src/CCL/mono.ML

--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/src/CCL/mono.ML	Thu Sep 16 12:20:38 1993 +0200
@@ -0,0 +1,46 @@
+(*  Title: 	CCL/mono
+    ID:         $Id$
+
+Modified version of
+    Title: 	HOL/mono
+    Author: 	Lawrence C Paulson, Cambridge University Computer Laboratory
+    Copyright   1991  University of Cambridge
+
+Monotonicity of various operations
+*)
+
+writeln"File HOL/mono";
+
+val prems = goal Set.thy "A<=B ==> Union(A) <= Union(B)";
+by (cfast_tac prems 1);
+val Union_mono = result();
+
+val prems = goal Set.thy "[| B<=A |] ==> Inter(A) <= Inter(B)";
+by (cfast_tac prems 1);
+val Inter_anti_mono = result();
+
+val prems = goal Set.thy
+    "[| A<=B;  !!x. x:A ==> f(x)<=g(x) |] ==> \
+\    (UN x:A. f(x)) <= (UN x:B. g(x))";
+by (REPEAT (eresolve_tac [UN_E,ssubst] 1
+     ORELSE ares_tac ((prems RL [subsetD]) @ [subsetI,UN_I]) 1));
+val UN_mono = result();
+
+val prems = goal Set.thy
+    "[| B<=A;  !!x. x:A ==> f(x)<=g(x) |] ==> \
+\    (INT x:A. f(x)) <= (INT x:A. g(x))";
+by (REPEAT (ares_tac ((prems RL [subsetD]) @ [subsetI,INT_I]) 1
+     ORELSE etac INT_D 1));
+val INT_anti_mono = result();
+
+val prems = goal Set.thy "[| A<=C;  B<=D |] ==> A Un B <= C Un D";
+by (cfast_tac prems 1);
+val Un_mono = result();
+
+val prems = goal Set.thy "[| A<=C;  B<=D |] ==> A Int B <= C Int D";
+by (cfast_tac prems 1);
+val Int_mono = result();
+
+val prems = goal Set.thy "[| A<=B |] ==> Compl(B) <= Compl(A)";
+by (cfast_tac prems 1);
+val Compl_anti_mono = result();