src/ZF/domrange.ML

--- a/src/ZF/domrange.ML	Wed Dec 07 12:34:47 1994 +0100
+++ b/src/ZF/domrange.ML	Wed Dec 07 13:12:04 1994 +0100
@@ -8,19 +8,19 @@
 
 (*** converse ***)
 
-val converse_iff = prove_goalw ZF.thy [converse_def]
+qed_goalw "converse_iff" ZF.thy [converse_def]
     "<a,b>: converse(r) <-> <b,a>:r"
  (fn _ => [ (fast_tac pair_cs 1) ]);
 
-val converseI = prove_goalw ZF.thy [converse_def]
+qed_goalw "converseI" ZF.thy [converse_def]
     "!!a b r. <a,b>:r ==> <b,a>:converse(r)"
  (fn _ => [ (fast_tac pair_cs 1) ]);
 
-val converseD = prove_goalw ZF.thy [converse_def]
+qed_goalw "converseD" ZF.thy [converse_def]
     "!!a b r. <a,b> : converse(r) ==> <b,a> : r"
  (fn _ => [ (fast_tac pair_cs 1) ]);
 
-val converseE = prove_goalw ZF.thy [converse_def]
+qed_goalw "converseE" ZF.thy [converse_def]
     "[| yx : converse(r);  \
 \       !!x y. [| yx=<y,x>;  <x,y>:r |] ==> P \
 \    |] ==> P"
@@ -33,51 +33,51 @@
 val converse_cs = pair_cs addSIs [converseI] 
 			  addSEs [converseD,converseE];
 
-val converse_of_converse = prove_goal ZF.thy
+qed_goal "converse_of_converse" ZF.thy
     "!!A B r. r<=Sigma(A,B) ==> converse(converse(r)) = r"
  (fn _ => [ (fast_tac (converse_cs addSIs [equalityI]) 1) ]);
 
-val converse_type = prove_goal ZF.thy "!!A B r. r<=A*B ==> converse(r)<=B*A"
+qed_goal "converse_type" ZF.thy "!!A B r. r<=A*B ==> converse(r)<=B*A"
  (fn _ => [ (fast_tac converse_cs 1) ]);
 
-val converse_of_prod = prove_goal ZF.thy "converse(A*B) = B*A"
+qed_goal "converse_of_prod" ZF.thy "converse(A*B) = B*A"
  (fn _ => [ (fast_tac (converse_cs addSIs [equalityI]) 1) ]);
 
-val converse_empty = prove_goal ZF.thy "converse(0) = 0"
+qed_goal "converse_empty" ZF.thy "converse(0) = 0"
  (fn _ => [ (fast_tac (converse_cs addSIs [equalityI]) 1) ]);
 
 (*** domain ***)
 
-val domain_iff = prove_goalw ZF.thy [domain_def]
+qed_goalw "domain_iff" ZF.thy [domain_def]
     "a: domain(r) <-> (EX y. <a,y>: r)"
  (fn _=> [ (fast_tac pair_cs 1) ]);
 
-val domainI = prove_goal ZF.thy "!!a b r. <a,b>: r ==> a: domain(r)"
+qed_goal "domainI" ZF.thy "!!a b r. <a,b>: r ==> a: domain(r)"
  (fn _ => [ (etac (exI RS (domain_iff RS iffD2)) 1) ]);
 
-val domainE = prove_goal ZF.thy
+qed_goal "domainE" ZF.thy
     "[| a : domain(r);  !!y. <a,y>: r ==> P |] ==> P"
  (fn prems=>
   [ (rtac (domain_iff RS iffD1 RS exE) 1),
     (REPEAT (ares_tac prems 1)) ]);
 
-val domain_subset = prove_goal ZF.thy "domain(Sigma(A,B)) <= A"
+qed_goal "domain_subset" ZF.thy "domain(Sigma(A,B)) <= A"
  (fn _ => [ (rtac subsetI 1), (etac domainE 1), (etac SigmaD1 1) ]);
 
 
 (*** range ***)
 
