# HG changeset patch
# User clasohm
# Date 787315872 -3600
# Node ID 4ab9176b45b71ef0ba205d7dec10534118acf5a0
# Parent  9a03ed31ea2fa97a29945b22c630c40f2219d8db
removed FOL_Lemmas and IFOL_Lemmas; added qed_goal

diff -r 9a03ed31ea2f -r 4ab9176b45b7 src/FOL/FOL.ML
--- a/src/FOL/FOL.ML	Mon Dec 12 10:26:05 1994 +0100
+++ b/src/FOL/FOL.ML	Tue Dec 13 11:51:12 1994 +0100
@@ -8,25 +8,10 @@
 
 open FOL;
 
-signature FOL_LEMMAS = 
-  sig
-  val disjCI 		: thm
-  val excluded_middle 	: thm
-  val excluded_middle_tac: string -> int -> tactic
-  val exCI 		: thm
-  val ex_classical 	: thm
-  val iffCE 		: thm
-  val impCE 		: thm
-  val notnotD 		: thm
-  end;
-
-
-structure FOL_Lemmas : FOL_LEMMAS = 
-struct
 
 (*** Classical introduction rules for | and EX ***)
 
-val disjCI = prove_goal FOL.thy 
+qed_goal "disjCI" FOL.thy 
    "(~Q ==> P) ==> P|Q"
  (fn prems=>
   [ (resolve_tac [classical] 1),
@@ -34,14 +19,14 @@
     (REPEAT (ares_tac (prems@[disjI2,notE]) 1)) ]);
 
 (*introduction rule involving only EX*)
-val ex_classical = prove_goal FOL.thy 
+qed_goal "ex_classical" FOL.thy 
    "( ~(EX x. P(x)) ==> P(a)) ==> EX x.P(x)"
  (fn prems=>
   [ (resolve_tac [classical] 1),
     (eresolve_tac (prems RL [exI]) 1) ]);
 
 (*version of above, simplifying ~EX to ALL~ *)
-val exCI = prove_goal FOL.thy 
+qed_goal "exCI" FOL.thy 
    "(ALL x. ~P(x) ==> P(a)) ==> EX x.P(x)"
  (fn [prem]=>
   [ (resolve_tac [ex_classical] 1),
@@ -49,7 +34,7 @@
     (eresolve_tac [notE] 1),
     (eresolve_tac [exI] 1) ]);
 
-val excluded_middle = prove_goal FOL.thy "~P | P"
+qed_goal "excluded_middle" FOL.thy "~P | P"
  (fn _=> [ rtac disjCI 1, assume_tac 1 ]);
 
 (*For disjunctive case analysis*)
@@ -60,14 +45,14 @@
 
 
 (*Classical implies (-->) elimination. *)
-val impCE = prove_goal FOL.thy 
+qed_goal "impCE" FOL.thy 
     "[| 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)) ]);
 
 (*Double negation law*)
-val notnotD = prove_goal FOL.thy "~~P ==> P"
+qed_goal "notnotD" FOL.thy "~~P ==> P"
  (fn [major]=>
   [ (resolve_tac [classical] 1), (eresolve_tac [major RS notE] 1) ]);
 
@@ -76,14 +61,9 @@
 
 (*Classical <-> elimination.  Proof substitutes P=Q in 
     ~P ==> ~Q    and    P ==> Q  *)
-val iffCE = prove_goalw FOL.thy [iff_def]
+qed_goalw "iffCE" FOL.thy [iff_def]
     "[| P<->Q;  [| P; Q |] ==> R;  [| ~P; ~Q |] ==> R |] ==> R"
  (fn prems =>
   [ (resolve_tac [conjE] 1),
     (REPEAT (DEPTH_SOLVE_1 
 	(etac impCE 1  ORELSE  mp_tac 1  ORELSE  ares_tac prems 1))) ]);
-
-
-end;
-
-open FOL_Lemmas;
diff -r 9a03ed31ea2f -r 4ab9176b45b7 src/FOL/IFOL.ML
--- a/src/FOL/IFOL.ML	Mon Dec 12 10:26:05 1994 +0100
+++ b/src/FOL/IFOL.ML	Tue Dec 13 11:51:12 1994 +0100
@@ -8,88 +8,29 @@
 
 open IFOL;
 
