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<b>let </b><font color="Maroon">Y</font> be  non <a href="struct_0.html#V3">empty</a>  <a href="pre_topc.html#L1">TopStruct</a> ;<br/><b>let </b><font color="Maroon">Y0</font> be    <a href="pre_topc.html#M1">SubSpace</a> of <font color="Maroon">Y</font>;<br/><b>let </b><font color="Maroon">A</font> be   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">Y</font>;<br/>





<b>assume </b><a NAME="E1:92"/><i><font color="Green">E13</font></i>: 
<font color="Maroon">A</font> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">Y0</font>
 ;<br/>

<b>assume </b><a NAME="E2:92"/>
<font color="Maroon">Y0</font> is <a href="tdlat_3.html#V2">anti-discrete</a>
 ;<br/>

<a NAME="E3:92"/><b>then </b><i><font color="Green">E20</font></i>: 
the <a href="pre_topc.html#U1">topology</a> of <font color="Maroon">Y0</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">Y0</font></span><a href="tarski.html#K2">}</a></span>
 
<b>by </b><i><a class="ref" href="tdlat_3.html#D2">TDLAT_3:def 2</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="92_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">G</font> be   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">Y</font>;<br/><b>assume </b><a NAME="E1:92_1"/><i><font color="Green">E21</font></i>: 
<font color="Maroon">G</font> is <a href="pre_topc.html#V3">open</a>
 ;<br/><b>reconsider </b><font color="Maroon">H</font> = <font color="Maroon">A</font> <a href="subset_1.html#K9">/\</a> <font color="Maroon">G</font> as   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">Y0</font> <b>by </b><i><a class="ref" href="tex_4.html#T12" target="_self">Th12</a>, <a class="ref" href="xboole_1.html#T17">XBOOLE_1:17</a></i>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="92_1_1"><b>now </b></a><div class="add"><b>take </b><font color="Maroon">G</font> = <font color="Maroon">G</font>;<br/><b>thus </b><a NAME="E1:92_1_1"/>
<font color="Maroon">G</font> <a href="hidden.html#R2">in</a> the <a href="pre_topc.html#U1">topology</a> of <font color="Maroon">Y</font>
 <b>by </b><i><a class="ref" href="tex_4.html#T14" target="_self">Th14</a>, <a class="ref" href="pre_topc.html#D5">PRE_TOPC:def 5</a></i>;<br/><b>thus </b><a NAME="E2:92_1_1"/>
<font color="Maroon">H</font> <a href="hidden.html#R1">=</a> <font color="Maroon">G</font> <a href="subset_1.html#K9">/\</a> <span class="p1">(<span class="default"><a href="pre_topc.html#K2">[#]</a> <font color="Maroon">Y0</font></span>)</span>
 <b>by </b><i><a class="ref" href="tex_4.html#T12" target="_self">Th12</a></i>;<br/></div><b>end;</b></div><a NAME="E4:92_1"/><b>then </b>
<font color="Maroon">H</font> <a href="hidden.html#R2">in</a> the <a href="pre_topc.html#U1">topology</a> of <font color="Maroon">Y0</font>
 <b>by </b><i><a class="ref" href="pre_topc.html#D9">PRE_TOPC:def 9</a></i>;<br/><a NAME="E5:92_1"/><b>then </b>
( <font color="Maroon">A</font> <a href="subset_1.html#K9">/\</a> <font color="Maroon">G</font> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a>  or <font color="Maroon">A</font> <a href="subset_1.html#K9">/\</a> <font color="Maroon">G</font> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">Y0</font> )
 <b>by </b><i><a class="ref" href="tex_4.html#T13" target="_self">Th13</a>, <a class="ref" href="tarski.html#D2">TARSKI:def 2</a></i>;<br/><b>hence </b><a NAME="E6:92_1"/>
( <font color="Maroon">A</font> <a href="xboole_0.html#R1">misses</a> <font color="Maroon">G</font> or <font color="Maroon">A</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">G</font> )
 <b>by </b><i><a class="ref" href="tex_4.html#T12" target="_self">Th12</a>, <a class="ref" href="xboole_0.html#D7">XBOOLE_0:def 7</a>, <a class="ref" href="xboole_1.html#T17">XBOOLE_1:17</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E5:92"/>
<font color="Maroon">A</font> is <a href="tex_4.html#V1" target="_self">anti-discrete</a>
 <b>by </b><i/>;<br/>


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