# HG changeset patch # User blanchet # Date 1283292451 -7200 # Node ID 0e2798f30087573783d228596ed0aea9fda8374a # Parent 7fba3ccc755aaecdea7ce4fb1e241741d61b40fe rename sledgehammer config attributes diff -r 7fba3ccc755a -r 0e2798f30087 src/HOL/Metis_Examples/Abstraction.thy --- a/src/HOL/Metis_Examples/Abstraction.thy Wed Sep 01 00:03:15 2010 +0200 +++ b/src/HOL/Metis_Examples/Abstraction.thy Wed Sep 01 00:07:31 2010 +0200 @@ -21,7 +21,7 @@ pset :: "'a set => 'a set" order :: "'a set => ('a * 'a) set" -declare [[ atp_problem_prefix = "Abstraction__Collect_triv" ]] +declare [[ sledgehammer_problem_prefix = "Abstraction__Collect_triv" ]] lemma (*Collect_triv:*) "a \ {x. P x} ==> P a" proof - assume "a \ {x. P x}" @@ -34,11 +34,11 @@ by (metis mem_Collect_eq) -declare [[ atp_problem_prefix = "Abstraction__Collect_mp" ]] +declare [[ sledgehammer_problem_prefix = "Abstraction__Collect_mp" ]] lemma "a \ {x. P x --> Q x} ==> a \ {x. P x} ==> a \ {x. Q x}" by (metis Collect_imp_eq ComplD UnE) -declare [[ atp_problem_prefix = "Abstraction__Sigma_triv" ]] +declare [[ sledgehammer_problem_prefix = "Abstraction__Sigma_triv" ]] lemma "(a,b) \ Sigma A B ==> a \ A & b \ B a" proof - assume A1: "(a, b) \ Sigma A B" @@ -51,7 +51,7 @@ lemma Sigma_triv: "(a,b) \ Sigma A B ==> a \ A & b \ B a" by (metis SigmaD1 SigmaD2) -declare [[ atp_problem_prefix = "Abstraction__Sigma_Collect" ]] +declare [[ sledgehammer_problem_prefix = "Abstraction__Sigma_Collect" ]] lemma "(a, b) \ (SIGMA x:A. {y. x = f y}) \ a \ A \ a = f b" (* Metis says this is satisfiable! by (metis CollectD SigmaD1 SigmaD2) @@ -85,7 +85,7 @@ qed -declare [[ atp_problem_prefix = "Abstraction__CLF_eq_in_pp" ]] +declare [[ sledgehammer_problem_prefix = "Abstraction__CLF_eq_in_pp" ]] lemma "(cl,f) \ CLF ==> CLF = (SIGMA cl: CL.{f. f \ pset cl}) ==> f \ pset cl" by (metis Collect_mem_eq SigmaD2) @@ -100,7 +100,7 @@ thus "f \ pset cl" by metis qed -declare [[ atp_problem_prefix = "Abstraction__Sigma_Collect_Pi" ]] +declare [[ sledgehammer_problem_prefix = "Abstraction__Sigma_Collect_Pi" ]] lemma "(cl,f) \ (SIGMA cl: CL. {f. f \ pset cl \ pset cl}) ==> f \ pset cl \ pset cl" @@ -112,7 +112,7 @@ thus "f \ pset cl \ pset cl" by metis qed -declare [[ atp_problem_prefix = "Abstraction__Sigma_Collect_Int" ]] +declare [[ sledgehammer_problem_prefix = "Abstraction__Sigma_Collect_Int" ]] lemma "(cl,f) \ (SIGMA cl: CL. {f. f \ pset cl \ cl}) ==> f \ pset cl \ cl" @@ -127,27 +127,27 @@ qed -declare [[ atp_problem_prefix = "Abstraction__Sigma_Collect_Pi_mono" ]] +declare [[ sledgehammer_problem_prefix = "Abstraction__Sigma_Collect_Pi_mono" ]] lemma "(cl,f) \ (SIGMA cl: CL. {f. f \ pset cl \ pset cl & monotone f (pset cl) (order cl)}) ==> (f \ pset cl \ pset cl) & (monotone f (pset cl) (order cl))" by auto -declare [[ atp_problem_prefix = "Abstraction__CLF_subset_Collect_Int" ]] +declare [[ sledgehammer_problem_prefix = "Abstraction__CLF_subset_Collect_Int" ]] lemma "(cl,f) \ CLF ==> CLF \ (SIGMA cl: CL. {f. f \ pset cl \ cl}) ==> f \ pset cl \ cl" by auto -declare [[ atp_problem_prefix = "Abstraction__CLF_eq_Collect_Int" ]] +declare [[ sledgehammer_problem_prefix = "Abstraction__CLF_eq_Collect_Int" ]] lemma "(cl,f) \ CLF ==> CLF = (SIGMA cl: CL. {f. f \ pset cl \ cl}) ==> f \ pset cl \ cl" by auto -declare [[ atp_problem_prefix = "Abstraction__CLF_subset_Collect_Pi" ]] +declare [[ sledgehammer_problem_prefix = "Abstraction__CLF_subset_Collect_Pi" ]] lemma "(cl,f) \ CLF ==> CLF \ (SIGMA cl': CL. {f. f \ pset cl' \ pset cl'}) ==> @@ -155,7 +155,7 @@ by fast -declare [[ atp_problem_prefix = "Abstraction__CLF_eq_Collect_Pi" ]] +declare [[ sledgehammer_problem_prefix = "Abstraction__CLF_eq_Collect_Pi" ]] lemma "(cl,f) \ CLF ==> CLF = (SIGMA cl: CL. {f. f \ pset cl \ pset cl}) ==> @@ -163,46 +163,46 @@ by auto -declare [[ atp_problem_prefix = "Abstraction__CLF_eq_Collect_Pi_mono" ]] +declare [[ sledgehammer_problem_prefix = "Abstraction__CLF_eq_Collect_Pi_mono" ]] lemma "(cl,f) \ CLF ==> CLF = (SIGMA cl: CL. {f. f \ pset cl \ pset cl & monotone f (pset cl) (order cl)}) ==> (f \ pset cl \ pset cl) & (monotone f (pset cl) (order cl))" by auto -declare [[ atp_problem_prefix = "Abstraction__map_eq_zipA" ]] +declare [[ sledgehammer_problem_prefix = "Abstraction__map_eq_zipA" ]] lemma "map (%x. (f x, g x)) xs = zip (map f xs) (map g xs)" apply (induct xs) apply (metis map_is_Nil_conv zip.simps(1)) by auto -declare [[ atp_problem_prefix = "Abstraction__map_eq_zipB" ]] +declare [[ sledgehammer_problem_prefix = "Abstraction__map_eq_zipB" ]] lemma "map (%w. (w -> w, w \ w)) xs = zip (map (%w. w -> w) xs) (map (%w. w \ w) xs)" apply (induct xs) apply (metis Nil_is_map_conv zip_Nil) by auto -declare [[ atp_problem_prefix = "Abstraction__image_evenA" ]] +declare [[ sledgehammer_problem_prefix = "Abstraction__image_evenA" ]] lemma "(%x. Suc(f x)) ` {x. even x} <= A ==> (\x. even x --> Suc(f x) \ A)" by (metis Collect_def image_subset_iff mem_def) -declare [[ atp_problem_prefix = "Abstraction__image_evenB" ]] +declare [[ sledgehammer_problem_prefix = "Abstraction__image_evenB" ]] lemma "(%x. f (f x)) ` ((%x. Suc(f x)) ` {x. even x}) <= A ==> (\x. even x --> f (f (Suc(f x))) \ A)"; by (metis Collect_def imageI image_image image_subset_iff mem_def) -declare [[ atp_problem_prefix = "Abstraction__image_curry" ]] +declare [[ sledgehammer_problem_prefix = "Abstraction__image_curry" ]] lemma "f \ (%u v. b \ u \ v) ` A ==> \u v. P (b \ u \ v) ==> P(f y)" (*sledgehammer*) by auto -declare [[ atp_problem_prefix = "Abstraction__image_TimesA" ]] +declare [[ sledgehammer_problem_prefix = "Abstraction__image_TimesA" ]] lemma image_TimesA: "(%(x,y). (f x, g y)) ` (A \ B) = (f`A) \ (g`B)" (*sledgehammer*) apply (rule equalityI) (***Even the two inclusions are far too difficult -using [[ atp_problem_prefix = "Abstraction__image_TimesA_simpler"]] +using [[ sledgehammer_problem_prefix = "Abstraction__image_TimesA_simpler"]] ***) apply (rule subsetI) apply (erule imageE) @@ -225,13 +225,13 @@ (*Given the difficulty of the previous problem, these two are probably impossible*) -declare [[ atp_problem_prefix = "Abstraction__image_TimesB" ]] +declare [[ sledgehammer_problem_prefix = "Abstraction__image_TimesB" ]] lemma image_TimesB: "(%(x,y,z). (f x, g y, h z)) ` (A \ B \ C) = (f`A) \ (g`B) \ (h`C)" (*sledgehammer*) by force -declare [[ atp_problem_prefix = "Abstraction__image_TimesC" ]] +declare [[ sledgehammer_problem_prefix = "Abstraction__image_TimesC" ]] lemma image_TimesC: "(%(x,y). (x \ x, y \ y)) ` (A \ B) = ((%x. x \ x) ` A) \ ((%y. y \ y) ` B)" diff -r 7fba3ccc755a -r 0e2798f30087 src/HOL/Metis_Examples/BT.thy --- a/src/HOL/Metis_Examples/BT.thy Wed Sep 01 00:03:15 2010 +0200 +++ b/src/HOL/Metis_Examples/BT.thy Wed Sep 01 00:07:31 2010 +0200 @@ -65,7 +65,7 @@ text {* \medskip BT simplification *} -declare [[ atp_problem_prefix = "BT__n_leaves_reflect" ]] +declare [[ sledgehammer_problem_prefix = "BT__n_leaves_reflect" ]] lemma n_leaves_reflect: "n_leaves (reflect t) = n_leaves t" proof (induct t) @@ -81,7 +81,7 @@ by (metis n_leaves.simps(2) nat_add_commute reflect.simps(2)) qed -declare [[ atp_problem_prefix = "BT__n_nodes_reflect" ]] +declare [[ sledgehammer_problem_prefix = "BT__n_nodes_reflect" ]] lemma n_nodes_reflect: "n_nodes (reflect t) = n_nodes t" proof (induct t) @@ -91,7 +91,7 @@ by (metis add_commute n_nodes.simps(2) reflect.simps(2)) qed -declare [[ atp_problem_prefix = "BT__depth_reflect" ]] +declare [[ sledgehammer_problem_prefix = "BT__depth_reflect" ]] lemma depth_reflect: "depth (reflect t) = depth t" apply (induct t) @@ -102,14 +102,14 @@ The famous relationship between the numbers of leaves and nodes. *} -declare [[ atp_problem_prefix = "BT__n_leaves_nodes" ]] +declare [[ sledgehammer_problem_prefix = "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)) by auto -declare [[ atp_problem_prefix = "BT__reflect_reflect_ident" ]] +declare [[ sledgehammer_problem_prefix = "BT__reflect_reflect_ident" ]] lemma reflect_reflect_ident: "reflect (reflect t) = t" apply (induct t) @@ -127,7 +127,7 @@ thus "reflect (reflect (Br a t1 t2)) = Br a t1 t2" by blast qed -declare [[ atp_problem_prefix = "BT__bt_map_ident" ]] +declare [[ sledgehammer_problem_prefix = "BT__bt_map_ident" ]] lemma bt_map_ident: "bt_map (%x. x) = (%y. y)" apply (rule ext) @@ -135,35 +135,35 @@ apply (metis bt_map.simps(1)) by (metis bt_map.simps(2)) -declare [[ atp_problem_prefix = "BT__bt_map_appnd" ]] +declare [[ sledgehammer_problem_prefix = "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)) by (metis appnd.simps(2) bt_map.simps(2)) -declare [[ atp_problem_prefix = "BT__bt_map_compose" ]] +declare [[ sledgehammer_problem_prefix = "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)) by (metis bt_map.simps(2) o_eq_dest_lhs) -declare [[ atp_problem_prefix = "BT__bt_map_reflect" ]] +declare [[ sledgehammer_problem_prefix = "BT__bt_map_reflect" ]] lemma bt_map_reflect: "bt_map f (reflect t) = reflect (bt_map f t)" apply (induct t) apply (metis bt_map.simps(1) reflect.simps(1)) by (metis bt_map.simps(2) reflect.simps(2)) -declare [[ atp_problem_prefix = "BT__preorder_bt_map" ]] +declare [[ sledgehammer_problem_prefix = "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)) by simp -declare [[ atp_problem_prefix = "BT__inorder_bt_map" ]] +declare [[ sledgehammer_problem_prefix = "BT__inorder_bt_map" ]] lemma inorder_bt_map: "inorder (bt_map f t) = map f (inorder t)" proof (induct t) @@ -178,21 +178,21 @@ case (Br a t1 t2) thus ?case by simp qed -declare [[ atp_problem_prefix = "BT__postorder_bt_map" ]] +declare [[ sledgehammer_problem_prefix = "BT__postorder_bt_map" ]] lemma postorder_bt_map: "postorder (bt_map f t) = map f (postorder t)" apply (induct t) apply (metis Nil_is_map_conv bt_map.simps(1) postorder.simps(1)) by simp -declare [[ atp_problem_prefix = "BT__depth_bt_map" ]] +declare [[ sledgehammer_problem_prefix = "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)) by simp -declare [[ atp_problem_prefix = "BT__n_leaves_bt_map" ]] +declare [[ sledgehammer_problem_prefix = "BT__n_leaves_bt_map" ]] lemma n_leaves_bt_map [simp]: "n_leaves (bt_map f t) = n_leaves t" apply (induct t) @@ -213,7 +213,7 @@ using F1 by metis qed -declare [[ atp_problem_prefix = "BT__preorder_reflect" ]] +declare [[ sledgehammer_problem_prefix = "BT__preorder_reflect" ]] lemma preorder_reflect: "preorder (reflect t) = rev (postorder t)" apply (induct t) @@ -222,7 +222,7 @@ by (metis append.simps(1) append.simps(2) postorder.simps(2) preorder.simps(2) reflect.simps(2) rev.simps(2) rev_append rev_swap) -declare [[ atp_problem_prefix = "BT__inorder_reflect" ]] +declare [[ sledgehammer_problem_prefix = "BT__inorder_reflect" ]] lemma inorder_reflect: "inorder (reflect t) = rev (inorder t)" apply (induct t) @@ -233,7 +233,7 @@ reflect.simps(2) rev.simps(2) rev_append) *) -declare [[ atp_problem_prefix = "BT__postorder_reflect" ]] +declare [[ sledgehammer_problem_prefix = "BT__postorder_reflect" ]] lemma postorder_reflect: "postorder (reflect t) = rev (preorder t)" apply (induct t) @@ -245,14 +245,14 @@ Analogues of the standard properties of the append function for lists. *} -declare [[ atp_problem_prefix = "BT__appnd_assoc" ]] +declare [[ sledgehammer_problem_prefix = "BT__appnd_assoc" ]] lemma appnd_assoc [simp]: "appnd (appnd t1 t2) t3 = appnd t1 (appnd t2 t3)" apply (induct t1) apply (metis appnd.simps(1)) by (metis appnd.simps(2)) -declare [[ atp_problem_prefix = "BT__appnd_Lf2" ]] +declare [[ sledgehammer_problem_prefix = "BT__appnd_Lf2" ]] lemma appnd_Lf2 [simp]: "appnd t Lf = t" apply (induct t) @@ -261,14 +261,14 @@ declare max_add_distrib_left [simp] -declare [[ atp_problem_prefix = "BT__depth_appnd" ]] +declare [[ sledgehammer_problem_prefix = "BT__depth_appnd" ]] lemma depth_appnd [simp]: "depth (appnd t1 t2) = depth t1 + depth t2" apply (induct t1) apply (metis appnd.simps(1) depth.simps(1) plus_nat.simps(1)) by simp -declare [[ atp_problem_prefix = "BT__n_leaves_appnd" ]] +declare [[ sledgehammer_problem_prefix = "BT__n_leaves_appnd" ]] lemma n_leaves_appnd [simp]: "n_leaves (appnd t1 t2) = n_leaves t1 * n_leaves t2" @@ -277,7 +277,7 @@ semiring_norm(111)) by (simp add: left_distrib) -declare [[ atp_problem_prefix = "BT__bt_map_appnd" ]] +declare [[ sledgehammer_problem_prefix = "BT__bt_map_appnd" ]] lemma (*bt_map_appnd:*) "bt_map f (appnd t1 t2) = appnd (bt_map f t1) (bt_map f t2)" diff -r 7fba3ccc755a -r 0e2798f30087 src/HOL/Metis_Examples/BigO.thy --- a/src/HOL/Metis_Examples/BigO.thy Wed Sep 01 00:03:15 2010 +0200 +++ b/src/HOL/Metis_Examples/BigO.thy Wed Sep 01 00:07:31 2010 +0200 @@ -15,7 +15,7 @@ definition bigo :: "('a => 'b::linordered_idom) => ('a => 'b) set" ("(1O'(_'))") where "O(f::('a => 'b)) == {h. EX c. ALL x. abs (h x) <= c * abs (f x)}" -declare [[ atp_problem_prefix = "BigO__bigo_pos_const" ]] +declare [[ sledgehammer_problem_prefix = "BigO__bigo_pos_const" ]] lemma bigo_pos_const: "(EX (c::'a::linordered_idom). ALL x. (abs (h x)) <= (c * (abs (f x)))) = (EX c. 0 < c & (ALL x. (abs(h x)) <= (c * (abs (f x)))))" @@ -124,7 +124,7 @@ {h. EX c. (0 < c & (ALL x. abs (h x) <= c * abs (f x)))}" by (auto simp add: bigo_def bigo_pos_const) -declare [[ atp_problem_prefix = "BigO__bigo_elt_subset" ]] +declare [[ sledgehammer_problem_prefix = "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) @@ -142,12 +142,12 @@ done -declare [[ atp_problem_prefix = "BigO__bigo_refl" ]] +declare [[ sledgehammer_problem_prefix = "BigO__bigo_refl" ]] lemma bigo_refl [intro]: "f : O(f)" apply (auto simp add: bigo_def) by (metis mult_1 order_refl) -declare [[ atp_problem_prefix = "BigO__bigo_zero" ]] +declare [[ sledgehammer_problem_prefix = "BigO__bigo_zero" ]] lemma bigo_zero: "0 : O(g)" apply (auto simp add: bigo_def func_zero) by (metis mult_zero_left order_refl) @@ -230,7 +230,7 @@ apply (auto del: subsetI simp del: bigo_plus_idemp) done -declare [[ atp_problem_prefix = "BigO__bigo_plus_eq" ]] +declare [[ sledgehammer_problem_prefix = "BigO__bigo_plus_eq" ]] lemma bigo_plus_eq: "ALL x. 0 <= f x ==> ALL x. 0 <= g x ==> O(f + g) = O(f) \ O(g)" apply (rule equalityI) @@ -253,13 +253,13 @@ apply (rule abs_triangle_ineq) apply (metis add_nonneg_nonneg) apply (rule add_mono) -using [[ atp_problem_prefix = "BigO__bigo_plus_eq_simpler" ]] +using [[ sledgehammer_problem_prefix = "BigO__bigo_plus_eq_simpler" ]] (*Found by SPASS; SLOW*) apply (metis le_maxI2 linorder_linear linorder_not_le min_max.sup_absorb1 mult_le_cancel_right order_trans) apply (metis le_maxI2 linorder_not_le mult_le_cancel_right order_trans) done -declare [[ atp_problem_prefix = "BigO__bigo_bounded_alt" ]] +declare [[ sledgehammer_problem_prefix = "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) @@ -277,14 +277,14 @@ qed text{*So here is the easier (and more natural) problem using transitivity*} -declare [[ atp_problem_prefix = "BigO__bigo_bounded_alt_trans" ]] +declare [[ sledgehammer_problem_prefix = "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-line proof *) by (metis abs_ge_self abs_mult order_trans) text{*So here is the easier (and more natural) problem using transitivity*} -declare [[ atp_problem_prefix = "BigO__bigo_bounded_alt_trans" ]] +declare [[ sledgehammer_problem_prefix = "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: structured proof *) @@ -299,7 +299,7 @@ apply simp done -declare [[ atp_problem_prefix = "BigO__bigo_bounded2" ]] +declare [[ sledgehammer_problem_prefix = "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) @@ -314,13 +314,13 @@ thus "(0\'b) \ f x + - lb x" by (metis not_leE diff_minus less_iff_diff_less_0 less_le_not_le) qed -declare [[ atp_problem_prefix = "BigO__bigo_abs" ]] +declare [[ sledgehammer_problem_prefix = "BigO__bigo_abs" ]] lemma bigo_abs: "(%x. abs(f x)) =o O(f)" apply (unfold bigo_def) apply auto by (metis mult_1 order_refl) -declare [[ atp_problem_prefix = "BigO__bigo_abs2" ]] +declare [[ sledgehammer_problem_prefix = "BigO__bigo_abs2" ]] lemma bigo_abs2: "f =o O(%x. abs(f x))" apply (unfold bigo_def) apply auto @@ -383,7 +383,7 @@ by (simp add: bigo_abs3 [symmetric]) qed -declare [[ atp_problem_prefix = "BigO__bigo_mult" ]] +declare [[ sledgehammer_problem_prefix = "BigO__bigo_mult" ]] lemma bigo_mult [intro]: "O(f)\O(g) <= O(f * g)" apply (rule subsetI) apply (subst bigo_def) @@ -395,7 +395,7 @@ 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))") -using [[ atp_problem_prefix = "BigO__bigo_mult_simpler" ]] +using [[ sledgehammer_problem_prefix = "BigO__bigo_mult_simpler" ]] prefer 2 apply (metis mult_assoc mult_left_commute abs_of_pos mult_left_commute @@ -406,14 +406,14 @@ abs_mult has just been done *) by (metis abs_ge_zero mult_mono') -declare [[ atp_problem_prefix = "BigO__bigo_mult2" ]] +declare [[ sledgehammer_problem_prefix = "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) -using [[ atp_problem_prefix = "BigO__bigo_mult2_simpler" ]] +using [[ sledgehammer_problem_prefix = "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) @@ -421,11 +421,11 @@ apply (rule abs_ge_zero) done -declare [[ atp_problem_prefix = "BigO__bigo_mult3" ]] +declare [[ sledgehammer_problem_prefix = "BigO__bigo_mult3" ]] lemma bigo_mult3: "f : O(h) ==> g : O(j) ==> f * g : O(h * j)" by (metis bigo_mult set_rev_mp set_times_intro) -declare [[ atp_problem_prefix = "BigO__bigo_mult4" ]] +declare [[ sledgehammer_problem_prefix = "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) @@ -459,13 +459,13 @@ qed qed -declare [[ atp_problem_prefix = "BigO__bigo_mult6" ]] +declare [[ sledgehammer_problem_prefix = "BigO__bigo_mult6" ]] lemma bigo_mult6: "ALL x. f x ~= 0 ==> O(f * g) = (f::'a => ('b::linordered_field)) *o O(g)" by (metis bigo_mult2 bigo_mult5 order_antisym) (*proof requires relaxing relevance: 2007-01-25*) -declare [[ atp_problem_prefix = "BigO__bigo_mult7" ]] +declare [[ sledgehammer_problem_prefix = "BigO__bigo_mult7" ]] declare bigo_mult6 [simp] lemma bigo_mult7: "ALL x. f x ~= 0 ==> O(f * g) <= O(f::'a => ('b::linordered_field)) \ O(g)" @@ -477,7 +477,7 @@ done declare bigo_mult6 [simp del] -declare [[ atp_problem_prefix = "BigO__bigo_mult8" ]] +declare [[ sledgehammer_problem_prefix = "BigO__bigo_mult8" ]] declare bigo_mult7[intro!] lemma bigo_mult8: "ALL x. f x ~= 0 ==> O(f * g) = O(f::'a => ('b::linordered_field)) \ O(g)" @@ -528,7 +528,7 @@ qed qed -declare [[ atp_problem_prefix = "BigO__bigo_plus_absorb" ]] +declare [[ sledgehammer_problem_prefix = "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); @@ -555,7 +555,7 @@ lemma bigo_const1: "(%x. c) : O(%x. 1)" by (auto simp add: bigo_def