OpenMath Content Dictionary: multiset1
Canonical URL:
http://www.openmath.org/cd/multiset1.ocd
CD Base:
http://www.openmath.org/cd
CD File:
multiset1.ocd
CD as XML Encoded OpenMath:
multiset1.omcd
Defines:
cartesian_product , emptyset , in , intersect , multiset , notin , notprsubset , notsubset , prsubset , setdiff , size , subset , union
Date:
2004-03-30
Version:
3
(Revision 1)
Review Date:
2006-03-30
Status:
official
This document is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.
The copyright holder grants you permission to redistribute this
document freely as a verbatim copy. Furthermore, the copyright
holder permits you to develop any derived work from this document
provided that the following conditions are met.
a) The derived work acknowledges the fact that it is derived from
this document, and maintains a prominent reference in the
work to the original source.
b) The fact that the derived work is not the original OpenMath
document is stated prominently in the derived work. Moreover if
both this document and the derived work are Content Dictionaries
then the derived work must include a different CDName element,
chosen so that it cannot be confused with any works adopted by
the OpenMath Society. In particular, if there is a Content
Dictionary Group whose name is, for example, `math' containing
Content Dictionaries named `math1', `math2' etc., then you should
not name a derived Content Dictionary `mathN' where N is an integer.
However you are free to name it `private_mathN' or some such. This
is because the names `mathN' may be used by the OpenMath Society
for future extensions.
c) The derived work is distributed under terms that allow the
compilation of derived works, but keep paragraphs a) and b)
intact. The simplest way to do this is to distribute the derived
work under the OpenMath license, but this is not a requirement.
If you have questions about this license please contact the OpenMath
society at http://www.openmath.org .
Author: OpenMath Consortium
SourceURL: https://github.com/OpenMath/CDs
This CD defines the set functions and constructors for basic
multiset theory. It is intended to be `compatible' with the
corresponding elements in MathML i.e. set operations acting
on sets of type=multiset.
Based on set1.ocd
Role:
application
Description:
This symbol is used to denote the number of elements in a multiset. It is
either a non-negative integer, or an infinite cardinal number. The
symbol infinity may be used for an unspecified infinite cardinal.
Example:
The size of the multiset{3,3,9} = 3
OpenMath XML (source)
<OMOBJ xmlns="http://www.openmath.org/OpenMath" version="2.0" cdbase="http://www.openmath.org/cd">
<OMA>
<OMS cd="relation1" name="eq"/>
<OMA>
<OMS cd="multiset1" name="size"/>
<OMA>
<OMS cd="multiset1" name="multiset"/>
<OMI> 3 </OMI>
<OMI> 3 </OMI>
<OMI> 9 </OMI>
</OMA>
</OMA>
<OMI> 3 </OMI>
</OMA>
</OMOBJ>
Strict Content MathML
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply><csymbol cd="relation1">eq</csymbol>
<apply><csymbol cd="multiset1">size</csymbol>
<apply><csymbol cd="multiset1">multiset</csymbol>
<cn type="integer">3</cn>
<cn type="integer">3</cn>
<cn type="integer">9</cn>
</apply>
</apply>
<cn type="integer">3</cn>
</apply>
</math>
Prefix
Popcorn
multiset1.size(multiset1.multiset(3, 3, 9)) = 3
Rendered Presentation MathML
size
(
multiset
(
3
,
3
,
9
)
)
=
3
Signatures:
sts
Role:
application
Description:
This symbol represents an n-ary construction function for constructing
the Cartesian product of multisets. It takes n multiset arguments in order to
construct their Cartesian product.
Example:
An example to show the representation of the Cartesian product of
multisets: AxBxC.
OpenMath XML (source)
<OMOBJ xmlns="http://www.openmath.org/OpenMath" version="2.0" cdbase="http://www.openmath.org/cd">
<OMA>
<OMS cd="multiset1" name="cartesian_product"/>
<OMV name="A"/>
<OMV name="B"/>
<OMV name="C"/>
</OMA>
</OMOBJ>
Strict Content MathML
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply><csymbol cd="multiset1">cartesian_product</csymbol><ci>A</ci><ci>B</ci><ci>C</ci></apply>
</math>
Prefix
Popcorn
multiset1.cartesian_product($A, $B, $C)
Rendered Presentation MathML
Signatures:
sts
Role:
constant
Description:
This symbol is used to represent the empty multiset, that is the multiset which
contains no members. It takes no parameters.
