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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>assume </b><a NAME="E1:47"/>
<font color="Maroon">X</font> is <a href="supinf_1.html#V4" target="_self">bounded_below</a>
 ;<br/>

<a NAME="E2:47"/><b>then </b>
( ( <font color="Maroon">X</font> is <a href="supinf_1.html#V4" target="_self">bounded_below</a> &amp; <font color="Maroon">X</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><a href="supinf_1.html#K1" target="_self">+infty</a> </span><a href="domain_1.html#K6">}</a></span> ) or ( <font color="Maroon">X</font> is <a href="supinf_1.html#V4" target="_self">bounded_below</a> &amp; <font color="Maroon">X</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><a href="supinf_1.html#K1" target="_self">+infty</a> </span><a href="domain_1.html#K6">}</a></span> ) )
 
;<br/>
<b>hence </b><a NAME="E3:47"/>
 ex <font color="Olive">LB</font> being  <a href="supinf_1.html#NM3">R_eal</a> st <br/>( <font color="Olive">LB</font> is    <a href="supinf_1.html#M2" target="_self">minorant</a> of <font color="Maroon">X</font> &amp; ( for <font color="Olive">y</font> being  <a href="supinf_1.html#NM3">R_eal</a>  st <font color="Olive">y</font> is    <a href="supinf_1.html#M2" target="_self">minorant</a> of <font color="Maroon">X</font> holds <br/><font color="Olive">y</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Olive">LB</font> ) )
 <b>by </b><i>, <a class="ref" href="supinf_1.html#T22" target="_self">Th22</a></i>;<br/>


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