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



<b>assume </b><a NAME="E1:47"/><i><font color="Green">E36</font></i>: 
<font color="Maroon">c<sub>1</sub></font> is <a href="comseq_1.html#V1" target="_self">non-zero</a>
 ;<br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="47_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="E1:47_1"/><i><font color="Green">E37</font></i>: 
<font color="Maroon">c<sub>1</sub></font> <a href="comseq_1.html#K1" target="_self">.</a> <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="complex1.html#K5">0c</a> 
 <b>by </b><i><a class="txt" href="comseq_1.html#E1:47"><i><font color="Green">E36</font></i></a>, <a class="ref" href="comseq_1.html#T4" target="_self">Th4</a></i>;<br/><b>thus </b><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>1</sub></font></span>)</span> <a href="comseq_1.html#K3" target="_self">(#)</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="comseq_1.html#K1" target="_self">.</a> <font color="Maroon">c<sub>3</sub></font> = 
<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>1</sub></font></span>)</span> <a href="comseq_1.html#K1" target="_self">.</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="complex1.html#K9">*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="comseq_1.html#K1" target="_self">.</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="comseq_1.html#D5" target="_self">Def5</a></i>
<br/>.= 
<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>1</sub></font> <a href="comseq_1.html#K7" target="_self">"</a> </span>)</span></span>)</span> <a href="comseq_1.html#K1" target="_self">.</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="complex1.html#K9">*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="comseq_1.html#K1" target="_self">.</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>

<br/>.= 
<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#K1" target="_self">.</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="complex1.html#K9">*</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#K1" target="_self">.</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span> <a href="complex1.html#K9">*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="comseq_1.html#K1" target="_self">.</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="comseq_1.html#D5" target="_self">Def5</a></i>
<br/>.= 
<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#K1" target="_self">.</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="complex1.html#K9">*</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#K1" target="_self">.</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="complex1.html#K12">"</a> </span>)</span></span>)</span> <a href="complex1.html#K9">*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="comseq_1.html#K1" target="_self">.</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="comseq_1.html#D11" target="_self">Def11</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="comseq_1.html#K1" target="_self">.</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="complex1.html#K9">*</a> <span class="p1">(<span class="default"><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#K1" target="_self">.</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="complex1.html#K12">"</a> </span>)</span> <a href="complex1.html#K9">*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="comseq_1.html#K1" target="_self">.</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span>

<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="comseq_1.html#K1" target="_self">.</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="complex1.html#K9">*</a> <a href="complex1.html#K6">1r</a> 
<b>by </b><i><a class="txt" href="comseq_1.html#E1:47_1"><i><font color="Green">E37</font></i></a>, <a class="ref" href="complex1.html#D7">COMPLEX1:def 7</a>, <a class="ref" href="xcmplx_0.html#D7">XCMPLX_0:def 7</a></i>
<br/>.= 
<font color="Maroon">c<sub>2</sub></font> <a href="comseq_1.html#K1" target="_self">.</a> <font color="Maroon">c<sub>3</sub></font>
<b>by </b><i><a class="ref" href="complex1.html#D7">COMPLEX1:def 7</a></i>
;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E3:47"/>
<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>1</sub></font></span>)</span> <a href="comseq_1.html#K3" target="_self">(#)</a> <font color="Maroon">c<sub>1</sub></font> <a href="funct_2.html#R2">=</a> <font color="Maroon">c<sub>2</sub></font>
 <b>by </b><i><a class="ref" href="comseq_1.html#T6" target="_self">Th6</a></i>;<br/>


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