Commented Mathematical property (CMP):
The intersection of A with the empty (multi) set is the empty
(multi) set
Formal Mathematical property (FMP):
OpenMath XML (source)
<OMOBJ xmlns="http://www.openmath.org/OpenMath" version="2.0" cdbase="http://www.openmath.org/cd">
<OMA>
<OMS cd="relation1" name="eq"/>
<OMA>
<OMS cd="multiset1" name="intersect"/>
<OMV name="A"/>
<OMS cd="multiset1" name="emptyset"/>
</OMA>
<OMS cd="multiset1" name="emptyset"/>
</OMA>
</OMOBJ>
Strict Content MathML
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply><csymbol cd="relation1">eq</csymbol>
<apply><csymbol cd="multiset1">intersect</csymbol><ci>A</ci><csymbol cd="multiset1">emptyset</csymbol></apply>
<csymbol cd="multiset1">emptyset</csymbol>
</apply>
</math>
Prefix
Popcorn
multiset1.intersect($A, multiset1.emptyset) = multiset1.emptyset
Rendered Presentation MathML
Commented Mathematical property (CMP):
The union of A with the empty (multi) set is A
Formal Mathematical property (FMP):
OpenMath XML (source)
<OMOBJ xmlns="http://www.openmath.org/OpenMath" version="2.0" cdbase="http://www.openmath.org/cd">
<OMA>
<OMS cd="relation1" name="eq"/>
<OMA>
<OMS cd="multiset1" name="union"/>
<OMV name="A"/>
<OMS cd="multiset1" name="emptyset"/>
</OMA>
<OMV name="A"/>
</OMA>
</OMOBJ>
Strict Content MathML
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply><csymbol cd="relation1">eq</csymbol>
<apply><csymbol cd="multiset1">union</csymbol><ci>A</ci><csymbol cd="multiset1">emptyset</csymbol></apply>
<ci>A</ci>
</apply>
</math>
Prefix
Popcorn
multiset1.union($A, multiset1.emptyset) = $A
Rendered Presentation MathML
Signatures:
sts
Role:
application
Description:
This symbol represents the multiset construct. It is either an
n-ary function, in which case the multiset entries are given
explicitly, or it works on an elements construct. There is no
implied ordering to the elements of a multiset.
Example:
The multiset {4, 1, 0, 1 4}
OpenMath XML (source)
<OMOBJ xmlns="http://www.openmath.org/OpenMath" version="2.0" cdbase="http://www.openmath.org/cd">
<OMA>
<OMS cd="multiset1" name="multiset"/>
<OMI> 4 </OMI>
<OMI> 1 </OMI>
<OMI> 0 </OMI>
<OMI> 1 </OMI>
<OMI> 4 </OMI>
</OMA>
</OMOBJ>
Strict Content MathML
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply><csymbol cd="multiset1">multiset</csymbol>
<cn type="integer">4</cn>
<cn type="integer">1</cn>
<cn type="integer">0</cn>
<cn type="integer">1</cn>
<cn type="integer">4</cn>
</apply>
</math>
Prefix
Popcorn
multiset1.multiset(4, 1, 0, 1, 4)
Rendered Presentation MathML
multiset
(
4
,
1
,
0
,
1
,
4
)
Signatures:
sts
Role:
application
Description:
This symbol is used to denote the n-ary intersection of
multisets. It takes multisets as arguments, and denotes the
multiset that contains all the elements that occur in all of
them, with multiplicity the minimum of their multiplicities
in all multisets.
