
by (blast dest: Fake_parts_insert [THEN subsetD, dest])
-ML{*ResAtp.problem_name := "Message__Fake_analz_insert"*}
+ML{*AtpThread.problem_name := "Message__Fake_analz_insert"*}
declare analz_mono [intro] synth_mono [intro]
lemma Fake_analz_insert:
"X\<in> synth (analz G) ==>
analz (insert X H) \<subseteq> synth (analz G) \<union> analz (G \<union> H)"
by (metis Un_commute Un_insert_left Un_insert_right Un_upper1 analz_analz_Un analz_mono analz_synth_Un equalityE insert_absorb order_le_less xt1(12))
-ML{*ResAtp.problem_name := "Message__Fake_analz_insert_simpler"*}
+ML{*AtpThread.problem_name := "Message__Fake_analz_insert_simpler"*}
(*simpler problems? BUT METIS CAN'T PROVE
lemma Fake_analz_insert_simpler:
"X\<in> synth (analz G) ==>
--- a/src/HOL/MetisExamples/Tarski.thy Fri Oct 03 19:35:18 2008 +0200
+++ b/src/HOL/MetisExamples/Tarski.thy Fri Oct 03 20:10:43 2008 +0200
@@ -416,7 +416,7 @@
(*never proved, 2007-01-22: Tarski__CLF_unnamed_lemma
NOT PROVABLE because of the conjunction used in the definition: we don't
allow reasoning with rules like conjE, which is essential here.*)
-ML_command{*ResAtp.problem_name:="Tarski__CLF_unnamed_lemma"*}
+ML_command{*AtpThread.problem_name:="Tarski__CLF_unnamed_lemma"*}
lemma (in CLF) [simp]:
"f: pset cl -> pset cl & monotone f (pset cl) (order cl)"
apply (insert f_cl)
@@ -433,7 +433,7 @@
by (simp add: A_def r_def)
(*never proved, 2007-01-22*)
-ML_command{*ResAtp.problem_name:="Tarski__CLF_CLF_dual"*}
+ML_command{*AtpThread.problem_name:="Tarski__CLF_CLF_dual"*}
declare (in CLF) CLF_set_def [simp] CL_dualCL [simp] monotone_dual [simp] dualA_iff [simp]
lemma (in CLF) CLF_dual: "(dual cl, f) \<in> CLF_set"
@@ -461,7 +461,7 @@
subsection {* lemmas for Tarski, lub *}
(*never proved, 2007-01-22*)
-ML{*ResAtp.problem_name:="Tarski__CLF_lubH_le_flubH"*}
+ML{*AtpThread.problem_name:="Tarski__CLF_lubH_le_flubH"*}
declare CL.lub_least[intro] CLF.f_in_funcset[intro] funcset_mem[intro] CL.lub_in_lattice[intro] PO.transE[intro] PO.monotoneE[intro] CLF.monotone_f[intro] CL.lub_upper[intro]
lemma (in CLF) lubH_le_flubH:
"H = {x. (x, f x) \<in> r & x \<in> A} ==> (lub H cl, f (lub H cl)) \<in> r"
@@ -471,7 +471,7 @@
-- {* @{text "\<forall>x:H. (x, f (lub H r)) \<in> r"} *}
apply (rule ballI)
(*never proved, 2007-01-22*)
-ML_command{*ResAtp.problem_name:="Tarski__CLF_lubH_le_flubH_simpler"*}
+ML_command{*AtpThread.problem_name:="Tarski__CLF_lubH_le_flubH_simpler"*}
apply (rule transE)
-- {* instantiates @{text "(x, ?z) \<in> order cl to (x, f x)"}, *}
-- {* because of the def of @{text H} *}
@@ -489,7 +489,7 @@
CLF.monotone_f[rule del] CL.lub_upper[rule del]
(*never proved, 2007-01-22*)
-ML{*ResAtp.problem_name:="Tarski__CLF_flubH_le_lubH"*}
+ML{*AtpThread.problem_name:="Tarski__CLF_flubH_le_lubH"*}
declare CLF.f_in_funcset[intro] funcset_mem[intro] CL.lub_in_lattice[intro]
PO.monotoneE[intro] CLF.monotone_f[intro] CL.lub_upper[intro]
CLF.lubH_le_flubH[simp]
@@ -499,7 +499,7 @@
