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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">a</font>, <font color="Maroon" title="c3">b</font>, <font color="Maroon" title="c4">c</font>, <font color="Maroon" title="c5">d</font>, <font color="Maroon" title="c6">e</font>, <font color="Maroon" title="c7">f</font>, <font color="Maroon" title="c8">g</font>, <font color="Maroon" title="c9">h</font>, <font color="Maroon" title="c10">i</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">K</font>;<br/><b>let </b><font color="Maroon" title="c11">M</font> be   <a href="matrix_1.html#NM5" title="MATRIX_1:NM.5">Matrix</a> of 3,<font color="Maroon" title="c1">K</font>;<br/>





<b>assume </b><a NAME="E1:61"/><i><font color="Green" title="E48">A1</font></i>: 
<font color="Maroon" title="c11">M</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="finseq_4.html#K3" title="FINSEQ_4:func.3">&lt;*</a><span class="default"><span class="p2"><a href="finseq_4.html#K3" title="FINSEQ_4:func.3">&lt;*</a><span class="default"><font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c4">c</font></span><a href="finseq_4.html#K3" title="FINSEQ_4:func.3">*&gt;</a></span>,<span class="p2"><a href="finseq_4.html#K3" title="FINSEQ_4:func.3">&lt;*</a><span class="default"><font color="Maroon" title="c5">d</font>,<font color="Maroon" title="c6">e</font>,<font color="Maroon" title="c7">f</font></span><a href="finseq_4.html#K3" title="FINSEQ_4:func.3">*&gt;</a></span>,<span class="p2"><a href="finseq_4.html#K3" title="FINSEQ_4:func.3">&lt;*</a><span class="default"><font color="Maroon" title="c8">g</font>,<font color="Maroon" title="c9">h</font>,<font color="Maroon" title="c10">i</font></span><a href="finseq_4.html#K3" title="FINSEQ_4:func.3">*&gt;</a></span></span><a href="finseq_4.html#K3" title="FINSEQ_4:func.3">*&gt;</a></span>
 ;<br/>

<b>reconsider </b><font color="Maroon" title="c12">id3</font> =  <a href="finseq_2.html#K1" title="FINSEQ_2:func.1">idseq</a> 3 as   <a href="funct_2.html#NM2" title="FUNCT_2:NM.2">Permutation</a> of  <a href="setwop_2.html#K2" title="SETWOP_2:func.2">Seg</a> 3 ;<br/>
<b>reconsider </b><font color="Maroon" title="c13">Id3</font> =  <a href="finseq_2.html#K1" title="FINSEQ_2:func.1">idseq</a> 3 as    <a href="matrix_2.html#M3" title="MATRIX_2:mode.3">Element</a> of  <a href="matrix_2.html#K12" title="MATRIX_2:func.12">Permutations</a> 3 <b>by </b><i><a class="ref" href="matrix_2.html#D11" title="MATRIX_2:def.11">MATRIX_2:def 11</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c14">rid3</font> =  <a href="finseq_5.html#K3" title="FINSEQ_5:func.3">Rev</a> <span class="p1">(<span class="default"><a href="finseq_2.html#K1" title="FINSEQ_2:func.1">idseq</a> 3</span>)</span> as    <a href="matrix_2.html#M3" title="MATRIX_2:mode.3">Element</a> of  <a href="matrix_2.html#K12" title="MATRIX_2:func.12">Permutations</a> 3 <b>by </b><i><a class="ref" href="matrix_9.html#T4" target="_self" title="MATRIX_9:th.4">Th4</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c15">a3</font> = <span class="p1"><a href="finseq_4.html#K3" title="FINSEQ_4:func.3">&lt;*</a><span class="default">1,3,2</span><a href="finseq_4.html#K3" title="FINSEQ_4:func.3">*&gt;</a></span>, <font color="Maroon" title="c16">a4</font> = <span class="p1"><a href="finseq_4.html#K3" title="FINSEQ_4:func.3">&lt;*</a><span class="default">2,3,1</span><a href="finseq_4.html#K3" title="FINSEQ_4:func.3">*&gt;</a></span>, <font color="Maroon" title="c17">a5</font> = <span class="p1"><a href="finseq_4.html#K3" title="FINSEQ_4:func.3">&lt;*</a><span class="default">2,1,3</span><a href="finseq_4.html#K3" title="FINSEQ_4:func.3">*&gt;</a></span>, <font color="Maroon" title="c18">a6</font> = <span class="p1"><a href="finseq_4.html#K3" title="FINSEQ_4:func.3">&lt;*</a><span class="default">3,1,2</span><a href="finseq_4.html#K3" title="FINSEQ_4:func.3">*&gt;</a></span> as    <a href="matrix_2.html#M3" title="MATRIX_2:mode.3">Element</a> of  <a href="matrix_2.html#K12" title="MATRIX_2:func.12">Permutations</a> 3 <b>by </b><i><a class="ref" href="matrix_9.html#T27" target="_self" title="MATRIX_9:th.27">Th27</a></i>;<br/>
<b>set </b><font color="Maroon" title="c19">F</font> = the <a href="rlvect_1.html#U1" title="RLVECT_1:sel.1">add</a> of <font color="Maroon" title="c1">K</font>;<br/>
<b>set </b><font color="Maroon" title="c20">r</font> =  <a href="matrix_3.html#K11" title="MATRIX_3:func.11">Path_product</a> <font color="Maroon" title="c11">M</font>;<br/>
<a NAME="E6:61"/><i><font color="Green" title="E49">A2</font></i>: 
<font color="Maroon" title="c12">id3</font> is <a href="matrix_2.html#V3" title="MATRIX_2:attr.3">even</a>
 
<b>by </b><i><a class="ref" href="matrix_2.html#T29" title="MATRIX_2:th.29">MATRIX_2:29</a></i>;<br/>
<a NAME="E7:61"/><i><font color="Green" title="E50">A3</font></i>: 
3 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="matrix_2.html#K11" title="MATRIX_2:func.11">len</a> <span class="p1">(<span class="default"><a href="matrix_2.html#K12" title="MATRIX_2:func.12">Permutations</a> 3</span>)</span>
 
