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

<span class="kw">let </span><font color="Maroon" title="c1">n</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">x1</font>, <font color="Olive" title="b2">x2</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="urysohn1.html#K1" title="URYSOHN1:func.1">dyadic</a> <font color="Maroon" title="c1">n</font>  st <font color="Olive" title="b1">x1</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Olive" title="b2">x2</font> holds <br/> <a href="urysohn1.html#K6" title="URYSOHN1:func.6">axis</a> <font color="Olive" title="b1">x1</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="urysohn1.html#K6" title="URYSOHN1:func.6">axis</a> <font color="Olive" title="b2">x2</font></span><br/><span class="kw">let </span><font color="Maroon" title="c2">x1</font>, <font color="Maroon" title="c3">x2</font> be    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="urysohn1.html#K1" title="URYSOHN1:func.1">dyadic</a> <font color="Maroon" title="c1">n</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c2">x1</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c3">x2</font> implies  <a href="urysohn1.html#K6" title="URYSOHN1:func.6">axis</a> <font color="Maroon" title="c2">x1</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="urysohn1.html#K6" title="URYSOHN1:func.6">axis</a> <font color="Maroon" title="c3">x2</font> )</span><br/>



<a NAME="E1:23"/><span class="lab"><font color="Green" title="E16">A1</font></span>: 
 <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> 2 <a href="newton.html#K15" title="NEWTON:func.15">|^</a> <font color="Maroon" title="c1">n</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="newton.html#T83" title="NEWTON:th.83">NEWTON:83</a></span>;<br/>
<a NAME="E2:23"/>
( <font color="Maroon" title="c2">x1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="urysohn1.html#K6" title="URYSOHN1:func.6">axis</a> <font color="Maroon" title="c2">x1</font></span>)</span> <a href="real_1.html#K6" title="REAL_1:func.6">/</a> <span class="p1">(<span class="default">2 <a href="newton.html#K15" title="NEWTON:func.15">|^</a> <font color="Maroon" title="c1">n</font></span>)</span> &amp; <font color="Maroon" title="c3">x2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="urysohn1.html#K6" title="URYSOHN1:func.6">axis</a> <font color="Maroon" title="c3">x2</font></span>)</span> <a href="real_1.html#K6" title="REAL_1:func.6">/</a> <span class="p1">(<span class="default">2 <a href="newton.html#K15" title="NEWTON:func.15">|^</a> <font color="Maroon" title="c1">n</font></span>)</span> )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="urysohn1.html#T10" target="_self" title="URYSOHN1:th.10">Th16</a></span>;<br/>
<span class="kw">hence </span><a NAME="E3:23"/>
( <font color="Maroon" title="c2">x1</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c3">x2</font> implies  <a href="urysohn1.html#K6" title="URYSOHN1:func.6">axis</a> <font color="Maroon" title="c2">x1</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="urysohn1.html#K6" title="URYSOHN1:func.6">axis</a> <font color="Maroon" title="c3">x2</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:23"><span class="lab"><font color="Green" title="E16">A1</font></span></a>, <a class="ref" href="xreal_1.html#T72" title="XREAL_1:th.72">XREAL_1:72</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div>
