src/HOL/AxClasses/Lattice/LatMorph.ML

--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/AxClasses/Lattice/LatMorph.ML	Mon Jan 15 15:49:21 1996 +0100
@@ -0,0 +1,53 @@
+
+open LatMorph;
+
+
+(** monotone functions vs. "&&"- / "||"-semi-morphisms **)
+
+goalw thy [is_mono_def] "is_mono f = (ALL x y. f (x && y) [= f x && f y)";
+  by (safe_tac set_cs);
+  (*==> (level 1)*)
+    by (stac le_inf_eq 1);
+    br conjI 1;
+    by (step_tac set_cs 1);
+    by (step_tac set_cs 1);
+    be mp 1;
+    br inf_lb1 1;
+    by (step_tac set_cs 1);
+    by (step_tac set_cs 1);
+    be mp 1;
+    br inf_lb2 1;
+  (*==> (level 11)*)
+    br (conjI RS (le_trans RS mp)) 1;
+    br inf_lb2 2;
+    by (subgoal_tac "x && y = x" 1);
+    be subst 1;
+    by (fast_tac set_cs 1);
+    by (stac inf_connect 1);
+    ba 1;
+qed "mono_inf_eq";
+
+goalw thy [is_mono_def] "is_mono f = (ALL x y. f x || f y [= f (x || y))";
+  by (safe_tac set_cs);
+  (*==> (level 1)*)
+    by (stac ge_sup_eq 1);
+    br conjI 1;
+    by (step_tac set_cs 1);
+    by (step_tac set_cs 1);
+    be mp 1;
+    br sup_ub1 1;
+    by (step_tac set_cs 1);
+    by (step_tac set_cs 1);
+    be mp 1;
+    br sup_ub2 1;
+  (*==> (level 11)*)
+    br (conjI RS (le_trans RS mp)) 1;
+    br sup_ub1 1;
+    by (subgoal_tac "x || y = y" 1);
+    be subst 1;
+    by (fast_tac set_cs 1);
+    by (stac sup_connect 1);
+    ba 1;
+qed "mono_sup_eq";
+
+