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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#K2">[:</a><span class="default">the <a href="cat_1.html#U1">Objects</a> of <font color="Maroon">C</font>,the <a href="cat_1.html#U1">Objects</a> of <font color="Maroon">C</font></span><a href="zfmisc_1.html#K2">:]</a></span>, <font color="Maroon">M2</font> be    <a href="pboole.html#M1">ManySortedSet</a> of <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default">the <a href="cat_1.html#U1">Objects</a> of <font color="Maroon">C</font>,the <a href="cat_1.html#U1">Objects</a> of <font color="Maroon">C</font></span><a href="zfmisc_1.html#K2">:]</a></span>;<br/>

<b>assume </b><b>that </b><br/><a NAME="E1:22_1_2"/><i><font color="Green">E16</font></i>: 
for <font color="Olive">i</font>, <font color="Olive">j</font> being  <a href="cat_1.html#NM1">Object</a> of <font color="Maroon">C</font> holds  <font color="Maroon">M1</font> <a href="binop_1.html#K1">.</a> <font color="Olive">i</font>,<font color="Olive">j</font> <a href="hidden.html#R1">=</a>  <a href="cat_1.html#K6">Hom</a> <font color="Olive">i</font>,<font color="Olive">j</font>
 <b>and </b><br/><a NAME="E2:22_1_2"/><i><font color="Green">E17</font></i>: 
for <font color="Olive">i</font>, <font color="Olive">j</font> being  <a href="cat_1.html#NM1">Object</a> of <font color="Maroon">C</font> holds  <font color="Maroon">M2</font> <a href="binop_1.html#K1">.</a> <font color="Olive">i</font>,<font color="Olive">j</font> <a href="hidden.html#R1">=</a>  <a href="cat_1.html#K6">Hom</a> <font color="Olive">i</font>,<font color="Olive">j</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">i</font> be   <a href="cat_1.html#NM1">Object</a> of <font color="Maroon">C</font>, <font color="Maroon">j</font> be   <a href="cat_1.html#NM1">Object</a> of <font color="Maroon">C</font>;<br/><b>thus </b><font color="Maroon">M1</font> <a href="binop_1.html#K1">.</a> <font color="Maroon">i</font>,<font color="Maroon">j</font> = 
 <a href="cat_1.html#K6">Hom</a> <font color="Maroon">i</font>,<font color="Maroon">j</font>
<b>by </b><i/>
<br/>.= 
<font color="Maroon">M2</font> <a href="binop_1.html#K1">.</a> <font color="Maroon">i</font>,<font color="Maroon">j</font>
<b>by </b><i/>
;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E4:22_1_2"/>
<font color="Maroon">M1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">M2</font>
 <b>by </b><i><a class="ref" href="altcat_1.html#T9">ALTCAT_1:9</a></i>;<br/>


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