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<b>let </b><font color="Maroon">c<sub>1</sub></font>, <font color="Maroon">c<sub>2</sub></font> be    <a href="hidden.html#M1">set</a> ;<br/>



<a NAME="E1:48"/><i><font color="Green">E26</font></i>: 
( <font color="Maroon">c<sub>1</sub></font> is   <a href="monoid_1.html#NM2">Multiset</a> of <font color="Maroon">c<sub>2</sub></font> iff <font color="Maroon">c<sub>1</sub></font> is    <a href="fraenkel.html#M2">Element</a> of  <a href="fraenkel.html#K1">Funcs</a> <font color="Maroon">c<sub>2</sub></font>,<a href="numbers.html#K5">NAT</a>  )
 
<b>by </b><i><a class="ref" href="monoid_1.html#T27" target="_self">Th27</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="48_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c<sub>3</sub></font> be   <a href="funct_2.html#NM1">Function</a> of <font color="Maroon">c<sub>2</sub></font>, <a href="numbers.html#K5">NAT</a> ;<br/><a NAME="E1:48_1"/>
(  <a href="relset_1.html#K4">dom</a> <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>2</sub></font> &amp;  <a href="relset_1.html#K5">rng</a> <font color="Maroon">c<sub>3</sub></font> <a href="tarski.html#R1">c=</a>  <a href="numbers.html#K5">NAT</a>  )
 <b>by </b><i><a class="ref" href="funct_2.html#D1">FUNCT_2:def 1</a></i>;<br/><b>hence </b><a NAME="E2:48_1"/>
<font color="Maroon">c<sub>3</sub></font> is    <a href="fraenkel.html#M2">Element</a> of  <a href="fraenkel.html#K1">Funcs</a> <font color="Maroon">c<sub>2</sub></font>,<a href="numbers.html#K5">NAT</a> 
 <b>by </b><i><a class="ref" href="funct_2.html#D2">FUNCT_2:def 2</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E3:48"/>
( <font color="Maroon">c<sub>1</sub></font> is   <a href="monoid_1.html#NM2">Multiset</a> of <font color="Maroon">c<sub>2</sub></font> iff <font color="Maroon">c<sub>1</sub></font> is   <a href="funct_2.html#NM1">Function</a> of <font color="Maroon">c<sub>2</sub></font>, <a href="numbers.html#K5">NAT</a>  )
 <b>by </b><i><a class="txt" href="monoid_1.html#E1:48"><i><font color="Green">E26</font></i></a></i>;<br/>


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