src/HOL/AxClasses/Lattice/LatPreInsts.ML
changeset 1440 de6f18da81bb
child 1573 6d66b59f94a9
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/AxClasses/Lattice/LatPreInsts.ML	Mon Jan 15 15:49:21 1996 +0100
@@ -0,0 +1,76 @@
+
+open LatPreInsts;
+
+
+(** complete lattices **)
+
+goal thy "is_inf x y (Inf {x, y})";
+  br (bin_is_Inf_eq RS subst) 1;
+  br Inf_is_Inf 1;
+qed "Inf_is_inf";
+
+goal thy "is_sup x y (Sup {x, y})";
+  br (bin_is_Sup_eq RS subst) 1;
+  br Sup_is_Sup 1;
+qed "Sup_is_sup";
+
+
+
+(** product lattices **)
+
+(* pairs *)
+
+goalw thy [is_inf_def, le_prod_def] "is_inf p q (fst p && fst q, snd p && snd q)";
+  by (simp_tac prod_ss 1);
+  by (safe_tac HOL_cs);
+  by (REPEAT_FIRST (fn i => resolve_tac [inf_lb1, inf_lb2, inf_ub_lbs] i ORELSE atac i));
+qed "prod_is_inf";
+
+goalw thy [is_sup_def, le_prod_def] "is_sup p q (fst p || fst q, snd p || snd q)";
+  by (simp_tac prod_ss 1);
+  by (safe_tac HOL_cs);
+  by (REPEAT_FIRST (fn i => resolve_tac [sup_ub1, sup_ub2, sup_lb_ubs] i ORELSE atac i));
+qed "prod_is_sup";
+
+
+(* functions *)
+
+goalw thy [is_inf_def, le_fun_def] "is_inf f g (%x. f x && g x)";
+  by (safe_tac HOL_cs);
+  br inf_lb1 1;
+  br inf_lb2 1;
+  br inf_ub_lbs 1;
+  by (REPEAT_FIRST (fast_tac HOL_cs));
+qed "fun_is_inf";
+
+goalw thy [is_sup_def, le_fun_def] "is_sup f g (%x. f x || g x)";
+  by (safe_tac HOL_cs);
+  br sup_ub1 1;
+  br sup_ub2 1;
+  br sup_lb_ubs 1;
+  by (REPEAT_FIRST (fast_tac HOL_cs));
+qed "fun_is_sup";
+
+
+
+(** dual lattices **)
+
+goalw thy [is_inf_def, le_dual_def] "is_inf x y (Abs_dual (Rep_dual x || Rep_dual y))";
+  by (stac Abs_dual_inverse' 1);
+  by (safe_tac HOL_cs);
+  br sup_ub1 1;
+  br sup_ub2 1;
+  br sup_lb_ubs 1;
+  ba 1;
+  ba 1;
+qed "dual_is_inf";
+
+goalw thy [is_sup_def, le_dual_def] "is_sup x y (Abs_dual (Rep_dual x && Rep_dual y))";
+  by (stac Abs_dual_inverse' 1);
+  by (safe_tac HOL_cs);
+  br inf_lb1 1;
+  br inf_lb2 1;
+  br inf_ub_lbs 1;
+  ba 1;
+  ba 1;
+qed "dual_is_sup";