<?xml version="1.0"?>
<div class="add">

<b>let </b><font color="Maroon">n</font> be   <a href="nat_1.html#NM1">Nat</a>;<br/><b>let </b><font color="Maroon">M</font> be   <a href="matrix_1.html#NM3">Matrix</a> of <font color="Maroon">n</font>, <a href="numbers.html#K1">REAL</a> ;<br/>



<b>assume </b><a NAME="E1:41"/>
<font color="Maroon">M</font> is <a href="matrix10.html#V2" target="_self">Negative</a>
 ;<br/>

<a NAME="E2:41"/><b>then </b>
for <font color="Olive">i</font>, <font color="Olive">j</font> being  <a href="nat_1.html#NM1">Nat</a>  st <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Olive">i</font>,<font color="Olive">j</font></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a>  <a href="matrix_1.html#K2">Indices</a> <font color="Maroon">M</font> holds <br/><font color="Maroon">M</font> <a href="matrix_1.html#K3">*</a> <font color="Olive">i</font>,<font color="Olive">j</font> <a href="xxreal_0.html#R1">&lt;=</a> 0
 
<b>by </b><i/>;<br/>
<b>hence </b><a NAME="E3:41"/>
<font color="Maroon">M</font> is <a href="matrix10.html#V3" target="_self">Nonpositive</a>
 <b>by </b><i/>;<br/>


</div>