<b>by </b><i><a class="ref" href="matrix_2.html#T20" title="MATRIX_2:th.20">MATRIX_2:20</a></i>;<br/>
<a NAME="E8:61"/><b>then </b><i><font color="Green" title="E51">A4</font></i>: 
<font color="Maroon" title="c13">Id3</font> is <a href="matrix_2.html#V3" title="MATRIX_2:attr.3">even</a>
 
<b>by </b><i><a class="ref" href="matrix_2.html#T29" title="MATRIX_2:th.29">MATRIX_2:29</a></i>;<br/>
<i><font color="Green" title="E52">A5</font></i>: <span class="p1">(<span class="default"><a href="matrix_3.html#K11" title="MATRIX_3:func.11">Path_product</a> <font color="Maroon" title="c11">M</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c12">id3</font> = 
 <a href="matrix_2.html#K14" title="MATRIX_2:func.14">-</a> <span class="p1">(<span class="default">the <a href="group_1.html#U1" title="GROUP_1:sel.1">mult</a> of <font color="Maroon" title="c1">K</font> <a href="finsop_1.html#K2" title="FINSOP_1:func.2">$$</a> <span class="p2">(<span class="default"><a href="matrix_3.html#K10" title="MATRIX_3:func.10">Path_matrix</a> <font color="Maroon" title="c13">Id3</font>,<font color="Maroon" title="c11">M</font></span>)</span></span>)</span>,<font color="Maroon" title="c13">Id3</font>
<b>by </b><i><a class="ref" href="matrix_3.html#D8" title="MATRIX_3:def.8">MATRIX_3:def 8</a></i>
<br/>.= 
the <a href="group_1.html#U1" title="GROUP_1:sel.1">mult</a> of <font color="Maroon" title="c1">K</font> <a href="finsop_1.html#K2" title="FINSOP_1:func.2">$$</a> <span class="p1">(<span class="default"><a href="matrix_3.html#K10" title="MATRIX_3:func.10">Path_matrix</a> <font color="Maroon" title="c13">Id3</font>,<font color="Maroon" title="c11">M</font></span>)</span>
<b>by </b><i><a class="txt" href="matrix_9.html#E6:61"><i><font color="Green" title="E49">A2</font></i></a>, <a class="txt" href="matrix_9.html#E7:61"><i><font color="Green" title="E50">A3</font></i></a>, <a class="ref" href="matrix_2.html#D16" title="MATRIX_2:def.16">MATRIX_2:def 16</a></i>
<br/>.= 
the <a href="group_1.html#U1" title="GROUP_1:sel.1">mult</a> of <font color="Maroon" title="c1">K</font> <a href="finsop_1.html#K2" title="FINSOP_1:func.2">$$</a> <span class="p1"><a href="finseq_4.html#K3" title="FINSEQ_4:func.3">&lt;*</a><span class="default"><font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c6">e</font>,<font color="Maroon" title="c10">i</font></span><a href="finseq_4.html#K3" title="FINSEQ_4:func.3">*&gt;</a></span>
<b>by </b><i><a class="txt" href="matrix_9.html#E1:61"><i><font color="Green" title="E48">A1</font></i></a>, <a class="ref" href="matrix_9.html#T20" target="_self" title="MATRIX_9:th.20">Th20</a>, <a class="ref" href="finseq_2.html#T62" title="FINSEQ_2:th.62">FINSEQ_2:62</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="group_1.html#K10" title="GROUP_1:func.10">*</a> <font color="Maroon" title="c6">e</font></span>)</span> <a href="group_1.html#K10" title="GROUP_1:func.10">*</a> <font color="Maroon" title="c10">i</font>
<b>by </b><i><a class="ref" href="matrix_9.html#T26" target="_self" title="MATRIX_9:th.26">Th26</a></i>
;<br/>
<i><font color="Green" title="E53">A6</font></i>: <span class="p1">(<span class="default"><a href="matrix_3.html#K11" title="MATRIX_3:func.11">Path_product</a> <font color="Maroon" title="c11">M</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c14">rid3</font> = 
 <a href="matrix_2.html#K14" title="MATRIX_2:func.14">-</a> <span class="p1">(<span class="default">the <a href="group_1.html#U1" title="GROUP_1:sel.1">mult</a> of <font color="Maroon" title="c1">K</font> <a href="finsop_1.html#K2" title="FINSOP_1:func.2">$$</a> <span class="p2">(<span class="default"><a href="matrix_3.html#K10" title="MATRIX_3:func.10">Path_matrix</a> <font color="Maroon" title="c14">rid3</font>,<font color="Maroon" title="c11">M</font></span>)</span></span>)</span>,<font color="Maroon" title="c14">rid3</font>
<b>by </b><i><a class="ref" href="matrix_3.html#D8" title="MATRIX_3:def.8">MATRIX_3:def 8</a></i>
<br/>.= 
 <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <span class="p1">(<span class="default">the <a href="group_1.html#U1" title="GROUP_1:sel.1">mult</a> of <font color="Maroon" title="c1">K</font> <a href="finsop_1.html#K2" title="FINSOP_1:func.2">$$</a> <span class="p2">(<span class="default"><a href="matrix_3.html#K10" title="MATRIX_3:func.10">Path_matrix</a> <font color="Maroon" title="c14">rid3</font>,<font color="Maroon" title="c11">M</font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="matrix_9.html#E7:61"><i><font color="Green" title="E50">A3</font></i></a>, <a class="ref" href="matrix_9.html#T15" target="_self" title="MATRIX_9:th.15">Th15</a>, <a class="ref" href="matrix_9.html#T42" target="_self" title="MATRIX_9:th.42">Th42</a>, <a class="ref" href="matrix_2.html#D16" title="MATRIX_2:def.16">MATRIX_2:def 16</a></i>
<br/>.= 
 <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <span class="p1">(<span class="default">the <a href="group_1.html#U1" title="GROUP_1:sel.1">mult</a> of <font color="Maroon" title="c1">K</font> <a href="finsop_1.html#K2" title="FINSOP_1:func.2">$$</a> <span class="p2"><a href="finseq_4.html#K3" title="FINSEQ_4:func.3">&lt;*</a><span class="default"><font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c6">e</font>,<font color="Maroon" title="c8">g</font></span><a href="finseq_4.html#K3" title="FINSEQ_4:func.3">*&gt;</a></span></span>)</span>
<b>by </b><i><a class="txt" href="matrix_9.html#E1:61"><i><font color="Green" title="E48">A1</font></i></a>, <a class="ref" href="matrix_9.html#T15" target="_self" title="MATRIX_9:th.15">Th15</a>, <a class="ref" href="matrix_9.html#T21" target="_self" title="MATRIX_9:th.21">Th21</a></i>
<br/>.= 
