ex/set.ML

--- a/ex/set.ML	Fri Nov 11 10:35:03 1994 +0100
+++ b/ex/set.ML	Mon Nov 21 17:50:34 1994 +0100
@@ -21,7 +21,7 @@
 goal Set.thy "~ (? f:: 'a=>'a set. ! S. ? x. f(x) = S)";
 (*requires best-first search because it is undirectional*)
 by (best_tac (set_cs addSEs [equalityCE]) 1);
-val cantor1 = result();
+qed "cantor1";
 
 (*This form displays the diagonal term*)
 goal Set.thy "! f:: 'a=>'a set. ! x. f(x) ~= ?S(f)";
@@ -48,15 +48,15 @@
 by (rtac equalityI 1);
 by (fast_tac (set_cs addEs [Inv_f_f RS ssubst]) 1);
 by (fast_tac (set_cs addEs [Inv_f_f RS ssubst]) 1);
-val inv_image_comp = result();
+qed "inv_image_comp";
 
 val prems = goal Set.thy "f(a) ~: (f``X) ==> a~:X";
 by (cfast_tac prems 1);
-val contra_imageI = result();
+qed "contra_imageI";
 
 goal Lfp.thy "(a ~: Compl(X)) = (a:X)";
 by (fast_tac set_cs 1);
-val not_Compl = result();
+qed "not_Compl";
 
 (*Lots of backtracking in this proof...*)
 val [compl,fg,Xa] = goal Lfp.thy
@@ -64,7 +64,7 @@
 by (EVERY1 [rtac (not_Compl RS subst), rtac contra_imageI,
 	    rtac (compl RS subst), rtac (fg RS subst), stac not_Compl,
 	    rtac imageI, rtac Xa]);
-val disj_lemma = result();
+qed "disj_lemma";
 
 goal Lfp.thy "range(%z. if(z:X, f(z), g(z))) = f``X Un g``Compl(X)";
 by (rtac equalityI 1);
@@ -77,21 +77,21 @@
 by (rtac (excluded_middle RS disjE) 1);
 by (EVERY' [rtac (if_P     RS ssubst), atac, fast_tac set_cs] 2);
 by (EVERY' [rtac (if_not_P RS ssubst), atac, fast_tac set_cs] 1);
-val range_if_then_else = result();
+qed "range_if_then_else";
 
 goal Lfp.thy "a : X Un Compl(X)";
 by (fast_tac set_cs 1);
-val X_Un_Compl = result();
+qed "X_Un_Compl";
 
 goalw Lfp.thy [surj_def] "surj(f) = (!a. a : range(f))";
 by (fast_tac (set_cs addEs [ssubst]) 1);
-val surj_iff_full_range = result();
+qed "surj_iff_full_range";
 
 val [compl] = goal Lfp.thy
     "Compl(f``X) = g``Compl(X) ==> surj(%z. if(z:X, f(z), g(z)))";
 by (sstac [surj_iff_full_range, range_if_then_else, compl RS sym] 1);
 by (rtac (X_Un_Compl RS allI) 1);
-val surj_if_then_else = result();
+qed "surj_if_then_else";
 
 val [injf,injg,compl,bij] = goal Lfp.thy
     "[| inj_onto(f,X);  inj_onto(g,Compl(X));  Compl(f``X) = g``Compl(X); \
@@ -107,13 +107,13 @@
 by (fast_tac (set_cs addEs  [inj_ontoD, sym RS f_eq_gE]) 1);
 by (stac expand_if 1);
 by (fast_tac (set_cs addEs  [inj_ontoD, f_eq_gE]) 1);
-val bij_if_then_else = result();
+qed "bij_if_then_else";
 
 goal Lfp.thy "? X. X = Compl(g``Compl((f:: 'a=>'b)``X))";
 by (rtac exI 1);
 by (rtac lfp_Tarski 1);
 by (REPEAT (ares_tac [monoI, image_mono, Compl_anti_mono] 1));
-val decomposition = result();
+qed "decomposition";
 
 val [injf,injg] = goal Lfp.thy
    "[| inj(f:: 'a=>'b);  inj(g:: 'b=>'a) |] ==> \
@@ -127,6 +127,6 @@
 	    etac imageE, etac ssubst, rtac rangeI]);
 by (EVERY1 [etac ssubst, stac double_complement, 
 	    rtac (injg RS inv_image_comp RS sym)]);
-val schroeder_bernstein = result();
+qed "schroeder_bernstein";
 
 writeln"Reached end of file.";