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<b>set </b><font color="Maroon" title="c1">D</font> = <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> ,1</span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span>;<br/>
<b>reconsider </b><font color="Maroon" title="c2">a</font> =  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  as    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> ,1</span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span> <b>by </b><i><a class="ref" href="tarski.html#D2" title="TARSKI:def.2">TARSKI:def 2</a></i>;<br/>
<b>set </b><font color="Maroon" title="c3">Y</font> =  <a href="tex_1.html#K3" title="TEX_1:func.3">STS</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> ,1</span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span>,<font color="Maroon" title="c2">a</font>;<br/>
<b>take </b>
 <a href="tex_1.html#K3" title="TEX_1:func.3">STS</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> ,1</span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span>,<font color="Maroon" title="c2">a</font>
;<br/>

<b>reconsider </b><font color="Maroon" title="c4">A</font> = <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c2">a</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> as  non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="tex_1.html#K3" title="TEX_1:func.3">STS</a> <span class="p2"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> ,1</span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span>,<font color="Maroon" title="c2">a</font></span>)</span> ;<br/>
<a NAME="E3:40_1_1"/><i><font color="Green" title="E17">A1</font></i>: 
( 1 <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> ,1</span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span> &amp; not 1 <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">A</font> )
 
<b>by </b><i><a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a>, <a class="ref" href="tarski.html#D2" title="TARSKI:def.2">TARSKI:def 2</a></i>;<br/>
<a NAME="E4:40_1_1"/><b>then </b>
not <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> ,1</span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span> <a href="subset_1.html#K6" title="SUBSET_1:func.6">\</a> <font color="Maroon" title="c4">A</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>
 
<b>by </b><i><a class="ref" href="xboole_0.html#D4" title="XBOOLE_0:def.4">XBOOLE_0:def 4</a></i>;<br/>
<a NAME="E5:40_1_1"/><b>then </b><i><font color="Green" title="E18">A2</font></i>: 
( <font color="Maroon" title="c4">A</font> is <a href="pre_topc.html#V4" title="PRE_TOPC:attr.4">closed</a> &amp; <font color="Maroon" title="c4">A</font> is <a href="tops_1.html#V2" title="TOPS_1:attr.2">boundary</a> )
 
<b>by </b><i><a class="ref" href="tex_1.html#T25" target="_self" title="TEX_1:th.25">Th25</a></i>;<br/>
<a NAME="E6:40_1_1"/><b>then </b>
 <a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <font color="Maroon" title="c4">A</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c4">A</font>
 
<b>by </b><i><a class="ref" href="tops_1.html#T84" title="TOPS_1:th.84">TOPS_1:84</a></i>;<br/>
<a NAME="E7:40_1_1"/><b>then </b>
not <font color="Maroon" title="c4">A</font> is <a href="pre_topc.html#V3" title="PRE_TOPC:attr.3">open</a>
 
<b>by </b><i><a class="ref" href="tops_1.html#T55" title="TOPS_1:th.55">TOPS_1:55</a></i>;<br/>
<b>hence </b><a NAME="E8:40_1_1"/>
( not  <a href="tex_1.html#K3" title="TEX_1:func.3">STS</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> ,1</span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span>,<font color="Maroon" title="c2">a</font> is <a href="tdlat_3.html#V2" title="TDLAT_3:attr.2">anti-discrete</a> &amp; not  <a href="tex_1.html#K3" title="TEX_1:func.3">STS</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> ,1</span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span>,<font color="Maroon" title="c2">a</font> is <a href="tdlat_3.html#V1" title="TDLAT_3:attr.1">discrete</a> &amp;  <a href="tex_1.html#K3" title="TEX_1:func.3">STS</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> ,1</span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span>,<font color="Maroon" title="c2">a</font> is <a href="pre_topc.html#V1" title="PRE_TOPC:attr.1">strict</a> &amp; not  <a href="tex_1.html#K3" title="TEX_1:func.3">STS</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> ,1</span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span>,<font color="Maroon" title="c2">a</font> is <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a> )
 <b>by </b><i><a class="txt" href="tex_1.html#E3:40_1_1"><i><font color="Green" title="E17">A1</font></i></a>, <a class="txt" href="tex_1.html#E5:40_1_1"><i><font color="Green" title="E18">A2</font></i></a>, <a class="ref" href="tdlat_3.html#T17" title="TDLAT_3:th.17">TDLAT_3:17</a>, <a class="ref" href="tdlat_3.html#T21" title="TDLAT_3:th.21">TDLAT_3:21</a></i>;<br/>


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