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<b>let </b><font color="Maroon" title="c5">L1</font>, <font color="Maroon" title="c6">L2</font> be   <a href="struct_0.html#NM7" title="STRUCT_0:NM.7">FinSequence</a> of <font color="Maroon" title="c3">K</font>;<br/>

<b>assume </b><b>that </b><br/><a NAME="E1:34_1_2"/><i><font color="Green" title="E27">A6</font></i>: 
(  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c5">L1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">n</font> &amp; ( for <font color="Olive" title="b1">i</font> being  <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>  st <font color="Olive" title="b1">i</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Maroon" title="c5">L1</font> holds <br/><font color="Maroon" title="c5">L1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">M</font> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Olive" title="b1">i</font>,<font color="Maroon" title="c2">j</font></span>)</span> <a href="group_1.html#K9" title="GROUP_1:func.9">*</a> <span class="p1">(<span class="default"><a href="laplace.html#K6" title="LAPLACE:func.6">Cofactor</a> <font color="Maroon" title="c4">M</font>,<font color="Olive" title="b1">i</font>,<font color="Maroon" title="c2">j</font></span>)</span> ) )
 <b>and </b><br/><a NAME="E2:34_1_2"/><i><font color="Green" title="E28">A7</font></i>: 
(  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c6">L2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">n</font> &amp; ( for <font color="Olive" title="b1">i</font> being  <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>  st <font color="Olive" title="b1">i</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Maroon" title="c6">L2</font> holds <br/><font color="Maroon" title="c6">L2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">M</font> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Olive" title="b1">i</font>,<font color="Maroon" title="c2">j</font></span>)</span> <a href="group_1.html#K9" title="GROUP_1:func.9">*</a> <span class="p1">(<span class="default"><a href="laplace.html#K6" title="LAPLACE:func.6">Cofactor</a> <font color="Maroon" title="c4">M</font>,<font color="Olive" title="b1">i</font>,<font color="Maroon" title="c2">j</font></span>)</span> ) )
 ;<br/>

<a NAME="E3:34_1_2"/><i><font color="Green" title="E29">A8</font></i>: 
(  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Maroon" title="c5">L1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <font color="Maroon" title="c1">n</font> &amp;  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Maroon" title="c6">L2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <font color="Maroon" title="c1">n</font> )
 
<b>by </b><i><a class="txt" href="laplace.html#E1:34_1_2"><i><font color="Green" title="E27">A6</font></i></a>, <a class="txt" href="laplace.html#E2:34_1_2"><i><font color="Green" title="E28">A7</font></i></a>, <a class="ref" href="finseq_1.html#D3" title="FINSEQ_1:def.3">FINSEQ_1:def 3</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="34_1_2_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c7">k</font> be   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>;<br/><b>assume </b><a NAME="E1:34_1_2_1"/><i><font color="Green" title="E30">A9</font></i>: 
<font color="Maroon" title="c7">k</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Maroon" title="c5">L1</font>
 ;<br/><a NAME="E2:34_1_2_1"/>
( <font color="Maroon" title="c5">L1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">M</font> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c7">k</font>,<font color="Maroon" title="c2">j</font></span>)</span> <a href="group_1.html#K9" title="GROUP_1:func.9">*</a> <span class="p1">(<span class="default"><a href="laplace.html#K6" title="LAPLACE:func.6">Cofactor</a> <font color="Maroon" title="c4">M</font>,<font color="Maroon" title="c7">k</font>,<font color="Maroon" title="c2">j</font></span>)</span> &amp; <font color="Maroon" title="c6">L2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">M</font> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c7">k</font>,<font color="Maroon" title="c2">j</font></span>)</span> <a href="group_1.html#K9" title="GROUP_1:func.9">*</a> <span class="p1">(<span class="default"><a href="laplace.html#K6" title="LAPLACE:func.6">Cofactor</a> <font color="Maroon" title="c4">M</font>,<font color="Maroon" title="c7">k</font>,<font color="Maroon" title="c2">j</font></span>)</span> )
 <b>by </b><i><a class="txt" href="laplace.html#E1:34_1_2"><i><font color="Green" title="E27">A6</font></i></a>, <a class="txt" href="laplace.html#E2:34_1_2"><i><font color="Green" title="E28">A7</font></i></a>, <a class="txt" href="laplace.html#E3:34_1_2"><i><font color="Green" title="E29">A8</font></i></a>, <a class="txt" href="laplace.html#E1:34_1_2_1"><i><font color="Green" title="E30">A9</font></i></a></i>;<br/><b>hence </b><a NAME="E3:34_1_2_1"/>
<font color="Maroon" title="c5">L1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">L2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">k</font>
 ;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E5:34_1_2"/>
<font color="Maroon" title="c5">L1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">L2</font>
 <b>by </b><i><a class="txt" href="laplace.html#E3:34_1_2"><i><font color="Green" title="E29">A8</font></i></a>, <a class="ref" href="finseq_1.html#T17" title="FINSEQ_1:th.17">FINSEQ_1:17</a></i>;<br/>


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