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<b>let </b><font color="Maroon" title="c1">Y</font> be    <a href="pre_topc.html#L1" title="PRE_TOPC:struct.1">TopStruct</a> ;<br/><b>let </b><font color="Maroon" title="c2">A</font>, <font color="Maroon" title="c3">B</font> be   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">Y</font>;<br/>



<b>assume </b><a NAME="E1:66"/><i><font color="Green" title="E23">A1</font></i>: 
<font color="Maroon" title="c3">B</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c2">A</font>
 ;<br/>

<b>assume </b><a NAME="E2:66"/><i><font color="Green" title="E24">A2</font></i>: 
<font color="Maroon" title="c2">A</font> is <a href="tex_2.html#V3" title="TEX_2:attr.3">discrete</a>
 ;<br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="66_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c4">D</font> be   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">Y</font>;<br/><b>assume </b><a NAME="E1:66_1"/><i><font color="Green" title="E25">A3</font></i>: 
<font color="Maroon" title="c4">D</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c3">B</font>
 ;<br/><a NAME="E2:66_1"/><b>then </b>
<font color="Maroon" title="c4">D</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c2">A</font>
 <b>by </b><i><a class="txt" href="tex_2.html#E1:66"><i><font color="Green" title="E23">A1</font></i></a>, <a class="ref" href="xboole_1.html#T1" title="XBOOLE_1:th.1">XBOOLE_1:1</a></i>;<br/><b>then consider </b><font color="Maroon" title="c5">G</font> being   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">Y</font><b> such that </b><br/><a NAME="E4:66_1"/><i><font color="Green" title="E26">A4</font></i>: 
<font color="Maroon" title="c5">G</font> is <a href="pre_topc.html#V3" title="PRE_TOPC:attr.3">open</a>
 <b>and </b><br/><a NAME="E5:66_1"/><i><font color="Green" title="E27">A5</font></i>: 
<font color="Maroon" title="c2">A</font> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <font color="Maroon" title="c5">G</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">D</font>
 <b>by </b><i><a class="txt" href="tex_2.html#E2:66"><i><font color="Green" title="E24">A2</font></i></a>, <a class="ref" href="tex_2.html#D5" target="_self" title="TEX_2:def.5">Def5</a></i>;<br/><div><b>hereby </b>
<div class="add"><b>take </b><font color="Maroon" title="c6">G</font> = <font color="Maroon" title="c5">G</font>;<br/><a NAME="E1:66_1_1"/>
<font color="Maroon" title="c4">D</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c6">G</font>
 <b>by </b><i><a class="txt" href="tex_2.html#E5:66_1"><i><font color="Green" title="E27">A5</font></i></a>, <a class="ref" href="xboole_1.html#T17" title="XBOOLE_1:th.17">XBOOLE_1:17</a></i>;<br/><a NAME="E2:66_1_1"/><b>then </b><i><font color="Green" title="E28">A6</font></i>: 
<font color="Maroon" title="c4">D</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c3">B</font> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <font color="Maroon" title="c6">G</font>
 <b>by </b><i><a class="txt" href="tex_2.html#E1:66_1"><i><font color="Green" title="E25">A3</font></i></a>, <a class="ref" href="xboole_1.html#T19" title="XBOOLE_1:th.19">XBOOLE_1:19</a></i>;<br/><a NAME="E3:66_1_1"/>
<font color="Maroon" title="c3">B</font> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <font color="Maroon" title="c6">G</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c2">A</font> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <font color="Maroon" title="c6">G</font>
 <b>by </b><i><a class="txt" href="tex_2.html#E1:66"><i><font color="Green" title="E23">A1</font></i></a>, <a class="ref" href="xboole_1.html#T26" title="XBOOLE_1:th.26">XBOOLE_1:26</a></i>;<br/><b>hence </b><a NAME="E4:66_1_1"/>
( <font color="Maroon" title="c6">G</font> is <a href="pre_topc.html#V3" title="PRE_TOPC:attr.3">open</a> &amp; <font color="Maroon" title="c3">B</font> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <font color="Maroon" title="c6">G</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">D</font> )
 <b>by </b><i><a class="txt" href="tex_2.html#E4:66_1"><i><font color="Green" title="E26">A4</font></i></a>, <a class="txt" href="tex_2.html#E5:66_1"><i><font color="Green" title="E27">A5</font></i></a>, <a class="txt" href="tex_2.html#E2:66_1_1"><i><font color="Green" title="E28">A6</font></i></a>, <a class="ref" href="xboole_0.html#D10" title="XBOOLE_0:def.10">XBOOLE_0:def 10</a></i>;<br/></div>
<b>end;</b></div></div><b>end;</b></div>
<b>hence </b><a NAME="E4:66"/>
<font color="Maroon" title="c3">B</font> is <a href="tex_2.html#V3" title="TEX_2:attr.3">discrete</a>
 <b>by </b><i><a class="ref" href="tex_2.html#D5" target="_self" title="TEX_2:def.5">Def5</a></i>;<br/>


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