-val rangeI = prove_goalw ZF.thy [range_def] "!!a b r.<a,b>: r ==> b : range(r)"
+qed_goalw "rangeI" ZF.thy [range_def] "!!a b r.<a,b>: r ==> b : range(r)"
  (fn _ => [ (etac (converseI RS domainI) 1) ]);
 
-val rangeE = prove_goalw ZF.thy [range_def]
+qed_goalw "rangeE" ZF.thy [range_def]
     "[| b : range(r);  !!x. <x,b>: r ==> P |] ==> P"
  (fn major::prems=>
   [ (rtac (major RS domainE) 1),
     (resolve_tac prems 1),
     (etac converseD 1) ]);
 
-val range_subset = prove_goalw ZF.thy [range_def] "range(A*B) <= B"
+qed_goalw "range_subset" ZF.thy [range_def] "range(A*B) <= B"
  (fn _ =>
   [ (rtac (converse_of_prod RS ssubst) 1),
     (rtac domain_subset 1) ]);
@@ -85,22 +85,22 @@
 
 (*** field ***)
 
-val fieldI1 = prove_goalw ZF.thy [field_def] "<a,b>: r ==> a : field(r)"
+qed_goalw "fieldI1" ZF.thy [field_def] "<a,b>: r ==> a : field(r)"
  (fn [prem]=>
   [ (rtac (prem RS domainI RS UnI1) 1) ]);
 
-val fieldI2 = prove_goalw ZF.thy [field_def] "<a,b>: r ==> b : field(r)"
+qed_goalw "fieldI2" ZF.thy [field_def] "<a,b>: r ==> b : field(r)"
  (fn [prem]=>
   [ (rtac (prem RS rangeI RS UnI2) 1) ]);
 
-val fieldCI = prove_goalw ZF.thy [field_def]
+qed_goalw "fieldCI" ZF.thy [field_def]
     "(~ <c,a>:r ==> <a,b>: r) ==> a : field(r)"
  (fn [prem]=>
   [ (rtac (prem RS domainI RS UnCI) 1),
     (swap_res_tac [rangeI] 1),
     (etac notnotD 1) ]);
 
-val fieldE = prove_goalw ZF.thy [field_def]
+qed_goalw "fieldE" ZF.thy [field_def]
      "[| a : field(r);  \
 \        !!x. <a,x>: r ==> P;  \
 \        !!x. <x,a>: r ==> P        |] ==> P"
@@ -108,74 +108,74 @@
   [ (rtac (major RS UnE) 1),
     (REPEAT (eresolve_tac (prems@[domainE,rangeE]) 1)) ]);
 
-val field_subset = prove_goal ZF.thy "field(A*B) <= A Un B"
+qed_goal "field_subset" ZF.thy "field(A*B) <= A Un B"
  (fn _ => [ (fast_tac (pair_cs addIs  [fieldCI] addSEs [fieldE]) 1) ]);
 
-val domain_subset_field = prove_goalw ZF.thy [field_def]
+qed_goalw "domain_subset_field" ZF.thy [field_def]
     "domain(r) <= field(r)"
  (fn _ => [ (rtac Un_upper1 1) ]);
 
-val range_subset_field = prove_goalw ZF.thy [field_def]
+qed_goalw "range_subset_field" ZF.thy [field_def]
     "range(r) <= field(r)"
  (fn _ => [ (rtac Un_upper2 1) ]);
 
-val domain_times_range = prove_goal ZF.thy
+qed_goal "domain_times_range" ZF.thy
     "!!A B r. r <= Sigma(A,B) ==> r <= domain(r)*range(r)"
  (fn _ => [ (fast_tac (pair_cs addIs [domainI,rangeI]) 1) ]);
 
-val field_times_field = prove_goal ZF.thy
+qed_goal "field_times_field" ZF.thy
     "!!A B r. r <= Sigma(A,B) ==> r <= field(r)*field(r)"
  (fn _ => [ (fast_tac (pair_cs addIs [fieldI1,fieldI2]) 1) ]);
 
 
 (*** Image of a set under a function/relation ***)
 
