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



<b>given </b><font color="Maroon">y</font> being   <a href="supinf_1.html#NM3">R_eal</a><b> such that </b><a NAME="E1:70"/><i><font color="Green">E22</font></i>: 
( <font color="Maroon">y</font> <a href="hidden.html#R2">in</a> <font color="Maroon">X</font> &amp; <font color="Maroon">y</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">x</font> )
 ;<br/>

<a NAME="E2:70"/>
 <a href="supinf_1.html#K7" target="_self">inf</a> <font color="Maroon">X</font> is    <a href="supinf_1.html#M2" target="_self">minorant</a> of <font color="Maroon">X</font>
 
<b>by </b><i><a class="ref" href="supinf_1.html#T33" target="_self">Th33</a></i>;<br/>
<a NAME="E3:70"/><b>then </b>
 <a href="supinf_1.html#K7" target="_self">inf</a> <font color="Maroon">X</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">y</font>
 
<b>by </b><i>, </i>;<br/>
<b>hence </b><a NAME="E4:70"/>
 <a href="supinf_1.html#K7" target="_self">inf</a> <font color="Maroon">X</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">x</font>
 <b>by </b><i>, </i>;<br/>


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