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<b>set </b><font color="Maroon">c<sub>1</sub></font> = <span class="p1"><a href="tarski.html#K2">{</a><span class="default">0,1</span><a href="tarski.html#K2">}</a></span>;<br/>
<b>reconsider </b><font color="Maroon">c<sub>2</sub></font> =  <a href="pcomps_1.html#K1">bool</a> <span class="p1"><a href="tarski.html#K2">{</a><span class="default">0,1</span><a href="tarski.html#K2">}</a></span> as   <a href="setfam_1.html#NM1">Subset-Family</a> of <span class="p1"><a href="tarski.html#K2">{</a><span class="default">0,1</span><a href="tarski.html#K2">}</a></span> ;<br/>
<b>reconsider </b><font color="Maroon">c<sub>3</sub></font> = <font color="Maroon">c<sub>2</sub></font> as   <a href="setfam_1.html#NM1">Subset-Family</a> of <span class="p1"><a href="tarski.html#K2">{</a><span class="default">0,1</span><a href="tarski.html#K2">}</a></span> ;<br/>
<b>reconsider </b><font color="Maroon">c<sub>4</sub></font> =  <a href="pre_topc.html#G1">TopStruct</a>(# <span class="p1"><a href="tarski.html#K2">{</a><span class="default">0,1</span><a href="tarski.html#K2">}</a></span>,<font color="Maroon">c<sub>3</sub></font> #) as  non <a href="struct_0.html#V3">empty</a> <a href="tdlat_3.html#V1">discrete</a>  <a href="pre_topc.html#L1">TopStruct</a>  <b>by </b><i><a class="ref" href="tdlat_3.html#D1">TDLAT_3:def 1</a></i>;<br/>
<b>take </b>
<font color="Maroon">c<sub>4</sub></font>
;<br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="15_1_1_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:15_1_1_1"/>
<font color="Maroon">c<sub>4</sub></font> is <a href="realset2.html#V3">trivial</a>
 ;<br/><b>then consider </b><font color="Maroon">c<sub>5</sub></font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>4</sub></font><b> such that </b><br/><a NAME="E3:15_1_1_1"/><i><font color="Green">E9</font></i>: 
the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>5</sub></font></span><a href="domain_1.html#K6">}</a></span>
 <b>by </b><i><a class="ref" href="tex_1.html#D1" target="_self">Def1</a></i>;<br/><a NAME="E4:15_1_1_1"/>
( <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> 0 &amp; <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> 1 )
 <b>by </b><i><a class="txt" href="tex_1.html#E3:15_1_1_1"><i><font color="Green">E9</font></i></a>, <a class="ref" href="zfmisc_1.html#T8">ZFMISC_1:8</a></i>;<br/><b>hence </b><a NAME="E5:15_1_1_1"/>
contradiction
 ;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E5:15_1_1"/>
( not <font color="Maroon">c<sub>4</sub></font> is <a href="realset2.html#V3">trivial</a> &amp; <font color="Maroon">c<sub>4</sub></font> is <a href="pre_topc.html#V1">strict</a> &amp; not <font color="Maroon">c<sub>4</sub></font> is <a href="struct_0.html#V3">empty</a> )
 ;<br/>


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