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<b>let </b><font color="Maroon">F</font> be   <a href="vectsp_1.html#NM2">Field</a>;<br/><b>let </b><font color="Maroon">V</font> be  <a href="matrlin.html#V2">finite-dimensional</a> <a href="vectsp_1.html#NM6">VectSp</a> of <font color="Maroon">F</font>;<br/><b>let </b><font color="Maroon">v</font> be   <a href="vectsp_1.html#NM5">Vector</a> of <font color="Maroon">V</font>;<br/>





<b>assume </b><a NAME="E1:15"/><i><font color="Green">E24</font></i>: 
<font color="Maroon">v</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="rlvect_1.html#K1">0.</a> <font color="Maroon">V</font>
 ;<br/>

<a NAME="E2:15"/>
<font color="Maroon">v</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">v</font></span><a href="domain_1.html#K6">}</a></span>
 
<b>by </b><i><a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/>
<a NAME="E3:15"/><b>then </b>
<font color="Maroon">v</font> <a href="rlvect_1.html#R1">in</a>  <a href="vectsp_7.html#K1">Lin</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">v</font></span><a href="domain_1.html#K6">}</a></span>
 
<b>by </b><i><a class="ref" href="vectsp_7.html#T13">VECTSP_7:13</a></i>;<br/>
<b>then reconsider </b><font color="Maroon">v0</font> = <font color="Maroon">v</font> as   <a href="vectsp_1.html#NM5">Vector</a> of <span class="p1">(<span class="default"><a href="vectsp_7.html#K1">Lin</a> <span class="p2"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">v</font></span><a href="domain_1.html#K6">}</a></span></span>)</span> <b>by </b><i><a class="ref" href="rlvect_1.html#D1">RLVECT_1:def 1</a></i>;<br/>
<a NAME="E5:15"/><i><font color="Green">E29</font></i>: 
 <a href="vectsp_7.html#K1">Lin</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">v0</font></span><a href="domain_1.html#K6">}</a></span> <a href="hidden.html#R1">=</a>  <a href="vectsp_7.html#K1">Lin</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">v</font></span><a href="domain_1.html#K6">}</a></span>
 
<b>by </b><i><a class="ref" href="vectsp_9.html#T21">VECTSP_9:21</a></i>;<br/>
<a NAME="E6:15"/><i><font color="Green">E31</font></i>: 
<font color="Maroon">v</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="rlvect_1.html#K1">0.</a> <span class="p1">(<span class="default"><a href="vectsp_7.html#K1">Lin</a> <span class="p2"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">v</font></span><a href="domain_1.html#K6">}</a></span></span>)</span>
 
<b>by </b><i>, <a class="ref" href="vectsp_4.html#T19">VECTSP_4:19</a></i>;<br/>
<a NAME="E7:15"/>
 <a href="vectsp_4.html#K2">(Omega).</a> <span class="p1">(<span class="default"><a href="vectsp_7.html#K1">Lin</a> <span class="p2"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">v0</font></span><a href="domain_1.html#K6">}</a></span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="vectsp_7.html#K1">Lin</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">v0</font></span><a href="domain_1.html#K6">}</a></span>
 
;<br/>
<b>hence </b><a NAME="E8:15"/>
 <a href="vectsp_9.html#K1">dim</a> <span class="p1">(<span class="default"><a href="vectsp_7.html#K1">Lin</a> <span class="p2"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">v</font></span><a href="domain_1.html#K6">}</a></span></span>)</span> <a href="hidden.html#R1">=</a> 1
 <b>by </b><i>, , <a class="ref" href="vectsp_9.html#T34">VECTSP_9:34</a></i>;<br/>


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