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<b>let </b><font color="Maroon">c<sub>1</sub></font> be    <a href="hidden.html#M1">set</a> ;<br/>

<b>assume </b><a NAME="E1:91"/><i><font color="Green">E22</font></i>: 
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 <a href="membered.html#V3" target="_self">rational-membered</a>
 ;<br/>

<b>let </b><font color="Maroon">c<sub>2</sub></font> be    <a href="hidden.html#M1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="membered.html#D3" target="_self">MEMBERED:def 3</a><br/>

<b>assume </b><a NAME="E2:91"/>
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</a>  <a href="tarski.html#K3">union</a> <font color="Maroon">c<sub>1</sub></font>
 ;<br/>

<b>then consider </b><font color="Maroon">c<sub>3</sub></font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E4:91"/><i><font color="Green">E23</font></i>: 
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>3</sub></font>
 <b>and </b><br/><a NAME="E5:91"/><i><font color="Green">E24</font></i>: 
<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="ref" href="tarski.html#D4">TARSKI:def 4</a></i>;<br/>
<a NAME="E6:91"/>
<font color="Maroon">c<sub>3</sub></font> is <a href="membered.html#V3" target="_self">rational-membered</a>
 
<b>by </b><i><a class="txt" href="membered.html#E1:91"><i><font color="Green">E22</font></i></a>, <a class="txt" href="membered.html#E5:91"><i><font color="Green">E24</font></i></a></i>;<br/>
<b>hence </b><a NAME="E7:91"/>
<font color="Maroon">c<sub>2</sub></font> is <a href="rat_1.html#V1">rational</a>
 <b>by </b><i><a class="txt" href="membered.html#E4:91"><i><font color="Green">E23</font></i></a>, <a class="ref" href="membered.html#D3" target="_self">Def3</a></i>;<br/>


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