apply (rule_tac t = "H" in ssubst, assumption)
apply (rule CollectI)
apply (rule conjI)
-ML_command{*ResAtp.problem_name:="Tarski__CLF_flubH_le_lubH_simpler"*}
+ML_command{*AtpThread.problem_name:="Tarski__CLF_flubH_le_lubH_simpler"*}
(*??no longer terminates, with combinators
apply (metis CO_refl lubH_le_flubH monotone_def monotone_f reflD1 reflD2)
*)
@@ -513,7 +513,7 @@
(*never proved, 2007-01-22*)
-ML{*ResAtp.problem_name:="Tarski__CLF_lubH_is_fixp"*}
+ML{*AtpThread.problem_name:="Tarski__CLF_lubH_is_fixp"*}
(*Single-step version fails. The conjecture clauses refer to local abstraction
functions (Frees), which prevents expand_defs_tac from removing those
"definitions" at the end of the proof. *)
@@ -588,7 +588,7 @@
"H = {x. (x, f x) \<in> r & x \<in> A} ==> lub H cl \<in> fix f A"
apply (simp add: fix_def)
apply (rule conjI)
-ML_command{*ResAtp.problem_name:="Tarski__CLF_lubH_is_fixp_simpler"*}
+ML_command{*AtpThread.problem_name:="Tarski__CLF_lubH_is_fixp_simpler"*}
apply (metis CO_refl lubH_le_flubH reflD1)
apply (metis antisymE flubH_le_lubH lubH_le_flubH)
done
@@ -607,7 +607,7 @@
apply (simp_all add: P_def)
done
-ML{*ResAtp.problem_name:="Tarski__CLF_lubH_least_fixf"*}
+ML{*AtpThread.problem_name:="Tarski__CLF_lubH_least_fixf"*}
lemma (in CLF) lubH_least_fixf:
"H = {x. (x, f x) \<in> r & x \<in> A}
==> \<forall>L. (\<forall>y \<in> fix f A. (y,L) \<in> r) --> (lub H cl, L) \<in> r"
@@ -615,7 +615,7 @@
done
subsection {* Tarski fixpoint theorem 1, first part *}
-ML{*ResAtp.problem_name:="Tarski__CLF_T_thm_1_lub"*}
+ML{*AtpThread.problem_name:="Tarski__CLF_T_thm_1_lub"*}
declare CL.lubI[intro] fix_subset[intro] CL.lub_in_lattice[intro]
CLF.fixf_le_lubH[simp] CLF.lubH_least_fixf[simp]
lemma (in CLF) T_thm_1_lub: "lub P cl = lub {x. (x, f x) \<in> r & x \<in> A} cl"
@@ -623,7 +623,7 @@
apply (rule sym)
apply (simp add: P_def)
apply (rule lubI)
-ML_command{*ResAtp.problem_name:="Tarski__CLF_T_thm_1_lub_simpler"*}
+ML_command{*AtpThread.problem_name:="Tarski__CLF_T_thm_1_lub_simpler"*}
apply (metis P_def fix_subset)
apply (metis Collect_conj_eq Collect_mem_eq Int_commute Int_lower1 lub_in_lattice vimage_def)
(*??no longer terminates, with combinators
@@ -638,7 +638,7 @@
(*never proved, 2007-01-22*)
-ML{*ResAtp.problem_name:="Tarski__CLF_glbH_is_fixp"*}
+ML{*AtpThread.problem_name:="Tarski__CLF_glbH_is_fixp"*}
declare glb_dual_lub[simp] PO.dualA_iff[intro] CLF.lubH_is_fixp[intro]
PO.dualPO[intro] CL.CL_dualCL[intro] PO.dualr_iff[simp]
lemma (in CLF) glbH_is_fixp: "H = {x. (f x, x) \<in> r & x \<in> A} ==> glb H cl \<in> P"
@@ -662,13 +662,13 @@
(*never proved, 2007-01-22*)
-ML{*ResAtp.problem_name:="Tarski__T_thm_1_glb"*} (*ALL THEOREMS*)
+ML{*AtpThread.problem_name:="Tarski__T_thm_1_glb"*} (*ALL THEOREMS*)
lemma (in CLF) T_thm_1_glb: "glb P cl = glb {x. (f x, x) \<in> r & x \<in> A} cl"
(*sledgehammer;*)
apply (simp add: glb_dual_lub P_def A_def r_def)
apply (rule dualA_iff [THEN subst])
