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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="E1:27"/><i><font color="Green">E21</font></i>: 
for <font color="Olive">b<sub>1</sub></font> being  <a href="real_1.html#NM1">Real</a> holds <font color="Maroon">c<sub>1</sub></font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a>  <a href="measure6.html#K1">R_EAL</a> <font color="Olive">b<sub>1</sub></font>
 ;<br/>

<b>assume </b><a NAME="E2:27"/><i><font color="Green">E22</font></i>: 
not <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a>  <a href="supinf_1.html#K2">-infty</a> 
 ;<br/>

<a NAME="E3:27"/>
 <a href="supinf_1.html#K2">-infty</a>  <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>1</sub></font>
 
<b>by </b><i><a class="ref" href="xxreal_0.html#T5">XXREAL_0:5</a></i>;<br/>
<a NAME="E4:27"/><b>then </b>
 <a href="supinf_1.html#K2">-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="mesfunc1.html#E2:27"><i><font color="Green">E22</font></i></a>, <a class="ref" href="xxreal_0.html#T1">XXREAL_0:1</a></i>;<br/>
<b>then consider </b><font color="Maroon">c<sub>2</sub></font> being   <a href="supinf_1.html#NM3">R_eal</a><b> such that </b><br/><a NAME="E6:27"/><i><font color="Green">E23</font></i>: 
(  <a href="supinf_1.html#K2">-infty</a>  <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">c<sub>2</sub></font> &amp; <font color="Maroon">c<sub>2</sub></font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">c<sub>1</sub></font> &amp; <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</a>  <a href="supinf_1.html#K3">REAL</a>  )
 <b>by </b><i><a class="ref" href="measure5.html#T17">MEASURE5:17</a></i>;<br/>
<b>reconsider </b><font color="Maroon">c<sub>3</sub></font> = <font color="Maroon">c<sub>2</sub></font> as   <a href="real_1.html#NM1">Real</a> <b>by </b><i><a class="txt" href="mesfunc1.html#E6:27"><i><font color="Green">E23</font></i></a></i>;<br/>
<a NAME="E8:27"/>
 <a href="measure6.html#K1">R_EAL</a> <font color="Maroon">c<sub>3</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>1</sub></font>
 
<b>by </b><i><a class="txt" href="mesfunc1.html#E6:27"><i><font color="Green">E23</font></i></a></i>;<br/>
<b>hence </b><a NAME="E9:27"/>
contradiction
 <b>by </b><i><a class="txt" href="mesfunc1.html#E1:27"><i><font color="Green">E21</font></i></a></i>;<br/>


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