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<a NAME="E1:14_2_1"/>
for <font color="Olive" title="b1">i</font>, <font color="Olive" title="b2">j</font> being  <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>  st <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Olive" title="b1">i</font>,<font color="Olive" title="b2">j</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="matrix_1.html#K2" title="MATRIX_1:func.2">Indices</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c1">n</font> <a href="matrix_2.html#K2" title="MATRIX_2:func.2">--&gt;</a> <span class="p2">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> 1</span>)</span></span>)</span> holds <br/><span class="p1">(<span class="default"><font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c1">n</font> <a href="matrix_2.html#K2" title="MATRIX_2:func.2">--&gt;</a> <span class="p2">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> 1</span>)</span></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Olive" title="b1">i</font>,<font color="Olive" title="b2">j</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> 0
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="14_2_1_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c2">i</font>, <font color="Maroon" title="c3">j</font> be   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>;<br/>



<b>assume </b><a NAME="E1:14_2_1_1"/>
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c2">i</font>,<font color="Maroon" title="c3">j</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="matrix_1.html#K2" title="MATRIX_1:func.2">Indices</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c1">n</font> <a href="matrix_2.html#K2" title="MATRIX_2:func.2">--&gt;</a> <span class="p2">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> 1</span>)</span></span>)</span>
 ;<br/>

<a NAME="E2:14_2_1_1"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c1">n</font> <a href="matrix_2.html#K2" title="MATRIX_2:func.2">--&gt;</a> <span class="p2">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> 1</span>)</span></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c2">i</font>,<font color="Maroon" title="c3">j</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="real_1.html#K1" title="REAL_1:func.1">-</a> 1
 
<b>by </b><i><a class="ref" href="matrix_2.html#T1" title="MATRIX_2:th.1">MATRIX_2:1</a></i>;<br/>
<b>hence </b><a NAME="E3:14_2_1_1"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c1">n</font> <a href="matrix_2.html#K2" title="MATRIX_2:func.2">--&gt;</a> <span class="p2">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> 1</span>)</span></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c2">i</font>,<font color="Maroon" title="c3">j</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> 0
 ;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E2:14_2_1"/>
<font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c1">n</font> <a href="matrix_2.html#K2" title="MATRIX_2:func.2">--&gt;</a> <span class="p1">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> 1</span>)</span> is  <a href="matrix10.html#V2" title="MATRIX10:attr.2">Negative</a> <a href="matrix_1.html#NM3" title="MATRIX_1:NM.3">Matrix</a> of <font color="Maroon" title="c1">n</font>, <a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a> 
 <b>by </b><i><a class="ref" href="matrix10.html#D2" target="_self" title="MATRIX10:def.2">Def2</a></i>;<br/>


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