(*never proved, 2007-01-22*)
-ML_command{*ResAtp.problem_name:="Tarski__T_thm_1_glb_simpler"*} (*ALL THEOREMS*)
+ML_command{*AtpThread.problem_name:="Tarski__T_thm_1_glb_simpler"*} (*ALL THEOREMS*)
(*sledgehammer;*)
apply (simp add: CLF.T_thm_1_lub [of _ f, OF CLF.intro, OF CL.intro CLF_axioms.intro, OF PO.intro CL_axioms.intro,
OF dualPO CL_dualCL] dualPO CL_dualCL CLF_dual dualr_iff)
@@ -677,13 +677,13 @@
subsection {* interval *}
-ML{*ResAtp.problem_name:="Tarski__rel_imp_elem"*}
+ML{*AtpThread.problem_name:="Tarski__rel_imp_elem"*}
declare (in CLF) CO_refl[simp] refl_def [simp]
lemma (in CLF) rel_imp_elem: "(x, y) \<in> r ==> x \<in> A"
by (metis CO_refl reflD1)
declare (in CLF) CO_refl[simp del] refl_def [simp del]
-ML{*ResAtp.problem_name:="Tarski__interval_subset"*}
+ML{*AtpThread.problem_name:="Tarski__interval_subset"*}
declare (in CLF) rel_imp_elem[intro]
declare interval_def [simp]
lemma (in CLF) interval_subset: "[| a \<in> A; b \<in> A |] ==> interval r a b \<subseteq> A"
@@ -718,7 +718,7 @@
"[| a \<in> A; b \<in> A; S \<subseteq> interval r a b |]==> S \<subseteq> A"
by (simp add: subset_trans [OF _ interval_subset])
-ML{*ResAtp.problem_name:="Tarski__L_in_interval"*} (*ALL THEOREMS*)
+ML{*AtpThread.problem_name:="Tarski__L_in_interval"*} (*ALL THEOREMS*)
lemma (in CLF) L_in_interval:
"[| a \<in> A; b \<in> A; S \<subseteq> interval r a b;
S \<noteq> {}; isLub S cl L; interval r a b \<noteq> {} |] ==> L \<in> interval r a b"
@@ -737,7 +737,7 @@
done
(*never proved, 2007-01-22*)
-ML{*ResAtp.problem_name:="Tarski__G_in_interval"*} (*ALL THEOREMS*)
+ML{*AtpThread.problem_name:="Tarski__G_in_interval"*} (*ALL THEOREMS*)
lemma (in CLF) G_in_interval:
"[| a \<in> A; b \<in> A; interval r a b \<noteq> {}; S \<subseteq> interval r a b; isGlb S cl G;
S \<noteq> {} |] ==> G \<in> interval r a b"
@@ -746,7 +746,7 @@
dualA_iff A_def dualPO CL_dualCL CLF_dual isGlb_dual_isLub)
done
-ML{*ResAtp.problem_name:="Tarski__intervalPO"*} (*ALL THEOREMS*)
+ML{*AtpThread.problem_name:="Tarski__intervalPO"*} (*ALL THEOREMS*)
lemma (in CLF) intervalPO:
"[| a \<in> A; b \<in> A; interval r a b \<noteq> {} |]
==> (| pset = interval r a b, order = induced (interval r a b) r |)
@@ -819,7 +819,7 @@
lemmas (in CLF) intv_CL_glb = intv_CL_lub [THEN Rdual]
(*never proved, 2007-01-22*)
-ML{*ResAtp.problem_name:="Tarski__interval_is_sublattice"*} (*ALL THEOREMS*)
+ML{*AtpThread.problem_name:="Tarski__interval_is_sublattice"*} (*ALL THEOREMS*)
lemma (in CLF) interval_is_sublattice:
"[| a \<in> A; b \<in> A; interval r a b \<noteq> {} |]
==> interval r a b <<= cl"
@@ -827,7 +827,7 @@
apply (rule sublatticeI)
apply (simp add: interval_subset)
(*never proved, 2007-01-22*)
-ML_command{*ResAtp.problem_name:="Tarski__interval_is_sublattice_simpler"*}
+ML_command{*AtpThread.problem_name:="Tarski__interval_is_sublattice_simpler"*}
(*sledgehammer *)
apply (rule CompleteLatticeI)
apply (simp add: intervalPO)
