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<b>let </b><font color="Maroon">c<sub>1</sub></font> be   <a href="supinf_1.html#NM3">R_eal</a>;<br/>

<b>assume </b><a NAME="E1:14"/><i><font color="Green">E8</font></i>: 
<font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R2">in</a>  <a href="numbers.html#K1">REAL</a> 
 ;<br/>

<a NAME="E2:14"/>
(  <a href="supinf_1.html#K2" target="_self">-infty</a>  <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>1</sub></font> &amp; not  <a href="supinf_1.html#K2" target="_self">-infty</a>  <a href="hidden.html#R2">in</a>  <a href="numbers.html#K1">REAL</a>  )
 
<b>by </b><i><a class="ref" href="xxreal_0.html#T5">XXREAL_0:5</a>, <a class="ref" href="xreal_0.html#D1">XREAL_0:def 1</a></i>;<br/>
<b>hence </b><a NAME="E3:14"/>
 <a href="supinf_1.html#K2" target="_self">-infty</a>  <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="supinf_1.html#E1:14"><i><font color="Green">E8</font></i></a>, <a class="ref" href="supinf_1.html#T22" target="_self">Th22</a></i>;<br/>

<a NAME="E4:14"/>
( <font color="Maroon">c<sub>1</sub></font> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="supinf_1.html#K1" target="_self">+infty</a>  &amp; not  <a href="supinf_1.html#K1" target="_self">+infty</a>  <a href="hidden.html#R2">in</a>  <a href="numbers.html#K1">REAL</a>  )
 
<b>by </b><i><a class="ref" href="xxreal_0.html#T4">XXREAL_0:4</a></i>;<br/>
<b>hence </b><a NAME="E5:14"/>
<font color="Maroon">c<sub>1</sub></font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a>  <a href="supinf_1.html#K1" target="_self">+infty</a> 
 <b>by </b><i><a class="txt" href="supinf_1.html#E1:14"><i><font color="Green">E8</font></i></a>, <a class="ref" href="supinf_1.html#T22" target="_self">Th22</a></i>;<br/>


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