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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/>







<b>assume </b><a NAME="E1:54"/><i><font color="Green">E7</font></i>: 
<font color="Maroon">c<sub>2</sub></font> <a href="pboole.html#R1">in</a> <font color="Maroon">c<sub>4</sub></font>
 ;<br/>

<a NAME="E2:54"/>
<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="E3:54"/><b>then </b>
<font color="Maroon">c<sub>2</sub></font> <a href="pboole.html#R1">in</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#E1:54"><i><font color="Green">E7</font></i></a>, <a class="ref" href="pboole.html#T9">PBOOLE:9</a></i>;<br/>
<a NAME="E4:54"/><b>then </b>
<font color="Maroon">c<sub>2</sub></font> <a href="pboole.html#R2">c=</a> <font color="Maroon">c<sub>3</sub></font>
 
<b>by </b><i><a class="ref" href="mboolean.html#T19">MBOOLEAN:19</a></i>;<br/>
<b>hence </b><a NAME="E5:54"/>
<font color="Maroon">c<sub>2</sub></font> is    <a href="pboole.html#M4">ManySortedSubset</a> of <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/>


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