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<b>let </b><font color="Maroon">c<sub>1</sub></font>, <font color="Maroon">c<sub>2</sub></font>, <font color="Maroon">c<sub>3</sub></font>, <font color="Maroon">c<sub>4</sub></font> be   <a href="comseq_1.html#NM1">Complex_Sequence</a>;<br/>







<b>assume </b><b>that </b><br/><a NAME="E1:59"/><i><font color="Green">E43</font></i>: 
<font color="Maroon">c<sub>1</sub></font> is <a href="comseq_1.html#V1" target="_self">non-zero</a>
 <b>and </b><br/><a NAME="E2:59"/><i><font color="Green">E44</font></i>: 
<font color="Maroon">c<sub>2</sub></font> is <a href="comseq_1.html#V1" target="_self">non-zero</a>
 ;<br/>

<b>assume </b><a NAME="E3:59"/>
<font color="Maroon">c<sub>3</sub></font> is <a href="comseq_1.html#V1" target="_self">non-zero</a>
 ;<br/>

<a NAME="E4:59"/><b>then </b><i><font color="Green">E45</font></i>: 
<font color="Maroon">c<sub>3</sub></font> <a href="comseq_1.html#K7" target="_self">"</a>  is <a href="comseq_1.html#V1" target="_self">non-zero</a>
 
<b>by </b><i><a class="ref" href="comseq_1.html#T30" target="_self">Th30</a></i>;<br/>
<b>thus </b><span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="comseq_1.html#K8" target="_self">/"</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="comseq_1.html#K8" target="_self">/"</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="comseq_1.html#K8" target="_self">/"</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> = 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="comseq_1.html#K8" target="_self">/"</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="comseq_1.html#K3" target="_self">(#)</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="comseq_1.html#K8" target="_self">/"</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="comseq_1.html#K7" target="_self">"</a> </span>)</span>

<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="comseq_1.html#K8" target="_self">/"</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="comseq_1.html#K3" target="_self">(#)</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="comseq_1.html#K3" target="_self">(#)</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="comseq_1.html#K7" target="_self">"</a> </span>)</span></span>)</span> <a href="comseq_1.html#K7" target="_self">"</a> </span>)</span>

<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="comseq_1.html#K8" target="_self">/"</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="comseq_1.html#K3" target="_self">(#)</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="comseq_1.html#K7" target="_self">"</a> </span>)</span> <a href="comseq_1.html#K3" target="_self">(#)</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="comseq_1.html#K7" target="_self">"</a> </span>)</span> <a href="comseq_1.html#K7" target="_self">"</a> </span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="comseq_1.html#E2:59"><i><font color="Green">E44</font></i></a>, <a class="txt" href="comseq_1.html#E4:59"><i><font color="Green">E45</font></i></a>, <a class="ref" href="comseq_1.html#T33" target="_self">Th33</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="comseq_1.html#K8" target="_self">/"</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="comseq_1.html#K3" target="_self">(#)</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="comseq_1.html#K3" target="_self">(#)</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="comseq_1.html#K7" target="_self">"</a> </span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="comseq_1.html#T31" target="_self">Th31</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="comseq_1.html#K3" target="_self">(#)</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="comseq_1.html#K7" target="_self">"</a> </span>)</span></span>)</span> <a href="comseq_1.html#K3" target="_self">(#)</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="comseq_1.html#K3" target="_self">(#)</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="comseq_1.html#K7" target="_self">"</a> </span>)</span></span>)</span>

<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="comseq_1.html#K3" target="_self">(#)</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="comseq_1.html#K7" target="_self">"</a> </span>)</span></span>)</span> <a href="comseq_1.html#K3" target="_self">(#)</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="comseq_1.html#K3" target="_self">(#)</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="comseq_1.html#K7" target="_self">"</a> </span>)</span>
<b>by </b><i><a class="ref" href="comseq_1.html#T11" target="_self">Th11</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="comseq_1.html#K3" target="_self">(#)</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="comseq_1.html#K3" target="_self">(#)</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="comseq_1.html#K7" target="_self">"</a> </span>)</span></span>)</span></span>)</span> <a href="comseq_1.html#K3" target="_self">(#)</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="comseq_1.html#K7" target="_self">"</a> </span>)</span>
<b>by </b><i><a class="ref" href="comseq_1.html#T11" target="_self">Th11</a></i>
<br/>.= 
<font color="Maroon">c<sub>4</sub></font> <a href="comseq_1.html#K3" target="_self">(#)</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="comseq_1.html#K3" target="_self">(#)</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="comseq_1.html#K7" target="_self">"</a> </span>)</span></span>)</span> <a href="comseq_1.html#K3" target="_self">(#)</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="comseq_1.html#K7" target="_self">"</a> </span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="comseq_1.html#T11" target="_self">Th11</a></i>
<br/>.= 
<font color="Maroon">c<sub>4</sub></font> <a href="comseq_1.html#K3" target="_self">(#)</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="comseq_1.html#K3" target="_self">(#)</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="comseq_1.html#K7" target="_self">"</a> </span>)</span> <a href="comseq_1.html#K3" target="_self">(#)</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="comseq_1.html#K7" target="_self">"</a> </span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="comseq_1.html#T11" target="_self">Th11</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="comseq_1.html#K3" target="_self">(#)</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="comseq_1.html#K3" target="_self">(#)</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="comseq_1.html#K7" target="_self">"</a> </span>)</span> <a href="comseq_1.html#K3" target="_self">(#)</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="comseq_1.html#K7" target="_self">"</a> </span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="comseq_1.html#T11" target="_self">Th11</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="comseq_1.html#K3" target="_self">(#)</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="comseq_1.html#K3" target="_self">(#)</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="comseq_1.html#K3" target="_self">(#)</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="comseq_1.html#K7" target="_self">"</a> </span>)</span>
<b>by </b><i><a class="txt" href="comseq_1.html#E1:59"><i><font color="Green">E43</font></i></a>, <a class="txt" href="comseq_1.html#E2:59"><i><font color="Green">E44</font></i></a>, <a class="ref" href="comseq_1.html#T33" target="_self">Th33</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="comseq_1.html#K3" target="_self">(#)</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="comseq_1.html#K8" target="_self">/"</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="comseq_1.html#K3" target="_self">(#)</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>

;<br/>


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