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<b>let </b><font color="Maroon">c<sub>1</sub></font> be   <a href="nat_1.html#NM1">Nat</a>;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font> be    <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">c<sub>3</sub></font>, <font color="Maroon">c<sub>4</sub></font> be    <a href="finseq_1.html#M2">FinSequence</a> of <font color="Maroon">c<sub>2</sub></font>;<br/><b>let </b><font color="Maroon">c<sub>5</sub></font> be   <a href="matrix_1.html#NM1">Matrix</a> of <font color="Maroon">c<sub>2</sub></font>;<br/>









<b>assume </b><b>that </b><br/><a NAME="E1:57"/><i><font color="Green">E37</font></i>: 
( 1 <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">c<sub>1</sub></font> &amp; <font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1 <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>3</sub></font> )
 <b>and </b><br/><a NAME="E2:57"/><i><font color="Green">E38</font></i>: 
<font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1 <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>4</sub></font>
 <b>and </b><br/><a NAME="E3:57"/><i><font color="Green">E39</font></i>: 
<font color="Maroon">c<sub>3</sub></font> <a href="goboard1.html#R1">is_sequence_on</a> <font color="Maroon">c<sub>5</sub></font>
 <b>and </b><br/><a NAME="E4:57"/><i><font color="Green">E40</font></i>: 
<font color="Maroon">c<sub>3</sub></font> <a href="finseq_1.html#K17">|</a> <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>4</sub></font> <a href="finseq_1.html#K17">|</a> <font color="Maroon">c<sub>1</sub></font>
 <b>and </b><br/><a NAME="E5:57"/><i><font color="Green">E41</font></i>: 
<font color="Maroon">c<sub>3</sub></font> <a href="gobrd13.html#R1" target="_self">turns_right</a> <font color="Maroon">c<sub>1</sub></font> <a href="binarith.html#K5">-'</a> 1,<font color="Maroon">c<sub>5</sub></font>
 <b>and </b><br/><a NAME="E6:57"/><i><font color="Green">E42</font></i>: 
<font color="Maroon">c<sub>4</sub></font> <a href="gobrd13.html#R1" target="_self">turns_right</a> <font color="Maroon">c<sub>1</sub></font> <a href="binarith.html#K5">-'</a> 1,<font color="Maroon">c<sub>5</sub></font>
 ;<br/>

<a NAME="E7:57"/><i><font color="Green">E43</font></i>: 
1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>1</sub></font> <a href="binarith.html#K5">-'</a> 1
 
<b>by </b><i><a class="txt" href="gobrd13.html#E1:57"><i><font color="Green">E37</font></i></a>, <a class="ref" href="jordan3.html#T12">JORDAN3:12</a></i>;<br/>
<a NAME="E8:57"/><i><font color="Green">E44</font></i>: 
<font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> 1
 
<b>by </b><i><a class="txt" href="gobrd13.html#E1:57"><i><font color="Green">E37</font></i></a>, <a class="ref" href="binarith.html#T53">BINARITH:53</a></i>;<br/>
<a NAME="E9:57"/>
<font color="Maroon">c<sub>1</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1
 
<b>by </b><i><a class="ref" href="nat_1.html#T37">NAT_1:37</a></i>;<br/>
<a NAME="E10:57"/><b>then </b><i><font color="Green">E45</font></i>: 
( <font color="Maroon">c<sub>1</sub></font> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>3</sub></font> &amp; <font color="Maroon">c<sub>1</sub></font> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>4</sub></font> )
 
<b>by </b><i><a class="txt" href="gobrd13.html#E1:57"><i><font color="Green">E37</font></i></a>, <a class="txt" href="gobrd13.html#E2:57"><i><font color="Green">E38</font></i></a>, <a class="ref" href="xxreal_0.html#T2">XXREAL_0:2</a></i>;<br/>
<a NAME="E11:57"/><b>then </b><i><font color="Green">E46</font></i>: 
<font color="Maroon">c<sub>1</sub></font> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="finseq_1.html#K17">|</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>
 
