diff -r d9527f97246e -r 89669c58e506 mono.ML
--- a/mono.ML	Thu Aug 25 10:47:33 1994 +0200
+++ b/mono.ML	Thu Aug 25 11:01:45 1994 +0200
@@ -6,15 +6,14 @@
 Monotonicity of various operations
 *)
 
-val [prem] = goal Set.thy
-    "[| !!x. P(x) ==> Q(x) |] ==> Collect(P) <= Collect(Q)";
-by (fast_tac (set_cs addIs [prem]) 1);
-val Collect_mono = result();
-
 goal Set.thy "!!A B. A<=B ==> f``A <= f``B";
 by (fast_tac set_cs 1);
 val image_mono = result();
 
+goal Set.thy "!!A B. A<=B ==> Pow(A) <= Pow(B)";
+by (fast_tac set_cs 1);
+val Pow_mono = result();
+
 goal Set.thy "!!A B. A<=B ==> Union(A) <= Union(B)";
 by (fast_tac set_cs 1);
 val Union_mono = result();
@@ -70,3 +69,55 @@
                      addSEs [SigmaE]) 1);
 val Sigma_mono = result();
 
+
+(** Monotonicity of implications.  For inductive definitions **)
+
+goal Set.thy "!!A B x. A<=B ==> x:A --> x:B";
+by (rtac impI 1);
+by (etac subsetD 1);
+by (assume_tac 1);
+val in_mono = result();
+
+goal HOL.thy "!!P1 P2 Q1 Q2. [| P1-->Q1; P2-->Q2 |] ==> (P1&P2) --> (Q1&Q2)";
+by (fast_tac HOL_cs 1);
+val conj_mono = result();
+
+goal HOL.thy "!!P1 P2 Q1 Q2. [| P1-->Q1; P2-->Q2 |] ==> (P1|P2) --> (Q1|Q2)";
+by (fast_tac HOL_cs 1);
+val disj_mono = result();
+
+goal HOL.thy "!!P1 P2 Q1 Q2.[| Q1-->P1; P2-->Q2 |] ==> (P1-->P2)-->(Q1-->Q2)";
+by (fast_tac HOL_cs 1);
+val imp_mono = result();
+
+goal HOL.thy "P-->P";
+by (rtac impI 1);
+by (assume_tac 1);
+val imp_refl = result();
+
+val [PQimp] = goal HOL.thy
+    "[| !!x. P(x) --> Q(x) |] ==> (EX x.P(x)) --> (EX x.Q(x))";
+by (fast_tac (HOL_cs addIs [PQimp RS mp]) 1);
+val ex_mono = result();
+
+val [PQimp] = goal HOL.thy
+    "[| !!x. P(x) --> Q(x) |] ==> (ALL x.P(x)) --> (ALL x.Q(x))";
+by (fast_tac (HOL_cs addIs [PQimp RS mp]) 1);
+val all_mono = result();
+
+val [PQimp] = goal Set.thy
+    "[| !!x. P(x) --> Q(x) |] ==> Collect(P) <= Collect(Q)";
+by (fast_tac (set_cs addIs [PQimp RS mp]) 1);
+val Collect_mono = result();
+
+(*Used in indrule.ML*)
+val [subs,PQimp] = goal Set.thy
+    "[| A<=B;  !!x. x:A ==> P(x) --> Q(x) \
+\    |] ==> A Int Collect(P) <= B Int Collect(Q)";
+by (fast_tac (set_cs addIs [subs RS subsetD, PQimp RS mp]) 1);
+val Int_Collect_mono = result();
+
+(*Used in intr_elim.ML and in individual datatype definitions*)
+val basic_monos = [subset_refl, imp_refl, disj_mono, conj_mono, 
+		   ex_mono, Collect_mono, Part_mono, in_mono];
+