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<b>let </b><font color="Maroon">C</font> be  non <a href="struct_0.html#V3">empty</a> <a href="altcat_1.html#V12">with_units</a>  <a href="altcat_1.html#L2">AltCatStr</a> ;<br/><b>let </b><font color="Maroon">D</font> be    <a href="altcat_2.html#M1">SubCatStr</a> of <font color="Maroon">C</font>;<br/>



<b>assume </b><a NAME="E1:39"/><i><font color="Green">E24</font></i>: 
( the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">C</font> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">D</font> &amp; the <a href="altcat_1.html#U1">Arrows</a> of <font color="Maroon">C</font> <a href="hidden.html#R1">=</a> the <a href="altcat_1.html#U1">Arrows</a> of <font color="Maroon">D</font> )
 ;<br/>

<a NAME="E2:39"/>
not <font color="Maroon">D</font> is <a href="struct_0.html#V3">empty</a>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="39_1"><b>proof </b></a><div class="add">

<b>thus </b><a NAME="E1:39_1"/>
not the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">D</font> is <a href="xboole_0.html#V1">empty</a>
 <b>by </b><i/>; <i><font color="Red">:: according to </font></i><a class="ref" href="struct_0.html#D1">STRUCT_0:def 1</a><br/>


</div><b>end;</b></div>
<b>then reconsider </b><font color="Maroon">D</font> = <font color="Maroon">D</font> as  non <a href="struct_0.html#V3">empty</a> <a href="altcat_2.html#V2">full</a>  <a href="altcat_2.html#M1">SubCatStr</a> of <font color="Maroon">C</font> <b>by </b><i>, </i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="39_2"><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">D</font>;<br/><b>let </b><font color="Maroon">o'</font> be   <a href="altcat_1.html#NM1">object</a> of <font color="Maroon">C</font>;<br/><b>assume </b><a NAME="E1:39_2"/><i><font color="Green">E25</font></i>: 
<font color="Maroon">o</font> <a href="hidden.html#R1">=</a> <font color="Maroon">o'</font>
 ;<br/><a NAME="E2:39_2"/>
<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> <a href="hidden.html#R1">=</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="ref" href="altcat_2.html#T29">ALTCAT_2:29</a></i>;<br/><b>hence </b><a NAME="E3:39_2"/>
 <a href="altcat_1.html#K8">idm</a> <font color="Maroon">o'</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>
 ;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E5:39"/>
<font color="Maroon">D</font> is <a href="altcat_2.html#V3">id-inheriting</a>
 <b>by </b><i><a class="ref" href="altcat_2.html#D14">ALTCAT_2:def 14</a></i>;<br/>


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