-signature IFOL_LEMMAS = 
-  sig
-  val allE: thm
-  val all_cong: thm
-  val all_dupE: thm
-  val all_impE: thm
-  val box_equals: thm
-  val conjE: thm
-  val conj_cong: thm
-  val conj_impE: thm
-  val contrapos: thm
-  val disj_cong: thm
-  val disj_impE: thm
-  val eq_cong: thm
-  val eq_mp_tac: int -> tactic
-  val ex1I: thm
-  val ex_ex1I: thm
-  val ex1E: thm
-  val ex1_equalsE: thm
-  val ex1_cong: thm
-  val ex_cong: thm
-  val ex_impE: thm
-  val iffD1: thm
-  val iffD2: thm
-  val iffE: thm
-  val iffI: thm
-  val iff_cong: thm
-  val iff_impE: thm
-  val iff_refl: thm
-  val iff_sym: thm
-  val iff_trans: thm
-  val impE: thm
-  val imp_cong: thm
-  val imp_impE: thm
-  val mp_tac: int -> tactic
-  val notE: thm
-  val notI: thm
-  val not_cong: thm
-  val not_impE: thm
-  val not_sym: thm
-  val not_to_imp: thm
-  val pred1_cong: thm
-  val pred2_cong: thm
-  val pred3_cong: thm
-  val pred_congs: thm list
-  val rev_mp: thm
-  val simp_equals: thm
-  val ssubst: thm
-  val subst_context: thm
-  val subst_context2: thm
-  val subst_context3: thm
-  val sym: thm
-  val trans: thm
-  val TrueI: thm
-  end;
 
-
-structure IFOL_Lemmas : IFOL_LEMMAS =
-struct
-
-val TrueI = prove_goalw IFOL.thy [True_def] "True"
+qed_goalw "TrueI" IFOL.thy [True_def] "True"
  (fn _ => [ (REPEAT (ares_tac [impI] 1)) ]);
 
 (*** Sequent-style elimination rules for & --> and ALL ***)
 
-val conjE = prove_goal IFOL.thy 
+qed_goal "conjE" IFOL.thy 
     "[| 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 impE = prove_goal IFOL.thy 
+qed_goal "impE" IFOL.thy 
     "[| P-->Q;  P;  Q ==> R |] ==> R"
  (fn prems=> [ (REPEAT (resolve_tac (prems@[mp]) 1)) ]);
 
-val allE = prove_goal IFOL.thy 
+qed_goal "allE" IFOL.thy 
     "[| ALL x.P(x); P(x) ==> R |] ==> R"
  (fn prems=> [ (REPEAT (resolve_tac (prems@[spec]) 1)) ]);
 
 (*Duplicates the quantifier; for use with eresolve_tac*)
-val all_dupE = prove_goal IFOL.thy 
+qed_goal "all_dupE" IFOL.thy 
     "[| ALL x.P(x);  [| P(x); ALL x.P(x) |] ==> R \
 \    |] ==> R"
  (fn prems=> [ (REPEAT (resolve_tac (prems@[spec]) 1)) ]);
@@ -97,16 +38,16 @@
 
 (*** Negation rules, which translate between ~P and P-->False ***)
 
-val notI = prove_goalw IFOL.thy [not_def] "(P ==> False) ==> ~P"
+qed_goalw "notI" IFOL.thy [not_def] "(P ==> False) ==> ~P"
  (fn prems=> [ (REPEAT (ares_tac (prems@[impI]) 1)) ]);
 
-val notE = prove_goalw IFOL.thy [not_def] "[| ~P;  P |] ==> R"
+qed_goalw "notE" IFOL.thy [not_def] "[| ~P;  P |] ==> R"
  (fn prems=>
   [ (resolve_tac [mp RS FalseE] 1),
     (REPEAT (resolve_tac prems 1)) ]);
 
 (*This is useful with the special implication rules for each kind of P. *)
-val not_to_imp = prove_goal IFOL.thy 
+qed_goal "not_to_imp" IFOL.thy 
     "[| ~P;  (P-->False) ==> Q |] ==> Q"
  (fn prems=> [ (REPEAT (ares_tac (prems@[impI,notE]) 1)) ]);
 
@@ -115,12 +56,12 @@
    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   *)
-val rev_mp = prove_goal IFOL.thy "[| P;  P --> Q |] ==> Q"
+qed_goal "rev_mp" IFOL.thy "[| P;  P --> Q |] ==> Q"
  (fn prems=> [ (REPEAT (resolve_tac (prems@[mp]) 1)) ]);
 
 
 (*Contrapositive of an inference rule*)
-val contrapos = prove_goal IFOL.thy "[| ~Q;  P==>Q |] ==> ~P"
+qed_goal "contrapos" IFOL.thy "[| ~Q;  P==>Q |] ==> ~P"
  (fn [major,minor]=> 
   [ (rtac (major RS notE RS notI) 1), 
     (etac minor 1) ]);
@@ -137,34 +78,34 @@
 
