--- a/src/HOL/Metis_Examples/Tarski.thy Thu Dec 01 13:34:12 2011 +0100
+++ b/src/HOL/Metis_Examples/Tarski.thy Thu Dec 01 13:34:12 2011 +0100
@@ -18,7 +18,6 @@
or explicit reasoning about connectives such as conjunction. The numerous
set comprehensions are to blame.*)
-
record 'a potype =
pset :: "'a set"
order :: "('a * 'a) set"
@@ -118,7 +117,6 @@
x: intY1}
(| pset=intY1, order=induced intY1 r|)"
-
subsection {* Partial Order *}
lemma (in PO) PO_imp_refl_on: "refl_on A r"
@@ -293,7 +291,6 @@
apply (simp add: reflE)
done
-
subsection {* sublattice *}
lemma (in PO) sublattice_imp_CL:
@@ -305,7 +302,6 @@
==> S <<= cl"
by (simp add: sublattice_def A_def r_def)
-
subsection {* lub *}
lemma (in CL) lub_unique: "[| S \<subseteq> A; isLub S cl x; isLub S cl L|] ==> x = L"
@@ -371,8 +367,6 @@
(\<forall>z \<in> A. (\<forall>y \<in> S. (y, z):r) --> (L, z) \<in> r)|] ==> isLub S cl L"
by (simp add: isLub_def A_def r_def)
-
-
subsection {* glb *}
lemma (in CL) glb_in_lattice: "S \<subseteq> A ==> glb S cl \<in> A"
@@ -408,7 +402,6 @@
declare (in CLF) f_cl [simp]
-declare [[ sledgehammer_problem_prefix = "Tarski__CLF_unnamed_lemma" ]]
lemma (in CLF) [simp]:
"f: pset cl -> pset cl & monotone f (pset cl) (order cl)"
proof -
@@ -430,7 +423,7 @@
by (simp add: A_def r_def)
(*never proved, 2007-01-22*)
-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) \<in> CLF_set"
@@ -441,7 +434,6 @@
declare (in CLF) CLF_set_def[simp del] CL_dualCL[simp del] monotone_dual[simp del]
dualA_iff[simp del]
-
subsection {* fixed points *}
lemma fix_subset: "fix f A \<subseteq> A"
@@ -454,12 +446,12 @@
"[| A \<subseteq> B; x \<in> fix (%y: A. f y) A |] ==> x \<in> fix f B"
by (simp add: fix_def, auto)
-
subsection {* lemmas for Tarski, lub *}
(*never proved, 2007-01-22*)
-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]
+
+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"
apply (rule lub_least, fast)
@@ -468,7 +460,6 @@
-- {* @{text "\<forall>x:H. (x, f (lub H r)) \<in> r"} *}
apply (rule ballI)
(*never proved, 2007-01-22*)
-using [[ sledgehammer_problem_prefix = "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} *}
@@ -480,37 +471,38 @@
apply (rule lub_upper, fast)
apply assumption
done
- declare CL.lub_least[rule del] CLF.f_in_funcset[rule del]
- funcset_mem[rule del] CL.lub_in_lattice[rule del]
- PO.transE[rule del] PO.monotoneE[rule del]
- CLF.monotone_f[rule del] CL.lub_upper[rule del]
+
+declare CL.lub_least[rule del] CLF.f_in_funcset[rule del]
+ funcset_mem[rule del] CL.lub_in_lattice[rule del]
+ PO.transE[rule del] PO.monotoneE[rule del]
+ CLF.monotone_f[rule del] CL.lub_upper[rule del]
(*never proved, 2007-01-22*)
-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]
+
+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]
+
lemma (in CLF) flubH_le_lubH:
"[| H = {x. (x, f x) \<in> r & x \<in> A} |] ==> (f (lub H cl), lub H cl) \<in> r"
apply (rule lub_upper, fast)
apply (rule_tac t = "H" in ssubst, assumption)
apply (rule CollectI)
apply (rule conjI)
-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)
*)
apply (metis CO_refl_on lubH_le_flubH monotoneE [OF monotone_f] refl_onD1 refl_onD2)
apply (metis CO_refl_on lubH_le_flubH refl_onD2)
done
- declare CLF.f_in_funcset[rule del] funcset_mem[rule del]
- CL.lub_in_lattice[rule del] PO.monotoneE[rule del]
- CLF.monotone_f[rule del] CL.lub_upper[rule del]
- CLF.lubH_le_flubH[simp del]
+declare CLF.f_in_funcset[rule del] funcset_mem[rule del]
+ CL.lub_in_lattice[rule del] PO.monotoneE[rule del]
+ CLF.monotone_f[rule del] CL.lub_upper[rule del]
+ CLF.lubH_le_flubH[simp del]
(*never proved, 2007-01-22*)
-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:
@@ -549,7 +541,6 @@
"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)
-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
@@ -559,7 +550,6 @@
by (simp add: P_def fix_imp_eq [of _ f A] reflE CO_refl_on
fix_subset [of f A, THEN subsetD])
-
lemma (in CLF) fixf_le_lubH:
"H = {x. (x, f x) \<in> r & x \<in> A} ==> \<forall>x \<in> fix f A. (x, lub H cl) \<in> r"
apply (rule ballI)
@@ -568,7 +558,6 @@
apply (simp_all add: P_def)
done
-declare [[ sledgehammer_problem_prefix = "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"
@@ -576,15 +565,15 @@
done
subsection {* Tarski fixpoint theorem 1, first part *}