@@ -846,7 +846,7 @@
lemma (in CLF) Bot_dual_Top: "Bot cl = Top (dual cl)"
by (simp add: Top_def Bot_def least_def greatest_def dualA_iff dualr_iff)
-ML_command{*ResAtp.problem_name:="Tarski__Bot_in_lattice"*} (*ALL THEOREMS*)
+ML_command{*AtpThread.problem_name:="Tarski__Bot_in_lattice"*} (*ALL THEOREMS*)
lemma (in CLF) Bot_in_lattice: "Bot cl \<in> A"
(*sledgehammer; *)
apply (simp add: Bot_def least_def)
@@ -856,12 +856,12 @@
done
(*first proved 2007-01-25 after relaxing relevance*)
-ML_command{*ResAtp.problem_name:="Tarski__Top_in_lattice"*} (*ALL THEOREMS*)
+ML_command{*AtpThread.problem_name:="Tarski__Top_in_lattice"*} (*ALL THEOREMS*)
lemma (in CLF) Top_in_lattice: "Top cl \<in> A"
(*sledgehammer;*)
apply (simp add: Top_dual_Bot A_def)
(*first proved 2007-01-25 after relaxing relevance*)
-ML_command{*ResAtp.problem_name:="Tarski__Top_in_lattice_simpler"*} (*ALL THEOREMS*)
+ML_command{*AtpThread.problem_name:="Tarski__Top_in_lattice_simpler"*} (*ALL THEOREMS*)
(*sledgehammer*)
apply (rule dualA_iff [THEN subst])
apply (blast intro!: CLF.Bot_in_lattice [OF CLF.intro, OF CL.intro CLF_axioms.intro, OF PO.intro CL_axioms.intro] dualPO CL_dualCL CLF_dual)
@@ -876,7 +876,7 @@
done
(*never proved, 2007-01-22*)
-ML_command{*ResAtp.problem_name:="Tarski__Bot_prop"*} (*ALL THEOREMS*)
+ML_command{*AtpThread.problem_name:="Tarski__Bot_prop"*} (*ALL THEOREMS*)
lemma (in CLF) Bot_prop: "x \<in> A ==> (Bot cl, x) \<in> r"
(*sledgehammer*)
apply (simp add: Bot_dual_Top r_def)
@@ -885,12 +885,12 @@
dualA_iff A_def dualPO CL_dualCL CLF_dual)
done
-ML_command{*ResAtp.problem_name:="Tarski__Bot_in_lattice"*} (*ALL THEOREMS*)
+ML_command{*AtpThread.problem_name:="Tarski__Bot_in_lattice"*} (*ALL THEOREMS*)
lemma (in CLF) Top_intv_not_empty: "x \<in> A ==> interval r x (Top cl) \<noteq> {}"
apply (metis Top_in_lattice Top_prop empty_iff intervalI reflE)
done
-ML_command{*ResAtp.problem_name:="Tarski__Bot_intv_not_empty"*} (*ALL THEOREMS*)
+ML_command{*AtpThread.problem_name:="Tarski__Bot_intv_not_empty"*} (*ALL THEOREMS*)
lemma (in CLF) Bot_intv_not_empty: "x \<in> A ==> interval r (Bot cl) x \<noteq> {}"
apply (metis Bot_prop ex_in_conv intervalI reflE rel_imp_elem)
done
@@ -902,7 +902,7 @@
by (simp add: P_def fix_subset po_subset_po)
(*first proved 2007-01-25 after relaxing relevance*)
-ML_command{*ResAtp.problem_name:="Tarski__Y_subset_A"*}
+ML_command{*AtpThread.problem_name:="Tarski__Y_subset_A"*}
declare (in Tarski) P_def[simp] Y_ss [simp]
declare fix_subset [intro] subset_trans [intro]
lemma (in Tarski) Y_subset_A: "Y \<subseteq> A"
@@ -918,7 +918,7 @@
by (rule Y_subset_A [THEN lub_in_lattice])
(*never proved, 2007-01-22*)
-ML_command{*ResAtp.problem_name:="Tarski__lubY_le_flubY"*} (*ALL THEOREMS*)
+ML_command{*AtpThread.problem_name:="Tarski__lubY_le_flubY"*} (*ALL THEOREMS*)
lemma (in Tarski) lubY_le_flubY: "(lub Y cl, f (lub Y cl)) \<in> r"
(*sledgehammer*)
apply (rule lub_least)
@@ -927,12 +927,12 @@
