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<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="E1:26"/><i><font color="Green" title="E18">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="E2:26"/>
<font color="Maroon" title="c2">Y</font> is <a href="supinf_1.html#V4" title="SUPINF_1:attr.4">bounded_below</a>
 ;<br/>

<a NAME="E3:26"/><b>then </b>
 ex <font color="Olive" title="b1">LB</font> being   <a href="supinf_1.html#M2" title="SUPINF_1:mode.2">minorant</a> of <font color="Maroon" title="c2">Y</font> st <font color="Olive" title="b1">LB</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="supinf_1.html#K3" title="SUPINF_1:func.3">REAL</a> 
 
<b>by </b><i><a class="ref" href="supinf_1.html#D12" target="_self" title="SUPINF_1:def.12">Def12</a></i>;<br/>
<b>then consider </b><font color="Maroon" title="c3">LB</font> being   <a href="supinf_1.html#NM3" title="SUPINF_1:NM.3">R_eal</a><b> such that </b><br/><a NAME="E5:26"/><i><font color="Green" title="E19">A2</font></i>: 
( <font color="Maroon" title="c3">LB</font> is    <a href="supinf_1.html#M2" title="SUPINF_1:mode.2">minorant</a> of <font color="Maroon" title="c2">Y</font> &amp; <font color="Maroon" title="c3">LB</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="supinf_1.html#K3" title="SUPINF_1:func.3">REAL</a>  )
 ;<br/>
<a NAME="E6:26"/>
( <font color="Maroon" title="c3">LB</font> is    <a href="supinf_1.html#M2" title="SUPINF_1:mode.2">minorant</a> of <font color="Maroon" title="c1">X</font> &amp; <font color="Maroon" title="c3">LB</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="supinf_1.html#K3" title="SUPINF_1:func.3">REAL</a>  )
 
<b>by </b><i><a class="txt" href="supinf_1.html#E1:26"><i><font color="Green" title="E18">A1</font></i></a>, <a class="txt" href="supinf_1.html#E5:26"><i><font color="Green" title="E19">A2</font></i></a>, <a class="ref" href="supinf_1.html#T39" target="_self" title="SUPINF_1:th.39">Th39</a></i>;<br/>
<b>hence </b><a NAME="E7:26"/>
<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="ref" href="supinf_1.html#D12" target="_self" title="SUPINF_1:def.12">Def12</a></i>;<br/>


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