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<b>let </b><font color="Maroon">M1</font> be    <a href="pboole.html#M1">ManySortedSet</a> of <span class="p1"><a href="zfmisc_1.html#K3">[:</a><span class="default"><font color="Maroon">I</font>,<font color="Maroon">I</font>,<font color="Maroon">I</font></span><a href="zfmisc_1.html#K3">:]</a></span>, <font color="Maroon">M2</font> be    <a href="pboole.html#M1">ManySortedSet</a> of <span class="p1"><a href="zfmisc_1.html#K3">[:</a><span class="default"><font color="Maroon">I</font>,<font color="Maroon">I</font>,<font color="Maroon">I</font></span><a href="zfmisc_1.html#K3">:]</a></span>;<br/>

<b>assume </b><b>that </b><br/><a NAME="E1:23_2_2"/><i><font color="Green">E29</font></i>: 
for <font color="Olive">i</font>, <font color="Olive">j</font>, <font color="Olive">k</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> &amp; <font color="Olive">j</font> <a href="hidden.html#R2">in</a> <font color="Maroon">I</font> &amp; <font color="Olive">k</font> <a href="hidden.html#R2">in</a> <font color="Maroon">I</font> holds <br/><font color="Maroon">M1</font> <a href="multop_1.html#K1">.</a> <font color="Olive">i</font>,<font color="Olive">j</font>,<font color="Olive">k</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">H</font> <a href="binop_1.html#K1">.</a> <font color="Olive">j</font>,<font color="Olive">k</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">G</font> <a href="binop_1.html#K1">.</a> <font color="Olive">i</font>,<font color="Olive">j</font></span>)</span></span><a href="zfmisc_1.html#K2">:]</a></span>
 <b>and </b><br/><a NAME="E2:23_2_2"/><i><font color="Green">E36</font></i>: 
for <font color="Olive">i</font>, <font color="Olive">j</font>, <font color="Olive">k</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> &amp; <font color="Olive">j</font> <a href="hidden.html#R2">in</a> <font color="Maroon">I</font> &amp; <font color="Olive">k</font> <a href="hidden.html#R2">in</a> <font color="Maroon">I</font> holds <br/><font color="Maroon">M2</font> <a href="multop_1.html#K1">.</a> <font color="Olive">i</font>,<font color="Olive">j</font>,<font color="Olive">k</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">H</font> <a href="binop_1.html#K1">.</a> <font color="Olive">j</font>,<font color="Olive">k</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">G</font> <a href="binop_1.html#K1">.</a> <font color="Olive">i</font>,<font color="Olive">j</font></span>)</span></span><a href="zfmisc_1.html#K2">:]</a></span>
 ;<br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="23_2_2_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">i</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">j</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">k</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>assume </b><a NAME="E1:23_2_2_1"/><i><font color="Green">E56</font></i>: 
( <font color="Maroon">i</font> <a href="hidden.html#R2">in</a> <font color="Maroon">I</font> &amp; <font color="Maroon">j</font> <a href="hidden.html#R2">in</a> <font color="Maroon">I</font> &amp; <font color="Maroon">k</font> <a href="hidden.html#R2">in</a> <font color="Maroon">I</font> )
 ;<br/><b>hence </b><font color="Maroon">M1</font> <a href="multop_1.html#K1">.</a> <font color="Maroon">i</font>,<font color="Maroon">j</font>,<font color="Maroon">k</font> = 
<span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">H</font> <a href="binop_1.html#K1">.</a> <font color="Maroon">j</font>,<font color="Maroon">k</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">G</font> <a href="binop_1.html#K1">.</a> <font color="Maroon">i</font>,<font color="Maroon">j</font></span>)</span></span><a href="zfmisc_1.html#K2">:]</a></span>
<b>by </b><i/>
<br/>.= 
<font color="Maroon">M2</font> <a href="multop_1.html#K1">.</a> <font color="Maroon">i</font>,<font color="Maroon">j</font>,<font color="Maroon">k</font>
<b>by </b><i>, </i>
;<br/><br/></div><b>end;</b></div>
<b>hence </b><a NAME="E4:23_2_2"/>
<font color="Maroon">M1</font> <a href="pboole.html#R6">=</a> <font color="Maroon">M2</font>
 <b>by </b><i/>;<br/>


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