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<b>let </b><font color="Maroon">X</font> be   <a href="subset_1.html#NM2">Subset</a> of <a href="numbers.html#K6">ExtREAL</a> , <font color="Maroon">Y</font> be   <a href="subset_1.html#NM2">Subset</a> of <a href="numbers.html#K6">ExtREAL</a> , <font color="Maroon">S</font> be   <a href="subset_1.html#NM2">Subset</a> of <a href="numbers.html#K6">ExtREAL</a> ;<br/><b>let </b><font color="Maroon">LB1</font> be    <a href="supinf_1.html#M2" target="_self">minorant</a> of <font color="Maroon">X</font>;<br/><b>let </b><font color="Maroon">LB2</font> be    <a href="supinf_1.html#M2" target="_self">minorant</a> of <font color="Maroon">Y</font>;<br/>





<b>assume </b><a NAME="E1:76"/><i><font color="Green">E22</font></i>: 
<font color="Maroon">S</font> <a href="hidden.html#R1">=</a> <font color="Maroon">X</font> <a href="subset_1.html#K9">/\</a> <font color="Maroon">Y</font>
 ;<br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="76_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">a</font> be   <a href="supinf_1.html#NM3">R_eal</a>;<br/><b>assume </b><a NAME="E1:76_1"/>
<font color="Maroon">a</font> <a href="hidden.html#R2">in</a> <font color="Maroon">S</font>
 ;<br/><a NAME="E2:76_1"/><b>then </b>
( <font color="Maroon">a</font> <a href="hidden.html#R2">in</a> <font color="Maroon">X</font> &amp; <font color="Maroon">a</font> <a href="hidden.html#R2">in</a> <font color="Maroon">Y</font> )
 <b>by </b><i><a class="ref" href="supinf_1.html#D13" target="_self">Def13</a>, <a class="ref" href="xboole_0.html#D3">XBOOLE_0:def 3</a></i>;<br/><a NAME="E3:76_1"/><b>then </b>
( <font color="Maroon">LB1</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">a</font> &amp; <font color="Maroon">LB2</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">a</font> )
 <b>by </b><i/>;<br/><b>hence </b><a NAME="E4:76_1"/>
 <a href="supinf_1.html#K6" target="_self">sup</a> <span class="p1"><a href="domain_1.html#K7">{</a><span class="default"><font color="Maroon">LB1</font>,<font color="Maroon">LB2</font></span><a href="domain_1.html#K7">}</a></span> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">a</font>
 <b>by </b><i><a class="ref" href="supinf_1.html#T36" target="_self">Th36</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E3:76"/>
 <a href="supinf_1.html#K6" target="_self">sup</a> <span class="p1"><a href="domain_1.html#K7">{</a><span class="default"><font color="Maroon">LB1</font>,<font color="Maroon">LB2</font></span><a href="domain_1.html#K7">}</a></span> is    <a href="supinf_1.html#M2" target="_self">minorant</a> of <font color="Maroon">S</font>
 <b>by </b><i/>;<br/>


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