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<b>let </b><font color="Maroon" title="c1">T</font> be  non <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a> <a href="compts_1.html#NV6" title="COMPTS_1:NV.6">Hausdorff</a> <a href="pre_topc.html#NM1" title="PRE_TOPC:NM.1">TopSpace</a>;<br/><b>let </b><font color="Maroon" title="c2">S</font> be  <a href="yellow_8.html#V2" title="YELLOW_8:attr.2">irreducible</a> <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">T</font>; <i><font color="Red">:: according to </font></i><a class="ref" href="yellow_8.html#D6" target="_self" title="YELLOW_8:def.6">YELLOW_8:def 6</a><br/>



<b>consider </b><font color="Maroon" title="c3">d</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of <font color="Maroon" title="c2">S</font><b> such that </b><br/><a NAME="E2:30"/><i><font color="Green" title="E22">A1</font></i>: 
<font color="Maroon" title="c2">S</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c3">d</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>
 <b>by </b><i><a class="ref" href="tex_2.html#D1" title="TEX_2:def.1">TEX_2:def 1</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c4">d</font> = <font color="Maroon" title="c3">d</font> as   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <font color="Maroon" title="c1">T</font> ;<br/>
<b>take </b>
<font color="Maroon" title="c4">d</font>
;<br/>

<b>thus </b><a NAME="E4:30"/>
<font color="Maroon" title="c4">d</font> <a href="yellow_8.html#R1" title="YELLOW_8:pred.1">is_dense_point_of</a> <font color="Maroon" title="c2">S</font>
 <b>by </b><i><a class="txt" href="yellow_8.html#E2:30"><i><font color="Green" title="E22">A1</font></i></a>, <a class="ref" href="yellow_8.html#T28" target="_self" title="YELLOW_8:th.28">Th28</a></i>;<br/>

<b>let </b><font color="Maroon" title="c5">p</font> be   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <font color="Maroon" title="c1">T</font>;<br/>

<b>assume </b><a NAME="E5:30"/>
<font color="Maroon" title="c5">p</font> <a href="yellow_8.html#R1" title="YELLOW_8:pred.1">is_dense_point_of</a> <font color="Maroon" title="c2">S</font>
 ;<br/>

<a NAME="E6:30"/><b>then </b>
<font color="Maroon" title="c5">p</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">S</font>
 
<b>by </b><i><a class="ref" href="yellow_8.html#D5" target="_self" title="YELLOW_8:def.5">Def5</a></i>;<br/>
<b>hence </b><a NAME="E7:30"/>
<font color="Maroon" title="c5">p</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="yellow_8.html#E2:30"><i><font color="Green" title="E22">A1</font></i></a>, <a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></i>;<br/>


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