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<b>let </b><font color="Maroon">x</font> be  <a href="xreal_0.html#V1">real</a>  <a href="ordinal1.html#NM1" target="_self">number</a> ;<br/>

<a NAME="E1:36"/><i><font color="Green">E34</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="numbers.html#K1">REAL</a> 
 
<b>by </b><i><a class="ref" href="xreal_0.html#D1">XREAL_0:def 1</a></i>;<br/>
<div><b>hereby </b>
<div class="add"><b>assume </b><a NAME="E1:36_1"/>
<font color="Maroon">x</font> is <a href="rat_1.html#V1">irrational</a>
 ;<br/><a NAME="E2:36_1"/><b>then </b>
not <font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="numbers.html#K3">RAT</a> 
 <b>by </b><i><a class="ref" href="rat_1.html#D2">RAT_1:def 2</a></i>;<br/><b>hence </b><a NAME="E3:36_1"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="borsuk_5.html#K1" target="_self">IRRAT</a> 
 <b>by </b><i>, <a class="ref" href="xboole_0.html#D4">XBOOLE_0:def 4</a></i>;<br/></div>
<b>end;</b></div>

<b>assume </b><a NAME="E3:36"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="borsuk_5.html#K1" target="_self">IRRAT</a> 
 ;<br/>

<a NAME="E4:36"/><b>then </b>
not <font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="numbers.html#K3">RAT</a> 
 
<b>by </b><i><a class="ref" href="xboole_0.html#D4">XBOOLE_0:def 4</a></i>;<br/>
<b>hence </b><a NAME="E5:36"/>
<font color="Maroon">x</font> is <a href="rat_1.html#V1">irrational</a>
 <b>by </b><i><a class="ref" href="rat_1.html#D2">RAT_1:def 2</a></i>;<br/>


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