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



<b>assume </b><a NAME="E1:18"/><i><font color="Green">E20</font></i>: 
( <font color="Maroon">r</font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0 &amp; <font color="Maroon">s</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> 0 )
 ;<br/>

<a NAME="E2:18"/><b>then </b><i><font color="Green">E21</font></i>: 
<font color="Maroon">r</font> <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">s</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">r</font> <a href="xcmplx_0.html#K3">*</a> 0
 
<b>by </b><i><a class="txt" href="xreal_0.html#E1:18"><i><font color="Green">E20</font></i></a></i>;<br/>
<b>assume </b><a NAME="E3:18"/>
0 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">r</font> <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">s</font>
 ;<br/>

<a NAME="E4:18"/><b>then </b>
<font color="Maroon">r</font> <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">s</font> <a href="hidden.html#R1">=</a> 0
 
<b>by </b><i>, </i>;<br/>
<b>hence </b><a NAME="E5:18"/>
contradiction
 <b>by </b><i>, </i>;<br/>


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