 <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">c</font> <a href="group_1.html#K10" title="GROUP_1:func.10">*</a> <font color="Maroon" title="c6">e</font></span>)</span> <a href="group_1.html#K10" title="GROUP_1:func.10">*</a> <font color="Maroon" title="c8">g</font></span>)</span>
<b>by </b><i><a class="ref" href="matrix_9.html#T26" target="_self" title="MATRIX_9:th.26">Th26</a></i>
;<br/>
<i><font color="Green" title="E54">A7</font></i>: <span class="p1">(<span class="default"><a href="matrix_3.html#K11" title="MATRIX_3:func.11">Path_product</a> <font color="Maroon" title="c11">M</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c15">a3</font> = 
 <a href="matrix_2.html#K14" title="MATRIX_2:func.14">-</a> <span class="p1">(<span class="default">the <a href="group_1.html#U1" title="GROUP_1:sel.1">mult</a> of <font color="Maroon" title="c1">K</font> <a href="finsop_1.html#K2" title="FINSOP_1:func.2">$$</a> <span class="p2">(<span class="default"><a href="matrix_3.html#K10" title="MATRIX_3:func.10">Path_matrix</a> <font color="Maroon" title="c15">a3</font>,<font color="Maroon" title="c11">M</font></span>)</span></span>)</span>,<font color="Maroon" title="c15">a3</font>
<b>by </b><i><a class="ref" href="matrix_3.html#D8" title="MATRIX_3:def.8">MATRIX_3:def 8</a></i>
<br/>.= 
 <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <span class="p1">(<span class="default">the <a href="group_1.html#U1" title="GROUP_1:sel.1">mult</a> of <font color="Maroon" title="c1">K</font> <a href="finsop_1.html#K2" title="FINSOP_1:func.2">$$</a> <span class="p2">(<span class="default"><a href="matrix_3.html#K10" title="MATRIX_3:func.10">Path_matrix</a> <font color="Maroon" title="c15">a3</font>,<font color="Maroon" title="c11">M</font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="matrix_9.html#E7:61"><i><font color="Green" title="E50">A3</font></i></a>, <a class="ref" href="matrix_9.html#T44" target="_self" title="MATRIX_9:th.44">Th44</a>, <a class="ref" href="matrix_2.html#D16" title="MATRIX_2:def.16">MATRIX_2:def 16</a></i>
<br/>.= 
 <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <span class="p1">(<span class="default">the <a href="group_1.html#U1" title="GROUP_1:sel.1">mult</a> of <font color="Maroon" title="c1">K</font> <a href="finsop_1.html#K2" title="FINSOP_1:func.2">$$</a> <span class="p2"><a href="finseq_4.html#K3" title="FINSEQ_4:func.3">&lt;*</a><span class="default"><font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c7">f</font>,<font color="Maroon" title="c9">h</font></span><a href="finseq_4.html#K3" title="FINSEQ_4:func.3">*&gt;</a></span></span>)</span>
<b>by </b><i><a class="ref" href="matrix_9.html#T22" target="_self" title="MATRIX_9:th.22">Th22</a>, <a class="txt" href="matrix_9.html#E1:61"><i><font color="Green" title="E48">A1</font></i></a></i>
<br/>.= 
 <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="group_1.html#K10" title="GROUP_1:func.10">*</a> <font color="Maroon" title="c7">f</font></span>)</span> <a href="group_1.html#K10" title="GROUP_1:func.10">*</a> <font color="Maroon" title="c9">h</font></span>)</span>
<b>by </b><i><a class="ref" href="matrix_9.html#T26" target="_self" title="MATRIX_9:th.26">Th26</a></i>
;<br/>
<i><font color="Green" title="E55">A8</font></i>: <span class="p1">(<span class="default"><a href="matrix_3.html#K11" title="MATRIX_3:func.11">Path_product</a> <font color="Maroon" title="c11">M</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c16">a4</font> = 
 <a href="matrix_2.html#K14" title="MATRIX_2:func.14">-</a> <span class="p1">(<span class="default">the <a href="group_1.html#U1" title="GROUP_1:sel.1">mult</a> of <font color="Maroon" title="c1">K</font> <a href="finsop_1.html#K2" title="FINSOP_1:func.2">$$</a> <span class="p2">(<span class="default"><a href="matrix_3.html#K10" title="MATRIX_3:func.10">Path_matrix</a> <font color="Maroon" title="c16">a4</font>,<font color="Maroon" title="c11">M</font></span>)</span></span>)</span>,<font color="Maroon" title="c16">a4</font>
<b>by </b><i><a class="ref" href="matrix_3.html#D8" title="MATRIX_3:def.8">MATRIX_3:def 8</a></i>
<br/>.= 
the <a href="group_1.html#U1" title="GROUP_1:sel.1">mult</a> of <font color="Maroon" title="c1">K</font> <a href="finsop_1.html#K2" title="FINSOP_1:func.2">$$</a> <span class="p1">(<span class="default"><a href="matrix_3.html#K10" title="MATRIX_3:func.10">Path_matrix</a> <font color="Maroon" title="c16">a4</font>,<font color="Maroon" title="c11">M</font></span>)</span>
<b>by </b><i><a class="txt" href="matrix_9.html#E7:61"><i><font color="Green" title="E50">A3</font></i></a>, <a class="txt" href="matrix_9.html#E47"><i><font color="Green" title="E39">Lm6</font></i></a>, <a class="ref" href="matrix_2.html#D16" title="MATRIX_2:def.16">MATRIX_2:def 16</a></i>
<br/>.= 
the <a href="group_1.html#U1" title="GROUP_1:sel.1">mult</a> of <font color="Maroon" title="c1">K</font> <a href="finsop_1.html#K2" title="FINSOP_1:func.2">$$</a> <span class="p1"><a href="finseq_4.html#K3" title="FINSEQ_4:func.3">&lt;*</a><span class="default"><font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c7">f</font>,<font color="Maroon" title="c8">g</font></span><a href="finseq_4.html#K3" title="FINSEQ_4:func.3">*&gt;</a></span>
<b>by </b><i><a class="ref" href="matrix_9.html#T23" target="_self" title="MATRIX_9:th.23">Th23</a>, <a class="txt" href="matrix_9.html#E1:61"><i><font color="Green" title="E48">A1</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c3">b</font> <a href="group_1.html#K10" title="GROUP_1:func.10">*</a> <font color="Maroon" title="c7">f</font></span>)</span> <a href="group_1.html#K10" title="GROUP_1:func.10">*</a> <font color="Maroon" title="c8">g</font>
