# HG changeset patch
# User paulson
# Date 962882916 -7200
# Node ID 051592f4236aedfa11e783a03005bcf27becac0b
# Parent  53e09e592278ef4cabaafb2b54f8d6dc0f422965
removal of batch style, and tidying

diff -r 53e09e592278 -r 051592f4236a src/FOL/FOL_lemmas1.ML
--- a/src/FOL/FOL_lemmas1.ML	Thu Jul 06 13:11:32 2000 +0200
+++ b/src/FOL/FOL_lemmas1.ML	Thu Jul 06 13:28:36 2000 +0200
@@ -12,39 +12,40 @@
 
 (*** Classical introduction rules for | and EX ***)
 
-qed_goal "disjCI" (the_context ()) 
-   "(~Q ==> P) ==> P|Q"
- (fn prems=>
-  [ (rtac classical 1),
-    (REPEAT (ares_tac (prems@[disjI1,notI]) 1)),
-    (REPEAT (ares_tac (prems@[disjI2,notE]) 1)) ]);
+val prems = Goal "(~Q ==> P) ==> P|Q";
+by (rtac classical 1);
+by (REPEAT (ares_tac (prems@[disjI1,notI]) 1));
+by (REPEAT (ares_tac (prems@[disjI2,notE]) 1)) ;
+qed "disjCI";
 
 (*introduction rule involving only EX*)
-qed_goal "ex_classical" (the_context ()) 
-   "( ~(EX x. P(x)) ==> P(a)) ==> EX x. P(x)"
- (fn prems=>
-  [ (rtac classical 1),
-    (eresolve_tac (prems RL [exI]) 1) ]);
+val prems = Goal "( ~(EX x. P(x)) ==> P(a)) ==> EX x. P(x)";
+by (rtac classical 1);
+by (eresolve_tac (prems RL [exI]) 1) ;
+qed "ex_classical";
 
 (*version of above, simplifying ~EX to ALL~ *)
-qed_goal "exCI" (the_context ()) 
-   "(ALL x. ~P(x) ==> P(a)) ==> EX x. P(x)"
- (fn [prem]=>
-  [ (rtac ex_classical 1),
-    (resolve_tac [notI RS allI RS prem] 1),
-    (etac notE 1),
-    (etac exI 1) ]);
+val [prem]= Goal "(ALL x. ~P(x) ==> P(a)) ==> EX x. P(x)";
+by (rtac ex_classical 1);
+by (resolve_tac [notI RS allI RS prem] 1);
+by (etac notE 1);
+by (etac exI 1) ;
+qed "exCI";
 
-qed_goal "excluded_middle" (the_context ()) "~P | P"
- (fn _=> [ rtac disjCI 1, assume_tac 1 ]);
+Goal"~P | P";
+by (rtac disjCI 1);
+by (assume_tac 1) ;
+qed "excluded_middle";
 
 (*For disjunctive case analysis*)
 fun excluded_middle_tac sP =
     res_inst_tac [("Q",sP)] (excluded_middle RS disjE);
 
-qed_goal "case_split_thm" (the_context ()) "[| P ==> Q; ~P ==> Q |] ==> Q"
-  (fn [p1,p2] => [rtac (excluded_middle RS disjE) 1,
-                  etac p2 1, etac p1 1]);
+val [p1,p2] = Goal"[| P ==> Q; ~P ==> Q |] ==> Q";
+by (rtac (excluded_middle RS disjE) 1);
+by (etac p2 1);
+by (etac p1 1);
+qed "case_split_thm";
 
 (*HOL's more natural case analysis tactic*)
 fun case_tac a = res_inst_tac [("P",a)] case_split_thm;
@@ -54,39 +55,41 @@
 
 
 (*Classical implies (-->) elimination. *)
-qed_goal "impCE" (the_context ()) 
-    "[| P-->Q;  ~P ==> R;  Q ==> R |] ==> R"
- (fn major::prems=>
-  [ (resolve_tac [excluded_middle RS disjE] 1),
-    (DEPTH_SOLVE (ares_tac (prems@[major RS mp]) 1)) ]);
+val major::prems = Goal "[| P-->Q;  ~P ==> R;  Q ==> R |] ==> R";
+by (resolve_tac [excluded_middle RS disjE] 1);
+by (DEPTH_SOLVE (ares_tac (prems@[major RS mp]) 1)) ;
+qed "impCE";
 
 (*This version of --> elimination works on Q before P.  It works best for
   those cases in which P holds "almost everywhere".  Can't install as
   default: would break old proofs.*)
-qed_goal "impCE'" (the_context ()) 
-    "[| P-->Q;  Q ==> R;  ~P ==> R |] ==> R"
- (fn major::prems=>
-  [ (resolve_tac [excluded_middle RS disjE] 1),
-    (DEPTH_SOLVE (ares_tac (prems@[major RS mp]) 1)) ]);
+val major::prems = Goal "[| P-->Q;  Q ==> R;  ~P ==> R |] ==> R";
+by (resolve_tac [excluded_middle RS disjE] 1);
+by (DEPTH_SOLVE (ares_tac (prems@[major RS mp]) 1)) ;
+qed "impCE'";
 
 (*Double negation law*)
-qed_goal "notnotD" (the_context ()) "~~P ==> P"
- (fn [major]=>
-  [ (rtac classical 1), (eresolve_tac [major RS notE] 1) ]);
+Goal"~~P ==> P";
+by (rtac classical 1);
+by (etac notE 1);
+by (assume_tac 1);
+qed "notnotD";
 
-qed_goal "contrapos2" (the_context ()) "[| Q; ~ P ==> ~ Q |] ==> P" (fn [p1,p2] => [
-        rtac classical 1,
-        dtac p2 1,
-        etac notE 1,
-        rtac p1 1]);
+val [p1,p2] = Goal"[| Q; ~ P ==> ~ Q |] ==> P";
+by (rtac classical 1);
+by (dtac p2 1);
+by (etac notE 1);
+by (rtac p1 1);
+qed "contrapos2";
 
 (*** Tactics for implication and contradiction ***)
 
 (*Classical <-> elimination.  Proof substitutes P=Q in 
     ~P ==> ~Q    and    P ==> Q  *)
-qed_goalw "iffCE" (the_context ()) [iff_def]
-    "[| P<->Q;  [| P; Q |] ==> R;  [| ~P; ~Q |] ==> R |] ==> R"
- (fn prems =>
-  [ (rtac conjE 1),
-    (REPEAT (DEPTH_SOLVE_1 
-        (etac impCE 1  ORELSE  mp_tac 1  ORELSE  ares_tac prems 1))) ]);
+val major::prems = 
+Goalw  [iff_def] "[| P<->Q;  [| P; Q |] ==> R;  [| ~P; ~Q |] ==> R |] ==> R";
+by (rtac (major RS conjE) 1);
+by (REPEAT_FIRST (etac impCE));
+by (REPEAT (DEPTH_SOLVE_1 (mp_tac 1  ORELSE  ares_tac prems 1)));
+qed "iffCE";
+
diff -r 53e09e592278 -r 051592f4236a src/FOL/FOL_lemmas2.ML
--- a/src/FOL/FOL_lemmas2.ML	Thu Jul 06 13:11:32 2000 +0200
+++ b/src/FOL/FOL_lemmas2.ML	Thu Jul 06 13:28:36 2000 +0200
@@ -1,4 +1,4 @@
 
