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<b>let </b><font color="Maroon" title="c1">A</font>, <font color="Maroon" title="c2">B</font> be   <a href="altcat_1.html#NM4" title="ALTCAT_1:NM.4">category</a>;<br/>

<b>assume </b><b>that </b><br/><a NAME="E1:28"/><i><font color="Green" title="E21">A1</font></i>: 
<font color="Maroon" title="c1">A</font>,<font color="Maroon" title="c2">B</font> <a href="yellow20.html#R1" title="YELLOW20:pred.1">have_the_same_composition</a> 
 <b>and </b><br/><a NAME="E2:28"/><i><font color="Green" title="E22">A2</font></i>: 
not  <a href="yellow20.html#K2" title="YELLOW20:func.2">Intersect</a> <font color="Maroon" title="c1">A</font>,<font color="Maroon" title="c2">B</font> is <a href="struct_0.html#V3" title="STRUCT_0:attr.3">empty</a>
 <b>and </b><br/><a NAME="E3:28"/><i><font color="Green" title="E23">A3</font></i>: 
for <font color="Olive" title="b1">a</font> being  <a href="altcat_1.html#NM1" title="ALTCAT_1:NM.1">object</a> of <font color="Maroon" title="c1">A</font><br/> for <font color="Olive" title="b2">b</font> being  <a href="altcat_1.html#NM1" title="ALTCAT_1:NM.1">object</a> of <font color="Maroon" title="c2">B</font>  st <font color="Olive" title="b1">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">b</font> holds <br/> <a href="altcat_1.html#K8" title="ALTCAT_1:func.8">idm</a> <font color="Olive" title="b1">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="altcat_1.html#K8" title="ALTCAT_1:func.8">idm</a> <font color="Olive" title="b2">b</font>
 ;<br/>

<b>reconsider </b><font color="Maroon" title="c3">AB</font> =  <a href="yellow20.html#K2" title="YELLOW20:func.2">Intersect</a> <font color="Maroon" title="c1">A</font>,<font color="Maroon" title="c2">B</font> as  non <a href="struct_0.html#V3" title="STRUCT_0:attr.3">empty</a> <a href="altcat_1.html#V2" title="ALTCAT_1:attr.2">transitive</a>  <a href="altcat_2.html#M1" title="ALTCAT_2:mode.1">SubCatStr</a> of <font color="Maroon" title="c1">A</font> <b>by </b><i><a class="txt" href="yellow20.html#E1:28"><i><font color="Green" title="E21">A1</font></i></a>, <a class="txt" href="yellow20.html#E2:28"><i><font color="Green" title="E22">A2</font></i></a>, <a class="ref" href="yellow20.html#T21" target="_self" title="YELLOW20:th.21">Th21</a>, <a class="ref" href="yellow20.html#T23" target="_self" title="YELLOW20:th.23">Th23</a></i>;<br/>
<a NAME="E5:28"/><i><font color="Green" title="E24">A4</font></i>: 
the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c3">AB</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">A</font> <a href="xboole_0.html#K3" title="XBOOLE_0:func.3">/\</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">B</font>
 
<b>by </b><i><a class="txt" href="yellow20.html#E1:28"><i><font color="Green" title="E21">A1</font></i></a>, <a class="ref" href="yellow20.html#D3" target="_self" title="YELLOW20:def.3">Def3</a></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" title="c4">o</font> be   <a href="altcat_1.html#NM1" title="ALTCAT_1:NM.1">object</a> of <font color="Maroon" title="c3">AB</font>;<br/><b>let </b><font color="Maroon" title="c5">a</font> be   <a href="altcat_1.html#NM1" title="ALTCAT_1:NM.1">object</a> of <font color="Maroon" title="c1">A</font>;<br/><b>assume </b><a NAME="E1:28_1"/><i><font color="Green" title="E25">A5</font></i>: 
<font color="Maroon" title="c4">o</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">a</font>
 ;<br/><b>reconsider </b><font color="Maroon" title="c6">b</font> = <font color="Maroon" title="c4">o</font> as   <a href="altcat_1.html#NM1" title="ALTCAT_1:NM.1">object</a> of <font color="Maroon" title="c2">B</font> <b>by </b><i><a class="txt" href="yellow20.html#E5:28"><i><font color="Green" title="E24">A4</font></i></a>, <a class="ref" href="xboole_0.html#D3" title="XBOOLE_0:def.3">XBOOLE_0:def 3</a></i>;<br/><a NAME="E3:28_1"/>
 <a href="altcat_1.html#K8" title="ALTCAT_1:func.8">idm</a> <font color="Maroon" title="c5">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="altcat_1.html#K8" title="ALTCAT_1:func.8">idm</a> <font color="Maroon" title="c6">b</font>
 <b>by </b><i><a class="txt" href="yellow20.html#E3:28"><i><font color="Green" title="E23">A3</font></i></a>, <a class="txt" href="yellow20.html#E1:28_1"><i><font color="Green" title="E25">A5</font></i></a></i>;<br/><b>hence </b><a NAME="E4:28_1"/>
 <a href="altcat_1.html#K8" title="ALTCAT_1:func.8">idm</a> <font color="Maroon" title="c5">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">&lt;^</a><span class="default"><font color="Maroon" title="c4">o</font>,<font color="Maroon" title="c4">o</font></span><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">^&gt;</a></span>
 <b>by </b><i><a class="txt" href="yellow20.html#E1:28"><i><font color="Green" title="E21">A1</font></i></a>, <a class="txt" href="yellow20.html#E1:28_1"><i><font color="Green" title="E25">A5</font></i></a>, <a class="ref" href="yellow20.html#T24" target="_self" title="YELLOW20:th.24">Th24</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E7:28"/>
 <a href="yellow20.html#K2" title="YELLOW20:func.2">Intersect</a> <font color="Maroon" title="c1">A</font>,<font color="Maroon" title="c2">B</font> is   <a href="altcat_2.html#NM2" title="ALTCAT_2:NM.2">subcategory</a> of <font color="Maroon" title="c1">A</font>
 <b>by </b><i><a class="ref" href="altcat_2.html#D14" title="ALTCAT_2:def.14">ALTCAT_2:def 14</a></i>;<br/>


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