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<b>let </b><font color="Maroon">A</font> be   <a href="altcat_1.html#NM4">category</a>, <font color="Maroon">B</font> be   <a href="altcat_1.html#NM4">category</a>;<br/>

<b>assume </b><b>that </b><br/><a NAME="E1:28"/><i><font color="Green">E25</font></i>: 
<font color="Maroon">A</font>,<font color="Maroon">B</font> <a href="yellow20.html#R1" target="_self">have_the_same_composition</a> 
 <b>and </b><br/><a NAME="E2:28"/><i><font color="Green">E32</font></i>: 
not  <a href="yellow20.html#K2" target="_self">Intersect</a> <font color="Maroon">A</font>,<font color="Maroon">B</font> is <a href="struct_0.html#V3">empty</a>
 <b>and </b><br/><a NAME="E3:28"/><i><font color="Green">E33</font></i>: 
for <font color="Olive">a</font> being  <a href="altcat_1.html#NM1">object</a> of <font color="Maroon">A</font><br/> for <font color="Olive">b</font> being  <a href="altcat_1.html#NM1">object</a> of <font color="Maroon">B</font>  st <font color="Olive">a</font> <a href="hidden.html#R1">=</a> <font color="Olive">b</font> holds <br/> <a href="altcat_1.html#K8">idm</a> <font color="Olive">a</font> <a href="hidden.html#R1">=</a>  <a href="altcat_1.html#K8">idm</a> <font color="Olive">b</font>
 ;<br/>

<b>reconsider </b><font color="Maroon">AB</font> =  <a href="yellow20.html#K2" target="_self">Intersect</a> <font color="Maroon">A</font>,<font color="Maroon">B</font> as  non <a href="struct_0.html#V3">empty</a> <a href="altcat_1.html#V2">transitive</a>  <a href="altcat_2.html#M1">SubCatStr</a> of <font color="Maroon">A</font> <b>by </b><i>, , , <a class="ref" href="yellow20.html#T1" target="_self">Th1</a></i>;<br/>
<a NAME="E5:28"/><i><font color="Green">E34</font></i>: 
the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">AB</font> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">A</font> <a href="xboole_0.html#K3">/\</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">B</font>
 
<b>by </b><i>, </i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="28_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">o</font> be   <a href="altcat_1.html#NM1">object</a> of <font color="Maroon">AB</font>;<br/><b>let </b><font color="Maroon">a</font> be   <a href="altcat_1.html#NM1">object</a> of <font color="Maroon">A</font>;<br/><b>assume </b><a NAME="E1:28_1"/><i><font color="Green">E39</font></i>: 
<font color="Maroon">o</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a</font>
 ;<br/><b>reconsider </b><font color="Maroon">b</font> = <font color="Maroon">o</font> as   <a href="altcat_1.html#NM1">object</a> of <font color="Maroon">B</font> <b>by </b><i>, <a class="ref" href="xboole_0.html#D3">XBOOLE_0:def 3</a></i>;<br/><a NAME="E3:28_1"/>
 <a href="altcat_1.html#K8">idm</a> <font color="Maroon">a</font> <a href="hidden.html#R1">=</a>  <a href="altcat_1.html#K8">idm</a> <font color="Maroon">b</font>
 <b>by </b><i>, <a class="txt" href="yellow20.html#E1:28"><i><font color="Green">E25</font></i></a></i>;<br/><b>hence </b><a NAME="E4:28_1"/>
 <a href="altcat_1.html#K8">idm</a> <font color="Maroon">a</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="altcat_1.html#K1">&lt;^</a><span class="default"><font color="Maroon">o</font>,<font color="Maroon">o</font></span><a href="altcat_1.html#K1">^&gt;</a></span>
 <b>by </b><i>, <a class="txt" href="yellow20.html#E1:28"><i><font color="Green">E25</font></i></a>, </i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E7:28"/>
 <a href="yellow20.html#K2" target="_self">Intersect</a> <font color="Maroon">A</font>,<font color="Maroon">B</font> is   <a href="altcat_2.html#NM2">subcategory</a> of <font color="Maroon">A</font>
 <b>by </b><i><a class="ref" href="altcat_2.html#D14">ALTCAT_2:def 14</a></i>;<br/>


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