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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/>

<b>thus </b><a NAME="E1:71"/>
( <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 0 implies 0 <a href="xxreal_0.html#NR3" target="_self">&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> )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="71_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:71_1"/>
<font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 0
 ;<br/>

<a NAME="E2:71_1"/><b>then </b>
( 0 <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> &amp; 0 <a href="hidden.html#NR2" target="_self">&lt;&gt;</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> )
 
<b>by </b><i><a class="ref" href="complex1.html#T131" target="_self">Th131</a>, <a class="ref" href="complex1.html#T132" target="_self">Th132</a></i>;<br/>
<b>hence </b><a NAME="E3:71_1"/>
0 <a href="xxreal_0.html#NR3" target="_self">&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>
 ;<br/>


</div><b>end;</b></div>

<b>thus </b><a NAME="E2:71"/>
( 0 <a href="xxreal_0.html#NR3" target="_self">&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> implies <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 0 )
 <b>by </b><i><a class="txt" href="complex1.html#E170"><i><font color="Green">Lemma54</font></i></a>, <a class="ref" href="complex1.html#T12" target="_self">Th12</a></i>;<br/>


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