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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E18">Th19</font></span>: <a NAME="T19"><span class="comment"><font color="firebrick">:: LAPLACE:19</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">c</font>, <font color="Olive" title="b2">m</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">D</font> being   non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>   <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a> <br/>  for <font color="Olive" title="b5">pD</font> being    <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of <font color="Olive" title="b4">D</font><br/>  for <font color="Olive" title="b6">A</font> being   <a href="matrix_0.html#NM2" title="MATRIX_0:NM.2">Matrix</a> of <font color="Olive" title="b3">n</font>,<font color="Olive" title="b2">m</font>,<font color="Olive" title="b4">D</font><br/>  for <font color="Olive" title="b7">A9</font> being   <a href="matrix_0.html#NM2" title="MATRIX_0:NM.2">Matrix</a> of <font color="Olive" title="b2">m</font>,<font color="Olive" title="b3">n</font>,<font color="Olive" title="b4">D</font>  st <font color="Olive" title="b7">A9</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b6">A</font> <a href="matrix_0.html#K4" title="MATRIX_0:func.4">@</a>  &amp; ( <font color="Olive" title="b2">m</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  implies <font color="Olive" title="b3">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  ) holds <br/> <a href="laplace.html#K3" title="LAPLACE:func.3">ReplaceCol</a> (<font color="Olive" title="b6">A</font>,<font color="Olive" title="b1">c</font>,<font color="Olive" title="b5">pD</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="matrix11.html#K3" title="MATRIX11:func.3">ReplaceLine</a> (<font color="Olive" title="b7">A9</font>,<font color="Olive" title="b1">c</font>,<font color="Olive" title="b5">pD</font>)</span>)</span> <a href="matrix_0.html#K4" title="MATRIX_0:func.4">@</a> </div></div>
