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

<b>let </b><font color="Maroon" title="c1">X</font>, <font color="Maroon" title="c2">Y</font> be   <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>assume </b><a NAME="E1:29"/><i><font color="Green" title="E19">A1</font></i>: 
<font color="Maroon" title="c1">X</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c2">Y</font>
 ;<br/>

<b>assume </b><a NAME="E2:29"/>
<font color="Maroon" title="c2">Y</font> is <a href="supinf_1.html#V5" title="SUPINF_1:attr.5">bounded</a>
 ;<br/>

<a NAME="E3:29"/><b>then </b>
( <font color="Maroon" title="c2">Y</font> is <a href="supinf_1.html#V3" title="SUPINF_1:attr.3">bounded_above</a> &amp; <font color="Maroon" title="c2">Y</font> is <a href="supinf_1.html#V4" title="SUPINF_1:attr.4">bounded_below</a> )
 
<b>by </b><i><a class="ref" href="supinf_1.html#D13" target="_self" title="SUPINF_1:def.13">Def13</a></i>;<br/>
<a NAME="E4:29"/><b>then </b>
( <font color="Maroon" title="c1">X</font> is <a href="supinf_1.html#V3" title="SUPINF_1:attr.3">bounded_above</a> &amp; <font color="Maroon" title="c1">X</font> is <a href="supinf_1.html#V4" title="SUPINF_1:attr.4">bounded_below</a> )
 
<b>by </b><i><a class="txt" href="supinf_1.html#E1:29"><i><font color="Green" title="E19">A1</font></i></a>, <a class="ref" href="supinf_1.html#T44" target="_self" title="SUPINF_1:th.44">Th44</a>, <a class="ref" href="supinf_1.html#T47" target="_self" title="SUPINF_1:th.47">Th47</a></i>;<br/>
<b>hence </b><a NAME="E5:29"/>
<font color="Maroon" title="c1">X</font> is <a href="supinf_1.html#V5" title="SUPINF_1:attr.5">bounded</a>
 <b>by </b><i><a class="ref" href="supinf_1.html#D13" target="_self" title="SUPINF_1:def.13">Def13</a></i>;<br/>


</div>