<b>by </b><i><a class="ref" href="matrix_9.html#T26" target="_self" title="MATRIX_9:th.26">Th26</a></i>
;<br/>
<i><font color="Green" title="E56">A9</font></i>: <span class="p1">(<span class="default"><a href="matrix_3.html#K11" title="MATRIX_3:func.11">Path_product</a> <font color="Maroon" title="c11">M</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c17">a5</font> = 
 <a href="matrix_2.html#K14" title="MATRIX_2:func.14">-</a> <span class="p1">(<span class="default">the <a href="group_1.html#U1" title="GROUP_1:sel.1">mult</a> of <font color="Maroon" title="c1">K</font> <a href="finsop_1.html#K2" title="FINSOP_1:func.2">$$</a> <span class="p2">(<span class="default"><a href="matrix_3.html#K10" title="MATRIX_3:func.10">Path_matrix</a> <font color="Maroon" title="c17">a5</font>,<font color="Maroon" title="c11">M</font></span>)</span></span>)</span>,<font color="Maroon" title="c17">a5</font>
<b>by </b><i><a class="ref" href="matrix_3.html#D8" title="MATRIX_3:def.8">MATRIX_3:def 8</a></i>
<br/>.= 
 <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <span class="p1">(<span class="default">the <a href="group_1.html#U1" title="GROUP_1:sel.1">mult</a> of <font color="Maroon" title="c1">K</font> <a href="finsop_1.html#K2" title="FINSOP_1:func.2">$$</a> <span class="p2">(<span class="default"><a href="matrix_3.html#K10" title="MATRIX_3:func.10">Path_matrix</a> <font color="Maroon" title="c17">a5</font>,<font color="Maroon" title="c11">M</font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="matrix_9.html#E7:61"><i><font color="Green" title="E50">A3</font></i></a>, <a class="ref" href="matrix_9.html#T43" target="_self" title="MATRIX_9:th.43">Th43</a>, <a class="ref" href="matrix_2.html#D16" title="MATRIX_2:def.16">MATRIX_2:def 16</a></i>
<br/>.= 
 <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <span class="p1">(<span class="default">the <a href="group_1.html#U1" title="GROUP_1:sel.1">mult</a> of <font color="Maroon" title="c1">K</font> <a href="finsop_1.html#K2" title="FINSOP_1:func.2">$$</a> <span class="p2"><a href="finseq_4.html#K3" title="FINSEQ_4:func.3">&lt;*</a><span class="default"><font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c5">d</font>,<font color="Maroon" title="c10">i</font></span><a href="finseq_4.html#K3" title="FINSEQ_4:func.3">*&gt;</a></span></span>)</span>
<b>by </b><i><a class="ref" href="matrix_9.html#T24" target="_self" title="MATRIX_9:th.24">Th24</a>, <a class="txt" href="matrix_9.html#E1:61"><i><font color="Green" title="E48">A1</font></i></a></i>
<br/>.= 
 <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">b</font> <a href="group_1.html#K10" title="GROUP_1:func.10">*</a> <font color="Maroon" title="c5">d</font></span>)</span> <a href="group_1.html#K10" title="GROUP_1:func.10">*</a> <font color="Maroon" title="c10">i</font></span>)</span>
<b>by </b><i><a class="ref" href="matrix_9.html#T26" target="_self" title="MATRIX_9:th.26">Th26</a></i>
;<br/>
<i><font color="Green" title="E57">A10</font></i>: <span class="p1">(<span class="default"><a href="matrix_3.html#K11" title="MATRIX_3:func.11">Path_product</a> <font color="Maroon" title="c11">M</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c18">a6</font> = 
 <a href="matrix_2.html#K14" title="MATRIX_2:func.14">-</a> <span class="p1">(<span class="default">the <a href="group_1.html#U1" title="GROUP_1:sel.1">mult</a> of <font color="Maroon" title="c1">K</font> <a href="finsop_1.html#K2" title="FINSOP_1:func.2">$$</a> <span class="p2">(<span class="default"><a href="matrix_3.html#K10" title="MATRIX_3:func.10">Path_matrix</a> <font color="Maroon" title="c18">a6</font>,<font color="Maroon" title="c11">M</font></span>)</span></span>)</span>,<font color="Maroon" title="c18">a6</font>
<b>by </b><i><a class="ref" href="matrix_3.html#D8" title="MATRIX_3:def.8">MATRIX_3:def 8</a></i>
<br/>.= 
the <a href="group_1.html#U1" title="GROUP_1:sel.1">mult</a> of <font color="Maroon" title="c1">K</font> <a href="finsop_1.html#K2" title="FINSOP_1:func.2">$$</a> <span class="p1">(<span class="default"><a href="matrix_3.html#K10" title="MATRIX_3:func.10">Path_matrix</a> <font color="Maroon" title="c18">a6</font>,<font color="Maroon" title="c11">M</font></span>)</span>
<b>by </b><i><a class="txt" href="matrix_9.html#E7:61"><i><font color="Green" title="E50">A3</font></i></a>, <a class="txt" href="matrix_9.html#E48"><i><font color="Green" title="E40">Lm7</font></i></a>, <a class="ref" href="matrix_2.html#D16" title="MATRIX_2:def.16">MATRIX_2:def 16</a></i>
<br/>.= 
the <a href="group_1.html#U1" title="GROUP_1:sel.1">mult</a> of <font color="Maroon" title="c1">K</font> <a href="finsop_1.html#K2" title="FINSOP_1:func.2">$$</a> <span class="p1"><a href="finseq_4.html#K3" title="FINSEQ_4:func.3">&lt;*</a><span class="default"><font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c5">d</font>,<font color="Maroon" title="c9">h</font></span><a href="finseq_4.html#K3" title="FINSEQ_4:func.3">*&gt;</a></span>
<b>by </b><i><a class="ref" href="matrix_9.html#T25" target="_self" title="MATRIX_9:th.25">Th25</a>, <a class="txt" href="matrix_9.html#E1:61"><i><font color="Green" title="E48">A1</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c4">c</font> <a href="group_1.html#K10" title="GROUP_1:func.10">*</a> <font color="Maroon" title="c5">d</font></span>)</span> <a href="group_1.html#K10" title="GROUP_1:func.10">*</a> <font color="Maroon" title="c9">h</font>
<b>by </b><i><a class="ref" href="matrix_9.html#T26" target="_self" title="MATRIX_9:th.26">Th26</a></i>
;<br/>
<a NAME="E15:61"/>
 <a href="matrix_2.html#K12" title="MATRIX_2:func.12">Permutations</a> 3 is <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a>
 
