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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E34">Th32</font></span>: <a NAME="T32"><span class="comment"><font color="firebrick">:: LAPLACE:32</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">i</font>, <font color="Olive" title="b2">j</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><br/>  for <font color="Olive" title="b5">M</font> being   <a href="matrix_1.html#NM2" title="MATRIX_1:NM.2">Matrix</a> of <font color="Olive" title="b3">n</font>,<font color="Olive" title="b4">K</font>  st <font color="Olive" title="b1">i</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <font color="Olive" title="b3">n</font> &amp; <font color="Olive" title="b2">j</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <font color="Olive" title="b3">n</font> holds <br/><span class="p1">(<span class="default"><a href="matrix_0.html#K7" title="MATRIX_0:func.7">Line</a> (<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="laplace.html#K7" title="LAPLACE:func.7">Matrix_of_Cofactor</a> <font color="Olive" title="b5">M</font></span>)</span> <a href="matrix_0.html#K4" title="MATRIX_0:func.4">@</a></span>)</span>,<font color="Olive" title="b1">i</font>)</span>)</span> <a href="fvsum_1.html#K13" title="FVSUM_1:func.13">"*"</a> <span class="p1">(<span class="default"><a href="matrix_0.html#K8" title="MATRIX_0:func.8">Col</a> (<font color="Olive" title="b5">M</font>,<font color="Olive" title="b2">j</font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="matrix_3.html#K12" title="MATRIX_3:func.12">Det</a> <span class="p1">(<span class="default"><a href="matrix11.html#NK5" title="MATRIX11:NK.5">RLine</a> (<span class="p2">(<span class="default"><font color="Olive" title="b5">M</font> <a href="matrix_0.html#K4" title="MATRIX_0:func.4">@</a></span>)</span>,<font color="Olive" title="b1">i</font>,<span class="p2">(<span class="default"><a href="matrix_0.html#K7" title="MATRIX_0:func.7">Line</a> (<span class="p3">(<span class="default"><font color="Olive" title="b5">M</font> <a href="matrix_0.html#K4" title="MATRIX_0:func.4">@</a></span>)</span>,<font color="Olive" title="b2">j</font>)</span>)</span>)</span>)</span></div></div>