 (*** If-and-only-if ***)
 
-val iffI = prove_goalw IFOL.thy [iff_def]
+qed_goalw "iffI" IFOL.thy [iff_def]
    "[| P ==> Q;  Q ==> P |] ==> P<->Q"
  (fn prems=> [ (REPEAT (ares_tac (prems@[conjI, impI]) 1)) ]);
 
 
 (*Observe use of rewrite_rule to unfold "<->" in meta-assumptions (prems) *)
-val iffE = prove_goalw IFOL.thy [iff_def]
+qed_goalw "iffE" IFOL.thy [iff_def]
     "[| P <-> Q;  [| P-->Q; Q-->P |] ==> R |] ==> R"
  (fn prems => [ (resolve_tac [conjE] 1), (REPEAT (ares_tac prems 1)) ]);
 
 (* Destruct rules for <-> similar to Modus Ponens *)
 
-val iffD1 = prove_goalw IFOL.thy [iff_def] "[| P <-> Q;  P |] ==> Q"
+qed_goalw "iffD1" IFOL.thy [iff_def] "[| P <-> Q;  P |] ==> Q"
  (fn prems => [ (rtac (conjunct1 RS mp) 1), (REPEAT (ares_tac prems 1)) ]);
 
-val iffD2 = prove_goalw IFOL.thy [iff_def] "[| P <-> Q;  Q |] ==> P"
+qed_goalw "iffD2" IFOL.thy [iff_def] "[| P <-> Q;  Q |] ==> P"
  (fn prems => [ (rtac (conjunct2 RS mp) 1), (REPEAT (ares_tac prems 1)) ]);
 
-val iff_refl = prove_goal IFOL.thy "P <-> P"
+qed_goal "iff_refl" IFOL.thy "P <-> P"
  (fn _ => [ (REPEAT (ares_tac [iffI] 1)) ]);
 
-val iff_sym = prove_goal IFOL.thy "Q <-> P ==> P <-> Q"
+qed_goal "iff_sym" IFOL.thy "Q <-> P ==> P <-> Q"
  (fn [major] =>
   [ (rtac (major RS iffE) 1),
     (rtac iffI 1),
     (REPEAT (eresolve_tac [asm_rl,mp] 1)) ]);
 
-val iff_trans = prove_goal IFOL.thy
+qed_goal "iff_trans" IFOL.thy
     "!!P Q R. [| P <-> Q;  Q<-> R |] ==> P <-> R"
  (fn _ =>
   [ (rtac iffI 1),
@@ -177,17 +118,17 @@
  do NOT mean the same thing.  The parser treats EX!x y.P(x,y) as sequential.
 ***)
 
-val ex1I = prove_goalw IFOL.thy [ex1_def]
+qed_goalw "ex1I" IFOL.thy [ex1_def]
     "[| P(a);  !!x. P(x) ==> x=a |] ==> EX! x. P(x)"
  (fn prems => [ (REPEAT (ares_tac (prems@[exI,conjI,allI,impI]) 1)) ]);
 
 (*Sometimes easier to use: the premises have no shared variables*)
-val ex_ex1I = prove_goal IFOL.thy
+qed_goal "ex_ex1I" IFOL.thy
     "[| 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 ex1E = prove_goalw IFOL.thy [ex1_def]
+qed_goalw "ex1E" IFOL.thy [ex1_def]
     "[| EX! x.P(x);  !!x. [| P(x);  ALL y. P(y) --> y=x |] ==> R |] ==> R"
  (fn prems =>
   [ (cut_facts_tac prems 1),
@@ -201,7 +142,7 @@
     resolve_tac (prems RL [iffE]) i THEN
     REPEAT1 (eresolve_tac [asm_rl,mp] i);
 
-val conj_cong = prove_goal IFOL.thy 
+qed_goal "conj_cong" IFOL.thy 
     "[| P <-> P';  P' ==> Q <-> Q' |] ==> (P&Q) <-> (P'&Q')"
  (fn prems =>
   [ (cut_facts_tac prems 1),
@@ -209,7 +150,7 @@
       ORELSE  eresolve_tac [iffE,conjE,mp] 1
       ORELSE  iff_tac prems 1)) ]);
 
-val disj_cong = prove_goal IFOL.thy 
+qed_goal "disj_cong" IFOL.thy 
     "[| P <-> P';  Q <-> Q' |] ==> (P|Q) <-> (P'|Q')"
  (fn prems =>
   [ (cut_facts_tac prems 1),
@@ -217,7 +158,7 @@
       ORELSE  ares_tac [iffI] 1
       ORELSE  mp_tac 1)) ]);
 
