src/CCL/genrec.ML

 qed "SPLITB";
 
 val prems = goalw Wfd.thy [letrec2_def]
     "[| a : A;  b : B;  \
 \     !!p q g.[| p:A; q:B; \
-\             ALL x:A.ALL y:{y: B. <<x,y>,<p,q>>:wf(R)}. g(x,y) : D(x,y) |] ==>\
+\             ALL x:A. ALL y:{y: B. <<x,y>,<p,q>>:wf(R)}. g(x,y) : D(x,y) |] ==>\
 \               h(p,q,g) : D(p,q) |] ==> \
 \    letrec g x y be h(x,y,g) in g(a,b) : D(a,b)";
 by (rtac (SPLITB RS subst) 1);
 by (REPEAT (ares_tac ([letrecT,pairT,splitT]@prems) 1));
 by (stac SPLITB 1);

 by (rtac (SPLITB RS subst) 1);
 by (REPEAT (ares_tac ([letrecT,SubtypeI,pairT,splitT]@prems) 1 ORELSE 
             eresolve_tac [bspec,SubtypeE,sym RS subst] 1));
 qed "letrec2T";
 
-goal Wfd.thy "SPLIT(<a,<b,c>>,%x xs.SPLIT(xs,%y z.B(x,y,z))) = B(a,b,c)";
+goal Wfd.thy "SPLIT(<a,<b,c>>,%x xs. SPLIT(xs,%y z. B(x,y,z))) = B(a,b,c)";
 by (simp_tac (ccl_ss addsimps [SPLITB]) 1);
 qed "lemma";
 
 val prems = goalw Wfd.thy [letrec3_def]
     "[| a : A;  b : B;  c : C;  \
 \    !!p q r g.[| p:A; q:B; r:C; \
-\      ALL x:A.ALL y:B.ALL z:{z:C. <<x,<y,z>>,<p,<q,r>>> : wf(R)}. \
+\      ALL x:A. ALL y:B. ALL z:{z:C. <<x,<y,z>>,<p,<q,r>>> : wf(R)}. \
 \                                                       g(x,y,z) : D(x,y,z) |] ==>\
 \               h(p,q,r,g) : D(p,q,r) |] ==> \
 \    letrec g x y z be h(x,y,z,g) in g(a,b,c) : D(a,b,c)";
 by (rtac (lemma RS subst) 1);
 by (REPEAT (ares_tac ([letrecT,pairT,splitT]@prems) 1));

 \   g(a) : E";
 by (REPEAT (ares_tac ([SubtypeI,major RS bspec,major]@prems) 1));
 qed "rcallT";
 
 val major::prems = goal Wfd.thy
-    "[| ALL x:A.ALL y:{y:B.<<x,y>,<p,q>>:wf(R)}.g(x,y):D(x,y); \
+    "[| ALL x:A. ALL y:{y:B.<<x,y>,<p,q>>:wf(R)}.g(x,y):D(x,y); \
 \       g(a,b) : D(a,b) ==> g(a,b) : E;  a:A;  b:B;  <<a,b>,<p,q>>:wf(R) |] ==> \
 \   g(a,b) : E";
 by (REPEAT (ares_tac ([SubtypeI,major RS bspec RS bspec,major]@prems) 1));
 qed "rcall2T";
 
 val major::prems = goal Wfd.thy
-    "[| ALL x:A.ALL y:B.ALL z:{z:C.<<x,<y,z>>,<p,<q,r>>>:wf(R)}. g(x,y,z):D(x,y,z); \
+    "[| ALL x:A. ALL y:B. ALL z:{z:C.<<x,<y,z>>,<p,<q,r>>>:wf(R)}. g(x,y,z):D(x,y,z); \
 \       g(a,b,c) : D(a,b,c) ==> g(a,b,c) : E;  \
 \       a:A;  b:B;  c:C;  <<a,<b,c>>,<p,<q,r>>> : wf(R) |] ==> \
 \   g(a,b,c) : E";
 by (REPEAT (ares_tac ([SubtypeI,major RS bspec RS bspec RS bspec,major]@prems) 1));
 qed "rcall3T";

 by (rtac rcallT 1);
 by (REPEAT (ares_tac prems 1));
 qed "hyprcallT";
 
 val prems = goal Wfd.thy
-    "[| g(a,b) = c; ALL x:A.ALL y:{y:B.<<x,y>,<p,q>>:wf(R)}.g(x,y):D(x,y); \
+    "[| g(a,b) = c; ALL x:A. ALL y:{y:B.<<x,y>,<p,q>>:wf(R)}.g(x,y):D(x,y); \
 \       [| c=g(a,b);  g(a,b) : D(a,b) |] ==> P; \
 \       a:A;  b:B;  <<a,b>,<p,q>>:wf(R) |] ==> \
 \   P";
 by (resolve_tac (prems) 1);
 by (resolve_tac (prems RL [sym]) 1);

 by (REPEAT (ares_tac prems 1));
 qed "hyprcall2T";
 
 val prems = goal Wfd.thy
   "[| g(a,b,c) = d; \
-\     ALL x:A.ALL y:B.ALL z:{z:C.<<x,<y,z>>,<p,<q,r>>>:wf(R)}.g(x,y,z):D(x,y,z); \
+\     ALL x:A. ALL y:B. ALL z:{z:C.<<x,<y,z>>,<p,<q,r>>>:wf(R)}.g(x,y,z):D(x,y,z); \
 \   [| d=g(a,b,c);  g(a,b,c) : D(a,b,c) |] ==> P; \
 \   a:A;  b:B;  c:C;  <<a,<b,c>>,<p,<q,r>>> : wf(R) |] ==> \
 \   P";
 by (resolve_tac (prems) 1);
 by (resolve_tac (prems RL [sym]) 1);

 \    P";
 by (REPEAT (ares_tac prems 1));
 qed "rmIH1";
 
 val prems = goal Wfd.thy
-    "[| ALL x:A.ALL y:{y:B.<<x,y>,<p,q>>:wf(R)}.g(x,y):D(x,y); P |] ==> \
+    "[| ALL x:A. ALL y:{y:B.<<x,y>,<p,q>>:wf(R)}.g(x,y):D(x,y); P |] ==> \
 \    P";
 by (REPEAT (ares_tac prems 1));
 qed "rmIH2";
 
 val prems = goal Wfd.thy
- "[| ALL x:A.ALL y:B.ALL z:{z:C.<<x,<y,z>>,<p,<q,r>>>:wf(R)}.g(x,y,z):D(x,y,z); \
+ "[| ALL x:A. ALL y:B. ALL z:{z:C.<<x,<y,z>>,<p,<q,r>>>:wf(R)}.g(x,y,z):D(x,y,z); \
 \    P |] ==> \
 \    P";
 by (REPEAT (ares_tac prems 1));
 qed "rmIH3";