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<b>let </b><font color="Maroon" title="c1">x</font> be   <a href="supinf_1.html#NM3" title="SUPINF_1:NM.3">R_eal</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c1">x</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="supinf_1.html#K2" title="SUPINF_1:func.2">-infty</a>  &amp; <font color="Maroon" title="c1">x</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="supinf_1.html#K1" title="SUPINF_1:func.1">+infty</a>  &amp; <font color="Maroon" title="c1">x</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="supinf_2.html#K1" title="SUPINF_2:func.1">0.</a>  implies <font color="Maroon" title="c1">x</font> <a href="extreal1.html#K2" title="EXTREAL1:func.2">/</a> <font color="Maroon" title="c1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 )</span><br/>

<b>assume </b><a NAME="E1:23"/><i><font color="Green" title="E16">A1</font></i>: 
( <font color="Maroon" title="c1">x</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="supinf_1.html#K2" title="SUPINF_1:func.2">-infty</a>  &amp; <font color="Maroon" title="c1">x</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="supinf_1.html#K1" title="SUPINF_1:func.1">+infty</a>  &amp; <font color="Maroon" title="c1">x</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="supinf_2.html#K1" title="SUPINF_2:func.1">0.</a>  )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c1">x</font> <a href="extreal1.html#K2" title="EXTREAL1:func.2">/</a> <font color="Maroon" title="c1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1</span><br/>

<b>then consider </b><font color="Maroon" title="c2">a</font>, <font color="Maroon" title="c3">b</font> being   <a href="real_1.html#NM1" title="REAL_1:NM.1">Real</a><b> such that </b><br/><a NAME="E3:23"/><i><font color="Green" title="E17">A2</font></i>: 
( <font color="Maroon" title="c1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">a</font> &amp; <font color="Maroon" title="c1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">b</font> &amp; <font color="Maroon" title="c1">x</font> <a href="extreal1.html#K2" title="EXTREAL1:func.2">/</a> <font color="Maroon" title="c1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">a</font> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <font color="Maroon" title="c3">b</font> )
 <b>by </b><i><a class="ref" href="extreal1.html#D2" target="_self" title="EXTREAL1:def.2">Def2</a></i>;<br/>
<b>thus </b><a NAME="E4:23"/>
<font color="Maroon" title="c1">x</font> <a href="extreal1.html#K2" title="EXTREAL1:func.2">/</a> <font color="Maroon" title="c1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1
 <b>by </b><i><a class="txt" href="#E1:23"><i><font color="Green" title="E16">A1</font></i></a>, <a class="txt" href="#E3:23"><i><font color="Green" title="E17">A2</font></i></a>, <a class="ref" href="xcmplx_1.html#T60" title="XCMPLX_1:th.60">XCMPLX_1:60</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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