-Goal "!!a b c. [| EX! z. P(a,z);  P(a,b);  P(a,c) |] ==> b = c";
+Goal "[| EX! z. P(a,z);  P(a,b);  P(a,c) |] ==> b = c";
   by (Blast_tac 1);
 qed "ex1_functional";
diff -r 53e09e592278 -r 051592f4236a src/FOL/IFOL_lemmas.ML
--- a/src/FOL/IFOL_lemmas.ML	Thu Jul 06 13:11:32 2000 +0200
+++ b/src/FOL/IFOL_lemmas.ML	Thu Jul 06 13:28:36 2000 +0200
@@ -32,63 +32,78 @@
 
 
 
-qed_goalw "TrueI" (the_context ()) [True_def] "True"
- (fn _ => [ (REPEAT (ares_tac [impI] 1)) ]);
+Goalw [True_def]  "True";
+by (REPEAT (ares_tac [impI] 1)) ;
+qed "TrueI";
 
 (*** Sequent-style elimination rules for & --> and ALL ***)
 
-qed_goal "conjE" (the_context ()) 
-    "[| P&Q; [| P; Q |] ==> R |] ==> R"
- (fn prems=>
-  [ (REPEAT (resolve_tac prems 1
-      ORELSE (resolve_tac [conjunct1, conjunct2] 1 THEN
-              resolve_tac prems 1))) ]);
+val major::prems = Goal 
+    "[| P&Q; [| P; Q |] ==> R |] ==> R";
+by (resolve_tac prems 1);
+by (rtac (major RS conjunct1) 1);
+by (rtac (major RS conjunct2) 1);
+qed "conjE";
 
-qed_goal "impE" (the_context ()) 
-    "[| P-->Q;  P;  Q ==> R |] ==> R"
- (fn prems=> [ (REPEAT (resolve_tac (prems@[mp]) 1)) ]);
+val major::prems = Goal 
+    "[| P-->Q;  P;  Q ==> R |] ==> R";
+by (resolve_tac prems 1);
+by (rtac (major RS mp) 1);
+by (resolve_tac prems 1);
+qed "impE";
 
-qed_goal "allE" (the_context ()) 
-    "[| ALL x. P(x); P(x) ==> R |] ==> R"
- (fn prems=> [ (REPEAT (resolve_tac (prems@[spec]) 1)) ]);
+val major::prems = Goal 
+    "[| ALL x. P(x); P(x) ==> R |] ==> R";
+by (resolve_tac prems 1);
+by (rtac (major RS spec) 1);
+qed "allE";
 
 (*Duplicates the quantifier; for use with eresolve_tac*)
-qed_goal "all_dupE" (the_context ()) 
+val major::prems = Goal 
     "[| ALL x. P(x);  [| P(x); ALL x. P(x) |] ==> R \
-\    |] ==> R"
- (fn prems=> [ (REPEAT (resolve_tac (prems@[spec]) 1)) ]);
+\    |] ==> R";
+by (resolve_tac prems 1);
+by (rtac (major RS spec) 1);
+by (rtac major 1);
+qed "all_dupE";
 
 
 (*** Negation rules, which translate between ~P and P-->False ***)
 
-qed_goalw "notI" (the_context ()) [not_def] "(P ==> False) ==> ~P"
- (fn prems=> [ (REPEAT (ares_tac (prems@[impI]) 1)) ]);
+val prems = Goalw [not_def]  "(P ==> False) ==> ~P";
+by (REPEAT (ares_tac (prems@[impI]) 1)) ;
+qed "notI";
 
-qed_goalw "notE" (the_context ()) [not_def] "[| ~P;  P |] ==> R"
- (fn prems=>
-  [ (resolve_tac [mp RS FalseE] 1),
-    (REPEAT (resolve_tac prems 1)) ]);
+Goalw [not_def]  "[| ~P;  P |] ==> R";
+by (etac (mp RS FalseE) 1);
+by (assume_tac 1);
+qed "notE";
 
-qed_goal "rev_notE" (the_context ()) "!!P R. [| P; ~P |] ==> R"
- (fn _ => [REPEAT (ares_tac [notE] 1)]);
+Goal "[| P; ~P |] ==> R";
+by (etac notE 1);
+by (assume_tac 1);
+qed "rev_notE";
 
 (*This is useful with the special implication rules for each kind of P. *)
-qed_goal "not_to_imp" (the_context ()) 
-    "[| ~P;  (P-->False) ==> Q |] ==> Q"
- (fn prems=> [ (REPEAT (ares_tac (prems@[impI,notE]) 1)) ]);
+val prems = Goal 
+    "[| ~P;  (P-->False) ==> Q |] ==> Q";
+by (REPEAT (ares_tac (prems@[impI,notE]) 1)) ;
+qed "not_to_imp";
 
 (* For substitution into an assumption P, reduce Q to P-->Q, substitute into
    this implication, then apply impI to move P back into the assumptions.
    To specify P use something like
       eres_inst_tac [ ("P","ALL y. ?S(x,y)") ] rev_mp 1   *)
-qed_goal "rev_mp" (the_context ()) "[| P;  P --> Q |] ==> Q"
- (fn prems=> [ (REPEAT (resolve_tac (prems@[mp]) 1)) ]);
+Goal "[| P;  P --> Q |] ==> Q";
+by (etac mp 1);
+by (assume_tac 1);
+qed "rev_mp";
 
 (*Contrapositive of an inference rule*)
-qed_goal "contrapos" (the_context ()) "[| ~Q;  P==>Q |] ==> ~P"
- (fn [major,minor]=> 
-  [ (rtac (major RS notE RS notI) 1), 
-    (etac minor 1) ]);
+val [major,minor]= Goal "[| ~Q;  P==>Q |] ==> ~P";
+by (rtac (major RS notE RS notI) 1);
+by (etac minor 1) ;
+qed "contrapos";
 
 
 (*** Modus Ponens Tactics ***)
@@ -102,44 +117,55 @@
 
 (*** If-and-only-if ***)
 
