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<a NAME="E1:83_1_1"/><i><font color="Green">E22</font></i>: 
( <font color="Maroon">F</font> is  non <a href="xboole_0.html#V1">empty</a> <a href="setfam_1.html#NM1">Subset-Family</a> of <a href="numbers.html#K6">ExtREAL</a>  &amp; ( for <font color="Olive">A</font> being   <a href="hidden.html#M1">set</a>   st <font color="Olive">A</font> <a href="hidden.html#R2">in</a> <font color="Maroon">F</font> holds <br/> not <font color="Olive">A</font> is <a href="xboole_0.html#V1">empty</a> ) )
 
<b>by </b><i><a class="ref" href="supinf_1.html#D13" target="_self">Def13</a></i>;<br/>
<b>consider </b><font color="Maroon">A</font> being    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">F</font>;<br/>
<b>reconsider </b><font color="Maroon">A</font> = <font color="Maroon">A</font> as  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>  <b>by </b><i><a class="ref" href="supinf_1.html#D14" target="_self">Def14</a>, <a class="ref" href="tarski.html#D3">TARSKI:def 3</a></i>;<br/>
<a NAME="E4:83_1_1"/>
 <a href="supinf_1.html#K6" target="_self">sup</a> <font color="Maroon">A</font> <a href="hidden.html#R1">=</a>  <a href="supinf_1.html#K6" target="_self">sup</a> <font color="Maroon">A</font>
 
;<br/>
<b>hence </b><a NAME="E5:83_1_1"/>
not  <a href="supinf_1.html#K8" target="_self">SUP</a> <font color="Maroon">F</font> is <a href="xboole_0.html#V1">empty</a>
 <b>by </b><i><a class="ref" href="supinf_1.html#D14" target="_self">Def14</a>, <a class="ref" href="supinf_1.html#T51" target="_self">Th51</a></i>;<br/>


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