Commented Mathematical property (CMP):
(A intersect B) is a subset of A and
(A intersect B) is a subset of B
Formal Mathematical property (FMP):
OpenMath XML (source)
<OMOBJ xmlns="http://www.openmath.org/OpenMath" version="2.0" cdbase="http://www.openmath.org/cd">
<OMA>
<OMS cd="logic1" name="and"/>
<OMA>
<OMS cd="multiset1" name="subset"/>
<OMA>
<OMS cd="multiset1" name="intersect"/>
<OMV name="A"/>
<OMV name="B"/>
</OMA>
<OMV name="A"/>
</OMA>
<OMA>
<OMS cd="multiset1" name="subset"/>
<OMA>
<OMS cd="multiset1" name="intersect"/>
<OMV name="A"/>
<OMV name="B"/>
</OMA>
<OMV name="B"/>
</OMA>
</OMA>
</OMOBJ>
Strict Content MathML
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply><csymbol cd="logic1">and</csymbol>
<apply><csymbol cd="multiset1">subset</csymbol>
<apply><csymbol cd="multiset1">intersect</csymbol><ci>A</ci><ci>B</ci></apply>
<ci>A</ci>
</apply>
<apply><csymbol cd="multiset1">subset</csymbol>
<apply><csymbol cd="multiset1">intersect</csymbol><ci>A</ci><ci>B</ci></apply>
<ci>B</ci>
</apply>
</apply>
</math>
Prefix
Popcorn
multiset1.subset(multiset1.intersect($A, $B), $A) and multiset1.subset(multiset1.intersect($A, $B), $B)
Rendered Presentation MathML
Signatures:
sts
Role:
application
Description:
This symbol is used to denote the n-ary union of multisets. It
takes multisets as arguments, and denotes the multiset that
contains all the elements that occur in any of them, with
multiplicity the sum of all the multiplicities in the multiset
arguments.
Commented Mathematical property (CMP):
A is a subset of (A union B) and B is a subset of (A union B)
Formal Mathematical property (FMP):
OpenMath XML (source)
<OMOBJ xmlns="http://www.openmath.org/OpenMath" version="2.0" cdbase="http://www.openmath.org/cd">
<OMA>
<OMS cd="logic1" name="and"/>
<OMA>
<OMS cd="multiset1" name="subset"/>
<OMV name="A"/>
<OMA>
<OMS cd="multiset1" name="union"/>
<OMV name="A"/>
<OMV name="B"/>
</OMA>
</OMA>
<OMA>
<OMS cd="multiset1" name="subset"/>
<OMV name="B"/>
<OMA>
<OMS cd="multiset1" name="union"/>
<OMV name="A"/>
<OMV name="B"/>
</OMA>
</OMA>
</OMA>
</OMOBJ>
Strict Content MathML
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply><csymbol cd="logic1">and</csymbol>
<apply><csymbol cd="multiset1">subset</csymbol>
<ci>A</ci>
<apply><csymbol cd="multiset1">union</csymbol><ci>A</ci><ci>B</ci></apply>
</apply>
<apply><csymbol cd="multiset1">subset</csymbol>
<ci>B</ci>
<apply><csymbol cd="multiset1">union</csymbol><ci>A</ci><ci>B</ci></apply>
</apply>
</apply>
</math>
Prefix
Popcorn
multiset1.subset($A, multiset1.union($A, $B)) and multiset1.subset($B, multiset1.union($A, $B))
Rendered Presentation MathML
Commented Mathematical property (CMP):
for all sets A,B and C
union(A,intersect(B,C)) = intersect(union(A,B),union(A,C))
Formal Mathematical property (FMP):
OpenMath XML (source)
<OMOBJ xmlns="http://www.openmath.org/OpenMath" version="2.0" cdbase="http://www.openmath.org/cd">
<OMBIND>
<OMS cd="quant1" name="forall"/>
<OMBVAR>
<OMV name="A"/>
<OMV name="B"/>
<OMV name="C"/>
</OMBVAR>
<OMA>
<OMS cd="relation1" name="eq"/>
<OMA>
<OMS cd="multiset1" name="union"/>
<OMV name="A"/>
<OMA>
<OMS cd="multiset1" name="intersect"/>
<OMV name="B"/>
<OMV name="C"/>
</OMA>
</OMA>
<OMA>
<OMS cd="multiset1" name="intersect"/>
<OMA>
<OMS cd="multiset1" name="union"/>
<OMV name="A"/>
<OMV name="B"/>
</OMA>
<OMA>
<OMS cd="multiset1" name="union"/>
<OMV name="A"/>
<OMV name="C"/>
</OMA>
</OMA>
</OMA>
</OMBIND>
</OMOBJ>
Strict Content MathML
