<?xml version="1.0"?>
<div class="add">

<b>let </b><font color="Maroon" title="c1">X</font> be  non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <a href="numbers.html#K6" title="NUMBERS:func.6">ExtREAL</a> ;<br/><b>let </b><font color="Maroon" title="c2">x</font> be   <a href="supinf_1.html#NM3" title="SUPINF_1:NM.3">R_eal</a>;<br/>



<b>given </b><font color="Maroon" title="c3">y</font> being   <a href="supinf_1.html#NM3" title="SUPINF_1:NM.3">R_eal</a><b> such that </b><a NAME="E1:69"/><i><font color="Green" title="E48">A1</font></i>: 
( <font color="Maroon" title="c3">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">X</font> &amp; <font color="Maroon" title="c2">x</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c3">y</font> )
 ;<br/>

<a NAME="E2:69"/>
 <a href="supinf_1.html#K6" title="SUPINF_1:func.6">sup</a> <font color="Maroon" title="c1">X</font> is    <a href="supinf_1.html#M1" title="SUPINF_1:mode.1">majorant</a> of <font color="Maroon" title="c1">X</font>
 
<b>by </b><i><a class="ref" href="supinf_1.html#D16" target="_self" title="SUPINF_1:def.16">Def16</a></i>;<br/>
<a NAME="E3:69"/><b>then </b>
<font color="Maroon" title="c3">y</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="supinf_1.html#K6" title="SUPINF_1:func.6">sup</a> <font color="Maroon" title="c1">X</font>
 
<b>by </b><i><a class="txt" href="supinf_1.html#E1:69"><i><font color="Green" title="E48">A1</font></i></a>, <a class="ref" href="supinf_1.html#D9" target="_self" title="SUPINF_1:def.9">Def9</a></i>;<br/>
<b>hence </b><a NAME="E4:69"/>
<font color="Maroon" title="c2">x</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="supinf_1.html#K6" title="SUPINF_1:func.6">sup</a> <font color="Maroon" title="c1">X</font>
 <b>by </b><i><a class="txt" href="supinf_1.html#E1:69"><i><font color="Green" title="E48">A1</font></i></a>, <a class="txt" href="supinf_1.html#E38"><i><font color="Green" title="E7">Lm4</font></i></a></i>;<br/>


</div>
