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<div><span class="kw">theorem </span><a NAME="T31"><span class="comment"><font color="firebrick">:: VECTSP_9:31</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">GF</font> being   <a href="vectsp_1.html#NM5" title="VECTSP_1:NM.5">Field</a><br/>  for <font color="Olive" title="b2">V</font> being   <a href="matrlin.html#V1" title="MATRLIN:attr.1">finite-dimensional</a>  <a href="vectsp_1.html#NM9" title="VECTSP_1:NM.9">VectSp</a> of <font color="Olive" title="b1">GF</font> holds <br/> (  <a href="vectsp_9.html#K1" title="VECTSP_9:func.1">dim</a> <font color="Olive" title="b2">V</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 2 iff  ex <font color="Olive" title="b3">u</font>, <font color="Olive" title="b4">v</font> being   <a href="vectsp_1.html#NM8" title="VECTSP_1:NM.8">Vector</a> of <font color="Olive" title="b2">V</font> st <br/>( <font color="Olive" title="b3">u</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b4">v</font> &amp; <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Olive" title="b3">u</font>,<font color="Olive" title="b4">v</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span> is  <a href="vectsp_7.html#V1" title="VECTSP_7:attr.1">linearly-independent</a>  &amp;  <a href="vectsp_4.html#K2" title="VECTSP_4:func.2">(Omega).</a> <font color="Olive" title="b2">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#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Olive" title="b3">u</font>,<font color="Olive" title="b4">v</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span> ) )</div></div>