<math xmlns="http://www.w3.org/1998/Math/MathML">
<bind><csymbol cd="quant1">forall</csymbol>
<bvar><ci>A</ci></bvar>
<bvar><ci>B</ci></bvar>
<bvar><ci>C</ci></bvar>
<apply><csymbol cd="relation1">eq</csymbol>
<apply><csymbol cd="multiset1">union</csymbol>
<ci>A</ci>
<apply><csymbol cd="multiset1">intersect</csymbol><ci>B</ci><ci>C</ci></apply>
</apply>
<apply><csymbol cd="multiset1">intersect</csymbol>
<apply><csymbol cd="multiset1">union</csymbol><ci>A</ci><ci>B</ci></apply>
<apply><csymbol cd="multiset1">union</csymbol><ci>A</ci><ci>C</ci></apply>
</apply>
</apply>
</bind>
</math>
Prefix
Popcorn
quant1.forall[$A, $B, $C -> multiset1.union($A, multiset1.intersect($B, $C)) = multiset1.intersect(multiset1.union($A, $B), multiset1.union($A, $C))]
Rendered Presentation MathML
∀
A
,
B
,
C
.
A
∪
B
∩
C
=
A
∪
B
∩
A
∪
C
Signatures:
sts
Role:
application
Description:
This symbol is used to denote the multiset difference of two
multisets. It takes two multisets as arguments, and denotes the
multiset that contains all the elements that occur in the first
multiset with strictly greater multiplicity than in the second.
The multiplicity in the result is the difference of the two.
Commented Mathematical property (CMP):
the difference of A and B is a subset of A
Formal Mathematical property (FMP):
OpenMath XML (source)
<OMOBJ xmlns="http://www.openmath.org/OpenMath" version="2.0" cdbase="http://www.openmath.org/cd">
<OMA>
<OMS cd="multiset1" name="subset"/>
<OMA>
<OMS cd="multiset1" name="setdiff"/>
<OMV name="A"/>
<OMV name="B"/>
</OMA>
<OMV name="A"/>
</OMA>
</OMOBJ>
Strict Content MathML
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply><csymbol cd="multiset1">subset</csymbol>
<apply><csymbol cd="multiset1">setdiff</csymbol><ci>A</ci><ci>B</ci></apply>
<ci>A</ci>
</apply>
</math>
Prefix
Popcorn
multiset1.subset(multiset1.setdiff($A, $B), $A)
Rendered Presentation MathML
Signatures:
sts
Role:
application
Description:
This symbol has two (multiset) arguments. It is used to denote
that the first set is a subset of the second, i.e. every element
of the first occurs with multiplicity at least as much in the
second.
Commented Mathematical property (CMP):
if B is a subset of A and C is a subset of B
then C is a subset of A
Formal Mathematical property (FMP):
OpenMath XML (source)
<OMOBJ xmlns="http://www.openmath.org/OpenMath" version="2.0" cdbase="http://www.openmath.org/cd">
<OMA>
<OMS cd="logic1" name="implies"/>
<OMA>
<OMS cd="logic1" name="and"/>
<OMA>
<OMS cd="multiset1" name="subset"/>
<OMV name="B"/>
<OMV name="A"/>
</OMA>
<OMA>
<OMS cd="multiset1" name="subset"/>
<OMV name="C"/>
<OMV name="B"/>
</OMA>
</OMA>
<OMA>
<OMS cd="multiset1" name="subset"/>
<OMV name="C"/>
<OMV name="A"/>
</OMA>
</OMA>
</OMOBJ>
Strict Content MathML
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply><csymbol cd="logic1">implies</csymbol>
<apply><csymbol cd="logic1">and</csymbol>
<apply><csymbol cd="multiset1">subset</csymbol><ci>B</ci><ci>A</ci></apply>
<apply><csymbol cd="multiset1">subset</csymbol><ci>C</ci><ci>B</ci></apply>
</apply>
<apply><csymbol cd="multiset1">subset</csymbol><ci>C</ci><ci>A</ci></apply>
</apply>
</math>
Prefix
Popcorn
multiset1.subset($B, $A) and multiset1.subset($C, $B) ==> multiset1.subset($C, $A)
Rendered Presentation MathML
Signatures:
sts
Role:
application
Description:
This symbol has two arguments, an element and a multiset. It is
used to denote that the element is in the given multiset.
