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

<b>let </b><font color="Maroon">RNS</font> be  non <a href="struct_0.html#V3">empty</a>  <a href="struct_0.html#L1">1-sorted</a> ;<br/><b>let </b><font color="Maroon">S</font> be   <a href="normsp_1.html#NM2">sequence</a> of <font color="Maroon">RNS</font>;<br/>



<b>assume </b><b>that </b><br/><a NAME="E1:26"/><i><font color="Green">E40</font></i>: 
for <font color="Olive">n</font>, <font color="Olive">m</font> being   <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a>  holds  <font color="Maroon">S</font> <a href="funct_2.html#K3">.</a> <font color="Olive">n</font> <a href="hidden.html#R1">=</a> <font color="Maroon">S</font> <a href="funct_2.html#K3">.</a> <font color="Olive">m</font>
 <b>and </b><br/><a NAME="E2:26"/><i><font color="Green">E46</font></i>: 
for <font color="Olive">x</font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">RNS</font>  ex <font color="Olive">n</font> being   <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a>  st <font color="Maroon">S</font> <a href="funct_2.html#K3">.</a> <font color="Olive">n</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Olive">x</font>
 ;<br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="26_1"><b>now </b></a><div class="add"><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>consider </b><font color="Maroon">z</font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">RNS</font><b> such that </b><br/><a NAME="E2:26_1"/><i><font color="Green">E72</font></i>: 
<font color="Maroon">S</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">n</font> <a href="hidden.html#R1">=</a> <font color="Maroon">z</font>
 ;<br/><a NAME="E3:26_1"/>
 ex <font color="Olive">k</font> being   <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a>  st <font color="Maroon">S</font> <a href="funct_2.html#K3">.</a> <font color="Olive">k</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">z</font>
 <b>by </b><i/>;<br/><b>hence </b><a NAME="E4:26_1"/>
contradiction
 <b>by </b><i>, </i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E4:26"/>
contradiction
 ;<br/>


</div>
