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



<b>assume </b><a NAME="E1:9"/><i><font color="Green">E15</font></i>: 
( <font color="Maroon">x</font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> <font color="Maroon">y</font> &amp; not <font color="Maroon">x</font> is <a href="xxreal_0.html#V2">positive</a> &amp; not <font color="Maroon">y</font> is <a href="xxreal_0.html#V3">negative</a> )
 ;<br/>

<a NAME="E2:9"/><b>then </b>
( <font color="Maroon">x</font> <a href="xxreal_0.html#R1">&lt;=</a> 0 &amp; <font color="Maroon">y</font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 0 )
 
<b>by </b><i><a class="ref" href="xxreal_0.html#D6">XXREAL_0:def 6</a>, <a class="ref" href="xxreal_0.html#D7">XXREAL_0:def 7</a></i>;<br/>
<b>hence </b><a NAME="E3:9"/>
contradiction
 <b>by </b><i>, </i>;<br/>


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