<b>by </b><i><a class="ref" href="finseq_1.html#T80">FINSEQ_1:80</a></i>;<br/>
<a NAME="E12:57"/>
<font color="Maroon">c<sub>1</sub></font> <a href="binarith.html#K5">-'</a> 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>1</sub></font>
 
<b>by </b><i><a class="ref" href="binarith.html#T52">BINARITH:52</a></i>;<br/>
<a NAME="E13:57"/><b>then </b>
<font color="Maroon">c<sub>1</sub></font> <a href="binarith.html#K5">-'</a> 1 <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="finseq_1.html#K17">|</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>
 
<b>by </b><i><a class="txt" href="gobrd13.html#E10:57"><i><font color="Green">E45</font></i></a>, <a class="ref" href="finseq_1.html#T80">FINSEQ_1:80</a></i>;<br/>
<a NAME="E14:57"/><b>then </b><i><font color="Green">E47</font></i>: 
( <font color="Maroon">c<sub>1</sub></font> <a href="binarith.html#K5">-'</a> 1 <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="finseq_1.html#K17">|</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> &amp; <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="finseq_1.html#K17">|</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> )
 
<b>by </b><i><a class="txt" href="gobrd13.html#E1:57"><i><font color="Green">E37</font></i></a>, <a class="txt" href="gobrd13.html#E7:57"><i><font color="Green">E43</font></i></a>, <a class="txt" href="gobrd13.html#E11:57"><i><font color="Green">E46</font></i></a>, <a class="ref" href="finseq_3.html#T27">FINSEQ_3:27</a></i>;<br/>
<a NAME="E15:57"/><b>then </b><i><font color="Green">E48</font></i>: 
( <font color="Maroon">c<sub>3</sub></font> <a href="finseq_4.html#K4">/.</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="finseq_1.html#K17">|</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="finseq_4.html#K4">/.</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span> &amp; <font color="Maroon">c<sub>3</sub></font> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="finseq_1.html#K17">|</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">c<sub>1</sub></font> )
 
<b>by </b><i><a class="ref" href="finseq_4.html#T85">FINSEQ_4:85</a></i>;<br/>
<a NAME="E16:57"/><i><font color="Green">E49</font></i>: 
( <font color="Maroon">c<sub>4</sub></font> <a href="finseq_4.html#K4">/.</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="finseq_1.html#K17">|</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="finseq_4.html#K4">/.</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span> &amp; <font color="Maroon">c<sub>4</sub></font> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="finseq_1.html#K17">|</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">c<sub>1</sub></font> )
 
<b>by </b><i><a class="txt" href="gobrd13.html#E4:57"><i><font color="Green">E40</font></i></a>, <a class="txt" href="gobrd13.html#E14:57"><i><font color="Green">E47</font></i></a>, <a class="ref" href="finseq_4.html#T85">FINSEQ_4:85</a></i>;<br/>
<a NAME="E17:57"/><i><font color="Green">E50</font></i>: 
<font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1 <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span>
 
