subset.ML

--- a/subset.ML	Fri Nov 11 10:35:03 1994 +0100
+++ b/subset.ML	Mon Nov 21 17:50:34 1994 +0100
@@ -17,35 +17,35 @@
 val prems = goal Set.thy
     "B:A ==> B <= Union(A)";
 by (REPEAT (ares_tac (prems@[subsetI,UnionI]) 1));
-val Union_upper = result();
+qed "Union_upper";
 
 val [prem] = goal Set.thy
     "[| !!X. X:A ==> X<=C |] ==> Union(A) <= C";
 br subsetI 1;
 by (REPEAT (eresolve_tac [asm_rl, UnionE, prem RS subsetD] 1));
-val Union_least = result();
+qed "Union_least";
 
 (** General union **)
 
 val prems = goal Set.thy
     "a:A ==> B(a) <= (UN x:A. B(x))";
 by (REPEAT (ares_tac (prems@[UN_I RS subsetI]) 1));
-val UN_upper = result();
+qed "UN_upper";
 
 val [prem] = goal Set.thy
     "[| !!x. x:A ==> B(x)<=C |] ==> (UN x:A. B(x)) <= C";
 br subsetI 1;
 by (REPEAT (eresolve_tac [asm_rl, UN_E, prem RS subsetD] 1));
-val UN_least = result();
+qed "UN_least";
 
 goal Set.thy "B(a) <= (UN x. B(x))";
 by (REPEAT (ares_tac [UN1_I RS subsetI] 1));
-val UN1_upper = result();
+qed "UN1_upper";
 
 val [prem] = goal Set.thy "[| !!x. B(x)<=C |] ==> (UN x. B(x)) <= C";
 br subsetI 1;
 by (REPEAT (eresolve_tac [asm_rl, UN1_E, prem RS subsetD] 1));
-val UN1_least = result();
+qed "UN1_least";
 
 
 (*** Big Intersection -- greatest lower bound of a set ***)
@@ -53,67 +53,67 @@
 val prems = goal Set.thy "B:A ==> Inter(A) <= B";
 br subsetI 1;
 by (REPEAT (resolve_tac prems 1 ORELSE etac InterD 1));
-val Inter_lower = result();
+qed "Inter_lower";
 
 val [prem] = goal Set.thy
     "[| !!X. X:A ==> C<=X |] ==> C <= Inter(A)";
 br (InterI RS subsetI) 1;
 by (REPEAT (eresolve_tac [asm_rl, prem RS subsetD] 1));
-val Inter_greatest = result();
+qed "Inter_greatest";
 
 val prems = goal Set.thy "a:A ==> (INT x:A. B(x)) <= B(a)";
 br subsetI 1;
 by (REPEAT (resolve_tac prems 1 ORELSE etac INT_D 1));
-val INT_lower = result();
+qed "INT_lower";
 
 val [prem] = goal Set.thy
     "[| !!x. x:A ==> C<=B(x) |] ==> C <= (INT x:A. B(x))";
 br (INT_I RS subsetI) 1;
 by (REPEAT (eresolve_tac [asm_rl, prem RS subsetD] 1));
-val INT_greatest = result();
+qed "INT_greatest";
 
 goal Set.thy "(INT x. B(x)) <= B(a)";
 br subsetI 1;
 by (REPEAT (resolve_tac prems 1 ORELSE etac INT1_D 1));
-val INT1_lower = result();
+qed "INT1_lower";
 
 val [prem] = goal Set.thy
     "[| !!x. C<=B(x) |] ==> C <= (INT x. B(x))";
 br (INT1_I RS subsetI) 1;
 by (REPEAT (eresolve_tac [asm_rl, prem RS subsetD] 1));
-val INT1_greatest = result();
+qed "INT1_greatest";
 
 (*** Finite Union -- the least upper bound of 2 sets ***)
 
 goal Set.thy "A <= A Un B";
 by (REPEAT (ares_tac [subsetI,UnI1] 1));
-val Un_upper1 = result();
+qed "Un_upper1";
 
 goal Set.thy "B <= A Un B";
 by (REPEAT (ares_tac [subsetI,UnI2] 1));
-val Un_upper2 = result();
+qed "Un_upper2";
 
 val prems = goal Set.thy "[| A<=C;  B<=C |] ==> A Un B <= C";
 by (cut_facts_tac prems 1);
 by (DEPTH_SOLVE (ares_tac [subsetI] 1 
           ORELSE eresolve_tac [UnE,subsetD] 1));
-val Un_least = result();
+qed "Un_least";
 
 (*** Finite Intersection -- the greatest lower bound of 2 sets *)
 
 goal Set.thy "A Int B <= A";
 by (REPEAT (ares_tac [subsetI] 1 ORELSE etac IntE 1));
-val Int_lower1 = result();
+qed "Int_lower1";
 
 goal Set.thy "A Int B <= B";
 by (REPEAT (ares_tac [subsetI] 1 ORELSE etac IntE 1));
-val Int_lower2 = result();
+qed "Int_lower2";
 
 val prems = goal Set.thy "[| C<=A;  C<=B |] ==> C <= A Int B";
 by (cut_facts_tac prems 1);
 by (REPEAT (ares_tac [subsetI,IntI] 1
      ORELSE etac subsetD 1));
-val Int_greatest = result();
+qed "Int_greatest";
 
 (*** Set difference ***)
 
@@ -126,10 +126,10 @@
 by (rtac Un_least 1);
 by (rtac (Un_upper1 RS (prem RS monoD)) 1);
 by (rtac (Un_upper2 RS (prem RS monoD)) 1);
-val mono_Un = result();
+qed "mono_Un";
 
 val [prem] = goal Set.thy "mono(f) ==> f(A Int B) <= f(A) Int f(B)";
 by (rtac Int_greatest 1);
 by (rtac (Int_lower1 RS (prem RS monoD)) 1);
 by (rtac (Int_lower2 RS (prem RS monoD)) 1);
-val mono_Int = result();
+qed "mono_Int";