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<b>let </b><font color="Maroon">K</font> be   <a href="vectsp_1.html#NM2">Field</a>;<br/><b>let </b><font color="Maroon">a</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">K</font>;<br/><b>let </b><font color="Maroon">b</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">K</font>;<br/><b>let </b><font color="Maroon">c</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">K</font>;<br/><b>let </b><font color="Maroon">d</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">K</font>;<br/><b>let </b><font color="Maroon">p</font> be    <a href="matrix_2.html#M3">Element</a> of  <a href="matrix_2.html#K12">Permutations</a> 2;<br/>











<b>assume </b><a NAME="E1:16"/><i><font color="Green">E31</font></i>: 
<font color="Maroon">p</font> <a href="hidden.html#R1">=</a>  <a href="finseq_2.html#K1">idseq</a> 2
 ;<br/>

<a NAME="E2:16"/><i><font color="Green">E34</font></i>: 
 <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><a href="matrix_3.html#K10">Path_matrix</a> <font color="Maroon">p</font>,<span class="p2">(<span class="default"><font color="Maroon">a</font>,<font color="Maroon">b</font> <a href="matrix_2.html#K6">][</a> <font color="Maroon">c</font>,<font color="Maroon">d</font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> 2
 
<b>by </b><i><a class="ref" href="matrix_3.html#D7">MATRIX_3:def 7</a></i>;<br/>
<a NAME="E3:16"/><b>then </b><i><font color="Green">E37</font></i>: 
 <a href="setwop_2.html#K3">dom</a> <span class="p1">(<span class="default"><a href="matrix_3.html#K10">Path_matrix</a> <font color="Maroon">p</font>,<span class="p2">(<span class="default"><font color="Maroon">a</font>,<font color="Maroon">b</font> <a href="matrix_2.html#K6">][</a> <font color="Maroon">c</font>,<font color="Maroon">d</font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="setwop_2.html#K2">Seg</a> 2
 
<b>by </b><i><a class="ref" href="finseq_1.html#D3">FINSEQ_1:def 3</a></i>;<br/>
<a NAME="E4:16"/><b>then </b><i><font color="Green">E38</font></i>: 
1 <a href="hidden.html#R2">in</a>  <a href="setwop_2.html#K3">dom</a> <span class="p1">(<span class="default"><a href="matrix_3.html#K10">Path_matrix</a> <font color="Maroon">p</font>,<span class="p2">(<span class="default"><font color="Maroon">a</font>,<font color="Maroon">b</font> <a href="matrix_2.html#K6">][</a> <font color="Maroon">c</font>,<font color="Maroon">d</font></span>)</span></span>)</span>
 
;<br/>
<a NAME="E5:16"/><b>then </b><i><font color="Green">E39</font></i>: 
1 <a href="hidden.html#R1">=</a> <font color="Maroon">p</font> <a href="funct_1.html#K1">.</a> 1
 
<b>by </b><i>, <a class="ref" href="funct_1.html#T35">FUNCT_1:35</a>, </i>;<br/>
<a NAME="E6:16"/><i><font color="Green">E40</font></i>: 
2 <a href="hidden.html#R2">in</a>  <a href="setwop_2.html#K3">dom</a> <span class="p1">(<span class="default"><a href="matrix_3.html#K10">Path_matrix</a> <font color="Maroon">p</font>,<span class="p2">(<span class="default"><font color="Maroon">a</font>,<font color="Maroon">b</font> <a href="matrix_2.html#K6">][</a> <font color="Maroon">c</font>,<font color="Maroon">d</font></span>)</span></span>)</span>
 
<b>by </b><i/>;<br/>
<a NAME="E7:16"/><b>then </b><i><font color="Green">E41</font></i>: 
2 <a href="hidden.html#R1">=</a> <font color="Maroon">p</font> <a href="funct_1.html#K1">.</a> 2
 
<b>by </b><i>, <a class="ref" href="funct_1.html#T35">FUNCT_1:35</a>, </i>;<br/>
<i><font color="Green">E42</font></i>: <span class="p1">(<span class="default"><a href="matrix_3.html#K10">Path_matrix</a> <font color="Maroon">p</font>,<span class="p2">(<span class="default"><font color="Maroon">a</font>,<font color="Maroon">b</font> <a href="matrix_2.html#K6">][</a> <font color="Maroon">c</font>,<font color="Maroon">d</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> 1 = 
<span class="p1">(<span class="default"><font color="Maroon">a</font>,<font color="Maroon">b</font> <a href="matrix_2.html#K6">][</a> <font color="Maroon">c</font>,<font color="Maroon">d</font></span>)</span> <a href="matrix_1.html#K3">*</a> 1,1
<b>by </b><i>, <a class="ref" href="matrix_3.html#D7">MATRIX_3:def 7</a>, </i>
<br/>.= 
<font color="Maroon">a</font>
<b>by </b><i><a class="ref" href="matrix_2.html#T6">MATRIX_2:6</a></i>
;<br/>
<span class="p1">(<span class="default"><a href="matrix_3.html#K10">Path_matrix</a> <font color="Maroon">p</font>,<span class="p2">(<span class="default"><font color="Maroon">a</font>,<font color="Maroon">b</font> <a href="matrix_2.html#K6">][</a> <font color="Maroon">c</font>,<font color="Maroon">d</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> 2 = 
<span class="p1">(<span class="default"><font color="Maroon">a</font>,<font color="Maroon">b</font> <a href="matrix_2.html#K6">][</a> <font color="Maroon">c</font>,<font color="Maroon">d</font></span>)</span> <a href="matrix_1.html#K3">*</a> 2,2
<b>by </b><i>, <a class="ref" href="matrix_3.html#D7">MATRIX_3:def 7</a>, </i>
<br/>.= 
<font color="Maroon">d</font>
<b>by </b><i><a class="ref" href="matrix_2.html#T6">MATRIX_2:6</a></i>
;<br/>
<b>hence </b><a NAME="E10:16"/>
 <a href="matrix_3.html#K10">Path_matrix</a> <font color="Maroon">p</font>,<span class="p1">(<span class="default"><font color="Maroon">a</font>,<font color="Maroon">b</font> <a href="matrix_2.html#K6">][</a> <font color="Maroon">c</font>,<font color="Maroon">d</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="finseq_4.html#K2">&lt;*</a><span class="default"><font color="Maroon">a</font>,<font color="Maroon">d</font></span><a href="finseq_4.html#K2">*&gt;</a></span>
 <b>by </b><i>, , <a class="ref" href="finseq_1.html#T61">FINSEQ_1:61</a></i>;<br/>


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