-qed_goalw "iffI" (the_context ()) [iff_def]
-   "[| P ==> Q;  Q ==> P |] ==> P<->Q"
- (fn prems=> [ (REPEAT (ares_tac (prems@[conjI, impI]) 1)) ]);
+val prems = Goalw [iff_def] 
+   "[| P ==> Q;  Q ==> P |] ==> P<->Q";
+by (REPEAT (ares_tac (prems@[conjI, impI]) 1)) ;
+qed "iffI";
 
 
 (*Observe use of rewrite_rule to unfold "<->" in meta-assumptions (prems) *)
-qed_goalw "iffE" (the_context ()) [iff_def]
-    "[| P <-> Q;  [| P-->Q; Q-->P |] ==> R |] ==> R"
- (fn prems => [ (rtac conjE 1), (REPEAT (ares_tac prems 1)) ]);
+val prems = Goalw [iff_def] 
+    "[| P <-> Q;  [| P-->Q; Q-->P |] ==> R |] ==> R";
+by (rtac conjE 1);
+by (REPEAT (ares_tac prems 1)) ;
+qed "iffE";
 
 (* Destruct rules for <-> similar to Modus Ponens *)
 
-qed_goalw "iffD1" (the_context ()) [iff_def] "[| P <-> Q;  P |] ==> Q"
- (fn prems => [ (rtac (conjunct1 RS mp) 1), (REPEAT (ares_tac prems 1)) ]);
-
-qed_goalw "iffD2" (the_context ()) [iff_def] "[| P <-> Q;  Q |] ==> P"
- (fn prems => [ (rtac (conjunct2 RS mp) 1), (REPEAT (ares_tac prems 1)) ]);
+Goalw [iff_def]  "[| P <-> Q;  P |] ==> Q";
+by (etac (conjunct1 RS mp) 1);
+by (assume_tac 1);
+qed "iffD1";
 
-qed_goal "rev_iffD1" (the_context ()) "!!P. [| P; P <-> Q |] ==> Q"
- (fn _ => [etac iffD1 1, assume_tac 1]);
+val prems = Goalw [iff_def]  "[| P <-> Q;  Q |] ==> P";
+by (etac (conjunct2 RS mp) 1);
+by (assume_tac 1);
+qed "iffD2";
 
-qed_goal "rev_iffD2" (the_context ()) "!!P. [| Q; P <-> Q |] ==> P"
- (fn _ => [etac iffD2 1, assume_tac 1]);
+Goal "[| P; P <-> Q |] ==> Q";
+by (etac iffD1 1);
+by (assume_tac 1);
+qed "rev_iffD1";
 
-qed_goal "iff_refl" (the_context ()) "P <-> P"
- (fn _ => [ (REPEAT (ares_tac [iffI] 1)) ]);
+Goal "[| Q; P <-> Q |] ==> P";
+by (etac iffD2 1);
+by (assume_tac 1);
+qed "rev_iffD2";
+
+Goal "P <-> P";
+by (REPEAT (ares_tac [iffI] 1)) ;
+qed "iff_refl";
 
-qed_goal "iff_sym" (the_context ()) "Q <-> P ==> P <-> Q"
- (fn [major] =>
-  [ (rtac (major RS iffE) 1),
-    (rtac iffI 1),
-    (REPEAT (eresolve_tac [asm_rl,mp] 1)) ]);
+Goal "Q <-> P ==> P <-> Q";
+by (etac iffE 1);
+by (rtac iffI 1);
+by (REPEAT (eresolve_tac [asm_rl,mp] 1)) ;
+qed "iff_sym";
 
-qed_goal "iff_trans" (the_context ())
-    "!!P Q R. [| P <-> Q;  Q<-> R |] ==> P <-> R"
- (fn _ =>
-  [ (rtac iffI 1),
-    (REPEAT (eresolve_tac [asm_rl,iffE] 1 ORELSE mp_tac 1)) ]);
+Goal "[| P <-> Q;  Q<-> R |] ==> P <-> R";
+by (rtac iffI 1);
+by (REPEAT (eresolve_tac [asm_rl,iffE] 1 ORELSE mp_tac 1)) ;
+qed "iff_trans";
 
 
 (*** Unique existence.  NOTE THAT the following 2 quantifications
@@ -148,21 +174,23 @@
  do NOT mean the same thing.  The parser treats EX!x y.P(x,y) as sequential.
 ***)
 
-qed_goalw "ex1I" (the_context ()) [ex1_def]
-    "[| P(a);  !!x. P(x) ==> x=a |] ==> EX! x. P(x)"
- (fn prems => [ (REPEAT (ares_tac (prems@[exI,conjI,allI,impI]) 1)) ]);
+val prems = Goalw [ex1_def] 
+    "[| P(a);  !!x. P(x) ==> x=a |] ==> EX! x. P(x)";
+by (REPEAT (ares_tac (prems@[exI,conjI,allI,impI]) 1)) ;
+qed "ex1I";
 
 (*Sometimes easier to use: the premises have no shared variables.  Safe!*)
-qed_goal "ex_ex1I" (the_context ())
-    "[| EX x. P(x);  !!x y. [| P(x); P(y) |] ==> x=y |] ==> EX! x. P(x)"
- (fn [ex,eq] => [ (rtac (ex RS exE) 1),
-                  (REPEAT (ares_tac [ex1I,eq] 1)) ]);
+val [ex,eq] = Goal
+    "[| EX x. P(x);  !!x y. [| P(x); P(y) |] ==> x=y |] ==> EX! x. P(x)";
+by (rtac (ex RS exE) 1);
+by (REPEAT (ares_tac [ex1I,eq] 1)) ;
+qed "ex_ex1I";
 
-qed_goalw "ex1E" (the_context ()) [ex1_def]
-    "[| EX! x. P(x);  !!x. [| P(x);  ALL y. P(y) --> y=x |] ==> R |] ==> R"
- (fn prems =>
-  [ (cut_facts_tac prems 1),
-    (REPEAT (eresolve_tac [exE,conjE] 1 ORELSE ares_tac prems 1)) ]);
+val prems = Goalw [ex1_def] 
+    "[| EX! x. P(x);  !!x. [| P(x);  ALL y. P(y) --> y=x |] ==> R |] ==> R";
+by (cut_facts_tac prems 1);
+by (REPEAT (eresolve_tac [exE,conjE] 1 ORELSE ares_tac prems 1)) ;
+qed "ex1E";
 
 
 (*** <-> congruence rules for simplification ***)
@@ -172,83 +200,78 @@
     resolve_tac (prems RL [iffE]) i THEN
     REPEAT1 (eresolve_tac [asm_rl,mp] i);
 