-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]
+
+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"
(*sledgehammer;*)
apply (rule sym)
apply (simp add: P_def)
apply (rule lubI)
-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
@@ -594,14 +583,15 @@
apply (simp add: fixf_le_lubH)
apply (simp add: lubH_least_fixf)
done
- declare CL.lubI[rule del] fix_subset[rule del] CL.lub_in_lattice[rule del]
- CLF.fixf_le_lubH[simp del] CLF.lubH_least_fixf[simp del]
+declare CL.lubI[rule del] fix_subset[rule del] CL.lub_in_lattice[rule del]
+ CLF.fixf_le_lubH[simp del] CLF.lubH_least_fixf[simp del]
(*never proved, 2007-01-22*)
-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]
+
+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"
-- {* Tarski for glb *}
(*sledgehammer;*)
@@ -618,18 +608,17 @@
apply (rule CLF_dual)
apply (simp add: dualr_iff dualA_iff)
done
- declare glb_dual_lub[simp del] PO.dualA_iff[rule del] CLF.lubH_is_fixp[rule del]
- PO.dualPO[rule del] CL.CL_dualCL[rule del] PO.dualr_iff[simp del]
+declare glb_dual_lub[simp del] PO.dualA_iff[rule del] CLF.lubH_is_fixp[rule del]
+ PO.dualPO[rule del] CL.CL_dualCL[rule del] PO.dualr_iff[simp del]
(*never proved, 2007-01-22*)
-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) \<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*)
-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)
@@ -637,21 +626,21 @@
subsection {* interval *}
+declare (in CLF) CO_refl_on[simp] refl_on_def [simp]
-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) \<in> r ==> x \<in> A"
by (metis CO_refl_on refl_onD1)
- declare (in CLF) CO_refl_on[simp del] refl_on_def [simp del]
+
+declare (in CLF) CO_refl_on[simp del] refl_on_def [simp del]
-declare [[ sledgehammer_problem_prefix = "Tarski__interval_subset" ]]
- declare (in CLF) rel_imp_elem[intro]
- declare interval_def [simp]
+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"
by (metis CO_refl_on interval_imp_mem refl_onD refl_onD2 rel_imp_elem subset_eq)
- declare (in CLF) rel_imp_elem[rule del]
- declare interval_def [simp del]
+declare (in CLF) rel_imp_elem[rule del]
+declare interval_def [simp del]
lemma (in CLF) intervalI:
"[| (a, x) \<in> r; (x, b) \<in> r |] ==> x \<in> interval r a b"
@@ -679,7 +668,7 @@
"[| a \<in> A; b \<in> A; S \<subseteq> interval r a b |]==> S \<subseteq> A"
by (simp add: subset_trans [OF _ interval_subset])
-declare [[ sledgehammer_problem_prefix = "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"
@@ -698,7 +687,7 @@
done
(*never proved, 2007-01-22*)
-declare [[ sledgehammer_problem_prefix = "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"
@@ -707,7 +696,7 @@
dualA_iff A_def dualPO CL_dualCL CLF_dual isGlb_dual_isLub)
done
-declare [[ sledgehammer_problem_prefix = "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 |)
@@ -775,7 +764,7 @@
lemmas (in CLF) intv_CL_glb = intv_CL_lub [THEN Rdual]
(*never proved, 2007-01-22*)
-declare [[ sledgehammer_problem_prefix = "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"
@@ -783,7 +772,6 @@
apply (rule sublatticeI)
apply (simp add: interval_subset)
(*never proved, 2007-01-22*)
-using [[ sledgehammer_problem_prefix = "Tarski__interval_is_sublattice_simpler" ]]
(*sledgehammer *)
apply (rule CompleteLatticeI)
apply (simp add: intervalPO)
@@ -794,7 +782,6 @@
lemmas (in CLF) interv_is_compl_latt =
interval_is_sublattice [THEN sublattice_imp_CL]
-
subsection {* Top and Bottom *}
lemma (in CLF) Top_dual_Bot: "Top cl = Bot (dual cl)"
by (simp add: Top_def Bot_def least_def greatest_def dualA_iff dualr_iff)
@@ -802,7 +789,7 @@
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 [[ sledgehammer_problem_prefix = "Tarski__Bot_in_lattice" ]] (*ALL THEOREMS*)
+
lemma (in CLF) Bot_in_lattice: "Bot cl \<in> A"
(*sledgehammer; *)
apply (simp add: Bot_def least_def)
@@ -812,12 +799,11 @@
done
(*first proved 2007-01-25 after relaxing relevance*)
-declare [[ sledgehammer_problem_prefix = "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*)
-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)
@@ -832,7 +818,7 @@
done
(*never proved, 2007-01-22*)
-declare [[ sledgehammer_problem_prefix = "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)
@@ -841,40 +827,40 @@
dualA_iff A_def dualPO CL_dualCL CLF_dual)