<b>by </b><i><a class="ref" href="matrix_2.html#T30" title="MATRIX_2:th.30">MATRIX_2:30</a></i>;<br/>
<a NAME="E16:61"/><b>then </b><i><font color="Green" title="E58">A11</font></i>: 
 <a href="matrix_2.html#K15" title="MATRIX_2:func.15">FinOmega</a> <span class="p1">(<span class="default"><a href="matrix_2.html#K12" title="MATRIX_2:func.12">Permutations</a> 3</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="matrix_2.html#K12" title="MATRIX_2:func.12">Permutations</a> 3
 
<b>by </b><i><a class="ref" href="matrix_2.html#D17" title="MATRIX_2:def.17">MATRIX_2:def 17</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c21">r1</font> = <span class="p1">(<span class="default"><a href="matrix_3.html#K11" title="MATRIX_3:func.11">Path_product</a> <font color="Maroon" title="c11">M</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c12">id3</font>, <font color="Maroon" title="c22">r2</font> = <span class="p1">(<span class="default"><a href="matrix_3.html#K11" title="MATRIX_3:func.11">Path_product</a> <font color="Maroon" title="c11">M</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c14">rid3</font>, <font color="Maroon" title="c23">r3</font> = <span class="p1">(<span class="default"><a href="matrix_3.html#K11" title="MATRIX_3:func.11">Path_product</a> <font color="Maroon" title="c11">M</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c15">a3</font>, <font color="Maroon" title="c24">r4</font> = <span class="p1">(<span class="default"><a href="matrix_3.html#K11" title="MATRIX_3:func.11">Path_product</a> <font color="Maroon" title="c11">M</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c16">a4</font>, <font color="Maroon" title="c25">r5</font> = <span class="p1">(<span class="default"><a href="matrix_3.html#K11" title="MATRIX_3:func.11">Path_product</a> <font color="Maroon" title="c11">M</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c17">a5</font>, <font color="Maroon" title="c26">r6</font> = <span class="p1">(<span class="default"><a href="matrix_3.html#K11" title="MATRIX_3:func.11">Path_product</a> <font color="Maroon" title="c11">M</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c18">a6</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">K</font> <b>by </b><i><a class="txt" href="matrix_9.html#E8:61"><i><font color="Green" title="E51">A4</font></i></a>, <a class="ref" href="funct_2.html#T7" title="FUNCT_2:th.7">FUNCT_2:7</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c27">X</font> = <span class="p1"><a href="enumset1.html#K4" title="ENUMSET1:func.4">{</a><span class="default"><font color="Maroon" title="c13">Id3</font>,<font color="Maroon" title="c14">rid3</font>,<font color="Maroon" title="c15">a3</font>,<font color="Maroon" title="c16">a4</font>,<font color="Maroon" title="c17">a5</font>,<font color="Maroon" title="c18">a6</font></span><a href="enumset1.html#K4" title="ENUMSET1:func.4">}</a></span> as    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="finsub_1.html#K5" title="FINSUB_1:func.5">Fin</a> <span class="p1">(<span class="default"><a href="matrix_2.html#K12" title="MATRIX_2:func.12">Permutations</a> 3</span>)</span> <b>by </b><i><a class="txt" href="matrix_9.html#E16:61"><i><font color="Green" title="E58">A11</font></i></a>, <a class="ref" href="matrix_9.html#T15" target="_self" title="MATRIX_9:th.15">Th15</a>, <a class="ref" href="matrix_9.html#T19" target="_self" title="MATRIX_9:th.19">Th19</a>, <a class="ref" href="finseq_2.html#T62" title="FINSEQ_2:th.62">FINSEQ_2:62</a></i>;<br/>
<a NAME="E19:61"/><i><font color="Green" title="E59">A12</font></i>: 
 <a href="matrix_2.html#K15" title="MATRIX_2:func.15">FinOmega</a> <span class="p1">(<span class="default"><a href="matrix_2.html#K12" title="MATRIX_2:func.12">Permutations</a> 3</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c27">X</font>
 
