mono.ML

--- a/mono.ML	Fri Nov 11 10:35:03 1994 +0100
+++ b/mono.ML	Mon Nov 21 17:50:34 1994 +0100
@@ -8,58 +8,58 @@
 
 goal Set.thy "!!A B. A<=B ==> f``A <= f``B";
 by (fast_tac set_cs 1);
-val image_mono = result();
+qed "image_mono";
 
 goal Set.thy "!!A B. A<=B ==> Pow(A) <= Pow(B)";
 by (fast_tac set_cs 1);
-val Pow_mono = result();
+qed "Pow_mono";
 
 goal Set.thy "!!A B. A<=B ==> Union(A) <= Union(B)";
 by (fast_tac set_cs 1);
-val Union_mono = result();
+qed "Union_mono";
 
 goal Set.thy "!!A B. B<=A ==> Inter(A) <= Inter(B)";
 by (fast_tac set_cs 1);
-val Inter_anti_mono = result();
+qed "Inter_anti_mono";
 
 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 (fast_tac (set_cs addIs (prems RL [subsetD])) 1);
-val UN_mono = result();
+qed "UN_mono";
 
 val [prem] = goal Set.thy
     "[| !!x. f(x)<=g(x) |] ==> (UN x. f(x)) <= (UN x. g(x))";
 by (fast_tac (set_cs addIs [prem RS subsetD]) 1);
-val UN1_mono = result();
+qed "UN1_mono";
 
 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 (fast_tac (set_cs addIs (prems RL [subsetD])) 1);
-val INT_anti_mono = result();
+qed "INT_anti_mono";
 
 (*The inclusion is POSITIVE! *)
 val [prem] = goal Set.thy
     "[| !!x. f(x)<=g(x) |] ==> (INT x. f(x)) <= (INT x. g(x))";
 by (fast_tac (set_cs addIs [prem RS subsetD]) 1);
-val INT1_mono = result();
+qed "INT1_mono";
 
 goal Set.thy "!!A B. [| A<=C;  B<=D |] ==> A Un B <= C Un D";
 by (fast_tac set_cs 1);
-val Un_mono = result();
+qed "Un_mono";
 
 goal Set.thy "!!A B. [| A<=C;  B<=D |] ==> A Int B <= C Int D";
 by (fast_tac set_cs 1);
-val Int_mono = result();
+qed "Int_mono";
 
 goal Set.thy "!!A::'a set. [| A<=C;  D<=B |] ==> A-B <= C-D";
 by (fast_tac set_cs 1);
-val Diff_mono = result();
+qed "Diff_mono";
 
 goal Set.thy "!!A B. A<=B ==> Compl(B) <= Compl(A)";
 by (fast_tac set_cs 1);
-val Compl_anti_mono = result();
+qed "Compl_anti_mono";
 
 val prems = goal Prod.thy
     "[| A<=C;  !!x. x:A ==> B<=D |] ==> Sigma(A,%x.B) <= Sigma(C,%x.D)";
@@ -67,7 +67,7 @@
 by (fast_tac (set_cs addIs (prems RL [subsetD]) 
                      addSIs [SigmaI] 
                      addSEs [SigmaE]) 1);
-val Sigma_mono = result();
+qed "Sigma_mono";
 
 
 (** Monotonicity of implications.  For inductive definitions **)
@@ -76,46 +76,46 @@
 by (rtac impI 1);
 by (etac subsetD 1);
 by (assume_tac 1);
-val in_mono = result();
+qed "in_mono";
 
 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();
+qed "conj_mono";
 
 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();
+qed "disj_mono";
 
 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();
+qed "imp_mono";
 
 goal HOL.thy "P-->P";
 by (rtac impI 1);
 by (assume_tac 1);
-val imp_refl = result();
+qed "imp_refl";
 
 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();
+qed "ex_mono";
 
 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();
+qed "all_mono";
 
 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();
+qed "Collect_mono";
 
 (*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();
+qed "Int_Collect_mono";
 
 (*Used in intr_elim.ML and in individual datatype definitions*)
 val basic_monos = [subset_refl, imp_refl, disj_mono, conj_mono,