-qed_goal "conj_cong" (the_context ()) 
-    "[| P <-> P';  P' ==> Q <-> Q' |] ==> (P&Q) <-> (P'&Q')"
- (fn prems =>
-  [ (cut_facts_tac prems 1),
-    (REPEAT  (ares_tac [iffI,conjI] 1
-      ORELSE  eresolve_tac [iffE,conjE,mp] 1
-      ORELSE  iff_tac prems 1)) ]);
+val prems = Goal 
+    "[| P <-> P';  P' ==> Q <-> Q' |] ==> (P&Q) <-> (P'&Q')";
+by (cut_facts_tac prems 1);
+by (REPEAT  (ares_tac [iffI,conjI] 1
+     ORELSE  eresolve_tac [iffE,conjE,mp] 1 
+     ORELSE  iff_tac prems 1)) ;
+qed "conj_cong";
 
 (*Reversed congruence rule!   Used in ZF/Order*)
-qed_goal "conj_cong2" (the_context ()) 
-    "[| P <-> P';  P' ==> Q <-> Q' |] ==> (Q&P) <-> (Q'&P')"
- (fn prems =>
-  [ (cut_facts_tac prems 1),
-    (REPEAT  (ares_tac [iffI,conjI] 1
-      ORELSE  eresolve_tac [iffE,conjE,mp] 1
-      ORELSE  iff_tac prems 1)) ]);
+val prems = Goal 
+    "[| P <-> P';  P' ==> Q <-> Q' |] ==> (Q&P) <-> (Q'&P')";
+by (cut_facts_tac prems 1);
+by (REPEAT  (ares_tac [iffI,conjI] 1
+     ORELSE  eresolve_tac [iffE,conjE,mp] 1 ORELSE  iff_tac prems 1)) ;
+qed "conj_cong2";
 
-qed_goal "disj_cong" (the_context ()) 
-    "[| P <-> P';  Q <-> Q' |] ==> (P|Q) <-> (P'|Q')"
- (fn prems =>
-  [ (cut_facts_tac prems 1),
-    (REPEAT  (eresolve_tac [iffE,disjE,disjI1,disjI2] 1
-      ORELSE  ares_tac [iffI] 1
-      ORELSE  mp_tac 1)) ]);
+val prems = Goal 
+    "[| P <-> P';  Q <-> Q' |] ==> (P|Q) <-> (P'|Q')";
+by (cut_facts_tac prems 1);
+by (REPEAT  (eresolve_tac [iffE,disjE,disjI1,disjI2] 1
+             ORELSE  ares_tac [iffI] 1 ORELSE  mp_tac 1)) ;
+qed "disj_cong";
 
-qed_goal "imp_cong" (the_context ()) 
-    "[| P <-> P';  P' ==> Q <-> Q' |] ==> (P-->Q) <-> (P'-->Q')"
- (fn prems =>
-  [ (cut_facts_tac prems 1),
-    (REPEAT   (ares_tac [iffI,impI] 1
-      ORELSE  etac iffE 1
-      ORELSE  mp_tac 1 ORELSE iff_tac prems 1)) ]);
+val prems = Goal 
+    "[| P <-> P';  P' ==> Q <-> Q' |] ==> (P-->Q) <-> (P'-->Q')";
+by (cut_facts_tac prems 1);
+by (REPEAT   (ares_tac [iffI,impI] 1
+      ORELSE  etac iffE 1 ORELSE  mp_tac 1 ORELSE iff_tac prems 1)) ;
+qed "imp_cong";
 
-qed_goal "iff_cong" (the_context ()) 
-    "[| P <-> P';  Q <-> Q' |] ==> (P<->Q) <-> (P'<->Q')"
- (fn prems =>
-  [ (cut_facts_tac prems 1),
-    (REPEAT   (etac iffE 1
-      ORELSE  ares_tac [iffI] 1
-      ORELSE  mp_tac 1)) ]);
+val prems = Goal 
+    "[| P <-> P';  Q <-> Q' |] ==> (P<->Q) <-> (P'<->Q')";
+by (cut_facts_tac prems 1);
+by (REPEAT   (etac iffE 1 ORELSE  ares_tac [iffI] 1 ORELSE  mp_tac 1)) ;
+qed "iff_cong";
 
-qed_goal "not_cong" (the_context ()) 
-    "P <-> P' ==> ~P <-> ~P'"
- (fn prems =>
-  [ (cut_facts_tac prems 1),
-    (REPEAT   (ares_tac [iffI,notI] 1
-      ORELSE  mp_tac 1
-      ORELSE  eresolve_tac [iffE,notE] 1)) ]);
+val prems = Goal 
+    "P <-> P' ==> ~P <-> ~P'";
+by (cut_facts_tac prems 1);
+by (REPEAT   (ares_tac [iffI,notI] 1
+      ORELSE  mp_tac 1 ORELSE  eresolve_tac [iffE,notE] 1)) ;
+qed "not_cong";
 
-qed_goal "all_cong" (the_context ()) 
-    "(!!x. P(x) <-> Q(x)) ==> (ALL x. P(x)) <-> (ALL x. Q(x))"
- (fn prems =>
-  [ (REPEAT   (ares_tac [iffI,allI] 1
-      ORELSE   mp_tac 1
-      ORELSE   etac allE 1 ORELSE iff_tac prems 1)) ]);
+val prems = Goal 
+    "(!!x. P(x) <-> Q(x)) ==> (ALL x. P(x)) <-> (ALL x. Q(x))";
+by (REPEAT   (ares_tac [iffI,allI] 1
+     ORELSE   mp_tac 1 ORELSE   etac allE 1 ORELSE iff_tac prems 1)) ;
+qed "all_cong";
 
-qed_goal "ex_cong" (the_context ()) 
-    "(!!x. P(x) <-> Q(x)) ==> (EX x. P(x)) <-> (EX x. Q(x))"
- (fn prems =>
-  [ (REPEAT   (etac exE 1 ORELSE ares_tac [iffI,exI] 1
-      ORELSE   mp_tac 1
-      ORELSE   iff_tac prems 1)) ]);
+val prems = Goal 
+    "(!!x. P(x) <-> Q(x)) ==> (EX x. P(x)) <-> (EX x. Q(x))";
+by (REPEAT   (etac exE 1 ORELSE ares_tac [iffI,exI] 1
+     ORELSE   mp_tac 1 ORELSE   iff_tac prems 1)) ;
+qed "ex_cong";
 
-qed_goal "ex1_cong" (the_context ()) 
-    "(!!x. P(x) <-> Q(x)) ==> (EX! x. P(x)) <-> (EX! x. Q(x))"
- (fn prems =>
-  [ (REPEAT   (eresolve_tac [ex1E, spec RS mp] 1 ORELSE ares_tac [iffI,ex1I] 1
-      ORELSE   mp_tac 1
-      ORELSE   iff_tac prems 1)) ]);
+val prems = Goal 
+    "(!!x. P(x) <-> Q(x)) ==> (EX! x. P(x)) <-> (EX! x. Q(x))";
+by (REPEAT   (eresolve_tac [ex1E, spec RS mp] 1
+       ORELSE ares_tac [iffI,ex1I] 1 ORELSE   mp_tac 1
+       ORELSE   iff_tac prems 1)) ;
+qed "ex1_cong";
 
