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<a NAME="E1:43_1_1"/>
( ( <font color="Maroon" title="c8">r</font> <a href="xreal_0.html#K1" title="XREAL_0:func.1">-'</a> <font color="Maroon" title="c9">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">r</font> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <font color="Maroon" title="c9">s</font> &amp; <font color="Maroon" title="c8">r</font> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <font color="Maroon" title="c9">s</font> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  ) or <font color="Maroon" title="c8">r</font> <a href="xreal_0.html#K1" title="XREAL_0:func.1">-'</a> <font color="Maroon" title="c9">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="xreal_0.html#D2" target="_self" title="XREAL_0:def.2">Def2</a></span>;<br/>
<span class="kw">hence </span><a NAME="E2:43_1_1"/>
 for <font color="Olive">b<sub>1</sub></font> being   <a href="xreal_0.html#V1" title="XREAL_0:attr.1">real</a>   <a href="ordinal1.html#NM1" title="ORDINAL1:NM.1">number</a>   st <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">r</font> <a href="xreal_0.html#K1" title="XREAL_0:func.1">-'</a> <font color="Maroon" title="c9">s</font> holds <br/> not <font color="Olive">b<sub>1</sub></font> is  <a href="xxreal_0.html#V3" title="XXREAL_0:attr.3">negative</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="xxreal_0.html#D7" title="XXREAL_0:def.7">XXREAL_0:def 7</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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