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<b>let </b><font color="Maroon" title="c1">T</font> be   <a href="pre_topc.html#NM1" title="PRE_TOPC:NM.1">TopSpace</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">A</font> being  <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">T</font>  holds <br/>( <font color="Olive" title="b1">A</font> is <a href="isomichi.html#V3" title="ISOMICHI:attr.3">1st_class</a> or <font color="Olive" title="b1">A</font> is <a href="isomichi.html#V4" title="ISOMICHI:attr.4">2nd_class</a> or <font color="Olive" title="b1">A</font> is <a href="isomichi.html#V5" title="ISOMICHI:attr.5">3rd_class</a> )</span><br/><b>let </b><font color="Maroon" title="c2">A</font> be   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">T</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c2">A</font> is <a href="isomichi.html#V3" title="ISOMICHI:attr.3">1st_class</a> or <font color="Maroon" title="c2">A</font> is <a href="isomichi.html#V4" title="ISOMICHI:attr.4">2nd_class</a> or <font color="Maroon" title="c2">A</font> is <a href="isomichi.html#V5" title="ISOMICHI:attr.5">3rd_class</a> )</span><br/>



<b>assume </b><a NAME="E1:60"/>
( not <font color="Maroon" title="c2">A</font> is <a href="isomichi.html#V3" title="ISOMICHI:attr.3">1st_class</a> &amp; not <font color="Maroon" title="c2">A</font> is <a href="isomichi.html#V4" title="ISOMICHI:attr.4">2nd_class</a> &amp; not <font color="Maroon" title="c2">A</font> is <a href="isomichi.html#V5" title="ISOMICHI:attr.5">3rd_class</a> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> contradiction</span><br/>

<a NAME="E2:60"/><b>then </b>
( not  <a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <span class="p1">(<span class="default"><a href="pre_topc.html#K2" title="PRE_TOPC:func.2">Cl</a> <font color="Maroon" title="c2">A</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="pre_topc.html#K2" title="PRE_TOPC:func.2">Cl</a> <span class="p1">(<span class="default"><a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <font color="Maroon" title="c2">A</font></span>)</span> &amp; not  <a href="pre_topc.html#K2" title="PRE_TOPC:func.2">Cl</a> <span class="p1">(<span class="default"><a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <font color="Maroon" title="c2">A</font></span>)</span> <a href="xboole_0.html#R2" title="XBOOLE_0:pred.2">c&lt;</a>  <a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <span class="p1">(<span class="default"><a href="pre_topc.html#K2" title="PRE_TOPC:func.2">Cl</a> <font color="Maroon" title="c2">A</font></span>)</span> &amp;  <a href="pre_topc.html#K2" title="PRE_TOPC:func.2">Cl</a> <span class="p1">(<span class="default"><a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <font color="Maroon" title="c2">A</font></span>)</span>, <a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <span class="p1">(<span class="default"><a href="pre_topc.html#K2" title="PRE_TOPC:func.2">Cl</a> <font color="Maroon" title="c2">A</font></span>)</span> <a href="xboole_0.html#R3" title="XBOOLE_0:pred.3">are_c=-comparable</a>  )
 
<b>by </b><i><a class="ref" href="isomichi.html#D6" target="_self" title="ISOMICHI:def.6">Def6</a>, <a class="ref" href="isomichi.html#D7" target="_self" title="ISOMICHI:def.7">Def7</a>, <a class="ref" href="isomichi.html#D8" target="_self" title="ISOMICHI:def.8">Def8</a></i>;<br/>
<b>hence </b><a NAME="E3:60"/>
contradiction
 <b>by </b><i><a class="ref" href="isomichi.html#T45" target="_self" title="ISOMICHI:th.45">Th45</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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