Commented Mathematical property (CMP):
if a is in A and a is in B then a is in A intersection B
Formal Mathematical property (FMP):
OpenMath XML (source)
<OMOBJ xmlns="http://www.openmath.org/OpenMath" version="2.0" cdbase="http://www.openmath.org/cd">
<OMA>
<OMS cd="logic1" name="implies"/>
<OMA>
<OMS cd="logic1" name="and"/>
<OMA>
<OMS cd="multiset1" name="in"/>
<OMV name="a"/>
<OMV name="A"/>
</OMA>
<OMA>
<OMS cd="multiset1" name="in"/>
<OMV name="a"/>
<OMV name="B"/>
</OMA>
</OMA>
<OMA>
<OMS cd="multiset1" name="in"/>
<OMV name="a"/>
<OMA>
<OMS cd="multiset1" name="intersect"/>
<OMV name="A"/>
<OMV name="B"/>
</OMA>
</OMA>
</OMA>
</OMOBJ>
Strict Content MathML
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply><csymbol cd="logic1">implies</csymbol>
<apply><csymbol cd="logic1">and</csymbol>
<apply><csymbol cd="multiset1">in</csymbol><ci>a</ci><ci>A</ci></apply>
<apply><csymbol cd="multiset1">in</csymbol><ci>a</ci><ci>B</ci></apply>
</apply>
<apply><csymbol cd="multiset1">in</csymbol>
<ci>a</ci>
<apply><csymbol cd="multiset1">intersect</csymbol><ci>A</ci><ci>B</ci></apply>
</apply>
</apply>
</math>
Prefix
Popcorn
multiset1.in($a, $A) and multiset1.in($a, $B) ==> multiset1.in($a, multiset1.intersect($A, $B))
Rendered Presentation MathML
a
∈
A
∧
a
∈
B
⇒
a
∈
A
∩
B
Signatures:
sts
Role:
application
Description:
This symbol has two arguments, an element and a multiset. It is
used to denote that the element is not in the given multiset.
Example:
4 is not in {1,1,2,3}
OpenMath XML (source)
<OMOBJ xmlns="http://www.openmath.org/OpenMath" version="2.0" cdbase="http://www.openmath.org/cd">
<OMA>
<OMS cd="multiset1" name="notin"/>
<OMI> 4 </OMI>
<OMA>
<OMS cd="multiset1" name="multiset"/>
<OMI> 1 </OMI>
<OMI> 1 </OMI>
<OMI> 2 </OMI>
<OMI> 3 </OMI>
</OMA>
</OMA>
</OMOBJ>
Strict Content MathML
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply><csymbol cd="multiset1">notin</csymbol>
<cn type="integer">4</cn>
<apply><csymbol cd="multiset1">multiset</csymbol>
<cn type="integer">1</cn>
<cn type="integer">1</cn>
<cn type="integer">2</cn>
<cn type="integer">3</cn>
</apply>
</apply>
</math>
Prefix
Popcorn
multiset1.notin(4, multiset1.multiset(1, 1, 2, 3))
Rendered Presentation MathML
4
∉
multiset
(
1
,
1
,
2
,
3
)
Signatures:
sts
Role:
application
Description:
This symbol has two (multiset) arguments. It is used to denote
that the first multiset is a proper subset of the second, that is
a subset of the second multiset but not actually equal to it.