apply (rule lubY_in_A)
-- {* @{text "Y \<subseteq> P ==> f x = x"} *}
apply (rule ballI)
-ML_command{*ResAtp.problem_name:="Tarski__lubY_le_flubY_simpler"*} (*ALL THEOREMS*)
+ML_command{*AtpThread.problem_name:="Tarski__lubY_le_flubY_simpler"*} (*ALL THEOREMS*)
(*sledgehammer *)
apply (rule_tac t = "x" in fix_imp_eq [THEN subst])
apply (erule Y_ss [simplified P_def, THEN subsetD])
-- {* @{text "reduce (f x, f (lub Y cl)) \<in> r to (x, lub Y cl) \<in> r"} by monotonicity *}
-ML_command{*ResAtp.problem_name:="Tarski__lubY_le_flubY_simplest"*} (*ALL THEOREMS*)
+ML_command{*AtpThread.problem_name:="Tarski__lubY_le_flubY_simplest"*} (*ALL THEOREMS*)
(*sledgehammer*)
apply (rule_tac f = "f" in monotoneE)
apply (rule monotone_f)
@@ -942,7 +942,7 @@
done
(*first proved 2007-01-25 after relaxing relevance*)
-ML_command{*ResAtp.problem_name:="Tarski__intY1_subset"*} (*ALL THEOREMS*)
+ML_command{*AtpThread.problem_name:="Tarski__intY1_subset"*} (*ALL THEOREMS*)
lemma (in Tarski) intY1_subset: "intY1 \<subseteq> A"
(*sledgehammer*)
apply (unfold intY1_def)
@@ -954,7 +954,7 @@
lemmas (in Tarski) intY1_elem = intY1_subset [THEN subsetD]
(*never proved, 2007-01-22*)
-ML_command{*ResAtp.problem_name:="Tarski__intY1_f_closed"*} (*ALL THEOREMS*)
+ML_command{*AtpThread.problem_name:="Tarski__intY1_f_closed"*} (*ALL THEOREMS*)
lemma (in Tarski) intY1_f_closed: "x \<in> intY1 \<Longrightarrow> f x \<in> intY1"
(*sledgehammer*)
apply (simp add: intY1_def interval_def)
@@ -962,7 +962,7 @@
apply (rule transE)
apply (rule lubY_le_flubY)
-- {* @{text "(f (lub Y cl), f x) \<in> r"} *}
-ML_command{*ResAtp.problem_name:="Tarski__intY1_f_closed_simpler"*} (*ALL THEOREMS*)
+ML_command{*AtpThread.problem_name:="Tarski__intY1_f_closed_simpler"*} (*ALL THEOREMS*)
(*sledgehammer [has been proved before now...]*)
apply (rule_tac f=f in monotoneE)
apply (rule monotone_f)
@@ -975,13 +975,13 @@
apply (simp add: intY1_def interval_def intY1_elem)
done
-ML_command{*ResAtp.problem_name:="Tarski__intY1_func"*} (*ALL THEOREMS*)
+ML_command{*AtpThread.problem_name:="Tarski__intY1_func"*} (*ALL THEOREMS*)
lemma (in Tarski) intY1_func: "(%x: intY1. f x) \<in> intY1 -> intY1"
apply (rule restrict_in_funcset)
apply (metis intY1_f_closed restrict_in_funcset)
done
-ML_command{*ResAtp.problem_name:="Tarski__intY1_mono"*} (*ALL THEOREMS*)
+ML_command{*AtpThread.problem_name:="Tarski__intY1_mono"*} (*ALL THEOREMS*)
lemma (in Tarski) intY1_mono:
"monotone (%x: intY1. f x) intY1 (induced intY1 r)"
(*sledgehammer *)
@@ -990,7 +990,7 @@
done
(*proof requires relaxing relevance: 2007-01-25*)
-ML_command{*ResAtp.problem_name:="Tarski__intY1_is_cl"*} (*ALL THEOREMS*)
+ML_command{*AtpThread.problem_name:="Tarski__intY1_is_cl"*} (*ALL THEOREMS*)
lemma (in Tarski) intY1_is_cl:
"(| pset = intY1, order = induced intY1 r |) \<in> CompleteLattice"
(*sledgehammer*)
@@ -1003,7 +1003,7 @@
done
(*never proved, 2007-01-22*)
-ML_command{*ResAtp.problem_name:="Tarski__v_in_P"*} (*ALL THEOREMS*)
