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

<b>let </b><font color="Maroon">c<sub>1</sub></font>, <font color="Maroon">c<sub>2</sub></font> be   <a href="seq_1.html#NM1">Real_Sequence</a>;<br/>



<b>thus </b><a NAME="E1:64"/>
( <font color="Maroon">c<sub>1</sub></font> is <a href="relat_1.html#V2">being_not_0</a> &amp; <font color="Maroon">c<sub>2</sub></font> is <a href="relat_1.html#V2">being_not_0</a> implies <font color="Maroon">c<sub>1</sub></font> <a href="seq_1.html#K11" target="_self">(#)</a> <font color="Maroon">c<sub>2</sub></font> is <a href="relat_1.html#V2">being_not_0</a> )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="64_1"><b>proof </b></a><div class="add">

<b>assume </b><b>that </b><br/><a NAME="E1:64_1"/><i><font color="Green">E37</font></i>: 
<font color="Maroon">c<sub>1</sub></font> is <a href="relat_1.html#V2">being_not_0</a>
 <b>and </b><br/><a NAME="E2:64_1"/><i><font color="Green">E38</font></i>: 
<font color="Maroon">c<sub>2</sub></font> is <a href="relat_1.html#V2">being_not_0</a>
 ;<br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="64_1_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c<sub>3</sub></font> be   <a href="nat_1.html#NM1">Nat</a>;<br/><a NAME="E1:64_1_1"/><i><font color="Green">E39</font></i>: 
<font color="Maroon">c<sub>1</sub></font> <a href="seq_1.html#K2" target="_self">.</a> <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 0
 <b>by </b><i><a class="txt" href="seq_1.html#E1:64_1"><i><font color="Green">E37</font></i></a>, <a class="ref" href="seq_1.html#T7" target="_self">Th7</a></i>;<br/><a NAME="E2:64_1_1"/><i><font color="Green">E40</font></i>: 
<font color="Maroon">c<sub>2</sub></font> <a href="seq_1.html#K2" target="_self">.</a> <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 0
 <b>by </b><i><a class="txt" href="seq_1.html#E2:64_1"><i><font color="Green">E38</font></i></a>, <a class="ref" href="seq_1.html#T7" target="_self">Th7</a></i>;<br/><a NAME="E3:64_1_1"/>
<span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="seq_1.html#K11" target="_self">(#)</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="seq_1.html#K2" target="_self">.</a> <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="seq_1.html#K2" target="_self">.</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="real_1.html#K4">*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="seq_1.html#K2" target="_self">.</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>
 <b>by </b><i><a class="ref" href="seq_1.html#T12" target="_self">Th12</a></i>;<br/><b>hence </b><a NAME="E4:64_1_1"/>
<span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="seq_1.html#K11" target="_self">(#)</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="seq_1.html#K2" target="_self">.</a> <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 0
 <b>by </b><i><a class="txt" href="seq_1.html#E1:64_1_1"><i><font color="Green">E39</font></i></a>, <a class="txt" href="seq_1.html#E2:64_1_1"><i><font color="Green">E40</font></i></a>, <a class="ref" href="xcmplx_1.html#T6">XCMPLX_1:6</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E4:64_1"/>
<font color="Maroon">c<sub>1</sub></font> <a href="seq_1.html#K11" target="_self">(#)</a> <font color="Maroon">c<sub>2</sub></font> is <a href="relat_1.html#V2">being_not_0</a>
 <b>by </b><i><a class="ref" href="seq_1.html#T7" target="_self">Th7</a></i>;<br/>


</div><b>end;</b></div>

<b>assume </b><a NAME="E2:64"/><i><font color="Green">E37</font></i>: 
<font color="Maroon">c<sub>1</sub></font> <a href="seq_1.html#K11" target="_self">(#)</a> <font color="Maroon">c<sub>2</sub></font> is <a href="relat_1.html#V2">being_not_0</a>
 ;<br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="64_2"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c<sub>3</sub></font> be   <a href="nat_1.html#NM1">Nat</a>;<br/><a NAME="E1:64_2"/>
<span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="seq_1.html#K11" target="_self">(#)</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="seq_1.html#K2" target="_self">.</a> <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="seq_1.html#K2" target="_self">.</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="real_1.html#K4">*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="seq_1.html#K2" target="_self">.</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>
 <b>by </b><i><a class="ref" href="seq_1.html#T12" target="_self">Th12</a></i>;<br/><b>hence </b><a NAME="E2:64_2"/>
<font color="Maroon">c<sub>1</sub></font> <a href="seq_1.html#K2" target="_self">.</a> <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 0
 <b>by </b><i><a class="txt" href="seq_1.html#E2:64"><i><font color="Green">E37</font></i></a>, <a class="ref" href="seq_1.html#T7" target="_self">Th7</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E4:64"/>
<font color="Maroon">c<sub>1</sub></font> is <a href="relat_1.html#V2">being_not_0</a>
 <b>by </b><i><a class="ref" href="seq_1.html#T7" target="_self">Th7</a></i>;<br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="64_3"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c<sub>3</sub></font> be   <a href="nat_1.html#NM1">Nat</a>;<br/><a NAME="E1:64_3"/>
<span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="seq_1.html#K11" target="_self">(#)</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="seq_1.html#K2" target="_self">.</a> <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="seq_1.html#K2" target="_self">.</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="real_1.html#K4">*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="seq_1.html#K2" target="_self">.</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>
 <b>by </b><i><a class="ref" href="seq_1.html#T12" target="_self">Th12</a></i>;<br/><b>hence </b><a NAME="E2:64_3"/>
<font color="Maroon">c<sub>2</sub></font> <a href="seq_1.html#K2" target="_self">.</a> <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 0
 <b>by </b><i><a class="txt" href="seq_1.html#E2:64"><i><font color="Green">E37</font></i></a>, <a class="ref" href="seq_1.html#T7" target="_self">Th7</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E6:64"/>
<font color="Maroon">c<sub>2</sub></font> is <a href="relat_1.html#V2">being_not_0</a>
 <b>by </b><i><a class="ref" href="seq_1.html#T7" target="_self">Th7</a></i>;<br/>


</div>
