<?xml version="1.0"?>
<div class="add">

<b>let </b><font color="Maroon">T</font> be  non <a href="struct_0.html#V3">empty</a> <a href="compts_1.html#V5">being_T4</a> <a href="pre_topc.html#NM1">TopSpace</a>;<br/><b>let </b><font color="Maroon">A</font> be  <a href="pre_topc.html#V4">closed</a> <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">T</font>, <font color="Maroon">B</font> be  <a href="pre_topc.html#V4">closed</a> <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">T</font>;<br/>



<b>assume </b><a NAME="E1:15"/><i><font color="Green">E31</font></i>: 
( <font color="Maroon">A</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="measure5.html#K6">{}</a>  &amp; <font color="Maroon">A</font> <a href="xboole_0.html#R1">misses</a> <font color="Maroon">B</font> )
 ;<br/>

<b>let </b><font color="Maroon">G</font> be    <a href="urysohn3.html#M2" target="_self">Rain</a> of <font color="Maroon">A</font>,<font color="Maroon">B</font>;<br/><b>let </b><font color="Maroon">x</font> be   <a href="real_1.html#NM1">Real</a>;<br/>



<b>assume </b><a NAME="E2:15"/><i><font color="Green">E33</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="urysohn1.html#K2">DYADIC</a> 
 ;<br/>

<b>reconsider </b><font color="Maroon">s</font> =  <a href="urysohn3.html#K2" target="_self">inf_number_dyadic</a> <font color="Maroon">x</font> as    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a>  ;<br/>
<a NAME="E4:15"/><i><font color="Green">E34</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="urysohn1.html#K1">dyadic</a> <font color="Maroon">s</font>
 
<b>by </b><i>, </i>;<br/>
<a NAME="E5:15"/>
<font color="Maroon">G</font> <a href="seqfunc.html#K1">.</a> <font color="Maroon">s</font> is    <a href="urysohn3.html#M1" target="_self">Drizzle</a> of <font color="Maroon">A</font>,<font color="Maroon">B</font>,<font color="Maroon">s</font>
 
<b>by </b><i>, </i>;<br/>
<b>then reconsider </b><font color="Maroon">y</font> = <span class="p1">(<span class="default"><font color="Maroon">G</font> <a href="seqfunc.html#K1">.</a> <font color="Maroon">s</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> as   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">T</font> <b>by </b><i>, <a class="ref" href="funct_2.html#T7">FUNCT_2:7</a></i>;<br/>
<b>take </b>
<font color="Maroon">y</font>
;<br/>

<b>let </b><font color="Maroon">n</font> be    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/>

<b>assume </b><a NAME="E7:15"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="urysohn1.html#K1">dyadic</a> <font color="Maroon">n</font>
 ;<br/>

<a NAME="E8:15"/><b>then </b>
<font color="Maroon">s</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">n</font>
 
<b>by </b><i/>;<br/>
<b>then consider </b><font color="Maroon">m</font> being   <a href="nat_1.html#NM1">Nat</a><b> such that </b><br/><a NAME="E10:15"/><i><font color="Green">E36</font></i>: 
<font color="Maroon">n</font> <a href="hidden.html#R1">=</a> <font color="Maroon">s</font> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">m</font>
 <b>by </b><i><a class="ref" href="nat_1.html#T28">NAT_1:28</a></i>;<br/>
<a NAME="E11:15"/>
<font color="Maroon">m</font> <a href="hidden.html#R2">in</a>  <a href="numbers.html#K5">NAT</a> 
 
<b>by </b><i><a class="ref" href="ordinal1.html#D13">ORDINAL1:def 13</a></i>;<br/>
<b>hence </b><a NAME="E12:15"/>
<font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">G</font> <a href="seqfunc.html#K1">.</a> <font color="Maroon">n</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font>
 <b>by </b><i>, , , </i>;<br/>


</div>
