src/CCL/Gfp.ML

--- a/src/CCL/Gfp.ML	Wed Nov 30 13:18:42 1994 +0100
+++ b/src/CCL/Gfp.ML	Wed Nov 30 13:53:46 1994 +0100
@@ -18,27 +18,27 @@
 val prems = goalw Gfp.thy [gfp_def] "[| A <= f(A) |] ==> A <= gfp(f)";
 by (rtac (CollectI RS Union_upper) 1);
 by (resolve_tac prems 1);
-val gfp_upperbound = result();
+qed "gfp_upperbound";
 
 val prems = goalw Gfp.thy [gfp_def]
     "[| !!u. u <= f(u) ==> u<=A |] ==> gfp(f) <= A";
 by (REPEAT (ares_tac ([Union_least]@prems) 1));
 by (etac CollectD 1);
-val gfp_least = result();
+qed "gfp_least";
 
 val [mono] = goal Gfp.thy "mono(f) ==> gfp(f) <= f(gfp(f))";
 by (EVERY1 [rtac gfp_least, rtac subset_trans, atac,
 	    rtac (mono RS monoD), rtac gfp_upperbound, atac]);
-val gfp_lemma2 = result();
+qed "gfp_lemma2";
 
 val [mono] = goal Gfp.thy "mono(f) ==> f(gfp(f)) <= gfp(f)";
 by (EVERY1 [rtac gfp_upperbound, rtac (mono RS monoD), 
 	    rtac gfp_lemma2, rtac mono]);
-val gfp_lemma3 = result();
+qed "gfp_lemma3";
 
 val [mono] = goal Gfp.thy "mono(f) ==> gfp(f) = f(gfp(f))";
 by (REPEAT (resolve_tac [equalityI,gfp_lemma2,gfp_lemma3,mono] 1));
-val gfp_Tarski = result();
+qed "gfp_Tarski";
 
 (*** Coinduction rules for greatest fixed points ***)
 
@@ -47,7 +47,7 @@
     "[| a: A;  A <= f(A) |] ==> a : gfp(f)";
 by (rtac (gfp_upperbound RS subsetD) 1);
 by (REPEAT (ares_tac prems 1));
-val coinduct = result();
+qed "coinduct";
 
 val [prem,mono] = goal Gfp.thy
     "[| A <= f(A) Un gfp(f);  mono(f) |] ==>  \
@@ -57,7 +57,7 @@
 by (rtac (mono RS gfp_Tarski RS subst) 1);
 by (rtac (prem RS Un_least) 1);
 by (rtac Un_upper2 1);
-val coinduct2_lemma = result();
+qed "coinduct2_lemma";
 
 (*strong version, thanks to Martin Coen*)
 val ainA::prems = goal Gfp.thy
@@ -65,7 +65,7 @@
 by (rtac coinduct 1);
 by (rtac (prems MRS coinduct2_lemma) 2);
 by (resolve_tac [ainA RS UnI1] 1);
-val coinduct2 = result();
+qed "coinduct2";
 
 (***  Even Stronger version of coinduct  [by Martin Coen]
          - instead of the condition  A <= f(A)
@@ -73,7 +73,7 @@
 
 val [prem] = goal Gfp.thy "mono(f) ==> mono(%x.f(x) Un A Un B)";
 by (REPEAT (ares_tac [subset_refl, monoI, Un_mono, prem RS monoD] 1));
-val coinduct3_mono_lemma= result();
+qed "coinduct3_mono_lemma";
 
 val [prem,mono] = goal Gfp.thy
     "[| A <= f(lfp(%x.f(x) Un A Un gfp(f)));  mono(f) |] ==> \
@@ -87,7 +87,7 @@
 by (rtac (mono RS monoD) 1);
 by (rtac (mono RS coinduct3_mono_lemma RS lfp_Tarski RS ssubst) 1);
 by (rtac Un_upper2 1);
-val coinduct3_lemma = result();
+qed "coinduct3_lemma";
 
 val ainA::prems = goal Gfp.thy
     "[| a:A;  A <= f(lfp(%x.f(x) Un A Un gfp(f))); mono(f) |] ==> a : gfp(f)";
@@ -95,7 +95,7 @@
 by (rtac (prems MRS coinduct3_lemma) 2);
 by (resolve_tac (prems RL [coinduct3_mono_lemma RS lfp_Tarski RS ssubst]) 1);
 by (rtac (ainA RS UnI2 RS UnI1) 1);
-val coinduct3 = result();
+qed "coinduct3";
 
 
 (** Definition forms of gfp_Tarski, to control unfolding **)
@@ -103,25 +103,25 @@
 val [rew,mono] = goal Gfp.thy "[| h==gfp(f);  mono(f) |] ==> h = f(h)";
 by (rewtac rew);
 by (rtac (mono RS gfp_Tarski) 1);
-val def_gfp_Tarski = result();
+qed "def_gfp_Tarski";
 
 val rew::prems = goal Gfp.thy
     "[| h==gfp(f);  a:A;  A <= f(A) |] ==> a: h";
 by (rewtac rew);
 by (REPEAT (ares_tac (prems @ [coinduct]) 1));
-val def_coinduct = result();
+qed "def_coinduct";
 
 val rew::prems = goal Gfp.thy
     "[| h==gfp(f);  a:A;  A <= f(A) Un h; mono(f) |] ==> a: h";
 by (rewtac rew);
 by (REPEAT (ares_tac (map (rewrite_rule [rew]) prems @ [coinduct2]) 1));
-val def_coinduct2 = result();
+qed "def_coinduct2";
 
 val rew::prems = goal Gfp.thy
     "[| h==gfp(f);  a:A;  A <= f(lfp(%x.f(x) Un A Un h)); mono(f) |] ==> a: h";
 by (rewtac rew);
 by (REPEAT (ares_tac (map (rewrite_rule [rew]) prems @ [coinduct3]) 1));
-val def_coinduct3 = result();
+qed "def_coinduct3";
 
 (*Monotonicity of gfp!*)
 val prems = goal Gfp.thy
@@ -131,4 +131,4 @@
 by (rtac gfp_lemma2 1);
 by (resolve_tac prems 1);
 by (resolve_tac prems 1);
-val gfp_mono = result();
+qed "gfp_mono";