<b>by </b><i><a class="ref" href="matrix_9.html#T15" target="_self" title="MATRIX_9:th.15">Th15</a>, <a class="ref" href="matrix_9.html#T19" target="_self" title="MATRIX_9:th.19">Th19</a>, <a class="ref" href="finseq_2.html#T62" title="FINSEQ_2:th.62">FINSEQ_2:62</a>, <a class="ref" href="matrix_2.html#D17" title="MATRIX_2:def.17">MATRIX_2:def 17</a></i>;<br/>
<a NAME="E20:61"/><i><font color="Green" title="E60">A13</font></i>: 
<font color="Maroon" title="c27">X</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="enumset1.html#K1" title="ENUMSET1:func.1">{</a><span class="default"><font color="Maroon" title="c13">Id3</font>,<font color="Maroon" title="c14">rid3</font>,<font color="Maroon" title="c15">a3</font></span><a href="enumset1.html#K1" title="ENUMSET1:func.1">}</a></span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1"><a href="enumset1.html#K1" title="ENUMSET1:func.1">{</a><span class="default"><font color="Maroon" title="c16">a4</font>,<font color="Maroon" title="c17">a5</font>,<font color="Maroon" title="c18">a6</font></span><a href="enumset1.html#K1" title="ENUMSET1:func.1">}</a></span>
 
<b>by </b><i><a class="ref" href="enumset1.html#T53" title="ENUMSET1:th.53">ENUMSET1:53</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c28">B1</font> = <span class="p1"><a href="setwiseo.html#K4" title="SETWISEO:func.4">{.</a><span class="default"><font color="Maroon" title="c13">Id3</font>,<font color="Maroon" title="c14">rid3</font>,<font color="Maroon" title="c15">a3</font></span><a href="setwiseo.html#K4" title="SETWISEO:func.4">.}</a></span>, <font color="Maroon" title="c29">B2</font> = <span class="p1"><a href="setwiseo.html#K4" title="SETWISEO:func.4">{.</a><span class="default"><font color="Maroon" title="c16">a4</font>,<font color="Maroon" title="c17">a5</font>,<font color="Maroon" title="c18">a6</font></span><a href="setwiseo.html#K4" title="SETWISEO:func.4">.}</a></span> as    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="finsub_1.html#K5" title="FINSUB_1:func.5">Fin</a> <span class="p1">(<span class="default"><a href="matrix_2.html#K12" title="MATRIX_2:func.12">Permutations</a> 3</span>)</span> ;<br/>
<a NAME="E22:61"/><i><font color="Green" title="E61">A14</font></i>: 
( <font color="Maroon" title="c28">B1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  &amp; <font color="Maroon" title="c29">B2</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  &amp; <font color="Maroon" title="c28">B1</font> <a href="xboole_0.html#R1" title="XBOOLE_0:pred.1">misses</a> <font color="Maroon" title="c29">B2</font> )
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="61_7"><b>proof </b></a><div class="add">

<a NAME="E1:61_7"/>
<font color="Maroon" title="c28">B1</font> <a href="finsub_1.html#K2" title="FINSUB_1:func.2">\</a> <font color="Maroon" title="c29">B2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c28">B1</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="61_7_1"><b>proof </b></a><div class="add">

<a NAME="E1:61_7_1"/>
for <font color="Olive" title="b1">x</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   st <font color="Olive" title="b1">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c28">B1</font> <a href="finsub_1.html#K2" title="FINSUB_1:func.2">\</a> <font color="Maroon" title="c29">B2</font> holds <br/><font color="Olive" title="b1">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c28">B1</font>
 
<b>by </b><i><a class="ref" href="xboole_0.html#D4" title="XBOOLE_0:def.4">XBOOLE_0:def 4</a></i>;<br/>
<a NAME="E2:61_7_1"/><b>then </b><i><font color="Green" title="E62">A15</font></i>: 
<font color="Maroon" title="c28">B1</font> <a href="finsub_1.html#K2" title="FINSUB_1:func.2">\</a> <font color="Maroon" title="c29">B2</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c28">B1</font>
 
<b>by </b><i><a class="ref" href="tarski.html#D3" title="TARSKI:def.3">TARSKI:def 3</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="61_7_1_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c30">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/><b>assume </b><a NAME="E1:61_7_1_1"/>
<font color="Maroon" title="c30">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c28">B1</font>
 ;<br/><a NAME="E2:61_7_1_1"/><b>then </b>
( <font color="Maroon" title="c30">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c13">Id3</font> or <font color="Maroon" title="c30">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c14">rid3</font> or <font color="Maroon" title="c30">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c15">a3</font> )
 <b>by </b><i><a class="ref" href="enumset1.html#D1" title="ENUMSET1:def.1">ENUMSET1:def 1</a></i>;<br/><a NAME="E3:61_7_1_1"/><b>then </b>
( <font color="Maroon" title="c30">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c28">B1</font> &amp; not <font color="Maroon" title="c30">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c29">B2</font> )
 <b>by </b><i><a class="txt" href="matrix_9.html#E33"><i><font color="Green" title="E27">Lm4</font></i></a>, <a class="ref" href="matrix_9.html#T15" target="_self" title="MATRIX_9:th.15">Th15</a>, <a class="ref" href="enumset1.html#D1" title="ENUMSET1:def.1">ENUMSET1:def 1</a>, <a class="ref" href="finseq_2.html#T62" title="FINSEQ_2:th.62">FINSEQ_2:62</a></i>;<br/><b>hence </b><a NAME="E4:61_7_1_1"/>
<font color="Maroon" title="c30">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c28">B1</font> <a href="finsub_1.html#K2" title="FINSUB_1:func.2">\</a> <font color="Maroon" title="c29">B2</font>
 <b>by </b><i><a class="ref" href="xboole_0.html#D4" title="XBOOLE_0:def.4">XBOOLE_0:def 4</a></i>;<br/></div><b>end;</b></div>
<a NAME="E4:61_7_1"/><b>then </b>
<font color="Maroon" title="c28">B1</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c28">B1</font> <a href="finsub_1.html#K2" title="FINSUB_1:func.2">\</a> <font color="Maroon" title="c29">B2</font>
 