 (*** Equality rules ***)
 
-qed_goal "sym" (the_context ()) "a=b ==> b=a"
- (fn [major] => [ (rtac (major RS subst) 1), (rtac refl 1) ]);
+Goal "a=b ==> b=a";
+by (etac subst 1);
+by (rtac refl 1) ;
+qed "sym";
 
-qed_goal "trans" (the_context ()) "[| a=b;  b=c |] ==> a=c"
- (fn [prem1,prem2] => [ (rtac (prem2 RS subst) 1), (rtac prem1 1) ]);
+Goal "[| a=b;  b=c |] ==> a=c";
+by (etac subst 1 THEN assume_tac 1) ;
+qed "trans";
 
 (** ~ b=a ==> ~ a=b **)
 bind_thm ("not_sym", hd (compose(sym,2,contrapos)));
@@ -257,12 +280,12 @@
 (* Two theorms for rewriting only one instance of a definition:
    the first for definitions of formulae and the second for terms *)
 
-val prems = goal (the_context ()) "(A == B) ==> A <-> B";
+val prems = goal (the_context()) "(A == B) ==> A <-> B";
 by (rewrite_goals_tac prems);
 by (rtac iff_refl 1);
 qed "def_imp_iff";
 
-val prems = goal (the_context ()) "(A == B) ==> A = B";
+val prems = goal (the_context()) "(A == B) ==> A = B";
 by (rewrite_goals_tac prems);
 by (rtac refl 1);
 qed "meta_eq_to_obj_eq";
@@ -279,75 +302,67 @@
   end;
 
 (*A special case of ex1E that would otherwise need quantifier expansion*)
-qed_goal "ex1_equalsE" (the_context ())
-    "[| EX! x. P(x);  P(a);  P(b) |] ==> a=b"
- (fn prems =>
-  [ (cut_facts_tac prems 1),
-    (etac ex1E 1),
-    (rtac trans 1),
-    (rtac sym 2),
-    (REPEAT (eresolve_tac [asm_rl, spec RS mp] 1)) ]);
+val prems = Goal
+    "[| EX! x. P(x);  P(a);  P(b) |] ==> a=b";
+by (cut_facts_tac prems 1);
+by (etac ex1E 1);
+by (rtac trans 1);
+by (rtac sym 2);
+by (REPEAT (eresolve_tac [asm_rl, spec RS mp] 1)) ;
+qed "ex1_equalsE";
 
 (** Polymorphic congruence rules **)
 
-qed_goal "subst_context" (the_context ()) 
-   "[| a=b |]  ==>  t(a)=t(b)"
- (fn prems=>
-  [ (resolve_tac (prems RL [ssubst]) 1),
-    (rtac refl 1) ]);
+Goal "[| a=b |]  ==>  t(a)=t(b)";
+by (etac ssubst 1);
+by (rtac refl 1) ;
+qed "subst_context";
 
-qed_goal "subst_context2" (the_context ()) 
-   "[| a=b;  c=d |]  ==>  t(a,c)=t(b,d)"
- (fn prems=>
-  [ (EVERY1 (map rtac ((prems RL [ssubst]) @ [refl]))) ]);
+Goal "[| a=b;  c=d |]  ==>  t(a,c)=t(b,d)";
+by (REPEAT (etac ssubst 1));
+by (rtac refl 1) ;
+qed "subst_context2";
 
-qed_goal "subst_context3" (the_context ()) 
-   "[| a=b;  c=d;  e=f |]  ==>  t(a,c,e)=t(b,d,f)"
- (fn prems=>
-  [ (EVERY1 (map rtac ((prems RL [ssubst]) @ [refl]))) ]);
+Goal "[| a=b;  c=d;  e=f |]  ==>  t(a,c,e)=t(b,d,f)";
+by (REPEAT (etac ssubst 1));
+by (rtac refl 1) ;
+qed "subst_context3";
 
 (*Useful with eresolve_tac for proving equalties from known equalities.
         a = b
         |   |
         c = d   *)
-qed_goal "box_equals" (the_context ())
-    "[| a=b;  a=c;  b=d |] ==> c=d"  
- (fn prems=>
-  [ (rtac trans 1),
-    (rtac trans 1),
-    (rtac sym 1),
-    (REPEAT (resolve_tac prems 1)) ]);
+Goal "[| a=b;  a=c;  b=d |] ==> c=d";
+by (rtac trans 1);
+by (rtac trans 1);
+by (rtac sym 1);
+by (REPEAT (assume_tac 1));
+qed "box_equals";
 
 (*Dual of box_equals: for proving equalities backwards*)
-qed_goal "simp_equals" (the_context ())
-    "[| a=c;  b=d;  c=d |] ==> a=b"  
- (fn prems=>
-  [ (rtac trans 1),
-    (rtac trans 1),
-    (REPEAT (resolve_tac (prems @ (prems RL [sym])) 1)) ]);
+Goal "[| a=c;  b=d;  c=d |] ==> a=b";
+by (rtac trans 1);
+by (rtac trans 1);
+by (REPEAT (assume_tac 1));
+by (etac sym 1);
+qed "simp_equals";
 
 (** Congruence rules for predicate letters **)
 
-qed_goal "pred1_cong" (the_context ())
-    "a=a' ==> P(a) <-> P(a')"
- (fn prems =>
-  [ (cut_facts_tac prems 1),
-    (rtac iffI 1),
-    (DEPTH_SOLVE (eresolve_tac [asm_rl, subst, ssubst] 1)) ]);
+Goal "a=a' ==> P(a) <-> P(a')";
+by (rtac iffI 1);
+by (DEPTH_SOLVE (eresolve_tac [asm_rl, subst, ssubst] 1)) ;
+qed "pred1_cong";
 
-qed_goal "pred2_cong" (the_context ())
-    "[| a=a';  b=b' |] ==> P(a,b) <-> P(a',b')"
- (fn prems =>
-  [ (cut_facts_tac prems 1),
-    (rtac iffI 1),
-    (DEPTH_SOLVE (eresolve_tac [asm_rl, subst, ssubst] 1)) ]);
+Goal "[| a=a';  b=b' |] ==> P(a,b) <-> P(a',b')";
+by (rtac iffI 1);
+by (DEPTH_SOLVE (eresolve_tac [asm_rl, subst, ssubst] 1)) ;
+qed "pred2_cong";
 