-val imp_cong = prove_goal IFOL.thy 
+qed_goal "imp_cong" IFOL.thy 
     "[| P <-> P';  P' ==> Q <-> Q' |] ==> (P-->Q) <-> (P'-->Q')"
  (fn prems =>
   [ (cut_facts_tac prems 1),
@@ -225,7 +166,7 @@
       ORELSE  eresolve_tac [iffE] 1
       ORELSE  mp_tac 1 ORELSE iff_tac prems 1)) ]);
 
-val iff_cong = prove_goal IFOL.thy 
+qed_goal "iff_cong" IFOL.thy 
     "[| P <-> P';  Q <-> Q' |] ==> (P<->Q) <-> (P'<->Q')"
  (fn prems =>
   [ (cut_facts_tac prems 1),
@@ -233,7 +174,7 @@
       ORELSE  ares_tac [iffI] 1
       ORELSE  mp_tac 1)) ]);
 
-val not_cong = prove_goal IFOL.thy 
+qed_goal "not_cong" IFOL.thy 
     "P <-> P' ==> ~P <-> ~P'"
  (fn prems =>
   [ (cut_facts_tac prems 1),
@@ -241,21 +182,21 @@
       ORELSE  mp_tac 1
       ORELSE  eresolve_tac [iffE,notE] 1)) ]);
 
-val all_cong = prove_goal IFOL.thy 
+qed_goal "all_cong" IFOL.thy 
     "(!!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   eresolve_tac [allE] 1 ORELSE iff_tac prems 1)) ]);
 
-val ex_cong = prove_goal IFOL.thy 
+qed_goal "ex_cong" IFOL.thy 
     "(!!x.P(x) <-> Q(x)) ==> (EX x.P(x)) <-> (EX x.Q(x))"
  (fn prems =>
   [ (REPEAT   (eresolve_tac [exE] 1 ORELSE ares_tac [iffI,exI] 1
       ORELSE   mp_tac 1
       ORELSE   iff_tac prems 1)) ]);
 
-val ex1_cong = prove_goal IFOL.thy 
+qed_goal "ex1_cong" IFOL.thy 
     "(!!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
@@ -264,20 +205,20 @@
 
 (*** Equality rules ***)
 
-val sym = prove_goal IFOL.thy "a=b ==> b=a"
+qed_goal "sym" IFOL.thy "a=b ==> b=a"
  (fn [major] => [ (rtac (major RS subst) 1), (rtac refl 1) ]);
 
-val trans = prove_goal IFOL.thy "[| a=b;  b=c |] ==> a=c"
+qed_goal "trans" IFOL.thy "[| a=b;  b=c |] ==> a=c"
  (fn [prem1,prem2] => [ (rtac (prem2 RS subst) 1), (rtac prem1 1) ]);
 
 (** ~ b=a ==> ~ a=b **)
 val [not_sym] = compose(sym,2,contrapos);
 
 (*calling "standard" reduces maxidx to 0*)
-val ssubst = standard (sym RS subst);
+bind_thm ("ssubst", (sym RS subst));
 
 (*A special case of ex1E that would otherwise need quantifier expansion*)
-val ex1_equalsE = prove_goal IFOL.thy
+qed_goal "ex1_equalsE" IFOL.thy
     "[| EX! x.P(x);  P(a);  P(b) |] ==> a=b"
  (fn prems =>
   [ (cut_facts_tac prems 1),
@@ -288,18 +229,18 @@
 
 (** Polymorphic congruence rules **)
 
-val subst_context = prove_goal IFOL.thy 
+qed_goal "subst_context" IFOL.thy 
    "[| a=b |]  ==>  t(a)=t(b)"
  (fn prems=>
   [ (resolve_tac (prems RL [ssubst]) 1),
     (resolve_tac [refl] 1) ]);
 
-val subst_context2 = prove_goal IFOL.thy 
+qed_goal "subst_context2" IFOL.thy 
    "[| a=b;  c=d |]  ==>  t(a,c)=t(b,d)"
  (fn prems=>
   [ (EVERY1 (map rtac ((prems RL [ssubst]) @ [refl]))) ]);
 
