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

<b>let </b><font color="Maroon">seq</font> be   <a href="toprns_1.html#NM1">Real_Sequence</a> of <font color="Maroon">N</font>;<br/><b>let </b><font color="Maroon">seq'</font> be   <a href="toprns_1.html#NM1">Real_Sequence</a> of <font color="Maroon">N</font>;<br/>



<b>assume </b><b>that </b><br/><a NAME="E1:9_1_2"/><i><font color="Green">E44</font></i>: 
for <font color="Olive">n</font> being   <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a>  holds  <font color="Maroon">seq</font> <a href="normsp_1.html#K2">.</a> <font color="Olive">n</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">seq1</font> <a href="normsp_1.html#K2">.</a> <font color="Olive">n</font></span>)</span> <a href="euclid.html#K17">+</a> <span class="p1">(<span class="default"><font color="Maroon">seq2</font> <a href="normsp_1.html#K2">.</a> <font color="Olive">n</font></span>)</span>
 <b>and </b><br/><a NAME="E2:9_1_2"/><i><font color="Green">E45</font></i>: 
for <font color="Olive">n</font> being   <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a>  holds  <font color="Maroon">seq'</font> <a href="normsp_1.html#K2">.</a> <font color="Olive">n</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">seq1</font> <a href="normsp_1.html#K2">.</a> <font color="Olive">n</font></span>)</span> <a href="euclid.html#K17">+</a> <span class="p1">(<span class="default"><font color="Maroon">seq2</font> <a href="normsp_1.html#K2">.</a> <font color="Olive">n</font></span>)</span>
 ;<br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="9_1_2_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/><a NAME="E1:9_1_2_1"/>
( <font color="Maroon">seq</font> <a href="normsp_1.html#K2">.</a> <font color="Maroon">n</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">seq1</font> <a href="normsp_1.html#K2">.</a> <font color="Maroon">n</font></span>)</span> <a href="euclid.html#K17">+</a> <span class="p1">(<span class="default"><font color="Maroon">seq2</font> <a href="normsp_1.html#K2">.</a> <font color="Maroon">n</font></span>)</span> &amp; <font color="Maroon">seq'</font> <a href="normsp_1.html#K2">.</a> <font color="Maroon">n</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">seq1</font> <a href="normsp_1.html#K2">.</a> <font color="Maroon">n</font></span>)</span> <a href="euclid.html#K17">+</a> <span class="p1">(<span class="default"><font color="Maroon">seq2</font> <a href="normsp_1.html#K2">.</a> <font color="Maroon">n</font></span>)</span> )
 <b>by </b><i>, </i>;<br/><b>hence </b><a NAME="E2:9_1_2_1"/>
<font color="Maroon">seq</font> <a href="normsp_1.html#K2">.</a> <font color="Maroon">n</font> <a href="hidden.html#R1">=</a> <font color="Maroon">seq'</font> <a href="normsp_1.html#K2">.</a> <font color="Maroon">n</font>
 ;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E4:9_1_2"/>
<font color="Maroon">seq</font> <a href="hidden.html#R1">=</a> <font color="Maroon">seq'</font>
 <b>by </b><i/>;<br/>


</div>
