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<a NAME="E1:50_2_1"/>
(  <a href="monoid_1.html#K13" target="_self">MultiSet_over</a> <font color="Maroon">A</font> <a href="hidden.html#R1">=</a>  <a href="monoid_1.html#K12" target="_self">.:</a> <a href="monoid_0.html#K6">&lt;NAT,+,0&gt;</a> ,<font color="Maroon">A</font> &amp; <font color="Maroon">H<sub>3</sub></font>( <a href="monoid_0.html#K6">&lt;NAT,+,0&gt;</a> ) <a href="hidden.html#R1">=</a>  <a href="numbers.html#K5">NAT</a>  )
 
<b>by </b><i><a class="ref" href="monoid_0.html#T52">MONOID_0:52</a></i>;<br/>
<a NAME="E2:50_2_1"/><b>then </b><i><font color="Green">E43</font></i>: 
(  <a href="relat_1.html#K2">rng</a> <font color="Maroon">m</font> <a href="tarski.html#R1">c=</a>  <a href="numbers.html#K5">NAT</a>  &amp;  <a href="relat_1.html#K1">dom</a> <font color="Maroon">m</font> <a href="hidden.html#R1">=</a> <font color="Maroon">A</font> )
 
<b>by </b><i/>;<br/>
<a NAME="E3:50_2_1"/><b>then </b>
<font color="Maroon">m</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">a</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K2">rng</a> <font color="Maroon">m</font>
 
<b>by </b><i><a class="ref" href="funct_1.html#D5">FUNCT_1:def 5</a></i>;<br/>
<b>hence </b><a NAME="E4:50_2_1"/>
<font color="Maroon">m</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">a</font> is    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a> 
 <b>by </b><i/>;<br/>


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