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<b>let </b><font color="Maroon" title="c1">x</font>, <font color="Maroon" title="c2">y</font> be  <a href="xreal_0.html#V1" title="XREAL_0:attr.1">real</a>  <a href="ordinal1.html#NM1" title="ORDINAL1:NM.1">number</a> ;<br/>



<b>assume </b><a NAME="E1:6"/><i><font color="Green" title="E3">A1</font></i>: 
( <font color="Maroon" title="c1">x</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c2">y</font> &amp; not <font color="Maroon" title="c2">y</font> is <a href="xxreal_0.html#V2" title="XXREAL_0:attr.2">positive</a> &amp; <font color="Maroon" title="c1">x</font> is <a href="xxreal_0.html#V2" title="XXREAL_0:attr.2">positive</a> )
 ;<br/>

<a NAME="E2:6"/><b>then </b>
<font color="Maroon" title="c1">x</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 
<b>by </b><i><a class="ref" href="xxreal_0.html#D6" title="XXREAL_0:def.6">XXREAL_0:def 6</a></i>;<br/>
<a NAME="E3:6"/><b>then </b>
<font color="Maroon" title="c2">y</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 
<b>by </b><i><a class="txt" href="real.html#E1:6"><i><font color="Green" title="E3">A1</font></i></a>, <a class="txt" href="real.html#E2"><i><font color="Green" title="E2">Lm2</font></i></a></i>;<br/>
<b>hence </b><a NAME="E4:6"/>
contradiction
 <b>by </b><i><a class="txt" href="real.html#E1:6"><i><font color="Green" title="E3">A1</font></i></a>, <a class="ref" href="xxreal_0.html#D6" title="XXREAL_0:def.6">XXREAL_0:def 6</a></i>;<br/>


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