mult_ac) -declare [[ atp_problem_prefix = "BigO__bigo_const2" ]] +declare [[ sledgehammer_problem_prefix = "BigO__bigo_const2" ]] lemma (*bigo_const2 [intro]:*) "O(%x. c) <= O(%x. 1)" by (metis bigo_const1 bigo_elt_subset); @@ -566,7 +566,7 @@ show "O(\x. c) \ O(\x. 1)" by (metis F1 bigo_elt_subset) qed -declare [[ atp_problem_prefix = "BigO__bigo_const3" ]] +declare [[ sledgehammer_problem_prefix = "BigO__bigo_const3" ]] lemma bigo_const3: "(c::'a::linordered_field) ~= 0 ==> (%x. 1) : O(%x. c)" apply (simp add: bigo_def) by (metis abs_eq_0 left_inverse order_refl) @@ -578,7 +578,7 @@ O(%x. c) = O(%x. 1)" by (rule equalityI, rule bigo_const2, rule bigo_const4, assumption) -declare [[ atp_problem_prefix = "BigO__bigo_const_mult1" ]] +declare [[ sledgehammer_problem_prefix = "BigO__bigo_const_mult1" ]] lemma bigo_const_mult1: "(%x. c * f x) : O(f)" apply (simp add: bigo_def abs_mult) by (metis le_less) @@ -586,7 +586,7 @@ lemma bigo_const_mult2: "O(%x. c * f x) <= O(f)" by (rule bigo_elt_subset, rule bigo_const_mult1) -declare [[ atp_problem_prefix = "BigO__bigo_const_mult3" ]] +declare [[ sledgehammer_problem_prefix = "BigO__bigo_const_mult3" ]] lemma bigo_const_mult3: "(c::'a::linordered_field) ~= 0 ==> f : O(%x. c * f x)" apply (simp add: bigo_def) (*sledgehammer [no luck]*) @@ -604,7 +604,7 @@ O(%x. c * f x) = O(f)" by (rule equalityI, rule bigo_const_mult2, erule bigo_const_mult4) -declare [[ atp_problem_prefix = "BigO__bigo_const_mult5" ]] +declare [[ sledgehammer_problem_prefix = "BigO__bigo_const_mult5" ]] lemma bigo_const_mult5 [simp]: "(c::'a::linordered_field) ~= 0 ==> (%x. c) *o O(f) = O(f)" apply (auto del: subsetI) @@ -624,7 +624,7 @@ done -declare [[ atp_problem_prefix = "BigO__bigo_const_mult6" ]] +declare [[ sledgehammer_problem_prefix = "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 @@ -681,7 +681,7 @@ apply (blast intro: order_trans mult_right_mono abs_ge_self) done -declare [[ atp_problem_prefix = "BigO__bigo_setsum1" ]] +declare [[ sledgehammer_problem_prefix = "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)" @@ -698,7 +698,7 @@ (%x. SUM y : A x. f y) =o O(%x. SUM y : A x. h y)" by (rule bigo_setsum1, auto) -declare [[ atp_problem_prefix = "BigO__bigo_setsum3" ]] +declare [[ sledgehammer_problem_prefix = "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)))" @@ -729,7 +729,7 @@ apply (erule set_plus_imp_minus) done -declare [[ atp_problem_prefix = "BigO__bigo_setsum5" ]] +declare [[ sledgehammer_problem_prefix = "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 @@ -786,7 +786,7 @@ apply (simp add: func_times) done -declare [[ atp_problem_prefix = "BigO__bigo_fix" ]] +declare [[ sledgehammer_problem_prefix = "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) @@ -849,7 +849,7 @@ apply (erule spec)+ done -declare [[ atp_problem_prefix = "BigO__bigo_lesso1" ]] +declare [[ sledgehammer_problem_prefix = "BigO__bigo_lesso1" ]] lemma bigo_lesso1: "ALL x. f x <= g x ==> f ALL x. 0 <= k x ==> ALL x. k x <= f x ==> k ALL x. 0 <= k x ==> ALL x. g x <= k x ==> f EX C. ALL x. f x <= g x + C * abs(h x)" apply (simp only: lesso_def bigo_alt_def) diff -r 7fba3ccc755a -r 0e2798f30087 src/HOL/Metis_Examples/Tarski.thy --- a/src/HOL/Metis_Examples/Tarski.thy Wed Sep 01 00:03:15 2010 +0200 +++ b/src/HOL/Metis_Examples/Tarski.thy Wed Sep 01 00:07:31 2010 +0200 @@ -409,7 +409,7 @@ (*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.*) -declare [[ atp_problem_prefix = "Tarski__CLF_unnamed_lemma" ]] +declare [[ sledgehammer_problem_prefix = "Tarski__CLF_unnamed_lemma" ]] lemma (in CLF) [simp]: "f: pset cl -> pset cl & monotone f (pset cl) (order cl)" apply (insert f_cl) @@ -426,7 +426,7 @@ by (simp add: A_def r_def) (*never proved, 2007-01-22*) -declare [[ atp_problem_prefix = "Tarski__CLF_CLF_dual" ]] +declare [[ sledgehammer_problem_prefix = "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) \ CLF_set" @@ -454,7 +454,7 @@ subsection {* lemmas for Tarski, lub *} (*never proved, 2007-01-22*) -declare [[ atp_problem_prefix = "Tarski__CLF_lubH_le_flubH" ]] +declare [[ sledgehammer_problem_prefix = "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) \ r & x \ A} ==> (lub H cl, f (lub H cl)) \ r" @@ -464,7 +464,7 @@ -- {* @{text "\x:H. (x, f (lub H r)) \ r"} *} apply (rule ballI) (*never proved, 2007-01-22*) -using [[ atp_problem_prefix = "Tarski__CLF_lubH_le_flubH_simpler" ]] +using [[ sledgehammer_problem_prefix = "Tarski__CLF_lubH_le_flubH_simpler" ]] apply (rule transE) -- {* instantiates @{text "(x, ?z) \ order cl to (x, f x)"}, *} -- {* because of the def of @{text H} *} @@ -482,7 +482,7 @@ CLF.monotone_f[rule del] CL.lub_upper[rule