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<b>let </b><font color="Maroon" title="c1">K</font> be   <a href="vectsp_1.html#NM3" title="VECTSP_1:NM.3">Field</a>;<br/><b>let </b><font color="Maroon" title="c2">M</font> be   <a href="matrix_1.html#NM4" title="MATRIX_1:NM.4">Matrix</a> of <font color="Maroon" title="c1">K</font>;<br/><b>let </b><font color="Maroon" title="c3">P</font>, <font color="Maroon" title="c4">Q</font> be  <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a> <a href="setfam_1.html#V1" title="SETFAM_1:attr.1">without_zero</a> <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> ;<br/>







<b>assume </b><b>that </b><br/><a NAME="E1:82"/><i><font color="Green" title="E72">A1</font></i>: 
<span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><font color="Maroon" title="c3">P</font>,<font color="Maroon" title="c4">Q</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="matrix_1.html#K2" title="MATRIX_1:func.2">Indices</a> <font color="Maroon" title="c2">M</font>
 <b>and </b><br/><a NAME="E2:82"/><i><font color="Green" title="E73">A2</font></i>: 
 <a href="card_1.html#K4" title="CARD_1:func.4">card</a> <font color="Maroon" title="c3">P</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="card_1.html#K4" title="CARD_1:func.4">card</a> <font color="Maroon" title="c4">Q</font>
 ;<br/>

<a NAME="E3:82"/><i><font color="Green" title="E74">A3</font></i>: 
(  <a href="card_1.html#K4" title="CARD_1:func.4">card</a> <font color="Maroon" title="c4">Q</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 0 implies  <a href="card_1.html#K4" title="CARD_1:func.4">card</a> <font color="Maroon" title="c3">P</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 0 )
 
<b>by </b><i><a class="txt" href="matrix13.html#E2:82"><i><font color="Green" title="E73">A2</font></i></a></i>;<br/>
 <a href="matrix13.html#K5" title="MATRIX13:func.5">EqSegm</a> <font color="Maroon" title="c2">M</font>,<font color="Maroon" title="c3">P</font>,<font color="Maroon" title="c4">Q</font> = 
 <a href="matrix13.html#K4" title="MATRIX13:func.4">Segm</a> <font color="Maroon" title="c2">M</font>,<font color="Maroon" title="c3">P</font>,<font color="Maroon" title="c4">Q</font>
<b>by </b><i><a class="txt" href="matrix13.html#E2:82"><i><font color="Green" title="E73">A2</font></i></a>, <a class="ref" href="matrix13.html#D3" target="_self" title="MATRIX13:def.3">Def4</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="matrix13.html#K4" title="MATRIX13:func.4">Segm</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">M</font> <a href="matrix_1.html#K4" title="MATRIX_1:func.4">@</a> </span>)</span>,<font color="Maroon" title="c4">Q</font>,<font color="Maroon" title="c3">P</font></span>)</span> <a href="matrix_1.html#K4" title="MATRIX_1:func.4">@</a> 
<b>by </b><i><a class="txt" href="matrix13.html#E1:82"><i><font color="Green" title="E72">A1</font></i></a>, <a class="txt" href="matrix13.html#E3:82"><i><font color="Green" title="E74">A3</font></i></a>, <a class="ref" href="matrix13.html#T62" target="_self" title="MATRIX13:th.62">TT62</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="matrix13.html#K5" title="MATRIX13:func.5">EqSegm</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">M</font> <a href="matrix_1.html#K4" title="MATRIX_1:func.4">@</a> </span>)</span>,<font color="Maroon" title="c4">Q</font>,<font color="Maroon" title="c3">P</font></span>)</span> <a href="matrix_7.html#K4" title="MATRIX_7:func.4">@</a> 
<b>by </b><i><a class="txt" href="matrix13.html#E2:82"><i><font color="Green" title="E73">A2</font></i></a>, <a class="ref" href="matrix13.html#D3" target="_self" title="MATRIX13:def.3">Def4</a></i>
;<br/>
<b>hence </b><a NAME="E5:82"/>
 <a href="matrix_3.html#K12" title="MATRIX_3:func.12">Det</a> <span class="p1">(<span class="default"><a href="matrix13.html#K5" title="MATRIX13:func.5">EqSegm</a> <font color="Maroon" title="c2">M</font>,<font color="Maroon" title="c3">P</font>,<font color="Maroon" title="c4">Q</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="matrix13.html#K5" title="MATRIX13:func.5">EqSegm</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">M</font> <a href="matrix_1.html#K4" title="MATRIX_1:func.4">@</a> </span>)</span>,<font color="Maroon" title="c4">Q</font>,<font color="Maroon" title="c3">P</font></span>)</span>
 <b>by </b><i><a class="txt" href="matrix13.html#E2:82"><i><font color="Green" title="E73">A2</font></i></a>, <a class="ref" href="matrixr2.html#T43" title="MATRIXR2:th.43">MATRIXR2:43</a></i>;<br/>


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