Example:
{2,3} is a proper subset of {2,2,3}
OpenMath XML (source)
<OMOBJ xmlns="http://www.openmath.org/OpenMath" version="2.0" cdbase="http://www.openmath.org/cd">
<OMA>
<OMS cd="multiset1" name="prsubset"/>
<OMA>
<OMS cd="multiset1" name="multiset"/>
<OMI> 2 </OMI>
<OMI> 3 </OMI>
</OMA>
<OMA>
<OMS cd="multiset1" name="multiset"/>
<OMI> 2 </OMI>
<OMI> 2 </OMI>
<OMI> 3 </OMI>
</OMA>
</OMA>
</OMOBJ>
Strict Content MathML
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply><csymbol cd="multiset1">prsubset</csymbol>
<apply><csymbol cd="multiset1">multiset</csymbol>
<cn type="integer">2</cn>
<cn type="integer">3</cn>
</apply>
<apply><csymbol cd="multiset1">multiset</csymbol>
<cn type="integer">2</cn>
<cn type="integer">2</cn>
<cn type="integer">3</cn>
</apply>
</apply>
</math>
Prefix
Popcorn
multiset1.prsubset(multiset1.multiset(2, 3), multiset1.multiset(2, 2, 3))
Rendered Presentation MathML
multiset
(
2
,
3
)
⊂
multiset
(
2
,
2
,
3
)
Signatures:
sts
Role:
application
Description:
This symbol has two (multiset) arguments. It is used to denote
that the first multiset is not a subset of the second.
Example:
{2,3,3} is not a subset of {1,2,3}
OpenMath XML (source)
<OMOBJ xmlns="http://www.openmath.org/OpenMath" version="2.0" cdbase="http://www.openmath.org/cd">
<OMA>
<OMS cd="multiset1" name="notsubset"/>
<OMA>
<OMS cd="multiset1" name="multiset"/>
<OMI> 2 </OMI>
<OMI> 3 </OMI>
<OMI> 3 </OMI>
</OMA>
<OMA>
<OMS cd="multiset1" name="multiset"/>
<OMI> 1 </OMI>
<OMI> 2 </OMI>
<OMI> 3 </OMI>
</OMA>
</OMA>
</OMOBJ>
Strict Content MathML
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply><csymbol cd="multiset1">notsubset</csymbol>
<apply><csymbol cd="multiset1">multiset</csymbol>
<cn type="integer">2</cn>
<cn type="integer">3</cn>
<cn type="integer">3</cn>
</apply>
<apply><csymbol cd="multiset1">multiset</csymbol>
<cn type="integer">1</cn>
<cn type="integer">2</cn>
<cn type="integer">3</cn>
</apply>
</apply>
</math>
Prefix
Popcorn
multiset1.notsubset(multiset1.multiset(2, 3, 3), multiset1.multiset(1, 2, 3))
Rendered Presentation MathML
multiset
(
2
,
3
,
3
)
⊄
multiset
(
1
,
2
,
3
)
Signatures:
sts
Role:
application
Description:
This symbol has two (multiset) arguments. It is used to denote
that the first multiset is not a proper subset of the second. A
proper subset of a multiset is a subset of the multiset but not
actually equal to it.
Example:
{1,2,1} is not a proper subset of {1,2,1}
OpenMath XML (source)
<OMOBJ xmlns="http://www.openmath.org/OpenMath" version="2.0" cdbase="http://www.openmath.org/cd">
<OMA>
<OMS cd="multiset1" name="notprsubset"/>
<OMA>
<OMS cd="multiset1" name="multiset"/>
<OMI> 1 </OMI>
<OMI> 2 </OMI>
<OMI> 1 </OMI>
</OMA>
<OMA>
<OMS cd="multiset1" name="multiset"/>
<OMI> 1 </OMI>
<OMI> 2 </OMI>
<OMI> 1 </OMI>
</OMA>
</OMA>
</OMOBJ>
Strict Content MathML
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply><csymbol cd="multiset1">notprsubset</csymbol>
<apply><csymbol cd="multiset1">multiset</csymbol>
<cn type="integer">1</cn>
<cn type="integer">2</cn>
<cn type="integer">1</cn>
</apply>
<apply><csymbol cd="multiset1">multiset</csymbol>
<cn type="integer">1</cn>
<cn type="integer">2</cn>
<cn type="integer">1</cn>
</apply>
</apply>
</math>
Prefix
Popcorn
multiset1.notprsubset(multiset1.multiset(1, 2, 1), multiset1.multiset(1, 2, 1))
Rendered Presentation MathML
multiset
(
1
,
2
,
1
)
⊄
multiset
(
1
,
2
,
1
)
Signatures:
sts