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<b>let </b><font color="Maroon">A</font> be  non <a href="xboole_0.html#V1">empty</a> <a href="subset_1.html#NM2">Subset</a> of <a href="numbers.html#K6">ExtREAL</a> ;<br/>

<b>assume </b><a NAME="E1:5"/><i><font color="Green">E23</font></i>: 
for <font color="Olive">r</font> being  <a href="supinf_1.html#NM3">R_eal</a>  st <font color="Olive">r</font> <a href="hidden.html#R2">in</a> <font color="Maroon">A</font> holds <br/> <a href="supinf_1.html#K1">+infty</a>  <a href="xxreal_0.html#R1">&lt;=</a> <font color="Olive">r</font>
 ;<br/>

<b>assume </b><a NAME="E2:5"/>
<font color="Maroon">A</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><a href="supinf_1.html#K1">+infty</a> </span><a href="domain_1.html#K6">}</a></span>
 ;<br/>

<b>then consider </b><font color="Maroon">a</font> being    <a href="subset_1.html#M2">Element</a> of <font color="Maroon">A</font><b> such that </b><br/><a NAME="E4:5"/><i><font color="Green">E24</font></i>: 
<font color="Maroon">a</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="supinf_1.html#K1">+infty</a> 
 <b>by </b><i/>;<br/>
<a NAME="E5:5"/>
 <a href="supinf_1.html#K1">+infty</a>  <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">a</font>
 
<b>by </b><i/>;<br/>
<b>hence </b><a NAME="E6:5"/>
contradiction
 <b>by </b><i>, <a class="ref" href="supinf_1.html#T24">SUPINF_1:24</a></i>;<br/>


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