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<b>let </b><font color="Maroon">c<sub>1</sub></font> be   <a href="pre_topc.html#NM1">TopSpace</a>;<br/><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="E1:70"/>
( not <font color="Maroon">c<sub>2</sub></font> is <a href="isomichi.html#V3" target="_self">1st_class</a> &amp; not <font color="Maroon">c<sub>2</sub></font> is <a href="isomichi.html#V4" target="_self">2nd_class</a> &amp; not <font color="Maroon">c<sub>2</sub></font> is <a href="isomichi.html#V5" target="_self">3rd_class</a> )
 ;<br/>

<a NAME="E2:70"/><b>then </b>
( not  <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="tarski.html#R1">c=</a>  <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> &amp; not  <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> &amp;  <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="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="xboole_0.html#R3">are_c=-comparable</a>  )
 
<b>by </b><i><a class="ref" href="isomichi.html#D6" target="_self">Def6</a>, <a class="ref" href="isomichi.html#D7" target="_self">Def7</a>, <a class="ref" href="isomichi.html#D8" target="_self">Def8</a></i>;<br/>
<b>hence </b><a NAME="E3:70"/>
contradiction
 <b>by </b><i><a class="ref" href="isomichi.html#T45" target="_self">Th45</a></i>;<br/>


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