done
-declare [[ sledgehammer_problem_prefix = "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
-declare [[ sledgehammer_problem_prefix = "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
-
subsection {* fixed points form a partial order *}
lemma (in CLF) fixf_po: "(| pset = P, order = induced P r|) \<in> PartialOrder"
by (simp add: P_def fix_subset po_subset_po)
(*first proved 2007-01-25 after relaxing relevance*)
-declare [[ sledgehammer_problem_prefix = "Tarski__Y_subset_A" ]]
- declare (in Tarski) P_def[simp] Y_ss [simp]
- declare fix_subset [intro] subset_trans [intro]
+
+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"
(*sledgehammer*)
apply (rule subset_trans [OF _ fix_subset])
apply (rule Y_ss [simplified P_def])
done
- declare (in Tarski) P_def[simp del] Y_ss [simp del]
- declare fix_subset [rule del] subset_trans [rule del]
+declare (in Tarski) P_def[simp del] Y_ss [simp del]
+declare fix_subset [rule del] subset_trans [rule del]
lemma (in Tarski) lubY_in_A: "lub Y cl \<in> A"
by (rule Y_subset_A [THEN lub_in_lattice])
(*never proved, 2007-01-22*)
-declare [[ sledgehammer_problem_prefix = "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)
@@ -883,12 +869,10 @@
apply (rule lubY_in_A)
-- {* @{text "Y \<subseteq> P ==> f x = x"} *}
apply (rule ballI)
-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)) \<in> r to (x, lub Y cl) \<in> r"} by monotonicity *}
-using [[ sledgehammer_problem_prefix = "Tarski__lubY_le_flubY_simplest" ]] (*ALL THEOREMS*)
(*sledgehammer*)
apply (rule_tac f = "f" in monotoneE)
apply (rule monotone_f)
@@ -898,7 +882,7 @@
done
(*first proved 2007-01-25 after relaxing relevance*)
-declare [[ sledgehammer_problem_prefix = "Tarski__intY1_subset" ]] (*ALL THEOREMS*)
+
lemma (in Tarski) intY1_subset: "intY1 \<subseteq> A"
(*sledgehammer*)
apply (unfold intY1_def)
@@ -910,7 +894,7 @@
lemmas (in Tarski) intY1_elem = intY1_subset [THEN subsetD]
(*never proved, 2007-01-22*)
-declare [[ sledgehammer_problem_prefix = "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)
@@ -918,7 +902,6 @@
apply (rule transE)
apply (rule lubY_le_flubY)
-- {* @{text "(f (lub Y cl), f x) \<in> r"} *}
-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)
@@ -931,13 +914,13 @@
apply (simp add: intY1_def interval_def intY1_elem)
done
-declare [[ sledgehammer_problem_prefix = "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
-declare [[ sledgehammer_problem_prefix = "Tarski__intY1_mono" ]] (*ALL THEOREMS*)
+
lemma (in Tarski) intY1_mono:
"monotone (%x: intY1. f x) intY1 (induced intY1 r)"
(*sledgehammer *)
@@ -946,7 +929,7 @@
done
(*proof requires relaxing relevance: 2007-01-25*)
-declare [[ sledgehammer_problem_prefix = "Tarski__intY1_is_cl" ]] (*ALL THEOREMS*)
+
lemma (in Tarski) intY1_is_cl:
"(| pset = intY1, order = induced intY1 r |) \<in> CompleteLattice"
(*sledgehammer*)
@@ -959,7 +942,7 @@
done
(*never proved, 2007-01-22*)
-declare [[ sledgehammer_problem_prefix = "Tarski__v_in_P" ]] (*ALL THEOREMS*)
+
lemma (in Tarski) v_in_P: "v \<in> P"
(*sledgehammer*)
apply (unfold P_def)
@@ -969,7 +952,7 @@
v_def CL_imp_PO intY1_is_cl CLF_set_def intY1_func intY1_mono)
done
-declare [[ sledgehammer_problem_prefix = "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 *)
@@ -983,14 +966,14 @@
apply (simp add: induced_def)
done
-declare [[ sledgehammer_problem_prefix = "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*)
-declare [[ sledgehammer_problem_prefix = "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)
@@ -1020,12 +1003,10 @@
prefer 2 apply (simp add: v_in_P)
apply (unfold v_def)
(*never proved, 2007-01-22*)
-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 [[ 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)
@@ -1041,19 +1022,18 @@
==> (| pset = A, order = r |) \<in> CompleteLattice"
by (simp add: CompleteLatticeI Rdual)
+(*never proved, 2007-01-22*)
-(*never proved, 2007-01-22*)
-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]
+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]
+
theorem (in CLF) Tarski_full:
"(| pset = P, order = induced P r|) \<in> CompleteLattice"
(*sledgehammer*)
apply (rule CompleteLatticeI_simp)
apply (rule fixf_po, clarify)
(*never proved, 2007-01-22*)
-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,