
diff -r 000000000000 -r a5a9c433f639 src/CCL/Set.thy
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/src/CCL/Set.thy	Thu Sep 16 12:20:38 1993 +0200
@@ -0,0 +1,71 @@
+(*  Title:      CCL/set.thy
+    ID:         $Id$
+
+Modified version of HOL/set.thy that extends FOL
+
+*)
+
+Set = FOL +
+
+types
+  set 1
+
+arities
+  set :: (term) term
+
+consts
+  Collect       :: "['a => o] => 'a set"                    (*comprehension*)
+  Compl         :: "('a set) => 'a set"                     (*complement*)
+  Int           :: "['a set, 'a set] => 'a set"         (infixl 70)
+  Un            :: "['a set, 'a set] => 'a set"         (infixl 65)
+  Union, Inter  :: "(('a set)set) => 'a set"                (*...of a set*)
+  UNION, INTER  :: "['a set, 'a => 'b set] => 'b set"       (*general*)
+  Ball, Bex     :: "['a set, 'a => o] => o"                 (*bounded quants*)
+  mono          :: "['a set => 'b set] => o"                (*monotonicity*)
+  ":"           :: "['a, 'a set] => o"                  (infixl 50) (*membership*)
+  "<="          :: "['a set, 'a set] => o"              (infixl 50)
+  singleton     :: "'a => 'a set"                       ("{_}")
+  empty         :: "'a set"                             ("{}")
+  "oo"          :: "['b => 'c, 'a => 'b, 'a] => 'c"     (infixr 50) (*composition*)
+
+  "@Coll"       :: "[idt, o] => 'a set"                 ("(1{_./ _})") (*collection*)
+
+  (* Big Intersection / Union *)
+
+  "@INTER"      :: "[idt, 'a set, 'b set] => 'b set"    ("(INT _:_./ _)" [0, 0, 0] 10)
+  "@UNION"      :: "[idt, 'a set, 'b set] => 'b set"    ("(UN _:_./ _)" [0, 0, 0] 10)
+
+  (* Bounded Quantifiers *)
+
+  "@Ball"       :: "[idt, 'a set, o] => o"              ("(ALL _:_./ _)" [0, 0, 0] 10)
+  "@Bex"        :: "[idt, 'a set, o] => o"              ("(EX _:_./ _)" [0, 0, 0] 10)
+
+
+translations
+  "{x. P}"      == "Collect(%x. P)"
+  "INT x:A. B"  == "INTER(A, %x. B)"
+  "UN x:A. B"   == "UNION(A, %x. B)"
+  "ALL x:A. P"  == "Ball(A, %x. P)"
+  "EX x:A. P"   == "Bex(A, %x. P)"
+
+
+rules
+  mem_Collect_iff       "(a : {x.P(x)}) <-> P(a)"
+  set_extension         "A=B <-> (ALL x.x:A <-> x:B)"
+
+  Ball_def      "Ball(A, P)  == ALL x. x:A --> P(x)"
+  Bex_def       "Bex(A, P)   == EX x. x:A & P(x)"
+  mono_def      "mono(f)     == (ALL A B. A <= B --> f(A) <= f(B))"
+  subset_def    "A <= B      == ALL x:A. x:B"
+  singleton_def "{a}         == {x.x=a}"
+  empty_def     "{}          == {x.False}"
+  Un_def        "A Un B      == {x.x:A | x:B}"
+  Int_def       "A Int B     == {x.x:A & x:B}"
+  Compl_def     "Compl(A)    == {x. ~x:A}"
+  INTER_def     "INTER(A, B) == {y. ALL x:A. y: B(x)}"
+  UNION_def     "UNION(A, B) == {y. EX x:A. y: B(x)}"
+  Inter_def     "Inter(S)    == (INT x:S. x)"
+  Union_def     "Union(S)    == (UN x:S. x)"
+
+end
+




