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<b>consider </b><font color="Maroon">A</font> being   <a href="subset_1.html#NM2">Subset</a> of <a href="numbers.html#K6">ExtREAL</a> <b> such that </b><br/><a NAME="E2:6_4_1"/><i><font color="Green">E29</font></i>: 
for <font color="Olive">x</font> being  <a href="supinf_1.html#NM3">R_eal</a> holds <br/> ( <font color="Olive">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">A</font> iff <font color="Maroon">S<sub>4</sub></font>[<font color="Olive">x</font>] )
 <b>from </b><i><a class="ref" href="supinf_1.html#S1">SUPINF_1:sch 1</a>();<br/></i>
<a NAME="E3:6_4_1"/>
for <font color="Olive">x</font> being   <a href="hidden.html#M1">set</a>   st <font color="Olive">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">A</font> holds <br/><font color="Olive">x</font> <a href="hidden.html#R2">in</a>  <a href="supinf_1.html#K3">REAL</a> 
 
<b>by </b><i/>;<br/>
<b>then reconsider </b><font color="Maroon">A</font> = <font color="Maroon">A</font> as   <a href="subset_1.html#NM2">Subset</a> of <a href="supinf_1.html#K3">REAL</a>  <b>by </b><i><a class="ref" href="tarski.html#D3">TARSKI:def 3</a></i>;<br/>
<b>take </b>
<font color="Maroon">A</font>
;<br/>

<b>thus </b><a NAME="E5:6_4_1"/>
for <font color="Olive">x</font> being  <a href="supinf_1.html#NM3">R_eal</a> holds <br/> ( <font color="Olive">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">A</font> iff ( <font color="Maroon">a</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Olive">x</font> &amp; <font color="Olive">x</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">b</font> &amp; <font color="Olive">x</font> <a href="hidden.html#R2">in</a>  <a href="supinf_1.html#K3">REAL</a>  ) )
 <b>by </b><i/>;<br/>


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