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

<a NAME="E1:43_1_1"/><i><font color="Green">E31</font></i>: 
 <a href="relat_1.html#K2">rng</a> <font color="Maroon">Nseq1</font> <a href="tarski.html#R1">c=</a>  <a href="numbers.html#K5">NAT</a> 
 
<b>by </b><i/>;<br/>
<a NAME="E2:43_1_1"/>
 <a href="relat_1.html#K2">rng</a> <span class="p1">(<span class="default"><font color="Maroon">Nseq1</font> <a href="seqm_3.html#K3" target="_self">*</a> <font color="Maroon">Nseq</font></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="relat_1.html#K2">rng</a> <font color="Maroon">Nseq1</font>
 
<b>by </b><i><a class="ref" href="relat_1.html#T45">RELAT_1:45</a></i>;<br/>
<a NAME="E3:43_1_1"/><b>then </b><i><font color="Green">E33</font></i>: 
 <a href="relat_1.html#K2">rng</a> <span class="p1">(<span class="default"><font color="Maroon">Nseq1</font> <a href="seqm_3.html#K3" target="_self">*</a> <font color="Maroon">Nseq</font></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="numbers.html#K5">NAT</a> 
 
<b>by </b><i>, <a class="ref" href="xboole_1.html#T1">XBOOLE_1:1</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="43_1_1_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="E1:43_1_1_1"/>
<font color="Maroon">Nseq</font> <a href="seqm_3.html#K2" target="_self">.</a> <font color="Maroon">n</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">Nseq</font> <a href="seqm_3.html#K2" target="_self">.</a> <span class="p1">(<span class="default"><font color="Maroon">n</font> <a href="nat_1.html#K1">+</a> 1</span>)</span>
 <b>by </b><i/>;<br/><a NAME="E2:43_1_1_1"/><b>then </b>
<font color="Maroon">Nseq1</font> <a href="seqm_3.html#K2" target="_self">.</a> <span class="p1">(<span class="default"><font color="Maroon">Nseq</font> <a href="seqm_3.html#K2" target="_self">.</a> <font color="Maroon">n</font></span>)</span> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">Nseq1</font> <a href="seqm_3.html#K2" target="_self">.</a> <span class="p1">(<span class="default"><font color="Maroon">Nseq</font> <a href="seqm_3.html#K2" target="_self">.</a> <span class="p2">(<span class="default"><font color="Maroon">n</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>
 <b>by </b><i/>;<br/><a NAME="E3:43_1_1_1"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon">Nseq1</font> <a href="seqm_3.html#K3" target="_self">*</a> <font color="Maroon">Nseq</font></span>)</span> <a href="seq_1.html#K2">.</a> <font color="Maroon">n</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">Nseq1</font> <a href="seqm_3.html#K2" target="_self">.</a> <span class="p1">(<span class="default"><font color="Maroon">Nseq</font> <a href="seqm_3.html#K2" target="_self">.</a> <span class="p2">(<span class="default"><font color="Maroon">n</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>
 <b>by </b><i/>;<br/><b>hence </b><a NAME="E4:43_1_1_1"/>
<span class="p1">(<span class="default"><font color="Maroon">Nseq1</font> <a href="seqm_3.html#K3" target="_self">*</a> <font color="Maroon">Nseq</font></span>)</span> <a href="seq_1.html#K2">.</a> <font color="Maroon">n</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <span class="p1">(<span class="default"><font color="Maroon">Nseq1</font> <a href="seqm_3.html#K3" target="_self">*</a> <font color="Maroon">Nseq</font></span>)</span> <a href="seq_1.html#K2">.</a> <span class="p1">(<span class="default"><font color="Maroon">n</font> <a href="nat_1.html#K1">+</a> 1</span>)</span>
 <b>by </b><i/>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E5:43_1_1"/>
<font color="Maroon">Nseq</font> <a href="relat_1.html#K5">*</a> <font color="Maroon">Nseq1</font> is  <a href="seqm_3.html#V1" target="_self">increasing</a> <a href="seqm_3.html#NM1">Seq_of_Nat</a>
 <b>by </b><i>, , </i>;<br/>


</div>