-val subst_context3 = prove_goal IFOL.thy 
+qed_goal "subst_context3" IFOL.thy 
    "[| a=b;  c=d;  e=f |]  ==>  t(a,c,e)=t(b,d,f)"
  (fn prems=>
   [ (EVERY1 (map rtac ((prems RL [ssubst]) @ [refl]))) ]);
@@ -308,7 +249,7 @@
 	a = b
 	|   |
 	c = d	*)
-val box_equals = prove_goal IFOL.thy
+qed_goal "box_equals" IFOL.thy
     "[| a=b;  a=c;  b=d |] ==> c=d"  
  (fn prems=>
   [ (resolve_tac [trans] 1),
@@ -317,7 +258,7 @@
     (REPEAT (resolve_tac prems 1)) ]);
 
 (*Dual of box_equals: for proving equalities backwards*)
-val simp_equals = prove_goal IFOL.thy
+qed_goal "simp_equals" IFOL.thy
     "[| a=c;  b=d;  c=d |] ==> a=b"  
  (fn prems=>
   [ (resolve_tac [trans] 1),
@@ -326,21 +267,21 @@
 
 (** Congruence rules for predicate letters **)
 
-val pred1_cong = prove_goal IFOL.thy
+qed_goal "pred1_cong" IFOL.thy
     "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)) ]);
 
-val pred2_cong = prove_goal IFOL.thy
+qed_goal "pred2_cong" IFOL.thy
     "[| 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)) ]);
 
-val pred3_cong = prove_goal IFOL.thy
+qed_goal "pred3_cong" IFOL.thy
     "[| a=a';  b=b';  c=c' |] ==> P(a,b,c) <-> P(a',b',c')"
  (fn prems =>
   [ (cut_facts_tac prems 1),
@@ -366,50 +307,45 @@
    R. Dyckhoff, Contraction-free sequent calculi for intuitionistic logic
     (preprint, University of St Andrews, 1991)  ***)
 
-val conj_impE = prove_goal IFOL.thy 
+qed_goal "conj_impE" IFOL.thy 
     "[| (P&Q)-->S;  P-->(Q-->S) ==> R |] ==> R"
  (fn major::prems=>
   [ (REPEAT (ares_tac ([conjI, impI, major RS mp]@prems) 1)) ]);
 
-val disj_impE = prove_goal IFOL.thy 
+qed_goal "disj_impE" IFOL.thy 
     "[| (P|Q)-->S;  [| P-->S; Q-->S |] ==> R |] ==> R"
  (fn major::prems=>
   [ (DEPTH_SOLVE (ares_tac ([disjI1, disjI2, impI, major RS mp]@prems) 1)) ]);
 
 (*Simplifies the implication.  Classical version is stronger. 
   Still UNSAFE since Q must be provable -- backtracking needed.  *)
-val imp_impE = prove_goal IFOL.thy 
+qed_goal "imp_impE" IFOL.thy 
     "[| (P-->Q)-->S;  [| P; Q-->S |] ==> Q;  S ==> R |] ==> R"
  (fn major::prems=>
   [ (REPEAT (ares_tac ([impI, major RS mp]@prems) 1)) ]);
 
 (*Simplifies the implication.  Classical version is stronger. 
   Still UNSAFE since ~P must be provable -- backtracking needed.  *)
-val not_impE = prove_goal IFOL.thy
+qed_goal "not_impE" IFOL.thy
     "[| ~P --> S;  P ==> False;  S ==> R |] ==> R"
  (fn major::prems=>
   [ (REPEAT (ares_tac ([notI, impI, major RS mp]@prems) 1)) ]);
 
 (*Simplifies the implication.   UNSAFE.  *)
-val iff_impE = prove_goal IFOL.thy 
+qed_goal "iff_impE" IFOL.thy 
     "[| (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)) ]);
 
 (*What if (ALL x.~~P(x)) --> ~~(ALL x.P(x)) is an assumption? UNSAFE*)
-val all_impE = prove_goal IFOL.thy 
+qed_goal "all_impE" IFOL.thy 
     "[| (ALL x.P(x))-->S;  !!x.P(x);  S ==> R |] ==> R"
  (fn major::prems=>
   [ (REPEAT (ares_tac ([allI, impI, major RS mp]@prems) 1)) ]);
 
 (*Unsafe: (EX x.P(x))-->S  is equivalent to  ALL x.P(x)-->S.  *)
-val ex_impE = prove_goal IFOL.thy 
+qed_goal "ex_impE" IFOL.thy 
     "[| (EX x.P(x))-->S;  P(x)-->S ==> R |] ==> R"
  (fn major::prems=>
   [ (REPEAT (ares_tac ([exI, impI, major RS mp]@prems) 1)) ]);
-
-end;
-
-open IFOL_Lemmas;
-