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<b>let </b><font color="Maroon" title="c3">M1</font>, <font color="Maroon" title="c4">M2</font> be    <a href="pboole.html#M1" title="PBOOLE:mode.1">ManySortedSet</a> of <span class="p1"><a href="zfmisc_1.html#K3" title="ZFMISC_1:func.3">[:</a><span class="default"><font color="Maroon" title="c1">I</font>,<font color="Maroon" title="c1">I</font>,<font color="Maroon" title="c1">I</font></span><a href="zfmisc_1.html#K3" title="ZFMISC_1:func.3">:]</a></span>;<br/>

<b>assume </b><b>that </b><br/><a NAME="E1:22_1_2"/><i><font color="Green" title="E10">A1</font></i>: 
for <font color="Olive" title="b1">i</font>, <font color="Olive" title="b2">j</font>, <font color="Olive" title="b3">k</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   st <font color="Olive" title="b1">i</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">I</font> &amp; <font color="Olive" title="b2">j</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">I</font> &amp; <font color="Olive" title="b3">k</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">I</font> holds <br/><font color="Maroon" title="c3">M1</font> <a href="multop_1.html#K1" title="MULTOP_1:func.1">.</a> <font color="Olive" title="b1">i</font>,<font color="Olive" title="b2">j</font>,<font color="Olive" title="b3">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">G</font> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> <font color="Olive" title="b1">i</font>,<font color="Olive" title="b3">k</font>
 <b>and </b><br/><a NAME="E2:22_1_2"/><i><font color="Green" title="E11">A2</font></i>: 
for <font color="Olive" title="b1">i</font>, <font color="Olive" title="b2">j</font>, <font color="Olive" title="b3">k</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   st <font color="Olive" title="b1">i</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">I</font> &amp; <font color="Olive" title="b2">j</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">I</font> &amp; <font color="Olive" title="b3">k</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">I</font> holds <br/><font color="Maroon" title="c4">M2</font> <a href="multop_1.html#K1" title="MULTOP_1:func.1">.</a> <font color="Olive" title="b1">i</font>,<font color="Olive" title="b2">j</font>,<font color="Olive" title="b3">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">G</font> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> <font color="Olive" title="b1">i</font>,<font color="Olive" title="b3">k</font>
 ;<br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="22_1_2_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c5">i</font>, <font color="Maroon" title="c6">j</font>, <font color="Maroon" title="c7">k</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/><b>assume </b><a NAME="E1:22_1_2_1"/><i><font color="Green" title="E12">A3</font></i>: 
( <font color="Maroon" title="c5">i</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">I</font> &amp; <font color="Maroon" title="c6">j</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">I</font> &amp; <font color="Maroon" title="c7">k</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">I</font> )
 ;<br/><b>hence </b><font color="Maroon" title="c3">M1</font> <a href="multop_1.html#K1" title="MULTOP_1:func.1">.</a> <font color="Maroon" title="c5">i</font>,<font color="Maroon" title="c6">j</font>,<font color="Maroon" title="c7">k</font> = 
<font color="Maroon" title="c2">G</font> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> <font color="Maroon" title="c5">i</font>,<font color="Maroon" title="c7">k</font>
<b>by </b><i><a class="txt" href="altcat_1.html#E1:22_1_2"><i><font color="Green" title="E10">A1</font></i></a></i>
<br/>.= 
<font color="Maroon" title="c4">M2</font> <a href="multop_1.html#K1" title="MULTOP_1:func.1">.</a> <font color="Maroon" title="c5">i</font>,<font color="Maroon" title="c6">j</font>,<font color="Maroon" title="c7">k</font>
<b>by </b><i><a class="txt" href="altcat_1.html#E2:22_1_2"><i><font color="Green" title="E11">A2</font></i></a>, <a class="txt" href="altcat_1.html#E1:22_1_2_1"><i><font color="Green" title="E12">A3</font></i></a></i>
;<br/><br/></div><b>end;</b></div>
<b>hence </b><a NAME="E4:22_1_2"/>
<font color="Maroon" title="c3">M1</font> <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a> <font color="Maroon" title="c4">M2</font>
 <b>by </b><i><a class="ref" href="altcat_1.html#T10" target="_self" title="ALTCAT_1:th.10">Th10</a></i>;<br/>


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