del] (*never proved, 2007-01-22*) -declare [[ atp_problem_prefix = "Tarski__CLF_flubH_le_lubH" ]] +declare [[ sledgehammer_problem_prefix = "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] @@ -492,7 +492,7 @@ apply (rule_tac t = "H" in ssubst, assumption) apply (rule CollectI) apply (rule conjI) -using [[ atp_problem_prefix = "Tarski__CLF_flubH_le_lubH_simpler" ]] +using [[ sledgehammer_problem_prefix = "Tarski__CLF_flubH_le_lubH_simpler" ]] (*??no longer terminates, with combinators apply (metis CO_refl_on lubH_le_flubH monotone_def monotone_f reflD1 reflD2) *) @@ -506,7 +506,7 @@ (*never proved, 2007-01-22*) -declare [[ atp_problem_prefix = "Tarski__CLF_lubH_is_fixp" ]] +declare [[ sledgehammer_problem_prefix = "Tarski__CLF_lubH_is_fixp" ]] (* Single-step version fails. The conjecture clauses refer to local abstraction functions (Frees). *) lemma (in CLF) lubH_is_fixp: @@ -557,7 +557,7 @@ "H = {x. (x, f x) \ r & x \ A} ==> lub H cl \ fix f A" apply (simp add: fix_def) apply (rule conjI) -using [[ atp_problem_prefix = "Tarski__CLF_lubH_is_fixp_simpler" ]] +using [[ sledgehammer_problem_prefix = "Tarski__CLF_lubH_is_fixp_simpler" ]] apply (metis CO_refl_on lubH_le_flubH refl_onD1) apply (metis antisymE flubH_le_lubH lubH_le_flubH) done @@ -576,7 +576,7 @@ apply (simp_all add: P_def) done -declare [[ atp_problem_prefix = "Tarski__CLF_lubH_least_fixf" ]] +declare [[ sledgehammer_problem_prefix = "Tarski__CLF_lubH_least_fixf" ]] lemma (in CLF) lubH_least_fixf: "H = {x. (x, f x) \ r & x \ A} ==> \L. (\y \ fix f A. (y,L) \ r) --> (lub H cl, L) \ r" @@ -584,7 +584,7 @@ done subsection {* Tarski fixpoint theorem 1, first part *} -declare [[ atp_problem_prefix = "Tarski__CLF_T_thm_1_lub" ]] +declare [[ sledgehammer_problem_prefix = "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) \ r & x \ A} cl" @@ -592,7 +592,7 @@ apply (rule sym) apply (simp add: P_def) apply (rule lubI) -using [[ atp_problem_prefix = "Tarski__CLF_T_thm_1_lub_simpler" ]] +using [[ sledgehammer_problem_prefix = "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 @@ -607,7 +607,7 @@ (*never proved, 2007-01-22*) -declare [[ atp_problem_prefix = "Tarski__CLF_glbH_is_fixp" ]] +declare [[ sledgehammer_problem_prefix = "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) \ r & x \ A} ==> glb H cl \ P" @@ -631,13 +631,13 @@ (*never proved, 2007-01-22*) -declare [[ atp_problem_prefix = "Tarski__T_thm_1_glb" ]] (*ALL THEOREMS*) +declare [[ sledgehammer_problem_prefix = "Tarski__T_thm_1_glb" ]] (*ALL THEOREMS*) lemma (in CLF) T_thm_1_glb: "glb P cl = glb {x. (f x, x) \ r & x \ 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*) -using [[ atp_problem_prefix = "Tarski__T_thm_1_glb_simpler" ]] (*ALL THEOREMS*) +using [[ sledgehammer_problem_prefix = "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) @@ -646,13 +646,13 @@ subsection {* interval *} -declare [[ atp_problem_prefix = "Tarski__rel_imp_elem" ]] +declare [[ sledgehammer_problem_prefix = "Tarski__rel_imp_elem" ]] declare (in CLF) CO_refl_on[simp] refl_on_def [simp] lemma (in CLF) rel_imp_elem: "(x, y) \ r ==> x \ A" by (metis CO_refl_on refl_onD1) declare (in CLF) CO_refl_on[simp del] refl_on_def [simp del] -declare [[ atp_problem_prefix = "Tarski__interval_subset" ]] +declare [[ sledgehammer_problem_prefix = "Tarski__interval_subset" ]] declare (in CLF) rel_imp_elem[intro] declare interval_def [simp] lemma (in CLF) interval_subset: "[| a \ A; b \ A |] ==> interval r a b \ A" @@ -687,7 +687,7 @@ "[| a \ A; b \ A; S \ interval r a b |]==> S \ A" by (simp add: subset_trans [OF _ interval_subset]) -declare [[ atp_problem_prefix = "Tarski__L_in_interval" ]] (*ALL THEOREMS*) +declare [[ sledgehammer_problem_prefix = "Tarski__L_in_interval" ]] (*ALL THEOREMS*) lemma (in CLF) L_in_interval: "[| a \ A; b \ A; S \ interval r a b; S \ {}; isLub S cl L; interval r a b \ {} |] ==> L \ interval r a b" @@ -706,7 +706,7 @@ done (*never proved, 2007-01-22*) -declare [[ atp_problem_prefix = "Tarski__G_in_interval" ]] (*ALL THEOREMS*) +declare [[ sledgehammer_problem_prefix = "Tarski__G_in_interval" ]] (*ALL THEOREMS*) lemma (in CLF) G_in_interval: "[| a \ A; b \ A; interval r a b \ {}; S \ interval r a b; isGlb S cl G; S \ {} |] ==> G \ interval r a b" @@ -715,7 +715,7 @@ dualA_iff A_def dualPO CL_dualCL CLF_dual isGlb_dual_isLub) done -declare [[ atp_problem_prefix = "Tarski__intervalPO" ]] (*ALL THEOREMS*) +declare [[ sledgehammer_problem_prefix = "Tarski__intervalPO" ]] (*ALL THEOREMS*) lemma (in CLF) intervalPO: "[| a \ A; b \ A; interval r a b \ {} |] ==> (| pset = interval r a b, order = induced (interval r a b) r |) @@ -783,7 +783,7 @@ lemmas (in CLF) intv_CL_glb = intv_CL_lub [THEN Rdual] (*never proved, 2007-01-22*) -declare [[ atp_problem_prefix = "Tarski__interval_is_sublattice" ]] (*ALL THEOREMS*) +declare [[ sledgehammer_problem_prefix = "Tarski__interval_is_sublattice" ]] (*ALL THEOREMS*) lemma (in CLF) interval_is_sublattice: "[| a \ A; b \ A; interval r a b \ {} |] ==> interval r a b <<= cl" @@ -791,7 +791,7 @@ apply (rule sublatticeI) apply (simp add: interval_subset) (*never proved, 2007-01-22*) -using [[ atp_problem_prefix = "Tarski__interval_is_sublattice_simpler" ]] +using [[ sledgehammer_problem_prefix = "Tarski__interval_is_sublattice_simpler" ]] (*sledgehammer *) apply (rule CompleteLatticeI) apply (simp add: intervalPO) @@ -810,7 +810,7 @@ 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) -declare [[ atp_problem_prefix = "Tarski__Bot_in_lattice" ]] (*ALL THEOREMS*) +declare [[ sledgehammer_problem_prefix = "Tarski__Bot_in_lattice" ]] (*ALL THEOREMS*) lemma (in CLF) Bot_in_lattice: "Bot cl \ A" (*sledgehammer; *) apply (simp add: Bot_def least_def) @@ -820,12 +820,12 @@ done (*first proved 2007-01-25 after relaxing relevance*) -declare [[ atp_problem_prefix = "Tarski__Top_in_lattice" ]] (*ALL THEOREMS*) +declare [[ sledgehammer_problem_prefix = "Tarski__Top_in_lattice" ]] (*ALL THEOREMS*) lemma (in CLF) Top_in_lattice: "Top cl \ A" (*sledgehammer;*) apply (simp add: Top_dual_Bot A_def) (*first proved 2007-01-25 after relaxing relevance*) -using [[ atp_problem_prefix = "Tarski__Top_in_lattice_simpler" ]] (*ALL THEOREMS*) +using [[ sledgehammer_problem_prefix = "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) @@ -840,7 +840,7 @@ done (*never proved, 2007-01-22*) -declare [[ atp_problem_prefix = "Tarski__Bot_prop" ]] (*ALL THEOREMS*) +declare [[ sledgehammer_problem_prefix = "Tarski__Bot_prop" ]] (*ALL THEOREMS*) lemma (in CLF) Bot_prop: "x \ A ==> (Bot cl, x) \ r" (*sledgehammer*) apply (simp add: Bot_dual_Top r_def) @@ -849,12 +849,12 @@ dualA_iff A_def dualPO CL_dualCL CLF_dual) done -declare [[ atp_problem_prefix = "Tarski__Bot_in_lattice" ]] (*ALL THEOREMS*) +declare [[ sledgehammer_problem_prefix = "Tarski__Bot_in_lattice" ]] (*ALL THEOREMS*) lemma (in CLF) Top_intv_not_empty: "x \ A ==> interval r x (Top cl) \ {}" apply (metis Top_in_lattice Top_prop empty_iff intervalI reflE) done -declare [[ atp_problem_prefix = "Tarski__Bot_intv_not_empty" ]] (*ALL THEOREMS*) +declare [[ sledgehammer_problem_prefix = "Tarski__Bot_intv_not_empty" ]] (*ALL THEOREMS*) lemma (in CLF) Bot_intv_not_empty: "x \ A ==> interval r (Bot cl) x \ {}" apply (metis Bot_prop ex_in_conv intervalI reflE rel_imp_elem) done @@ -866,7 +866,7 @@ by (simp add: P_def fix_subset po_subset_po) (*first proved 2007-01-25 after relaxing relevance*) -declare [[ atp_problem_prefix = "Tarski__Y_subset_A" ]] +declare [[ sledgehammer_problem_prefix = "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 \ A" @@ -882,7 +882,7 @@ by (rule Y_subset_A [THEN lub_in_lattice]) (*never proved, 2007-01-22*) -declare [[ atp_problem_prefix = "Tarski__lubY_le_flubY" ]] (*ALL THEOREMS*) +declare [[ sledgehammer_problem_prefix = "Tarski__lubY_le_flubY" ]] (*ALL THEOREMS*) lemma (in Tarski) lubY_le_flubY: "(lub Y cl, f (lub Y cl)) \ r" (*sledgehammer*) apply (rule lub_least) @@ -891,12 +891,12 @@ apply (rule lubY_in_A) -- {* @{text "Y \ P ==> f x = x"} *} apply (rule ballI) -using [[ atp_problem_prefix = "Tarski__lubY_le_flubY_simpler" ]] (*ALL THEOREMS*) +using [[ sledgehammer_problem_prefix = "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)) \ r to (x, lub Y cl) \ r"} by monotonicity *} -using [[ atp_problem_prefix = "Tarski__lubY_le_flubY_simplest" ]] (*ALL THEOREMS*) +using [[ sledgehammer_problem_prefix = "Tarski__lubY_le_flubY_simplest" ]] (*ALL THEOREMS*) (*sledgehammer*) apply (rule_tac f = "f" in monotoneE) apply (rule monotone_f) @@ -906,7 +906,7 @@ done (*first proved 2007-01-25 after relaxing relevance*) -declare [[ atp_problem_prefix = "Tarski__intY1_subset" ]] (*ALL THEOREMS*) +declare [[ sledgehammer_problem_prefix = "Tarski__intY1_subset" ]] (*ALL THEOREMS*) lemma (in Tarski) intY1_subset: "intY1 \ A" (*sledgehammer*) apply (unfold intY1_def) @@ -918,7 +918,7 @@ lemmas (in Tarski) intY1_elem = intY1_subset [THEN subsetD] (*never proved, 2007-01-22*) -declare [[ atp_problem_prefix = "Tarski__intY1_f_closed" ]] (*ALL THEOREMS*) +declare [[ sledgehammer_problem_prefix = "Tarski__intY1_f_closed" ]] (*ALL THEOREMS*) lemma (in Tarski) intY1_f_closed: "x \ intY1 \ f x \ intY1" (*sledgehammer*) apply (simp add: intY1_def interval_def) @@ -926,7 +926,7 @@ apply (rule transE) apply (rule lubY_le_flubY) -- {* @{text "(f (lub Y cl), f x) \ r"} *} -using [[ atp_problem_prefix = "Tarski__intY1_f_closed_simpler" ]] (*ALL THEOREMS*) +using [[ sledgehammer_problem_prefix = "Tarski__intY1_f_closed_simpler" ]] (*ALL THEOREMS*) (*sledgehammer [has been proved before now...]