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<b>let </b><font color="Maroon">c<sub>3</sub></font> be   <a href="mssubfam.html#NM1">MSSubsetFamily</a> of <font color="Maroon">c<sub>2</sub></font>;<br/>

<b>assume </b><a NAME="E1:82_1_1"/><i><font color="Green">E20</font></i>: 
<font color="Maroon">c<sub>3</sub></font> is <a href="mssubfam.html#V4" target="_self">absolutely-multiplicative</a>
 ;<br/>

<b>let </b><font color="Maroon">c<sub>4</sub></font> be    <a href="pboole.html#M1">ManySortedSet</a> of <font color="Maroon">c<sub>1</sub></font>; <i><font color="Red">:: according to </font></i><a class="ref" href="mssubfam.html#D5" target="_self">MSSUBFAM:def 5</a><br/><b>let </b><font color="Maroon">c<sub>5</sub></font> be    <a href="pboole.html#M1">ManySortedSet</a> of <font color="Maroon">c<sub>1</sub></font>;<br/>



<b>assume </b><a NAME="E2:82_1_1"/><i><font color="Green">E21</font></i>: 
( <font color="Maroon">c<sub>4</sub></font> <a href="pboole.html#R1">in</a> <font color="Maroon">c<sub>3</sub></font> &amp; <font color="Maroon">c<sub>5</sub></font> <a href="pboole.html#R1">in</a> <font color="Maroon">c<sub>3</sub></font> )
 ;<br/>

<a NAME="E3:82_1_1"/><b>then </b><i><font color="Green">E22</font></i>: 
( <font color="Maroon">c<sub>4</sub></font> is    <a href="pboole.html#M4">ManySortedSubset</a> of <font color="Maroon">c<sub>2</sub></font> &amp; <font color="Maroon">c<sub>5</sub></font> is    <a href="pboole.html#M4">ManySortedSubset</a> of <font color="Maroon">c<sub>2</sub></font> )
 
<b>by </b><i><a class="ref" href="mssubfam.html#T33" target="_self">Th33</a></i>;<br/>
<a NAME="E4:82_1_1"/><b>then </b>
( <font color="Maroon">c<sub>4</sub></font> <a href="pboole.html#R2">c=</a> <font color="Maroon">c<sub>2</sub></font> &amp; <font color="Maroon">c<sub>5</sub></font> <a href="pboole.html#R2">c=</a> <font color="Maroon">c<sub>2</sub></font> )
 
<b>by </b><i><a class="ref" href="pboole.html#D23">PBOOLE:def 23</a></i>;<br/>
<b>then reconsider </b><font color="Maroon">c<sub>6</sub></font> = <span class="p1"><a href="pzfmisc1.html#K2">{</a><span class="default"><font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font></span><a href="pzfmisc1.html#K2">}</a></span> as   <a href="mssubfam.html#NM1">MSSubsetFamily</a> of <font color="Maroon">c<sub>2</sub></font> <b>by </b><i><a class="ref" href="mssubfam.html#T39" target="_self">Th39</a></i>;<br/>
<a NAME="E6:82_1_1"/>
( <span class="p1"><a href="pzfmisc1.html#K1">{</a><span class="default"><font color="Maroon">c<sub>4</sub></font></span><a href="pzfmisc1.html#K1">}</a></span> <a href="pboole.html#R2">c=</a> <font color="Maroon">c<sub>3</sub></font> &amp; <span class="p1"><a href="pzfmisc1.html#K1">{</a><span class="default"><font color="Maroon">c<sub>5</sub></font></span><a href="pzfmisc1.html#K1">}</a></span> <a href="pboole.html#R2">c=</a> <font color="Maroon">c<sub>3</sub></font> )
 
<b>by </b><i><a class="txt" href="mssubfam.html#E2:82_1_1"><i><font color="Green">E21</font></i></a>, <a class="ref" href="pzfmisc1.html#T36">PZFMISC1:36</a></i>;<br/>
<a NAME="E7:82_1_1"/><b>then </b>
<span class="p1"><a href="pzfmisc1.html#K1">{</a><span class="default"><font color="Maroon">c<sub>4</sub></font></span><a href="pzfmisc1.html#K1">}</a></span> <a href="pboole.html#K2">\/</a> <span class="p1"><a href="pzfmisc1.html#K1">{</a><span class="default"><font color="Maroon">c<sub>5</sub></font></span><a href="pzfmisc1.html#K1">}</a></span> <a href="pboole.html#R2">c=</a> <font color="Maroon">c<sub>3</sub></font>
 
<b>by </b><i><a class="ref" href="pboole.html#T18">PBOOLE:18</a></i>;<br/>
<a NAME="E8:82_1_1"/><b>then </b>
<span class="p1"><a href="pzfmisc1.html#K2">{</a><span class="default"><font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font></span><a href="pzfmisc1.html#K2">}</a></span> <a href="pboole.html#R2">c=</a> <font color="Maroon">c<sub>3</sub></font>
 
<b>by </b><i><a class="ref" href="pzfmisc1.html#T11">PZFMISC1:11</a></i>;<br/>
<a NAME="E9:82_1_1"/><b>then </b>
 <a href="mssubfam.html#K6" target="_self">meet</a> <font color="Maroon">c<sub>6</sub></font> <a href="pboole.html#R1">in</a> <font color="Maroon">c<sub>3</sub></font>
 
<b>by </b><i><a class="txt" href="mssubfam.html#E1:82_1_1"><i><font color="Green">E20</font></i></a>, <a class="ref" href="mssubfam.html#D6" target="_self">Def6</a></i>;<br/>
<b>hence </b><a NAME="E10:82_1_1"/>
<font color="Maroon">c<sub>4</sub></font> <a href="pboole.html#K3">/\</a> <font color="Maroon">c<sub>5</sub></font> <a href="pboole.html#R1">in</a> <font color="Maroon">c<sub>3</sub></font>
 <b>by </b><i><a class="txt" href="mssubfam.html#E3:82_1_1"><i><font color="Green">E22</font></i></a>, <a class="ref" href="mssubfam.html#T51" target="_self">Th51</a></i>;<br/>


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