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<b>let </b><font color="Maroon">c<sub>1</sub></font> be   <a href="nat_1.html#NM1">Nat</a>;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font> be   <a href="vectsp_1.html#NM2">Field</a>;<br/>



<b>assume </b><a NAME="E1:29"/>
<font color="Maroon">c<sub>1</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0
 ;<br/>

<a NAME="E2:29"/><b>then </b>
<font color="Maroon">c<sub>1</sub></font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 0 <a href="nat_1.html#K1">+</a> 1
 
<b>by </b><i><a class="ref" href="int_1.html#T20">INT_1:20</a></i>;<br/>
<a NAME="E3:29"/><b>then </b><i><font color="Green">E7</font></i>: 
1 <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K2">Seg</a> <font color="Maroon">c<sub>1</sub></font>
 
;<br/>
<a NAME="E4:29"/><i><font color="Green">E8</font></i>: 
<span class="p1"><a href="tarski.html#K4">[</a><span class="default">1,1</span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K2">Seg</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<span class="p2">(<span class="default"><a href="finseq_1.html#K2">Seg</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span><a href="zfmisc_1.html#K2">:]</a></span>
 
<b>by </b><i><a class="txt" href="matrix_8.html#E3:29"><i><font color="Green">E7</font></i></a>, <a class="ref" href="zfmisc_1.html#T106">ZFMISC_1:106</a></i>;<br/>
<b>assume </b><a NAME="E5:29"/><i><font color="Green">E9</font></i>: 
 <a href="matrix_1.html#K11">0.</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a>  <a href="matrix_1.html#K12">1.</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>1</sub></font>
 ;<br/>

<a NAME="E6:29"/><i><font color="Green">E10</font></i>: 
(  <a href="matrix_1.html#K2">Indices</a> <span class="p1">(<span class="default"><a href="matrix_1.html#K11">0.</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="matrix_1.html#K2">Indices</a> <span class="p1">(<span class="default"><a href="matrix_1.html#K12">1.</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>1</sub></font></span>)</span> &amp;  <a href="matrix_1.html#K2">Indices</a> <span class="p1">(<span class="default"><a href="matrix_1.html#K12">1.</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K2">Seg</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<span class="p2">(<span class="default"><a href="finseq_1.html#K2">Seg</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span><a href="zfmisc_1.html#K2">:]</a></span> )
 
<b>by </b><i><a class="ref" href="matrix_1.html#T25">MATRIX_1:25</a>, <a class="ref" href="matrix_1.html#T27">MATRIX_1:27</a></i>;<br/>
<a NAME="E7:29"/>
<span class="p1">(<span class="default"><a href="matrix_1.html#K11">0.</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> 1,1 <a href="hidden.html#R1">=</a>  <a href="rlvect_1.html#K1">0.</a> <font color="Maroon">c<sub>2</sub></font>
 
<b>by </b><i><a class="txt" href="matrix_8.html#E4:29"><i><font color="Green">E8</font></i></a>, <a class="txt" href="matrix_8.html#E6:29"><i><font color="Green">E10</font></i></a>, <a class="ref" href="matrix_1.html#T30">MATRIX_1:30</a></i>;<br/>
<a NAME="E8:29"/><b>then </b>
 <a href="rlvect_1.html#K1">0.</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a>  <a href="group_1.html#K2">1.</a> <font color="Maroon">c<sub>2</sub></font>
 
<b>by </b><i><a class="txt" href="matrix_8.html#E5:29"><i><font color="Green">E9</font></i></a>, <a class="txt" href="matrix_8.html#E6:29"><i><font color="Green">E10</font></i></a>, <a class="txt" href="matrix_8.html#E4:29"><i><font color="Green">E8</font></i></a>, <a class="ref" href="matrix_1.html#D12">MATRIX_1:def 12</a></i>;<br/>
<b>hence </b><a NAME="E9:29"/>
contradiction
 <b>by </b><i><a class="ref" href="vectsp_1.html#D21">VECTSP_1:def 21</a></i>;<br/>


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