+ML_command{*AtpThread.problem_name:="Tarski__v_in_P"*} (*ALL THEOREMS*)
lemma (in Tarski) v_in_P: "v \<in> P"
(*sledgehammer*)
apply (unfold P_def)
@@ -1013,7 +1013,7 @@
v_def CL_imp_PO intY1_is_cl CLF_set_def intY1_func intY1_mono)
done
-ML_command{*ResAtp.problem_name:="Tarski__z_in_interval"*} (*ALL THEOREMS*)
+ML_command{*AtpThread.problem_name:="Tarski__z_in_interval"*} (*ALL THEOREMS*)
lemma (in Tarski) z_in_interval:
"[| z \<in> P; \<forall>y\<in>Y. (y, z) \<in> induced P r |] ==> z \<in> intY1"
(*sledgehammer *)
@@ -1027,14 +1027,14 @@
apply (simp add: induced_def)
done
-ML_command{*ResAtp.problem_name:="Tarski__fz_in_int_rel"*} (*ALL THEOREMS*)
+ML_command{*AtpThread.problem_name:="Tarski__fz_in_int_rel"*} (*ALL THEOREMS*)
lemma (in Tarski) f'z_in_int_rel: "[| z \<in> P; \<forall>y\<in>Y. (y, z) \<in> induced P r |]
==> ((%x: intY1. f x) z, z) \<in> induced intY1 r"
apply (metis P_def acc_def fix_imp_eq fix_subset indI reflE restrict_apply subset_eq z_in_interval)
done
(*never proved, 2007-01-22*)
-ML_command{*ResAtp.problem_name:="Tarski__tarski_full_lemma"*} (*ALL THEOREMS*)
+ML_command{*AtpThread.problem_name:="Tarski__tarski_full_lemma"*} (*ALL THEOREMS*)
lemma (in Tarski) tarski_full_lemma:
"\<exists>L. isLub Y (| pset = P, order = induced P r |) L"
apply (rule_tac x = "v" in exI)
@@ -1064,12 +1064,12 @@
prefer 2 apply (simp add: v_in_P)
apply (unfold v_def)
(*never proved, 2007-01-22*)
-ML_command{*ResAtp.problem_name:="Tarski__tarski_full_lemma_simpler"*}
+ML_command{*AtpThread.problem_name:="Tarski__tarski_full_lemma_simpler"*}
(*sledgehammer*)
apply (rule indE)
apply (rule_tac [2] intY1_subset)
(*never proved, 2007-01-22*)
-ML_command{*ResAtp.problem_name:="Tarski__tarski_full_lemma_simplest"*}
+ML_command{*AtpThread.problem_name:="Tarski__tarski_full_lemma_simplest"*}
(*sledgehammer*)
apply (rule CL.glb_lower [OF CL.intro, OF PO.intro CL_axioms.intro, OF _ intY1_is_cl, simplified])
apply (simp add: CL_imp_PO intY1_is_cl)
@@ -1087,7 +1087,7 @@
(*never proved, 2007-01-22*)
-ML_command{*ResAtp.problem_name:="Tarski__Tarski_full"*}
+ML_command{*AtpThread.problem_name:="Tarski__Tarski_full"*}
declare (in CLF) fixf_po[intro] P_def [simp] A_def [simp] r_def [simp]
Tarski.tarski_full_lemma [intro] cl_po [intro] cl_co [intro]
CompleteLatticeI_simp [intro]
@@ -1097,7 +1097,7 @@
apply (rule CompleteLatticeI_simp)
apply (rule fixf_po, clarify)
(*never proved, 2007-01-22*)
-ML_command{*ResAtp.problem_name:="Tarski__Tarski_full_simpler"*}
+ML_command{*AtpThread.problem_name:="Tarski__Tarski_full_simpler"*}
(*sledgehammer*)
apply (simp add: P_def A_def r_def)
apply (blast intro!: Tarski.tarski_full_lemma [OF Tarski.intro, OF CLF.intro Tarski_axioms.intro,
--- a/src/HOL/MetisExamples/TransClosure.thy Fri Oct 03 19:35:18 2008 +0200
+++ b/src/HOL/MetisExamples/TransClosure.thy Fri Oct 03 20:10:43 2008 +0200
@@ -22,7 +22,7 @@
consts f:: "addr \<Rightarrow> val"