-qed_goal "pred3_cong" (the_context ())
-    "[| a=a';  b=b';  c=c' |] ==> P(a,b,c) <-> P(a',b',c')"
- (fn prems =>
-  [ (cut_facts_tac prems 1),
-    (rtac iffI 1),
-    (DEPTH_SOLVE (eresolve_tac [asm_rl, subst, ssubst] 1)) ]);
+Goal "[| a=a';  b=b';  c=c' |] ==> P(a,b,c) <-> P(a',b',c')";
+by (rtac iffI 1);
+by (DEPTH_SOLVE (eresolve_tac [asm_rl, subst, ssubst] 1)) ;
+qed "pred3_cong";
 
 (*special cases for free variables P, Q, R, S -- up to 3 arguments*)
 
@@ -368,52 +383,52 @@
    R. Dyckhoff, Contraction-free sequent calculi for intuitionistic logic
     (preprint, University of St Andrews, 1991)  ***)
 
-qed_goal "conj_impE" (the_context ()) 
-    "[| (P&Q)-->S;  P-->(Q-->S) ==> R |] ==> R"
- (fn major::prems=>
-  [ (REPEAT (ares_tac ([conjI, impI, major RS mp]@prems) 1)) ]);
+val major::prems= Goal 
+    "[| (P&Q)-->S;  P-->(Q-->S) ==> R |] ==> R";
+by (REPEAT (ares_tac ([conjI, impI, major RS mp]@prems) 1)) ;
+qed "conj_impE";
 
-qed_goal "disj_impE" (the_context ()) 
-    "[| (P|Q)-->S;  [| P-->S; Q-->S |] ==> R |] ==> R"
- (fn major::prems=>
-  [ (DEPTH_SOLVE (ares_tac ([disjI1, disjI2, impI, major RS mp]@prems) 1)) ]);
+val major::prems= Goal 
+    "[| (P|Q)-->S;  [| P-->S; Q-->S |] ==> R |] ==> R";
+by (DEPTH_SOLVE (ares_tac ([disjI1, disjI2, impI, major RS mp]@prems) 1)) ;
+qed "disj_impE";
 
 (*Simplifies the implication.  Classical version is stronger. 
   Still UNSAFE since Q must be provable -- backtracking needed.  *)
-qed_goal "imp_impE" (the_context ()) 
-    "[| (P-->Q)-->S;  [| P; Q-->S |] ==> Q;  S ==> R |] ==> R"
- (fn major::prems=>
-  [ (REPEAT (ares_tac ([impI, major RS mp]@prems) 1)) ]);
+val major::prems= Goal 
+    "[| (P-->Q)-->S;  [| P; Q-->S |] ==> Q;  S ==> R |] ==> R";
+by (REPEAT (ares_tac ([impI, major RS mp]@prems) 1)) ;
+qed "imp_impE";
 
 (*Simplifies the implication.  Classical version is stronger. 
   Still UNSAFE since ~P must be provable -- backtracking needed.  *)
-qed_goal "not_impE" (the_context ())
-    "[| ~P --> S;  P ==> False;  S ==> R |] ==> R"
- (fn major::prems=>
-  [ (REPEAT (ares_tac ([notI, impI, major RS mp]@prems) 1)) ]);
+val major::prems= Goal
+    "[| ~P --> S;  P ==> False;  S ==> R |] ==> R";
+by (REPEAT (ares_tac ([notI, impI, major RS mp]@prems) 1)) ;
+qed "not_impE";
 
 (*Simplifies the implication.   UNSAFE.  *)
-qed_goal "iff_impE" (the_context ()) 
+val major::prems= Goal 
     "[| (P<->Q)-->S;  [| P; Q-->S |] ==> Q;  [| Q; P-->S |] ==> P;  \
-\       S ==> R |] ==> R"
- (fn major::prems=>
-  [ (REPEAT (ares_tac ([iffI, impI, major RS mp]@prems) 1)) ]);
+\       S ==> R |] ==> R";
+by (REPEAT (ares_tac ([iffI, impI, major RS mp]@prems) 1)) ;
+qed "iff_impE";
 
 (*What if (ALL x.~~P(x)) --> ~~(ALL x.P(x)) is an assumption? UNSAFE*)
-qed_goal "all_impE" (the_context ()) 
-    "[| (ALL x. P(x))-->S;  !!x. P(x);  S ==> R |] ==> R"
- (fn major::prems=>
-  [ (REPEAT (ares_tac ([allI, impI, major RS mp]@prems) 1)) ]);
+val major::prems= Goal 
+    "[| (ALL x. P(x))-->S;  !!x. P(x);  S ==> R |] ==> R";
+by (REPEAT (ares_tac ([allI, impI, major RS mp]@prems) 1)) ;
+qed "all_impE";
 
 (*Unsafe: (EX x.P(x))-->S  is equivalent to  ALL x.P(x)-->S.  *)
-qed_goal "ex_impE" (the_context ()) 
-    "[| (EX x. P(x))-->S;  P(x)-->S ==> R |] ==> R"
- (fn major::prems=>
-  [ (REPEAT (ares_tac ([exI, impI, major RS mp]@prems) 1)) ]);
+val major::prems= Goal 
+    "[| (EX x. P(x))-->S;  P(x)-->S ==> R |] ==> R";
+by (REPEAT (ares_tac ([exI, impI, major RS mp]@prems) 1)) ;
+qed "ex_impE";
 
 (*** Courtesy of Krzysztof Grabczewski ***)
 
-val major::prems = goal (the_context ()) "[| P|Q;  P==>R;  Q==>S |] ==> R|S";
+val major::prems = Goal "[| P|Q;  P==>R;  Q==>S |] ==> R|S";
 by (rtac (major RS disjE) 1);
 by (REPEAT (eresolve_tac (prems RL [disjI1, disjI2]) 1));
 qed "disj_imp_disj";
diff -r 53e09e592278 -r 051592f4236a src/ZF/Resid/Substitution.ML
--- a/src/ZF/Resid/Substitution.ML	Thu Jul 06 13:11:32 2000 +0200
+++ b/src/ZF/Resid/Substitution.ML	Thu Jul 06 13:28:36 2000 +0200
@@ -9,26 +9,23 @@
 (*   Arithmetic extensions                                                   *)
 (* ------------------------------------------------------------------------- *)
 
-goal Arith.thy
-    "!!m.[| p < n; n:nat|] ==> n~=p";
+Goal "[| p < n; n:nat|] ==> n~=p";
 by (Fast_tac 1);
 qed "gt_not_eq";
 
