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<span class="kw">let </span><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:()"><span class="comment"><font color="Red">::  thesis: </font></span></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/><span class="kw">let </span><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:()"><span class="comment"><font color="Red">::  thesis: </font></span></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/>



<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:70"/><span class="lab"><font color="Green" title="E26">A1</font></span>: 
not <font color="Maroon" title="c2">A</font> is  <a href="isomichi.html#V3" title="ISOMICHI:attr.3">1st_class</a> 
 <span class="kw">and </span><br/><a NAME="E2:70"/><span class="lab"><font color="Green" title="E27">A2</font></span>: 
not <font color="Maroon" title="c2">A</font> is  <a href="isomichi.html#V4" title="ISOMICHI:attr.4">2nd_class</a> 
 <span class="kw">and </span><br/><a NAME="E3:70"/><span class="lab"><font color="Green" title="E28">A3</font></span>: 
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:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/>

<a NAME="E4:70"/><span class="lab"><font color="Green" title="E29">A4</font></span>: 
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>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:70"><span class="lab"><font color="Green" title="E27">A2</font></span></a>, <a class="ref" href="isomichi.html#D7" target="_self" title="ISOMICHI:def.7">Def7</a></span>;<br/>
<a NAME="E5:70"/><span class="lab"><font color="Green" title="E30">A5</font></span>: 
 <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> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:70"><span class="lab"><font color="Green" title="E28">A3</font></span></a>, <a class="ref" href="isomichi.html#D8" target="_self" title="ISOMICHI:def.8">Def8</a></span>;<br/>
<a NAME="E6:70"/>
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>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:70"><span class="lab"><font color="Green" title="E26">A1</font></span></a>, <a class="ref" href="isomichi.html#D6" target="_self" title="ISOMICHI:def.6">Def6</a></span>;<br/>
<span class="kw">hence </span><a NAME="E7:70"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:70"><span class="lab"><font color="Green" title="E29">A4</font></span></a>, <a class="txt" href="#E5:70"><span class="lab"><font color="Green" title="E30">A5</font></span></a>, <a class="ref" href="isomichi.html#T45" target="_self" title="ISOMICHI:th.45">Th45</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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