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<b>let </b><font color="Maroon">c<sub>1</sub></font> be   <a href="nat_1.html#NM1">Nat</a>;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font> be   <a href="real_1.html#NM1">Real</a>;<br/>



<b>assume </b><a NAME="E1:8"/>
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</a>  <a href="urysohn1.html#K1" target="_self">dyadic</a> <font color="Maroon">c<sub>1</sub></font>
 ;<br/>

<b>then consider </b><font color="Maroon">c<sub>3</sub></font> being   <a href="nat_1.html#NM1">Nat</a><b> such that </b><br/><a NAME="E3:8"/><i><font color="Green">E4</font></i>: 
( 0 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>3</sub></font> &amp; <font color="Maroon">c<sub>3</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> 2 <a href="card_4.html#K1">|^</a> <font color="Maroon">c<sub>1</sub></font> &amp; <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font> <a href="real_1.html#K6">/</a> <span class="p1">(<span class="default">2 <a href="card_4.html#K1">|^</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> )
 <b>by </b><i><a class="ref" href="urysohn1.html#D3" target="_self">Def3</a></i>;<br/>
<a NAME="E4:8"/>
0 <a href="xxreal_0.html#NR3" target="_self">&lt;</a> 2 <a href="card_4.html#K1">|^</a> <font color="Maroon">c<sub>1</sub></font>
 
<b>by </b><i><a class="ref" href="newton.html#T102">NEWTON:102</a></i>;<br/>
<a NAME="E5:8"/><b>then </b><i><font color="Green">E5</font></i>: 
( 0 <a href="real_1.html#K6">/</a> <span class="p1">(<span class="default">2 <a href="card_4.html#K1">|^</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>3</sub></font> <a href="real_1.html#K6">/</a> <span class="p1">(<span class="default">2 <a href="card_4.html#K1">|^</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> &amp; <font color="Maroon">c<sub>3</sub></font> <a href="real_1.html#K6">/</a> <span class="p1">(<span class="default">2 <a href="card_4.html#K1">|^</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default">2 <a href="card_4.html#K1">|^</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="real_1.html#K6">/</a> <span class="p1">(<span class="default">2 <a href="card_4.html#K1">|^</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> )
 
<b>by </b><i><a class="txt" href="urysohn1.html#E3:8"><i><font color="Green">E4</font></i></a>, <a class="ref" href="real_1.html#T73">REAL_1:73</a></i>;<br/>
<b>thus </b><a NAME="E6:8"/>
( 0 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>2</sub></font> &amp; <font color="Maroon">c<sub>2</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> 1 )
 <b>by </b><i><a class="txt" href="urysohn1.html#E3:8"><i><font color="Green">E4</font></i></a>, <a class="txt" href="urysohn1.html#E5:8"><i><font color="Green">E5</font></i></a>, <a class="ref" href="xcmplx_1.html#T60">XCMPLX_1:60</a></i>;<br/>


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