-val succ_pred = prove_goal Arith.thy 
-    "!!i.[|j:nat; i:nat|] ==> i < j --> succ(j #- 1) = j"
- (fn prems =>[(induct_tac "j" 1),
-              (Fast_tac 1),
-              (Asm_simp_tac 1)]);
+Goal "[|j:nat; i:nat|] ==> i < j --> succ(j #- 1) = j";
+by (induct_tac "j" 1);
+by (Fast_tac 1);
+by (Asm_simp_tac 1);
+qed "succ_pred";
 
-goal Arith.thy 
-    "!!i.[|succ(x)<n; n:nat; x:nat|] ==> x < n #- 1 ";
+Goal "[|succ(x)<n; n:nat; x:nat|] ==> x < n #- 1 ";
 by (rtac succ_leE 1);
 by (forward_tac [nat_into_Ord RS le_refl RS lt_trans] 1 THEN assume_tac 1);
 by (asm_simp_tac (simpset() addsimps [succ_pred]) 1);
 qed "lt_pred";
 
-goal Arith.thy 
-    "!!i.[|n < succ(x); p<n; p:nat; n:nat; x:nat|] ==> n #- 1 < x ";
+Goal "[|n < succ(x); p<n; p:nat; n:nat; x:nat|] ==> n #- 1 < x ";
 by (rtac succ_leE 1);
 by (asm_simp_tac (simpset() addsimps [succ_pred]) 1);
 qed "gt_pred";
diff -r 53e09e592278 -r 051592f4236a src/ZF/ex/Limit.ML
--- a/src/ZF/ex/Limit.ML	Thu Jul 06 13:11:32 2000 +0200
+++ b/src/ZF/ex/Limit.ML	Thu Jul 06 13:28:36 2000 +0200
@@ -214,7 +214,7 @@
 
 AddTCs [pcpo_cpo, bot_least, bot_in];
 
-val prems = goal Limit.thy  (* bot_unique *)
+val prems = Goal  (* bot_unique *)
     "[| pcpo(D); x:set(D); !!y. y:set(D) ==> rel(D,x,y)|] ==> x = bot(D)";
 by (blast_tac (claset() addIs ([cpo_antisym,pcpo_cpo,bot_in,bot_least]@
                                prems)) 1);
@@ -364,14 +364,14 @@
 		                  xprem::yprem::prems));
 qed "matrix_chainI";
 
-val lemma = prove_goal Limit.thy
-    "!!z.[|m : nat; rel(D, (lam n:nat. M`n`n)`m, y)|] ==> rel(D,M`m`m, y)"
-    (fn prems => [Asm_full_simp_tac 1]);
+Goal "[|m : nat; rel(D, (lam n:nat. M`n`n)`m, y)|] ==> rel(D,M`m`m, y)";
+by (Asm_full_simp_tac 1);
+qed "lemma";
 
-val lemma2 = prove_goal Limit.thy
-    "!!z.[|x:nat; m:nat; rel(D,(lam n:nat. M`n`m1)`x,(lam n:nat. M`n`m1)`m)|] ==> \
-\        rel(D,M`x`m1,M`m`m1)"
-    (fn prems => [Asm_full_simp_tac 1]);
+Goal "[|x:nat; m:nat; rel(D,(lam n:nat. M`n`m1)`x,(lam n:nat. M`n`m1)`m)|] \
+\     ==> rel(D,M`x`m1,M`m`m1)";
+by (Asm_full_simp_tac 1);
+qed "lemma2";
 
 Goalw [isub_def]  (* isub_lemma *)
     "[|isub(D, lam n:nat. M`n`n, y); matrix(D,M); cpo(D)|] ==>  \
@@ -563,7 +563,7 @@
 (* rel_cf originally an equality. Now stated as two rules. Seemed easiest. 
    Besides, now complicated by typing assumptions. *)
 
-val prems = goal Limit.thy
+val prems = Goal
     "[|!!x. x:set(D) ==> rel(E,f`x,g`x); f:cont(D,E); g:cont(D,E)|] ==> \
 \    rel(cf(D,E),f,g)";
 by (asm_simp_tac (simpset() addsimps [rel_I, cf_def]@prems) 1);
@@ -1080,7 +1080,7 @@
 brr(lam_type::(chain_iprod RS cpo_lub RS islub_in)::iprodE::prems) 1;
 qed "islub_iprod";
 
-val prems = goal Limit.thy (* cpo_iprod *)
+val prems = Goal (* cpo_iprod *)
     "(!!n. n:nat ==> cpo(DD`n)) ==> cpo(iprod(DD))";
 brr[cpoI,poI] 1;
 by (rtac rel_iprodI 1); (* not repeated: want to solve 1 and leave 2 unchanged *)
@@ -1230,7 +1230,7 @@
                                chain_in,nat_succI]) 1);
 qed "chain_mkcpo";
 
-val prems = goal Limit.thy  (* subcpo_mkcpo *)
+val prems = Goal  (* subcpo_mkcpo *)
     "[|!!X. chain(mkcpo(D,P),X) ==> P(lub(D,X)); cpo(D)|] ==>   \
 \    subcpo(mkcpo(D,P),D)";
 brr(subcpoI::subsetI::prems) 1;
@@ -1250,15 +1250,16 @@
 by (REPEAT (ares_tac prems 1));
 qed "emb_chainI";
 
-val emb_chain_cpo = prove_goalw Limit.thy [emb_chain_def] 
-    "!!x. [|emb_chain(DD,ee); n:nat|] ==> cpo(DD`n)"
-  (fn prems => [Fast_tac 1]);
+Goalw [emb_chain_def] "[|emb_chain(DD,ee); n:nat|] ==> cpo(DD`n)";
+by (Fast_tac 1);
+qed "emb_chain_cpo";
 
 AddTCs [emb_chain_cpo];
 
-val emb_chain_emb = prove_goalw Limit.thy [emb_chain_def] 
-    "!!x. [|emb_chain(DD,ee); n:nat|] ==> emb(DD`n,DD`succ(n),ee`n)"
-  (fn prems => [Fast_tac 1]);
+Goalw [emb_chain_def] 
+    "[|emb_chain(DD,ee); n:nat|] ==> emb(DD`n,DD`succ(n),ee`n)";
+by (Fast_tac 1);
+qed "emb_chain_emb";
 
 (*----------------------------------------------------------------------*)
 (* Dinf, the inverse Limit.                                             *)
@@ -1358,12 +1359,11 @@
 
 (* Again, would like more theorems about arithmetic. *)
 
-val add1 = prove_goal Limit.thy
-    "!!x. n:nat ==> succ(n) = n #+ 1"
-  (fn prems => [Asm_simp_tac 1]);
+Goal "n:nat ==> succ(n) = n #+ 1";
+by (Asm_simp_tac 1);
+qed "add1";
 
