--- a/src/FOL/IFOL.ML Fri Oct 10 15:51:38 1997 +0200
+++ b/src/FOL/IFOL.ML Fri Oct 10 15:52:12 1997 +0200
@@ -26,12 +26,12 @@
(fn prems=> [ (REPEAT (resolve_tac (prems@[mp]) 1)) ]);
qed_goal "allE" IFOL.thy
- "[| ALL x.P(x); P(x) ==> R |] ==> R"
+ "[| ALL x. P(x); P(x) ==> R |] ==> R"
(fn prems=> [ (REPEAT (resolve_tac (prems@[spec]) 1)) ]);
(*Duplicates the quantifier; for use with eresolve_tac*)
qed_goal "all_dupE" IFOL.thy
- "[| ALL x.P(x); [| P(x); ALL x.P(x) |] ==> R \
+ "[| ALL x. P(x); [| P(x); ALL x. P(x) |] ==> R \
\ |] ==> R"
(fn prems=> [ (REPEAT (resolve_tac (prems@[spec]) 1)) ]);
@@ -126,12 +126,12 @@
(*Sometimes easier to use: the premises have no shared variables. Safe!*)
qed_goal "ex_ex1I" IFOL.thy
- "[| EX x.P(x); !!x y. [| P(x); P(y) |] ==> x=y |] ==> EX! x. P(x)"
+ "[| 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)) ]);
qed_goalw "ex1E" IFOL.thy [ex1_def]
- "[| EX! x.P(x); !!x. [| P(x); ALL y. P(y) --> y=x |] ==> R |] ==> R"
+ "[| 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)) ]);
@@ -194,21 +194,21 @@
ORELSE eresolve_tac [iffE,notE] 1)) ]);
qed_goal "all_cong" IFOL.thy
- "(!!x.P(x) <-> Q(x)) ==> (ALL x.P(x)) <-> (ALL x.Q(x))"
+ "(!!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)) ]);
qed_goal "ex_cong" IFOL.thy
- "(!!x.P(x) <-> Q(x)) ==> (EX x.P(x)) <-> (EX x.Q(x))"
+ "(!!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)) ]);
qed_goal "ex1_cong" IFOL.thy
- "(!!x.P(x) <-> Q(x)) ==> (EX! x.P(x)) <-> (EX! x.Q(x))"
+ "(!!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
@@ -231,7 +231,7 @@
(*A special case of ex1E that would otherwise need quantifier expansion*)
qed_goal "ex1_equalsE" IFOL.thy
- "[| EX! x.P(x); P(a); P(b) |] ==> a=b"
+ "[| EX! x. P(x); P(a); P(b) |] ==> a=b"
(fn prems =>
[ (cut_facts_tac prems 1),
(etac ex1E 1),
@@ -352,13 +352,13 @@
(*What if (ALL x.~~P(x)) --> ~~(ALL x.P(x)) is an assumption? UNSAFE*)
qed_goal "all_impE" IFOL.thy
- "[| (ALL x.P(x))-->S; !!x.P(x); S ==> R |] ==> R"
+ "[| (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. *)
qed_goal "ex_impE" IFOL.thy
- "[| (EX x.P(x))-->S; P(x)-->S ==> R |] ==> R"
+ "[| (EX x. P(x))-->S; P(x)-->S ==> R |] ==> R"
(fn major::prems=>
[ (REPEAT (ares_tac ([exI, impI, major RS mp]@prems) 1)) ]);