--- a/src/HOL/ex/ROOT.ML Wed Jun 21 10:34:33 2000 +0200
+++ b/src/HOL/ex/ROOT.ML Wed Jun 21 15:58:23 2000 +0200
@@ -26,7 +26,7 @@
time_use_thy "IntRing";
-time_use "set.ML";
+time_use_thy "set";
time_use_thy "MT";
time_use_thy "Tarski";
--- a/src/HOL/ex/set.ML Wed Jun 21 10:34:33 2000 +0200
+++ b/src/HOL/ex/set.ML Wed Jun 21 15:58:23 2000 +0200
@@ -6,72 +6,68 @@
Cantor's Theorem; the Schroeder-Berstein Theorem.
*)
-
-writeln"File HOL/ex/set.";
-
-context Lfp.thy;
-
-(*These two are cited in Benzmueller and Kohlhash's system description of LEO,
+(*These two are cited in Benzmueller and Kohlhase's system description of LEO,
CADE-15, 1998 (page 139-143) as theorems LEO could not prove.*)
Goal "(X = Y Un Z) = (Y<=X & Z<=X & (ALL V. Y<=V & Z<=V --> X<=V))";
by (Blast_tac 1);
-result();
+qed "";
Goal "(X = Y Int Z) = (X<=Y & X<=Z & (ALL V. V<=Y & V<=Z --> V<=X))";
by (Blast_tac 1);
-result();
+qed "";
(*trivial example of term synthesis: apparently hard for some provers!*)
Goal "a ~= b ==> a:?X & b ~: ?X";
by (Blast_tac 1);
-result();
+qed "";
(** Examples for the Blast_tac paper **)
(*Union-image, called Un_Union_image on equalities.ML*)
Goal "(UN x:C. f(x) Un g(x)) = Union(f``C) Un Union(g``C)";
by (Blast_tac 1);
-result();
+qed "";
(*Inter-image, called Int_Inter_image on equalities.ML*)
Goal "(INT x:C. f(x) Int g(x)) = Inter(f``C) Int Inter(g``C)";
by (Blast_tac 1);
-result();
+qed "";
(*Singleton I. Nice demonstration of blast_tac--and its limitations*)
Goal "!!S::'a set set. ALL x:S. ALL y:S. x<=y ==> EX z. S <= {z}";
(*for some unfathomable reason, UNIV_I increases the search space greatly*)
by (blast_tac (claset() delrules [UNIV_I]) 1);
-result();
+qed "";
(*Singleton II. variant of the benchmark above*)
Goal "ALL x:S. Union(S) <= x ==> EX z. S <= {z}";
by (blast_tac (claset() delrules [UNIV_I]) 1);
(*just Blast_tac takes 5 seconds instead of 1*)
-result();
+qed "";
(*** A unique fixpoint theorem --- fast/best/meson all fail ***)
Goal "?!x. f(g(x))=x ==> ?!y. g(f(y))=y";
by (EVERY1[etac ex1E, rtac ex1I, etac arg_cong,
rtac subst, atac, etac allE, rtac arg_cong, etac mp, etac arg_cong]);
-result();
+qed "";
+
(*** Cantor's Theorem: There is no surjection from a set to its powerset. ***)
-goal Set.thy "~ (? f:: 'a=>'a set. ! S. ? x. f(x) = S)";
+Goal "~ (? f:: 'a=>'a set. ! S. ? x. f(x) = S)";
(*requires best-first search because it is undirectional*)
by (best_tac (claset() addSEs [equalityCE]) 1);
qed "cantor1";
(*This form displays the diagonal term*)
-goal Set.thy "! f:: 'a=>'a set. ! x. f(x) ~= ?S(f)";
+Goal "! f:: 'a=>'a set. ! x. f(x) ~= ?S(f)";
by (best_tac (claset() addSEs [equalityCE]) 1);
uresult();
(*This form exploits the set constructs*)
-goal Set.thy "?S ~: range(f :: 'a=>'a set)";
+Goal "?S ~: range(f :: 'a=>'a set)";
by (rtac notI 1);
by (etac rangeE 1);
by (etac equalityCE 1);
@@ -82,6 +78,7 @@
choplev 0;
by (best_tac (claset() addSEs [equalityCE]) 1);
+qed "";
(*** The Schroder-Berstein Theorem ***)
@@ -110,7 +107,7 @@
by (REPEAT (ares_tac [monoI, image_mono, Compl_anti_mono] 1));
qed "decomposition";
-val [injf,injg] = goal Lfp.thy
+val [injf,injg] = goal (the_context ())
"[| inj (f:: 'a=>'b); inj (g:: 'b=>'a) |] ==> \
\ ? h:: 'a=>'b. inj(h) & surj(h)";
by (rtac (decomposition RS exE) 1);
@@ -125,5 +122,3 @@
by (EVERY1 [etac ssubst, stac double_complement,
rtac (injg RS inv_image_comp RS sym)]);
qed "schroeder_bernstein";
-
-writeln"Reached end of file.";
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/ex/set.thy Wed Jun 21 15:58:23 2000 +0200
@@ -0,0 +1,4 @@
+
+theory set = Main:
+
+end