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<b>defpred </b><font color="Maroon">S<sub>1</sub></font>[   <a href="hidden.html#M1">set</a> ] <b>means </b> ex <font color="Olive">i</font> being   <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a>  st <font color="Maroon">a<sub>1</sub></font> <a href="hidden.html#R2">in</a>  <a href="urysohn1.html#K1" target="_self">dyadic</a> <font color="Olive">i</font>;<br/>
<a NAME="E1:4_1_1"/>
 ex <font color="Olive">X</font> being  <a href="subset_1.html#NM2">Subset</a> of <a href="numbers.html#K1">REAL</a>  st <br/>for <font color="Olive">x</font> being  <a href="real_1.html#NM1">Real</a> holds <br/> ( <font color="Olive">x</font> <a href="hidden.html#R2">in</a> <font color="Olive">X</font> iff <font color="Maroon">S<sub>1</sub></font>[<font color="Olive">x</font>] )
 
<b>from </b><i><a class="ref" href="real_1.html#S1">REAL_1:sch 1</a>();<br/></i>
<b>hence </b><a NAME="E2:4_1_1"/>
 ex <font color="Olive">b<sub>1</sub></font> being  <a href="subset_1.html#NM2">Subset</a> of <a href="numbers.html#K1">REAL</a>  st <br/>for <font color="Olive">a</font> being  <a href="real_1.html#NM1">Real</a> holds <br/> ( <font color="Olive">a</font> <a href="hidden.html#R2">in</a> <font color="Olive">b<sub>1</sub></font> iff  ex <font color="Olive">n</font> being   <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a>  st <font color="Olive">a</font> <a href="hidden.html#R2">in</a>  <a href="urysohn1.html#K1" target="_self">dyadic</a> <font color="Olive">n</font> )
 ;<br/>


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