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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E31">Th31</font></span>: <a NAME="T37"><span class="comment"><font color="firebrick">:: ANPROJ_8:37</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">k</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a><br/>  for <font color="Olive" title="b2">M</font> being   <a href="matrix_1.html#NM2" title="MATRIX_1:NM.2">Matrix</a> of <font color="Olive" title="b1">k</font>,<a href="vectsp_1.html#K2" title="VECTSP_1:func.2">F_Real</a> holds <br/> ( (  <a href="matrix13.html#K9" title="MATRIX13:func.9">lines</a> <font color="Olive" title="b2">M</font> is  <a href="vectsp_7.html#NV2" title="VECTSP_7:NV.2">linearly-dependent</a>  or  not <font color="Olive" title="b2">M</font> is  <a href="matrix13.html#NV1" title="MATRIX13:NV.1">without_repeated_line</a>  ) iff  <a href="matrix13.html#K8" title="MATRIX13:func.8">the_rank_of</a> <font color="Olive" title="b2">M</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Olive" title="b1">k</font> )</div></div>