-ML {*ResAtp.problem_name := "TransClosure__test"*}
+ML {*AtpThread.problem_name := "TransClosure__test"*}
lemma "\<lbrakk> f c = Intg x; \<forall> y. f b = Intg y \<longrightarrow> y \<noteq> x; (a,b) \<in> R\<^sup>*; (b,c) \<in> R\<^sup>* \<rbrakk>
\<Longrightarrow> \<exists> c. (b,c) \<in> R \<and> (a,c) \<in> R\<^sup>*"
by (metis Transitive_Closure.rtrancl_into_rtrancl converse_rtranclE trancl_reflcl)
@@ -51,7 +51,7 @@
by (metis 10 3)
qed
-ML {*ResAtp.problem_name := "TransClosure__test_simpler"*}
+ML {*AtpThread.problem_name := "TransClosure__test_simpler"*}
lemma "\<lbrakk> f c = Intg x; \<forall> y. f b = Intg y \<longrightarrow> y \<noteq> x; (a,b) \<in> R\<^sup>*; (b,c) \<in> R\<^sup>* \<rbrakk>
\<Longrightarrow> \<exists> c. (b,c) \<in> R \<and> (a,c) \<in> R\<^sup>*"
apply (erule_tac x="b" in converse_rtranclE)
--- a/src/HOL/MetisExamples/set.thy Fri Oct 03 19:35:18 2008 +0200
+++ b/src/HOL/MetisExamples/set.thy Fri Oct 03 20:10:43 2008 +0200
@@ -20,9 +20,9 @@
lemma "P(n::nat) ==> ~P(0) ==> n ~= 0"
by metis
-declare [[sledgehammer_full = true]]
declare [[sledgehammer_modulus = 1]]
+
(*multiple versions of this example*)
lemma (*equal_union: *)
"(X = Y \<union> Z) =
@@ -198,7 +198,7 @@
by (metis 11 6 Un_upper2 sup_set_eq 1 sup_set_eq Un_upper1 sup_set_eq 0 sup_set_eq 9 Un_upper2 sup_set_eq 1 sup_set_eq Un_upper1 sup_set_eq 0 sup_set_eq)
qed
-ML {*ResAtp.problem_name := "set__equal_union"*}
+ML {*AtpThread.problem_name := "set__equal_union"*}
lemma (*equal_union: *)
"(X = Y \<union> Z) =
(Y \<subseteq> X \<and> Z \<subseteq> X \<and> (\<forall>V. Y \<subseteq> V \<and> Z \<subseteq> V \<longrightarrow> X \<subseteq> V))"
@@ -206,12 +206,12 @@
by (metis Un_least Un_upper1 Un_upper2 set_eq_subset)
-ML {*ResAtp.problem_name := "set__equal_inter"*}
+ML {*AtpThread.problem_name := "set__equal_inter"*}
lemma "(X = Y \<inter> Z) =
(X \<subseteq> Y \<and> X \<subseteq> Z \<and> (\<forall>V. V \<subseteq> Y \<and> V \<subseteq> Z \<longrightarrow> V \<subseteq> X))"
by (metis Int_greatest Int_lower1 Int_lower2 set_eq_subset)
-ML {*ResAtp.problem_name := "set__fixedpoint"*}
+ML {*AtpThread.problem_name := "set__fixedpoint"*}
lemma fixedpoint:
"\<exists>!x. f (g x) = x \<Longrightarrow> \<exists>!y. g (f y) = y"
by metis
@@ -230,7 +230,7 @@
by (metis 4 0)
qed
-ML {*ResAtp.problem_name := "set__singleton_example"*}
+ML {*AtpThread.problem_name := "set__singleton_example"*}
lemma (*singleton_example_2:*)
"\<forall>x \<in> S. \<Union>S \<subseteq> x \<Longrightarrow> \<exists>z. S \<subseteq> {z}"
by (metis Set.subsetI Union_upper insertCI set_eq_subset)
@@ -260,7 +260,7 @@
293-314.
*}
-ML {*ResAtp.problem_name := "set__Bledsoe_Fung"*}
+ML {*AtpThread.problem_name := "set__Bledsoe_Fung"*}
(*Notes: 1, the numbering doesn't completely agree with the paper.
2, we must rename set variables to avoid type clashes.*)
lemma "\<exists>B. (\<forall>x \<in> B. x \<le> (0::int))"
@@ -282,4 +282,3 @@
done
end
-