--- a/src/HOL/Induct/Multiset.thy Mon May 22 12:30:07 2000 +0200
+++ b/src/HOL/Induct/Multiset.thy Mon May 22 12:30:40 2000 +0200
@@ -23,9 +23,10 @@
set_of :: 'a multiset => 'a set
syntax
- elem :: ['a multiset, 'a] => bool
+ elem :: ['a multiset, 'a] => bool ("(_/ :# _)" [50, 51] 50)
+
translations
- "elem M a" == "0 < count M a"
+ "M :# a" == "0 < count M a"
defs
count_def "count == Rep_multiset"
@@ -33,13 +34,13 @@
single_def "{#a#} == Abs_multiset(%b. if b=a then 1 else 0)"
union_def "M+N == Abs_multiset(%a. Rep_multiset M a + Rep_multiset N a)"
diff_def "M-N == Abs_multiset(%a. Rep_multiset M a - Rep_multiset N a)"
- set_of_def "set_of M == {x. elem M x}"
+ set_of_def "set_of M == {x. M :# x}"
size_def "size (M) == setsum (count M) (set_of M)"
constdefs
mult1 :: "('a * 'a)set => ('a multiset * 'a multiset)set"
"mult1(r) == {(N,M) . ? a M0 K. M = M0 + {#a#} & N = M0 + K &
- (!b. elem K b --> (b,a) : r)}"
+ (!b. K :# b --> (b,a) : r)}"
mult :: "('a * 'a)set => ('a multiset * 'a multiset)set"
"mult(r) == (mult1 r)^+"
@@ -51,4 +52,9 @@
defines
W_def "W == acc(mult1 r)"
+
+defs
+ mult_less_def "M' < M == (M',M) : mult {(x',x). x'<x}"
+ mult_le_def "M' <= M == M'=M | M' < (M :: 'a multiset)"
+
end