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<b>let </b><font color="Maroon">c<sub>1</sub></font> be    <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font>, <font color="Maroon">c<sub>3</sub></font> be    <a href="pboole.html#M1">ManySortedSet</a> of <font color="Maroon">c<sub>1</sub></font>;<br/><b>let </b><font color="Maroon">c<sub>4</sub></font> be   <a href="mssubfam.html#NM1">MSSubsetFamily</a> of <font color="Maroon">c<sub>3</sub></font>;<br/>







<a NAME="E1:57"/>
<font color="Maroon">c<sub>4</sub></font> <a href="pboole.html#K4">\</a> <font color="Maroon">c<sub>2</sub></font> is    <a href="pboole.html#M4">ManySortedSubset</a> of  <a href="mssubfam.html#K3" target="_self">bool</a> <font color="Maroon">c<sub>3</sub></font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="57_1"><b>proof </b></a><div class="add">

<a NAME="E1:57_1"/>
<font color="Maroon">c<sub>4</sub></font> <a href="pboole.html#R2">c=</a>  <a href="mssubfam.html#K3" target="_self">bool</a> <font color="Maroon">c<sub>3</sub></font>
 
<b>by </b><i><a class="ref" href="pboole.html#D23">PBOOLE:def 23</a></i>;<br/>
<a NAME="E2:57_1"/><b>then </b><i><font color="Green">E9</font></i>: 
<font color="Maroon">c<sub>4</sub></font> <a href="pboole.html#K4">\</a> <font color="Maroon">c<sub>2</sub></font> <a href="pboole.html#R2">c=</a> <span class="p1">(<span class="default"><a href="mssubfam.html#K3" target="_self">bool</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="pboole.html#K4">\</a> <font color="Maroon">c<sub>2</sub></font>
 
<b>by </b><i><a class="ref" href="pboole.html#T59">PBOOLE:59</a></i>;<br/>
<a NAME="E3:57_1"/>
<span class="p1">(<span class="default"><a href="mssubfam.html#K3" target="_self">bool</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="pboole.html#K4">\</a> <font color="Maroon">c<sub>2</sub></font> <a href="pboole.html#R2">c=</a>  <a href="mssubfam.html#K3" target="_self">bool</a> <font color="Maroon">c<sub>3</sub></font>
 
<b>by </b><i><a class="ref" href="pboole.html#T62">PBOOLE:62</a></i>;<br/>
<b>hence </b><a NAME="E4:57_1"/>
<font color="Maroon">c<sub>4</sub></font> <a href="pboole.html#K4">\</a> <font color="Maroon">c<sub>2</sub></font> <a href="pboole.html#R2">c=</a>  <a href="mssubfam.html#K3" target="_self">bool</a> <font color="Maroon">c<sub>3</sub></font>
 <b>by </b><i><a class="txt" href="mssubfam.html#E2:57_1"><i><font color="Green">E9</font></i></a>, <a class="ref" href="pboole.html#T15">PBOOLE:15</a></i>; <i><font color="Red">:: according to </font></i><a class="ref" href="pboole.html#D23">PBOOLE:def 23</a><br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E2:57"/>
<font color="Maroon">c<sub>4</sub></font> <a href="pboole.html#K4">\</a> <font color="Maroon">c<sub>2</sub></font> is   <a href="mssubfam.html#NM1">MSSubsetFamily</a> of <font color="Maroon">c<sub>3</sub></font>
 ;<br/>


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