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<b>let </b><font color="Maroon">c<sub>1</sub></font> be    <a href="pre_topc.html#L1">TopStruct</a> ;<br/>

<b>assume </b><a NAME="E1:12"/>
(  <a href="xboole_0.html#K1">{}</a>  <a href="hidden.html#R2">in</a> the <a href="pre_topc.html#U1">topology</a> of <font color="Maroon">c<sub>1</sub></font> &amp; the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R2">in</a> the <a href="pre_topc.html#U1">topology</a> of <font color="Maroon">c<sub>1</sub></font> )
 ;<br/>

<a NAME="E2:12"/><b>then </b><i><font color="Green">E11</font></i>: 
<span class="p1"><a href="tarski.html#K2">{</a><span class="default"><a href="xboole_0.html#K1">{}</a> ,the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>1</sub></font></span><a href="tarski.html#K2">}</a></span> <a href="tarski.html#R1">c=</a> the <a href="pre_topc.html#U1">topology</a> of <font color="Maroon">c<sub>1</sub></font>
 
<b>by </b><i><a class="ref" href="zfmisc_1.html#T38">ZFMISC_1:38</a></i>;<br/>
<b>assume </b><a NAME="E3:12"/>
 <a href="pcomps_1.html#K1">bool</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K2">{</a><span class="default"><a href="xboole_0.html#K1">{}</a> ,the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>1</sub></font></span><a href="tarski.html#K2">}</a></span>
 ;<br/>

<a NAME="E4:12"/><b>then </b>
( the <a href="pre_topc.html#U1">topology</a> of <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a>  <a href="pcomps_1.html#K1">bool</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>1</sub></font> &amp; the <a href="pre_topc.html#U1">topology</a> of <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K2">{</a><span class="default"><a href="xboole_0.html#K1">{}</a> ,the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>1</sub></font></span><a href="tarski.html#K2">}</a></span> )
 
<b>by </b><i><a class="txt" href="tdlat_3.html#E2:12"><i><font color="Green">E11</font></i></a>, <a class="ref" href="xboole_0.html#D10">XBOOLE_0:def 10</a></i>;<br/>
<b>hence </b><a NAME="E5:12"/>
( <font color="Maroon">c<sub>1</sub></font> is <a href="tdlat_3.html#V1" target="_self">discrete</a> &amp; <font color="Maroon">c<sub>1</sub></font> is <a href="tdlat_3.html#V2" target="_self">anti-discrete</a> )
 <b>by </b><i><a class="ref" href="tdlat_3.html#D1" target="_self">Def1</a>, <a class="ref" href="tdlat_3.html#D2" target="_self">Def2</a></i>;<br/>


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