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<b>let </b><font color="Maroon">c<sub>1</sub></font> be  <a href="xreal_0.html#V1">real</a>  <a href="ordinal1.html#NM1" target="_self">number</a> ;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font> be   <a href="seq_1.html#NM1">Real_Sequence</a>;<br/>



<b>assume </b><b>that </b><br/><a NAME="E1:72"/><i><font color="Green">E42</font></i>: 
<font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 0
 <b>and </b><br/><a NAME="E2:72"/><i><font color="Green">E43</font></i>: 
<font color="Maroon">c<sub>2</sub></font> is <a href="relat_1.html#V2">being_not_0</a>
 <b>and </b><br/><a NAME="E3:72"/><i><font color="Green">E44</font></i>: 
not <font color="Maroon">c<sub>1</sub></font> <a href="seq_1.html#K14" target="_self">(#)</a> <font color="Maroon">c<sub>2</sub></font> is <a href="relat_1.html#V2">being_not_0</a>
 ;<br/>

<b>consider </b><font color="Maroon">c<sub>3</sub></font> being   <a href="nat_1.html#NM1">Nat</a><b> such that </b><br/><a NAME="E5:72"/><i><font color="Green">E45</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="seq_1.html#K14" 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> 0
 <b>by </b><i><a class="txt" href="seq_1.html#E3:72"><i><font color="Green">E44</font></i></a>, <a class="ref" href="seq_1.html#T7" target="_self">Th7</a></i>;<br/>
<a NAME="E6:72"/><i><font color="Green">E46</font></i>: 
<font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K3">*</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> <a href="hidden.html#R1">=</a> 0
 
<b>by </b><i><a class="txt" href="seq_1.html#E5:72"><i><font color="Green">E45</font></i></a>, <a class="ref" href="seq_1.html#T13" target="_self">Th13</a></i>;<br/>
<a NAME="E7:72"/>
<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#E2:72"><i><font color="Green">E43</font></i></a>, <a class="ref" href="seq_1.html#T7" target="_self">Th7</a></i>;<br/>
<b>hence </b><a NAME="E8:72"/>
contradiction
 <b>by </b><i><a class="txt" href="seq_1.html#E1:72"><i><font color="Green">E42</font></i></a>, <a class="txt" href="seq_1.html#E6:72"><i><font color="Green">E46</font></i></a>, <a class="ref" href="xcmplx_1.html#T6">XCMPLX_1:6</a></i>;<br/>


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