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<b>let </b><font color="Maroon">c<sub>2</sub></font> be   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">c<sub>1</sub></font>;<br/>

<b>assume </b><a NAME="E1:75_1_1"/><i><font color="Green">E42</font></i>: 
( <font color="Maroon">c<sub>2</sub></font> is <a href="tex_2.html#V1">proper</a> &amp; not <font color="Maroon">c<sub>2</sub></font> is <a href="xboole_0.html#V1">empty</a> )
 ;<br/>

<a NAME="E2:75_1_1"/>
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>1</sub></font>
 
<b>by </b><i><a class="txt" href="isomichi.html#E1:75_1_1"><i><font color="Green">E42</font></i></a>, <a class="ref" href="tex_2.html#T5">TEX_2:5</a></i>;<br/>
<a NAME="E3:75_1_1"/><b>then </b>
 <a href="tops_1.html#K1">Int</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a> 
 
<b>by </b><i><a class="ref" href="tex_1.html#T12">TEX_1:12</a></i>;<br/>
<a NAME="E4:75_1_1"/><b>then </b><i><font color="Green">E43</font></i>: 
 <a href="pre_topc.html#K4">Cl</a> <span class="p1">(<span class="default"><a href="tops_1.html#K1">Int</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a> 
 
<b>by </b><i><a class="ref" href="tex_1.html#T11">TEX_1:11</a></i>;<br/>
<a NAME="E5:75_1_1"/>
 <a href="pre_topc.html#K4">Cl</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>1</sub></font>
 
<b>by </b><i><a class="txt" href="isomichi.html#E1:75_1_1"><i><font color="Green">E42</font></i></a>, <a class="ref" href="tex_1.html#T11">TEX_1:11</a></i>;<br/>
<a NAME="E6:75_1_1"/><b>then </b>
 <a href="tops_1.html#K1">Int</a> <span class="p1">(<span class="default"><a href="pre_topc.html#K4">Cl</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>1</sub></font>
 
<b>by </b><i><a class="ref" href="tex_1.html#T12">TEX_1:12</a></i>;<br/>
<a NAME="E7:75_1_1"/><b>then </b>
 <a href="pre_topc.html#K4">Cl</a> <span class="p1">(<span class="default"><a href="tops_1.html#K1">Int</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="xboole_0.html#R2">c&lt;</a>  <a href="tops_1.html#K1">Int</a> <span class="p1">(<span class="default"><a href="pre_topc.html#K4">Cl</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>
 
<b>by </b><i><a class="txt" href="isomichi.html#E4:75_1_1"><i><font color="Green">E43</font></i></a>, <a class="ref" href="xboole_0.html#D8">XBOOLE_0:def 8</a></i>;<br/>
<b>hence </b><a NAME="E8:75_1_1"/>
<font color="Maroon">c<sub>2</sub></font> is <a href="isomichi.html#V4" target="_self">2nd_class</a>
 <b>by </b><i><a class="ref" href="isomichi.html#D7" target="_self">Def7</a></i>;<br/>


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