<b>by </b><i><a class="ref" href="tarski.html#D3" title="TARSKI:def.3">TARSKI:def 3</a></i>;<br/>
<b>hence </b><a NAME="E5:61_7_1"/>
<font color="Maroon" title="c28">B1</font> <a href="finsub_1.html#K2" title="FINSUB_1:func.2">\</a> <font color="Maroon" title="c29">B2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c28">B1</font>
 <b>by </b><i><a class="txt" href="matrix_9.html#E2:61_7_1"><i><font color="Green" title="E62">A15</font></i></a>, <a class="ref" href="xboole_0.html#D10" title="XBOOLE_0:def.10">XBOOLE_0:def 10</a></i>;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E2:61_7"/>
( <font color="Maroon" title="c28">B1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  &amp; <font color="Maroon" title="c29">B2</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  &amp; <font color="Maroon" title="c28">B1</font> <a href="xboole_0.html#R1" title="XBOOLE_0:pred.1">misses</a> <font color="Maroon" title="c29">B2</font> )
 <b>by </b><i><a class="ref" href="xboole_1.html#T83" title="XBOOLE_1:th.83">XBOOLE_1:83</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E23:61"/><i><font color="Green" title="E62">A16</font></i>: 
the <a href="rlvect_1.html#U1" title="RLVECT_1:sel.1">add</a> of <font color="Maroon" title="c1">K</font> <a href="setwiseo.html#K7" title="SETWISEO:func.7">$$</a> <font color="Maroon" title="c28">B1</font>,<span class="p1">(<span class="default"><a href="matrix_3.html#K11" title="MATRIX_3:func.11">Path_product</a> <font color="Maroon" title="c11">M</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c21">r1</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <font color="Maroon" title="c22">r2</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <font color="Maroon" title="c23">r3</font>
 
<b>by </b><i><a class="txt" href="matrix_9.html#E33"><i><font color="Green" title="E27">Lm4</font></i></a>, <a class="ref" href="matrix_9.html#T15" target="_self" title="MATRIX_9:th.15">Th15</a>, <a class="ref" href="finseq_2.html#T62" title="FINSEQ_2:th.62">FINSEQ_2:62</a>, <a class="ref" href="setwop_2.html#T5" title="SETWOP_2:th.5">SETWOP_2:5</a></i>;<br/>
<a NAME="E24:61"/><i><font color="Green" title="E63">A17</font></i>: 
the <a href="rlvect_1.html#U1" title="RLVECT_1:sel.1">add</a> of <font color="Maroon" title="c1">K</font> <a href="setwiseo.html#K7" title="SETWISEO:func.7">$$</a> <font color="Maroon" title="c29">B2</font>,<span class="p1">(<span class="default"><a href="matrix_3.html#K11" title="MATRIX_3:func.11">Path_product</a> <font color="Maroon" title="c11">M</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c24">r4</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <font color="Maroon" title="c25">r5</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <font color="Maroon" title="c26">r6</font>
 
