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<a NAME="E1:88_1_1"/><i><font color="Green">E58</font></i>: 
( <font color="Maroon">c<sub>1</sub></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">b<sub>1</sub></font> being   <a href="hidden.html#M1">set</a>  st <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>1</sub></font> holds <br/><font color="Olive">b<sub>1</sub></font> is  non <a href="xboole_0.html#V1">empty</a>  <a href="hidden.html#M1">set</a>  ) )
 
<b>by </b><i><a class="ref" href="supinf_1.html#D18" target="_self">Def18</a></i>;<br/>
<b>consider </b><font color="Maroon">c<sub>2</sub></font> being    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">c<sub>1</sub></font>;<br/>
<b>reconsider </b><font color="Maroon">c<sub>3</sub></font> = <font color="Maroon">c<sub>2</sub></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="txt" href="supinf_1.html#E1:88_1_1"><i><font color="Green">E58</font></i></a>, <a class="ref" href="tarski.html#D3">TARSKI:def 3</a></i>;<br/>
<a NAME="E4:88_1_1"/>
 <a href="supinf_1.html#K7" target="_self">inf</a> <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a>  <a href="supinf_1.html#K7" target="_self">inf</a> <font color="Maroon">c<sub>3</sub></font>
 
;<br/>
<b>hence </b><a NAME="E5:88_1_1"/>
not  <a href="supinf_1.html#K9" target="_self">INF</a> <font color="Maroon">c<sub>1</sub></font> is <a href="xboole_0.html#V1">empty</a>
 <b>by </b><i><a class="txt" href="supinf_1.html#E1:88_1_1"><i><font color="Green">E58</font></i></a>, <a class="ref" href="supinf_1.html#D20" target="_self">Def20</a></i>;<br/>


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