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<b>let </b><font color="Maroon">I</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">X</font> be    <a href="pboole.html#M1" target="_self">ManySortedSet</a> of <font color="Maroon">I</font>;<br/>



<div><b>hereby </b>
<div class="add"><b>assume </b><a NAME="E1:138_1"/>
<font color="Maroon">X</font> is <a href="relat_1.html#V3">empty-yielding</a>
 ;<br/><a NAME="E2:138_1"/><b>then </b>
for <font color="Olive">i</font> being   <a href="hidden.html#M1">set</a>   st <font color="Olive">i</font> <a href="hidden.html#R2">in</a> <font color="Maroon">I</font> holds <br/><font color="Maroon">X</font> <a href="funct_1.html#K1">.</a> <font color="Olive">i</font> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a> 
 <b>by </b><i><a class="ref" href="pboole.html#T17" target="_self">Th17</a></i>;<br/><b>hence </b><a NAME="E3:138_1"/>
<font color="Maroon">X</font> <a href="pboole.html#R6" target="_self">=</a>  <a href="pboole.html#K1" target="_self">[0]</a> <font color="Maroon">I</font>
 <b>by </b><i/>;<br/></div>
<b>end;</b></div>

<b>assume </b><a NAME="E2:138"/><i><font color="Green">E24</font></i>: 
<font color="Maroon">X</font> <a href="pboole.html#R6" target="_self">=</a>  <a href="pboole.html#K1" target="_self">[0]</a> <font color="Maroon">I</font>
 ;<br/>

<b>let </b><font color="Maroon">i</font> be    <a href="hidden.html#M1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="pboole.html#D15" target="_self">PBOOLE:def 15</a><br/>

<b>assume </b><a NAME="E3:138"/>
<font color="Maroon">i</font> <a href="hidden.html#R2">in</a> <font color="Maroon">I</font>
 ;<br/>

<b>thus </b><a NAME="E4:138"/>
<font color="Maroon">X</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font> is <a href="xboole_0.html#V1">empty</a>
 <b>by </b><i><a class="ref" href="pboole.html#T19" target="_self">Th19</a>, </i>;<br/>


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