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<b>let </b><font color="Maroon">c<sub>1</sub></font> be  <a href="xcmplx_0.html#V1">complex</a>  <a href="ordinal1.html#NM1" target="_self">number</a> ;<br/>

<a NAME="E1:1"/>
<font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R2">in</a>  <a href="numbers.html#K2">COMPLEX</a> 
 
<b>by </b><i><a class="ref" href="xcmplx_0.html#D2">XCMPLX_0:def 2</a></i>;<br/>
<b>then consider </b><font color="Maroon">c<sub>2</sub></font>, <font color="Maroon">c<sub>3</sub></font> being    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K1">REAL</a> <b> such that </b><br/><a NAME="E3:1"/><i><font color="Green">E2</font></i>: 
<font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="arytm_0.html#K5">[*</a><span class="default"><font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font></span><a href="arytm_0.html#K5">*]</a></span>
 <b>by </b><i><a class="ref" href="arytm_0.html#T11">ARYTM_0:11</a></i>;<br/>
<a NAME="E4:1"/>
0 <a href="hidden.html#R1">=</a> <span class="p1"><a href="arytm_0.html#K5">[*</a><span class="default">0,0</span><a href="arytm_0.html#K5">*]</a></span>
 
<b>by </b><i><a class="ref" href="arytm_0.html#D7">ARYTM_0:def 7</a></i>;<br/>
<b>then </b><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K2">+</a> 0 = 
<span class="p1"><a href="arytm_0.html#K5">[*</a><span class="default"><span class="p2">(<span class="default"><a href="arytm_0.html#K1">+</a> <font color="Maroon">c<sub>2</sub></font>,0</span>)</span>,<span class="p2">(<span class="default"><a href="arytm_0.html#K1">+</a> <font color="Maroon">c<sub>3</sub></font>,0</span>)</span></span><a href="arytm_0.html#K5">*]</a></span>
<b>by </b><i><a class="txt" href="arithm.html#E3:1"><i><font color="Green">E2</font></i></a>, <a class="ref" href="xcmplx_0.html#D4">XCMPLX_0:def 4</a></i>
<br/>.= 
<span class="p1"><a href="arytm_0.html#K5">[*</a><span class="default"><font color="Maroon">c<sub>2</sub></font>,<span class="p2">(<span class="default"><a href="arytm_0.html#K1">+</a> <font color="Maroon">c<sub>3</sub></font>,0</span>)</span></span><a href="arytm_0.html#K5">*]</a></span>
<b>by </b><i><a class="ref" href="arytm_0.html#T13">ARYTM_0:13</a></i>
<br/>.= 
<font color="Maroon">c<sub>1</sub></font>
<b>by </b><i><a class="txt" href="arithm.html#E3:1"><i><font color="Green">E2</font></i></a>, <a class="ref" href="arytm_0.html#T13">ARYTM_0:13</a></i>
;<br/>
<b>hence </b><a NAME="E6:1"/>
<font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K2">+</a> 0 <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>1</sub></font>
 ;<br/>


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