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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E119">Th121</font></span>: <a NAME="T121"><span class="comment"><font color="firebrick">:: MATRIX13:121</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">m</font>, <font color="Olive" title="b2">n</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a><br/>  for <font color="Olive" title="b3">K</font> being   <a href="vectsp_1.html#NM5" title="VECTSP_1:NM.5">Field</a><br/>  for <font color="Olive" title="b4">M</font> being   <a href="matrix_1.html#NM3" title="MATRIX_1:NM.3">Matrix</a> of <font color="Olive" title="b1">m</font>,<font color="Olive" title="b2">n</font>,<font color="Olive" title="b3">K</font> holds <br/> ( (  <a href="matrix13.html#K9" title="MATRIX13:func.9">lines</a> <font color="Olive" title="b4">M</font> is  <a href="vectsp_7.html#V1" title="VECTSP_7:attr.1">linearly-independent</a>  &amp; <font color="Olive" title="b4">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="b4">M</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">m</font> )</div></div>
