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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="seq_1.html#NM1">Real_Sequence</a>;<br/>



<b>assume </b><a NAME="E1:66"/><i><font color="Green">E38</font></i>: 
<font color="Maroon">c<sub>1</sub></font> is <a href="relat_1.html#V2">being_not_0</a>
 ;<br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="66_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="E1:66_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#E1:66"><i><font color="Green">E38</font></i></a>, <a class="ref" href="seq_1.html#T7" target="_self">Th7</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="seq_1.html#K19" target="_self">/"</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="seq_1.html#K11" target="_self">(#)</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="seq_1.html#K2" 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="seq_1.html#K19" target="_self">/"</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <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>1</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/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="seq_1.html#K11" target="_self">(#)</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="seq_1.html#K18" target="_self">"</a> </span>)</span></span>)</span> <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>1</sub></font> <a href="seq_1.html#K2" 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="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="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="seq_1.html#K18" target="_self">"</a> </span>)</span> <a href="seq_1.html#K2" target="_self">.</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span> <a href="real_1.html#K4">*</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>
<b>by </b><i><a class="ref" href="seq_1.html#T12" target="_self">Th12</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="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="p2">(<span class="default"><span class="p3">(<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#K2">"</a> </span>)</span></span>)</span> <a href="real_1.html#K4">*</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>
<b>by </b><i><a class="ref" href="seq_1.html#D8" target="_self">Def8</a></i>
<br/>.= 
<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> <a href="real_1.html#K4">*</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="seq_1.html#K2" target="_self">.</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="real_1.html#K2">"</a> </span>)</span> <a href="real_1.html#K4">*</a> <span class="p2">(<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></span>)</span>

<br/>.= 
<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> <a href="real_1.html#K4">*</a> 1
<b>by </b><i><a class="txt" href="seq_1.html#E1:66_1"><i><font color="Green">E39</font></i></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="seq_1.html#K2" target="_self">.</a> <font color="Maroon">c<sub>3</sub></font>

;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E3:66"/>
<span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="seq_1.html#K19" target="_self">/"</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="seq_1.html#K11" 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="funct_2.html#T113">FUNCT_2:113</a></i>;<br/>


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