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<b>let </b><font color="Maroon">c<sub>1</sub></font>, <font color="Maroon">c<sub>2</sub></font> be   <a href="subset_1.html#NM2">Subset</a> of <a href="numbers.html#K6">ExtREAL</a> ;<br/>

<b>assume </b><a NAME="E1:29"/><i><font color="Green">E19</font></i>: 
<font color="Maroon">c<sub>1</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>2</sub></font>
 ;<br/>

<b>assume </b><a NAME="E2:29"/>
<font color="Maroon">c<sub>2</sub></font> is <a href="supinf_1.html#V5" target="_self">bounded</a>
 ;<br/>

<a NAME="E3:29"/><b>then </b>
( <font color="Maroon">c<sub>2</sub></font> is <a href="supinf_1.html#V3" target="_self">bounded_above</a> &amp; <font color="Maroon">c<sub>2</sub></font> is <a href="supinf_1.html#V4" target="_self">bounded_below</a> )
 
<b>by </b><i><a class="ref" href="supinf_1.html#D13" target="_self">Def13</a></i>;<br/>
<a NAME="E4:29"/><b>then </b>
( <font color="Maroon">c<sub>1</sub></font> is <a href="supinf_1.html#V3" target="_self">bounded_above</a> &amp; <font color="Maroon">c<sub>1</sub></font> is <a href="supinf_1.html#V4" target="_self">bounded_below</a> )
 
<b>by </b><i><a class="txt" href="supinf_1.html#E1:29"><i><font color="Green">E19</font></i></a>, <a class="ref" href="supinf_1.html#T44" target="_self">Th44</a>, <a class="ref" href="supinf_1.html#T47" target="_self">Th47</a></i>;<br/>
<b>hence </b><a NAME="E5:29"/>
<font color="Maroon">c<sub>1</sub></font> is <a href="supinf_1.html#V5" target="_self">bounded</a>
 <b>by </b><i><a class="ref" href="supinf_1.html#D13" target="_self">Def13</a></i>;<br/>


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