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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="xcmplx_0.html#V1">complex</a>  <a href="ordinal1.html#NM1" target="_self">number</a> ;<br/>



<a NAME="E1:88"/>
<span class="p1"><a href="complex1.html#K17" target="_self">|.</a><span class="default"><font color="Maroon">c<sub>2</sub></font></span><a href="complex1.html#K17" target="_self">.|</a></span> <a href="real_1.html#K5">-</a> <span class="p1"><a href="complex1.html#K17" target="_self">|.</a><span class="default"><font color="Maroon">c<sub>1</sub></font></span><a href="complex1.html#K17" target="_self">.|</a></span> <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1"><a href="complex1.html#K17" target="_self">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span><a href="complex1.html#K17" target="_self">.|</a></span>
 
<b>by </b><i><a class="ref" href="complex1.html#T145" target="_self">Th145</a></i>;<br/>
<a NAME="E2:88"/><b>then </b>
 <a href="real_1.html#K1">-</a> <span class="p1">(<span class="default"><span class="p2"><a href="complex1.html#K17" target="_self">|.</a><span class="default"><font color="Maroon">c<sub>1</sub></font></span><a href="complex1.html#K17" target="_self">.|</a></span> <a href="real_1.html#K5">-</a> <span class="p2"><a href="complex1.html#K17" target="_self">|.</a><span class="default"><font color="Maroon">c<sub>2</sub></font></span><a href="complex1.html#K17" target="_self">.|</a></span></span>)</span> <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1"><a href="complex1.html#K17" target="_self">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span><a href="complex1.html#K17" target="_self">.|</a></span>
 
<b>by </b><i><a class="ref" href="complex1.html#T146" target="_self">Th146</a></i>;<br/>
<a NAME="E3:88"/><b>then </b>
 <a href="real_1.html#K1">-</a> <span class="p1"><a href="complex1.html#K17" target="_self">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span><a href="complex1.html#K17" target="_self">.|</a></span> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="real_1.html#K1">-</a> <span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> <span class="p2">(<span class="default"><span class="p3"><a href="complex1.html#K17" target="_self">|.</a><span class="default"><font color="Maroon">c<sub>1</sub></font></span><a href="complex1.html#K17" target="_self">.|</a></span> <a href="real_1.html#K5">-</a> <span class="p3"><a href="complex1.html#K17" target="_self">|.</a><span class="default"><font color="Maroon">c<sub>2</sub></font></span><a href="complex1.html#K17" target="_self">.|</a></span></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="xreal_1.html#T26">XREAL_1:26</a></i>;<br/>
<a NAME="E4:88"/><b>then </b>
(  <a href="real_1.html#K1">-</a> <span class="p1"><a href="complex1.html#K17" target="_self">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span><a href="complex1.html#K17" target="_self">.|</a></span> <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1"><a href="complex1.html#K17" target="_self">|.</a><span class="default"><font color="Maroon">c<sub>1</sub></font></span><a href="complex1.html#K17" target="_self">.|</a></span> <a href="real_1.html#K5">-</a> <span class="p1"><a href="complex1.html#K17" target="_self">|.</a><span class="default"><font color="Maroon">c<sub>2</sub></font></span><a href="complex1.html#K17" target="_self">.|</a></span> &amp; <span class="p1"><a href="complex1.html#K17" target="_self">|.</a><span class="default"><font color="Maroon">c<sub>1</sub></font></span><a href="complex1.html#K17" target="_self">.|</a></span> <a href="real_1.html#K5">-</a> <span class="p1"><a href="complex1.html#K17" target="_self">|.</a><span class="default"><font color="Maroon">c<sub>2</sub></font></span><a href="complex1.html#K17" target="_self">.|</a></span> <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1"><a href="complex1.html#K17" target="_self">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span><a href="complex1.html#K17" target="_self">.|</a></span> )
 
<b>by </b><i><a class="ref" href="complex1.html#T145" target="_self">Th145</a></i>;<br/>
<b>hence </b><a NAME="E5:88"/>
<span class="p1"><a href="complex1.html#K17" target="_self">|.</a><span class="default"><span class="p2">(<span class="default"><span class="p3"><a href="complex1.html#K17" target="_self">|.</a><span class="default"><font color="Maroon">c<sub>1</sub></font></span><a href="complex1.html#K17" target="_self">.|</a></span> <a href="real_1.html#K5">-</a> <span class="p3"><a href="complex1.html#K17" target="_self">|.</a><span class="default"><font color="Maroon">c<sub>2</sub></font></span><a href="complex1.html#K17" target="_self">.|</a></span></span>)</span></span><a href="complex1.html#K17" target="_self">.|</a></span> <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1"><a href="complex1.html#K17" target="_self">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span><a href="complex1.html#K17" target="_self">.|</a></span>
 <b>by </b><i><a class="txt" href="complex1.html#E198"><i><font color="Green">Lemma71</font></i></a></i>;<br/>


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