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<b>thus </b><a NAME="E1:86_1_1"/>
( <font color="Maroon">c<sub>1</sub></font> <a href="xboole_0.html#R1">misses</a> <font color="Maroon">c<sub>2</sub></font> implies for <font color="Olive">b<sub>1</sub></font> being <a href="rat_1.html#V1">rational</a>  <a href="ordinal1.html#NM1" target="_self">number</a>  holds <br/>(  not <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>1</sub></font> or  not <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>2</sub></font> ) )
 <b>by </b><i><a class="ref" href="xboole_0.html#T3">XBOOLE_0:3</a></i>;<br/>

<b>assume </b><a NAME="E2:86_1_1"/><i><font color="Green">E22</font></i>: 
for <font color="Olive">b<sub>1</sub></font> being <a href="rat_1.html#V1">rational</a>  <a href="ordinal1.html#NM1" target="_self">number</a>  holds <br/>(  not <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>1</sub></font> or  not <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>2</sub></font> )
 ;<br/>

<b>assume </b><a NAME="E3:86_1_1"/>
<font color="Maroon">c<sub>1</sub></font> <a href="xboole_0.html#R1">meets</a> <font color="Maroon">c<sub>2</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="E5:86_1_1"/><i><font color="Green">E23</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> &amp; <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>2</sub></font> )
 <b>by </b><i><a class="ref" href="xboole_0.html#T3">XBOOLE_0:3</a></i>;<br/>
<a NAME="E6:86_1_1"/>
<font color="Maroon">c<sub>3</sub></font> is <a href="rat_1.html#V1">rational</a>
 
<b>by </b><i><a class="txt" href="membered.html#E5:86_1_1"><i><font color="Green">E23</font></i></a>, <a class="ref" href="membered.html#D3" target="_self">Def3</a></i>;<br/>
<b>hence </b><a NAME="E7:86_1_1"/>
contradiction
 <b>by </b><i><a class="txt" href="membered.html#E2:86_1_1"><i><font color="Green">E22</font></i></a>, <a class="txt" href="membered.html#E5:86_1_1"><i><font color="Green">E23</font></i></a></i>;<br/>


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