<b>by </b><i><a class="txt" href="matrix_9.html#E33"><i><font color="Green" title="E27">Lm4</font></i></a>, <a class="ref" href="setwop_2.html#T5" title="SETWOP_2:th.5">SETWOP_2:5</a></i>;<br/>
 <a href="matrix_3.html#K12" title="MATRIX_3:func.12">Det</a> <font color="Maroon" title="c11">M</font> = 
the <a href="rlvect_1.html#U1" title="RLVECT_1:sel.1">add</a> of <font color="Maroon" title="c1">K</font> <a href="setwiseo.html#K7" title="SETWISEO:func.7">$$</a> <span class="p1">(<span class="default"><a href="matrix_2.html#K15" title="MATRIX_2:func.15">FinOmega</a> <span class="p2">(<span class="default"><a href="matrix_2.html#K12" title="MATRIX_2:func.12">Permutations</a> 3</span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="matrix_3.html#K11" title="MATRIX_3:func.11">Path_product</a> <font color="Maroon" title="c11">M</font></span>)</span>
<b>by </b><i><a class="ref" href="matrix_3.html#D9" title="MATRIX_3:def.9">MATRIX_3:def 9</a></i>
<br/>.= 
the <a href="rlvect_1.html#U1" title="RLVECT_1:sel.1">add</a> of <font color="Maroon" title="c1">K</font> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> <span class="p1">(<span class="default">the <a href="rlvect_1.html#U1" title="RLVECT_1:sel.1">add</a> of <font color="Maroon" title="c1">K</font> <a href="setwiseo.html#K7" title="SETWISEO:func.7">$$</a> <font color="Maroon" title="c28">B1</font>,<span class="p2">(<span class="default"><a href="matrix_3.html#K11" title="MATRIX_3:func.11">Path_product</a> <font color="Maroon" title="c11">M</font></span>)</span></span>)</span>,<span class="p1">(<span class="default">the <a href="rlvect_1.html#U1" title="RLVECT_1:sel.1">add</a> of <font color="Maroon" title="c1">K</font> <a href="setwiseo.html#K7" title="SETWISEO:func.7">$$</a> <font color="Maroon" title="c29">B2</font>,<span class="p2">(<span class="default"><a href="matrix_3.html#K11" title="MATRIX_3:func.11">Path_product</a> <font color="Maroon" title="c11">M</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="setwop_2.html#T6" title="SETWOP_2:th.6">SETWOP_2:6</a>, <a class="txt" href="matrix_9.html#E20:61"><i><font color="Green" title="E60">A13</font></i></a>, <a class="txt" href="matrix_9.html#E22:61"><i><font color="Green" title="E61">A14</font></i></a>, <a class="txt" href="matrix_9.html#E19:61"><i><font color="Green" title="E59">A12</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c21">r1</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <font color="Maroon" title="c22">r2</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <font color="Maroon" title="c23">r3</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c24">r4</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c25">r5</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <font color="Maroon" title="c26">r6</font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="matrix_9.html#E23:61"><i><font color="Green" title="E62">A16</font></i></a>, <a class="txt" href="matrix_9.html#E24:61"><i><font color="Green" title="E63">A17</font></i></a>, <a class="ref" href="rlvect_1.html#D6" title="RLVECT_1:def.6">RLVECT_1:def 6</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c21">r1</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <font color="Maroon" title="c22">r2</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <font color="Maroon" title="c23">r3</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <font color="Maroon" title="c24">r4</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c25">r5</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <font color="Maroon" title="c26">r6</font></span>)</span>
<b>by </b><i><a class="ref" href="rlvect_1.html#D6" title="RLVECT_1:def.6">RLVECT_1:def 6</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="group_1.html#K10" title="GROUP_1:func.10">*</a> <font color="Maroon" title="c6">e</font></span>)</span> <a href="group_1.html#K10" title="GROUP_1:func.10">*</a> <font color="Maroon" title="c10">i</font></span>)</span> <a href="rlvect_1.html#K5" title="RLVECT_1:func.5">-</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon" title="c4">c</font> <a href="group_1.html#K10" title="GROUP_1:func.10">*</a> <font color="Maroon" title="c6">e</font></span>)</span> <a href="group_1.html#K10" title="GROUP_1:func.10">*</a> <font color="Maroon" title="c8">g</font></span>)</span></span>)</span> <a href="rlvect_1.html#K5" title="RLVECT_1:func.5">-</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="group_1.html#K10" title="GROUP_1:func.10">*</a> <font color="Maroon" title="c7">f</font></span>)</span> <a href="group_1.html#K10" title="GROUP_1:func.10">*</a> <font color="Maroon" title="c9">h</font></span>)</span></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c3">b</font> <a href="group_1.html#K10" title="GROUP_1:func.10">*</a> <font color="Maroon" title="c7">f</font></span>)</span> <a href="group_1.html#K10" title="GROUP_1:func.10">*</a> <font color="Maroon" title="c8">g</font></span>)</span></span>)</span> <a href="rlvect_1.html#K5" title="RLVECT_1:func.5">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c3">b</font> <a href="group_1.html#K10" title="GROUP_1:func.10">*</a> <font color="Maroon" title="c5">d</font></span>)</span> <a href="group_1.html#K10" title="GROUP_1:func.10">*</a> <font color="Maroon" title="c10">i</font></span>)</span></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">c</font> <a href="group_1.html#K10" title="GROUP_1:func.10">*</a> <font color="Maroon" title="c5">d</font></span>)</span> <a href="group_1.html#K10" title="GROUP_1:func.10">*</a> <font color="Maroon" title="c9">h</font></span>)</span>
<b>by </b><i><a class="txt" href="matrix_9.html#E9:61"><i><font color="Green" title="E52">A5</font></i></a>, <a class="txt" href="matrix_9.html#E10:61"><i><font color="Green" title="E53">A6</font></i></a>, <a class="txt" href="matrix_9.html#E11:61"><i><font color="Green" title="E54">A7</font></i></a>, <a class="txt" href="matrix_9.html#E12:61"><i><font color="Green" title="E55">A8</font></i></a>, <a class="txt" href="matrix_9.html#E13:61"><i><font color="Green" title="E56">A9</font></i></a>, <a class="txt" href="matrix_9.html#E14:61"><i><font color="Green" title="E57">A10</font></i></a>, <a class="ref" href="rlvect_1.html#D6" title="RLVECT_1:def.6">RLVECT_1:def 6</a></i>
;<br/>
<b>hence </b><a NAME="E26:61"/>
 <a href="matrix_3.html#K12" title="MATRIX_3:func.12">Det</a> <font color="Maroon" title="c11">M</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="group_1.html#K10" title="GROUP_1:func.10">*</a> <font color="Maroon" title="c6">e</font></span>)</span> <a href="group_1.html#K10" title="GROUP_1:func.10">*</a> <font color="Maroon" title="c10">i</font></span>)</span> <a href="rlvect_1.html#K5" title="RLVECT_1:func.5">-</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon" title="c4">c</font> <a href="group_1.html#K10" title="GROUP_1:func.10">*</a> <font color="Maroon" title="c6">e</font></span>)</span> <a href="group_1.html#K10" title="GROUP_1:func.10">*</a> <font color="Maroon" title="c8">g</font></span>)</span></span>)</span> <a href="rlvect_1.html#K5" title="RLVECT_1:func.5">-</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="group_1.html#K10" title="GROUP_1:func.10">*</a> <font color="Maroon" title="c7">f</font></span>)</span> <a href="group_1.html#K10" title="GROUP_1:func.10">*</a> <font color="Maroon" title="c9">h</font></span>)</span></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c3">b</font> <a href="group_1.html#K10" title="GROUP_1:func.10">*</a> <font color="Maroon" title="c7">f</font></span>)</span> <a href="group_1.html#K10" title="GROUP_1:func.10">*</a> <font color="Maroon" title="c8">g</font></span>)</span></span>)</span> <a href="rlvect_1.html#K5" title="RLVECT_1:func.5">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c3">b</font> <a href="group_1.html#K10" title="GROUP_1:func.10">*</a> <font color="Maroon" title="c5">d</font></span>)</span> <a href="group_1.html#K10" title="GROUP_1:func.10">*</a> <font color="Maroon" title="c10">i</font></span>)</span></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">c</font> <a href="group_1.html#K10" title="GROUP_1:func.10">*</a> <font color="Maroon" title="c5">d</font></span>)</span> <a href="group_1.html#K10" title="GROUP_1:func.10">*</a> <font color="Maroon" title="c9">h</font></span>)</span>
 ;<br/>


</div>