-Goal  (* succ_sub1 *)
-    "x:nat ==> 0 < x --> succ(x #- 1)=x";
+Goal "x:nat ==> 0 < x --> succ(x #- 1)=x";
 by (induct_tac "x" 1);
 by Auto_tac;
 qed "succ_sub1";
@@ -1416,7 +1416,7 @@
 by (asm_simp_tac(simpset() addsimps[e_less_le, e_less_eq]) 1);
 qed "e_less_succ";
 
-val prems = goal Limit.thy  (* e_less_succ_emb *)
+val prems = Goal  (* e_less_succ_emb *)
     "[|!!n. n:nat ==> emb(DD`n,DD`succ(n),ee`n); m:nat|] ==>   \
 \    e_less(DD,ee,m,succ(m)) = ee`m";
 by (asm_simp_tac(simpset() addsimps e_less_succ::prems) 1);
@@ -1446,9 +1446,9 @@
 by (REPEAT (assume_tac 1));
 qed "emb_e_less";
 
-val comp_mono_eq = prove_goal Limit.thy
-    "!!z.[|f=f'; g=g'|] ==> f O g = f' O g'"
-  (fn prems => [Asm_simp_tac 1]);
+Goal "[|f=f'; g=g'|] ==> f O g = f' O g'";
+by (Asm_simp_tac 1);
+qed "comp_mono_eq";
 
 (* Typing, typing, typing, three irritating assumptions. Extra theorems
    needed in proof, but no real difficulty. *)
@@ -1695,7 +1695,7 @@
 by (REPEAT (assume_tac 1));
 qed "eps_e_gr";
 
-val prems = goal Limit.thy  (* eps_succ_ee *)
+val prems = Goal  (* eps_succ_ee *)
     "[|!!n. n:nat ==> emb(DD`n,DD`succ(n),ee`n); m:nat|] ==>  \
 \    eps(DD,ee,m,succ(m)) = ee`m";
 by (asm_simp_tac(simpset() addsimps eps_e_less::le_succ_iff::e_less_succ_emb::
@@ -1752,7 +1752,7 @@
 
 (* Arithmetic, little support in Isabelle/ZF. *)
 
-val prems = goal Limit.thy  (* le_exists_lemma *)
+val prems = Goal  (* le_exists_lemma *)
     "[|n le k; k le m;  \
 \      !!p q. [|p le q; k=n#+p; m=n#+q; p:nat; q:nat|] ==> R; \
 \      m:nat; n:nat; k:nat|]==>R";
@@ -1871,17 +1871,19 @@
 by (asm_full_simp_tac(simpset() addsimps[eps_succ_Rp, e_less_eq, id_conv, nat_succI]) 1);
 qed "rho_emb_fun";
 
-val rho_emb_apply1 = prove_goalw Limit.thy [rho_emb_def]
-    "!!z. x:set(DD`n) ==> rho_emb(DD,ee,n)`x = (lam m:nat. eps(DD,ee,n,m)`x)"
-  (fn prems => [Asm_simp_tac 1]);
+Goalw [rho_emb_def]
+    "x:set(DD`n) ==> rho_emb(DD,ee,n)`x = (lam m:nat. eps(DD,ee,n,m)`x)";
+by (Asm_simp_tac 1);
+qed "rho_emb_apply1";
 
-val rho_emb_apply2 = prove_goalw Limit.thy [rho_emb_def]
-    "!!z. [|x:set(DD`n); m:nat|] ==> rho_emb(DD,ee,n)`x`m = eps(DD,ee,n,m)`x"
-  (fn prems => [Asm_simp_tac 1]);
+Goalw [rho_emb_def]
+    "[|x:set(DD`n); m:nat|] ==> rho_emb(DD,ee,n)`x`m = eps(DD,ee,n,m)`x";
+by (Asm_simp_tac 1);
+qed "rho_emb_apply2";
 
-val rho_emb_id = prove_goal Limit.thy 
-  "!!z. [| x:set(DD`n); n:nat|] ==> rho_emb(DD,ee,n)`x`n = x"
-  (fn prems => [asm_simp_tac(simpset() addsimps[rho_emb_apply2,eps_id]) 1]);
+Goal "[| x:set(DD`n); n:nat|] ==> rho_emb(DD,ee,n)`x`n = x";
+by (asm_simp_tac(simpset() addsimps[rho_emb_apply2,eps_id]) 1);
+qed "rho_emb_id";
 
 (* Shorter proof, 23 against 62. *)
 
@@ -2078,10 +2080,9 @@
 by (auto_tac (claset() addIs [eps_fun], simpset()));
 qed "rho_emb_commute";
 
-val le_succ = prove_goal Arith.thy "n:nat ==> n le succ(n)"
- (fn prems =>
-   [REPEAT (ares_tac
-    ((disjI1 RS(le_succ_iff RS iffD2))::le_refl::nat_into_Ord::prems) 1)]);
+val prems = goal Arith.thy "n:nat ==> n le succ(n)";
+by (REPEAT (ares_tac ((disjI1 RS(le_succ_iff RS iffD2))::le_refl::nat_into_Ord::prems) 1));
+qed "le_succ";
 
 (* Shorter proof: 21 vs 83 (106 - 23, due to OAssoc complication) *)
 
@@ -2348,17 +2349,19 @@
 
 
 
-val mediatingI = prove_goalw Limit.thy [mediating_def]
-  "[|emb(E,G,t);  !!n. n:nat ==> f(n) = t O r(n) |]==>mediating(E,G,r,f,t)"
- (fn prems => [Safe_tac,REPEAT (ares_tac prems 1)]);
+val prems = Goalw [mediating_def]
+  "[|emb(E,G,t);  !!n. n:nat ==> f(n) = t O r(n) |]==>mediating(E,G,r,f,t)";
+by (Safe_tac);
+by (REPEAT (ares_tac prems 1));
+qed "mediatingI";
 
-val mediating_emb = prove_goalw Limit.thy [mediating_def]
-  "!!z. mediating(E,G,r,f,t) ==> emb(E,G,t)"
- (fn prems => [Fast_tac 1]);
+Goalw [mediating_def] "mediating(E,G,r,f,t) ==> emb(E,G,t)";
+by (Fast_tac 1);
+qed "mediating_emb";
 
-val mediating_eq = prove_goalw Limit.thy [mediating_def]
-  "!!z. [| mediating(E,G,r,f,t); n:nat |] ==> f(n) = t O r(n)"
- (fn prems => [Blast_tac 1]);
+Goalw [mediating_def] "[| mediating(E,G,r,f,t); n:nat |] ==> f(n) = t O r(n)";
+by (Blast_tac 1);
+qed "mediating_eq";
 
 Goal (* lub_universal_mediating *)
   "[| lub(cf(E,E), lam n:nat. r(n) O Rp(DD`n,E,r(n))) = id(set(E));  \