*) apply (rule_tac f=f in monotoneE) apply (rule monotone_f) @@ -939,13 +939,13 @@ apply (simp add: intY1_def interval_def intY1_elem) done -declare [[ atp_problem_prefix = "Tarski__intY1_func" ]] (*ALL THEOREMS*) +declare [[ sledgehammer_problem_prefix = "Tarski__intY1_func" ]] (*ALL THEOREMS*) lemma (in Tarski) intY1_func: "(%x: intY1. f x) \ intY1 -> intY1" apply (rule restrict_in_funcset) apply (metis intY1_f_closed restrict_in_funcset) done -declare [[ atp_problem_prefix = "Tarski__intY1_mono" ]] (*ALL THEOREMS*) +declare [[ sledgehammer_problem_prefix = "Tarski__intY1_mono" ]] (*ALL THEOREMS*) lemma (in Tarski) intY1_mono: "monotone (%x: intY1. f x) intY1 (induced intY1 r)" (*sledgehammer *) @@ -954,7 +954,7 @@ done (*proof requires relaxing relevance: 2007-01-25*) -declare [[ atp_problem_prefix = "Tarski__intY1_is_cl" ]] (*ALL THEOREMS*) +declare [[ sledgehammer_problem_prefix = "Tarski__intY1_is_cl" ]] (*ALL THEOREMS*) lemma (in Tarski) intY1_is_cl: "(| pset = intY1, order = induced intY1 r |) \ CompleteLattice" (*sledgehammer*) @@ -967,7 +967,7 @@ done (*never proved, 2007-01-22*) -declare [[ atp_problem_prefix = "Tarski__v_in_P" ]] (*ALL THEOREMS*) +declare [[ sledgehammer_problem_prefix = "Tarski__v_in_P" ]] (*ALL THEOREMS*) lemma (in Tarski) v_in_P: "v \ P" (*sledgehammer*) apply (unfold P_def) @@ -977,7 +977,7 @@ v_def CL_imp_PO intY1_is_cl CLF_set_def intY1_func intY1_mono) done -declare [[ atp_problem_prefix = "Tarski__z_in_interval" ]] (*ALL THEOREMS*) +declare [[ sledgehammer_problem_prefix = "Tarski__z_in_interval" ]] (*ALL THEOREMS*) lemma (in Tarski) z_in_interval: "[| z \ P; \y\Y. (y, z) \ induced P r |] ==> z \ intY1" (*sledgehammer *) @@ -991,14 +991,14 @@ apply (simp add: induced_def) done -declare [[ atp_problem_prefix = "Tarski__fz_in_int_rel" ]] (*ALL THEOREMS*) +declare [[ sledgehammer_problem_prefix = "Tarski__fz_in_int_rel" ]] (*ALL THEOREMS*) lemma (in Tarski) f'z_in_int_rel: "[| z \ P; \y\Y. (y, z) \ induced P r |] ==> ((%x: intY1. f x) z, z) \ 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*) -declare [[ atp_problem_prefix = "Tarski__tarski_full_lemma" ]] (*ALL THEOREMS*) +declare [[ sledgehammer_problem_prefix = "Tarski__tarski_full_lemma" ]] (*ALL THEOREMS*) lemma (in Tarski) tarski_full_lemma: "\L. isLub Y (| pset = P, order = induced P r |) L" apply (rule_tac x = "v" in exI) @@ -1028,12 +1028,12 @@ prefer 2 apply (simp add: v_in_P) apply (unfold v_def) (*never proved, 2007-01-22*) -using [[ atp_problem_prefix = "Tarski__tarski_full_lemma_simpler" ]] +using [[ sledgehammer_problem_prefix = "Tarski__tarski_full_lemma_simpler" ]] (*sledgehammer*) apply (rule indE) apply (rule_tac [2] intY1_subset) (*never proved, 2007-01-22*) -using [[ atp_problem_prefix = "Tarski__tarski_full_lemma_simplest" ]] +using [[ sledgehammer_problem_prefix = "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) @@ -1051,7 +1051,7 @@ (*never proved, 2007-01-22*) -declare [[ atp_problem_prefix = "Tarski__Tarski_full" ]] +declare [[ sledgehammer_problem_prefix = "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] @@ -1061,7 +1061,7 @@ apply (rule CompleteLatticeI_simp) apply (rule fixf_po, clarify) (*never proved, 2007-01-22*) -using [[ atp_problem_prefix = "Tarski__Tarski_full_simpler" ]] +using [[ sledgehammer_problem_prefix = "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, diff -r 7fba3ccc755a -r 0e2798f30087 src/HOL/Tools/Sledgehammer/sledgehammer.ML --- a/src/HOL/Tools/Sledgehammer/sledgehammer.ML Wed Sep 01 00:03:15 2010 +0200 +++ b/src/HOL/Tools/Sledgehammer/sledgehammer.ML Wed Sep 01 00:07:31 2010 +0200 @@ -118,14 +118,15 @@ (* configuration attributes *) -val (dest_dir, dest_dir_setup) = Attrib.config_string "atp_dest_dir" (K ""); - (*Empty string means create files in Isabelle's temporary files directory.*) +val (dest_dir, dest_dir_setup) = + Attrib.config_string "sledgehammer_dest_dir" (K ""); + (* Empty string means create files in Isabelle's temporary files directory. *) val (problem_prefix, problem_prefix_setup) = - Attrib.config_string "atp_problem_prefix" (K "prob"); + Attrib.config_string "sledgehammer_problem_prefix" (K "prob"); val (measure_runtime, measure_runtime_setup) = - Attrib.config_bool "atp_measure_runtime" (K false); + Attrib.config_bool "sledgehammer_measure_runtime" (K false); fun with_path cleanup after f path = Exn.capture f path