Subst/Setplus.ML

 
 (*** Rules for subsets ***)
 
 goal Set.thy "A <= B =  (! t.t:A --> t:B)";
 by (fast_tac set_cs 1);
-val subset_iff = result();
+qed "subset_iff";
 
 goalw Setplus.thy [ssubset_def] "A < B = ((A <= B) & ~(A=B))";
 by (rtac refl 1);
-val ssubset_iff = result();
+qed "ssubset_iff";
 
 goal Setplus.thy "((A::'a set) <= B) = ((A < B) | (A=B))";
 by (simp_tac (set_ss addsimps [ssubset_iff]) 1);
 by (fast_tac set_cs 1);
-val subseteq_iff_subset_eq = result();
+qed "subseteq_iff_subset_eq";
 
 (*Rule in Modus Ponens style*)
 goal Setplus.thy "A < B --> c:A --> c:B";
 by (simp_tac (set_ss addsimps [ssubset_iff]) 1);
 by (fast_tac set_cs 1);
-val ssubsetD = result();
+qed "ssubsetD";
 
 (*********)
 
 goalw Setplus.thy [empty_def] "~ a : {}";
 by (fast_tac set_cs 1);
-val not_in_empty = result();
+qed "not_in_empty";
 
 goalw Setplus.thy [empty_def] "(A = {}) = (ALL a.~ a:A)";
 by (fast_tac (set_cs addIs [set_ext]) 1);
-val empty_iff = result();
+qed "empty_iff";
 
 
 (*********)
 
 goal Set.thy "(~A=B)  = ((? x.x:A & ~x:B) | (? x.~x:A & x:B))";
 by (fast_tac (set_cs addIs [set_ext]) 1);
-val not_equal_iff = result();
+qed "not_equal_iff";
 
 (*********)
 
 val setplus_rews = [ssubset_iff,not_in_empty,empty_iff];
 

 (*Case analysis for rewriting; P also gets rewritten*)
 val [prem1,prem2] = goal HOL.thy "[| P-->Q;  ~P-->Q |] ==> Q";
 by (rtac (excluded_middle RS disjE) 1);
 by (etac (prem2 RS mp) 1);
 by (etac (prem1 RS mp) 1);
-val imp_excluded_middle = result();
+qed "imp_excluded_middle";
 
 fun imp_excluded_middle_tac s = res_inst_tac [("P",s)] imp_excluded_middle;