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<b>let </b><font color="Maroon">p1</font> be  <a href="xreal_0.html#V1">real</a>  <a href="ordinal1.html#NM1" target="_self">number</a> , <font color="Maroon">p2</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="E1:11"/><i><font color="Green">E38</font></i>: 
for <font color="Olive">e</font> being  <a href="real_1.html#NM1">Real</a>  st 0 <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Olive">e</font> holds <br/> <a href="complex1.html#K18">abs</a> <span class="p1">(<span class="default"><font color="Maroon">p1</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">p2</font></span>)</span> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Olive">e</font>
 ;<br/>

<b>assume </b><a NAME="E2:11"/>
<font color="Maroon">p1</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">p2</font>
 ;<br/>

<a NAME="E3:11"/><b>then </b>
<font color="Maroon">p1</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">p2</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 0
 
;<br/>
<a NAME="E4:11"/><b>then </b>
0 <a href="xxreal_0.html#NR3" target="_self">&lt;</a>  <a href="complex1.html#K18">abs</a> <span class="p1">(<span class="default"><font color="Maroon">p1</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">p2</font></span>)</span>
 
<b>by </b><i><a class="ref" href="complex1.html#T133">COMPLEX1:133</a></i>;<br/>
<b>hence </b><a NAME="E5:11"/>
contradiction
 <b>by </b><i/>;<br/>


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