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<span class="kw">take </span><font color="Maroon" title="c2">V</font> = 1 <a href="prvect_1.html#K6" title="PRVECT_1:func.6">-VectSp_over</a> <font color="Maroon" title="c1">K</font>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (  not <font color="Maroon" title="c2">V</font> is  <a href="struct_0.html#V7" title="STRUCT_0:attr.7">trivial</a>  &amp; <font color="Maroon" title="c2">V</font> is  <a href="matrlin.html#V1" title="MATRLIN:attr.1">finite-dimensional</a>  )</span><br/>

<a NAME="E1:10_1_1"/>
 <a href="vectsp_9.html#K1" title="VECTSP_9:func.1">dim</a> <font color="Maroon" title="c2">V</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="matrix13.html#T112" onmouseover="rs('matrix13/T112')" onmouseout="rh()">MATRIX13:112</a></span>;<br/>
<a NAME="E2:10_1_1"/><span class="kw">then </span>
 ex <font color="Olive" title="b1">v</font> being   <a href="vectsp_1.html#NM8" title="VECTSP_1:NM.8">Vector</a> of <font color="Maroon" title="c2">V</font> st <br/>( <font color="Olive" title="b1">v</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c2">V</font> &amp;  <a href="vectsp_4.html#K2" title="VECTSP_4:func.2">(Omega).</a> <font color="Maroon" title="c2">V</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="vectsp_7.html#K1" title="VECTSP_7:func.1">Lin</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Olive" title="b1">v</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="vectsp_9.html#T30" onmouseover="rs('vectsp_9/T30')" onmouseout="rh()">VECTSP_9:30</a></span>;<br/>
<span class="kw">hence </span><a NAME="E3:10_1_1"/>
(  not <font color="Maroon" title="c2">V</font> is  <a href="struct_0.html#V7" title="STRUCT_0:attr.7">trivial</a>  &amp; <font color="Maroon" title="c2">V</font> is  <a href="matrlin.html#V1" title="MATRLIN:attr.1">finite-dimensional</a>  )
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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