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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E16">Th12</font></span>: <a NAME="T12"><span class="comment"><font color="firebrick">:: MATRIX12:12</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">k</font>, <font color="Olive" title="b2">l</font>, <font color="Olive" title="b3">n</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a><br/>  for <font color="Olive" title="b4">K</font> being   <a href="vectsp_1.html#NM5" title="VECTSP_1:NM.5">Field</a>  st <font color="Olive" title="b2">l</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><a href="matrix_1.html#K3" title="MATRIX_1:func.3">1.</a> (<font color="Olive" title="b4">K</font>,<font color="Olive" title="b3">n</font>)</span>)</span> &amp; <font color="Olive" title="b1">k</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><a href="matrix_1.html#K3" title="MATRIX_1:func.3">1.</a> (<font color="Olive" title="b4">K</font>,<font color="Olive" title="b3">n</font>)</span>)</span> holds <br/>(  <a href="matrix12.html#NK4" title="MATRIX12:NK.4">ILine</a> (<span class="p1">(<span class="default"><a href="matrix_1.html#K3" title="MATRIX_1:func.3">1.</a> (<font color="Olive" title="b4">K</font>,<font color="Olive" title="b3">n</font>)</span>)</span>,<font color="Olive" title="b2">l</font>,<font color="Olive" title="b1">k</font>) is  <a href="matrix_6.html#V1" title="MATRIX_6:attr.1">invertible</a>  &amp; <span class="p1">(<span class="default"><a href="matrix12.html#NK4" title="MATRIX12:NK.4">ILine</a> (<span class="p2">(<span class="default"><a href="matrix_1.html#K3" title="MATRIX_1:func.3">1.</a> (<font color="Olive" title="b4">K</font>,<font color="Olive" title="b3">n</font>)</span>)</span>,<font color="Olive" title="b2">l</font>,<font color="Olive" title="b1">k</font>)</span>)</span> <a href="matrix_6.html#K1" title="MATRIX_6:func.1">~</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="matrix12.html#NK4" title="MATRIX12:NK.4">ILine</a> (<span class="p1">(<span class="default"><a href="matrix_1.html#K3" title="MATRIX_1:func.3">1.</a> (<font color="Olive" title="b4">K</font>,<font color="Olive" title="b3">n</font>)</span>)</span>,<font color="Olive" title="b2">l</font>,<font color="Olive" title="b1">k</font>) )</div></div>