-val image_iff = prove_goalw ZF.thy [image_def]
+qed_goalw "image_iff" ZF.thy [image_def]
     "b : r``A <-> (EX x:A. <x,b>:r)"
  (fn _ => [ fast_tac (pair_cs addIs [rangeI]) 1 ]);
 
-val image_singleton_iff = prove_goal ZF.thy
+qed_goal "image_singleton_iff" ZF.thy
     "b : r``{a} <-> <a,b>:r"
  (fn _ => [ rtac (image_iff RS iff_trans) 1,
 	    fast_tac pair_cs 1 ]);
 
-val imageI = prove_goalw ZF.thy [image_def]
+qed_goalw "imageI" ZF.thy [image_def]
     "!!a b r. [| <a,b>: r;  a:A |] ==> b : r``A"
  (fn _ => [ (REPEAT (ares_tac [CollectI,rangeI,bexI] 1)) ]);
 
-val imageE = prove_goalw ZF.thy [image_def]
+qed_goalw "imageE" ZF.thy [image_def]
     "[| b: r``A;  !!x.[| <x,b>: r;  x:A |] ==> P |] ==> P"
  (fn major::prems=>
   [ (rtac (major RS CollectE) 1),
     (REPEAT (etac bexE 1 ORELSE ares_tac prems 1)) ]);
 
-val image_subset = prove_goal ZF.thy
+qed_goal "image_subset" ZF.thy
     "!!A B r. r <= A*B ==> r``C <= B"
  (fn _ => [ (fast_tac (pair_cs addSEs [imageE]) 1) ]);
 
 
 (*** Inverse image of a set under a function/relation ***)
 
-val vimage_iff = prove_goalw ZF.thy [vimage_def,image_def,converse_def]
+qed_goalw "vimage_iff" ZF.thy [vimage_def,image_def,converse_def]
     "a : r-``B <-> (EX y:B. <a,y>:r)"
  (fn _ => [ fast_tac (pair_cs addIs [rangeI]) 1 ]);
 
-val vimage_singleton_iff = prove_goal ZF.thy
+qed_goal "vimage_singleton_iff" ZF.thy
     "a : r-``{b} <-> <a,b>:r"
  (fn _ => [ rtac (vimage_iff RS iff_trans) 1,
 	    fast_tac pair_cs 1 ]);
 
-val vimageI = prove_goalw ZF.thy [vimage_def]
+qed_goalw "vimageI" ZF.thy [vimage_def]
     "!!A B r. [| <a,b>: r;  b:B |] ==> a : r-``B"
  (fn _ => [ (REPEAT (ares_tac [converseI RS imageI] 1)) ]);
 
-val vimageE = prove_goalw ZF.thy [vimage_def]
+qed_goalw "vimageE" ZF.thy [vimage_def]
     "[| a: r-``B;  !!x.[| <a,x>: r;  x:B |] ==> P |] ==> P"
  (fn major::prems=>
   [ (rtac (major RS imageE) 1),
     (REPEAT (etac converseD 1 ORELSE ares_tac prems 1)) ]);
 
-val vimage_subset = prove_goalw ZF.thy [vimage_def]
+qed_goalw "vimage_subset" ZF.thy [vimage_def]
     "!!A B r. r <= A*B ==> r-``C <= A"
  (fn _ => [ (etac (converse_type RS image_subset) 1) ]);
 
@@ -193,10 +193,10 @@
 goal ZF.thy "!!S. (ALL x:S. EX A B. x <= A*B) ==>  \
 \                 Union(S) <= domain(Union(S)) * range(Union(S))";
 by (fast_tac ZF_cs 1);
-val rel_Union = result();
+qed "rel_Union";
 
 (** The Union of 2 relations is a relation (Lemma for fun_Un)  **)
-val rel_Un = prove_goal ZF.thy
+qed_goal "rel_Un" ZF.thy
     "!!r s. [| r <= A*B;  s <= C*D |] ==> (r Un s) <= (A Un C) * (B Un D)"
  (fn _ => [ (fast_tac ZF_cs 1) ]);