<b>by </b><i><a class="txt" href="gobrd13.html#E8:57"><i><font color="Green">E44</font></i></a></i>;<br/>
<b>consider </b><font color="Maroon">c<sub>6</sub></font>, <font color="Maroon">c<sub>7</sub></font>, <font color="Maroon">c<sub>8</sub></font>, <font color="Maroon">c<sub>9</sub></font> being   <a href="nat_1.html#NM1">Nat</a><b> such that </b><br/><a NAME="E19:57"/><i><font color="Green">E51</font></i>: 
( <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</sub></font></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a>  <a href="matrix_1.html#K2">Indices</a> <font color="Maroon">c<sub>5</sub></font> &amp; <font color="Maroon">c<sub>3</sub></font> <a href="finseq_4.html#K4">/.</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>5</sub></font> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</sub></font> )
 <b>and </b><br/><a NAME="E20:57"/><i><font color="Green">E52</font></i>: 
( <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>9</sub></font></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a>  <a href="matrix_1.html#K2">Indices</a> <font color="Maroon">c<sub>5</sub></font> &amp; <font color="Maroon">c<sub>3</sub></font> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>5</sub></font> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>9</sub></font> )
 <b>and </b><br/><a NAME="E21:57"/><i><font color="Green">E53</font></i>: 
( ( <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>8</sub></font> &amp; <font color="Maroon">c<sub>7</sub></font> <a href="nat_1.html#K1">+</a> 1 <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>9</sub></font> ) or ( <font color="Maroon">c<sub>6</sub></font> <a href="nat_1.html#K1">+</a> 1 <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>8</sub></font> &amp; <font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>9</sub></font> ) or ( <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>8</sub></font> <a href="nat_1.html#K1">+</a> 1 &amp; <font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>9</sub></font> ) or ( <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>8</sub></font> &amp; <font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>9</sub></font> <a href="nat_1.html#K1">+</a> 1 ) )
 <b>by </b><i><a class="txt" href="gobrd13.html#E3:57"><i><font color="Green">E39</font></i></a>, <a class="txt" href="gobrd13.html#E7:57"><i><font color="Green">E43</font></i></a>, <a class="txt" href="gobrd13.html#E8:57"><i><font color="Green">E44</font></i></a>, <a class="txt" href="gobrd13.html#E10:57"><i><font color="Green">E45</font></i></a>, <a class="ref" href="jordan8.html#T6">JORDAN8:6</a></i>;<br/>
<a NAME="E22:57"/><i><font color="Green">E54</font></i>: 
( <font color="Maroon">c<sub>6</sub></font> <a href="nat_1.html#K1">+</a> 1 <a href="xxreal_0.html#NR4" target="_self">&gt;</a> <font color="Maroon">c<sub>6</sub></font> &amp; <font color="Maroon">c<sub>8</sub></font> <a href="nat_1.html#K1">+</a> 1 <a href="xxreal_0.html#NR4" target="_self">&gt;</a> <font color="Maroon">c<sub>8</sub></font> &amp; <font color="Maroon">c<sub>7</sub></font> <a href="nat_1.html#K1">+</a> 1 <a href="xxreal_0.html#NR4" target="_self">&gt;</a> <font color="Maroon">c<sub>7</sub></font> &amp; <font color="Maroon">c<sub>9</sub></font> <a href="nat_1.html#K1">+</a> 1 <a href="xxreal_0.html#NR4" target="_self">&gt;</a> <font color="Maroon">c<sub>9</sub></font> )
 
<b>by </b><i><a class="ref" href="nat_1.html#T38">NAT_1:38</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="57_1"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="57_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:57_1_1"/>
( ( <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>8</sub></font> &amp; <font color="Maroon">c<sub>7</sub></font> <a href="nat_1.html#K1">+</a> 1 <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>9</sub></font> ) or ( <font color="Maroon">c<sub>6</sub></font> <a href="nat_1.html#K1">+</a> 1 <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>8</sub></font> &amp; <font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>9</sub></font> ) or ( <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>8</sub></font> <a href="nat_1.html#K1">+</a> 1 &amp; <font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>9</sub></font> ) or ( <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>8</sub></font> &amp; <font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>9</sub></font> <a href="nat_1.html#K1">+</a> 1 ) )
 </span><b>by </b><i><a class="txt" href="gobrd13.html#E21:57"><i><font color="Green">E53</font></i></a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="57_1_1_1"><b>suppose </b></a><a NAME="E1:57_1_1_1"/><i><font color="Green">E55</font></i>: 
( <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>8</sub></font> &amp; <font color="Maroon">c<sub>7</sub></font> <a href="nat_1.html#K1">+</a> 1 <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>9</sub></font> )
 ;<br/><div class="add"><b>hence </b><font color="Maroon">c<sub>3</sub></font> <a href="finseq_4.html#K4">/.</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> = 
<font color="Maroon">c<sub>5</sub></font> <a href="matrix_1.html#K3">*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>9</sub></font>
<b>by </b><i><a class="txt" href="gobrd13.html#E5:57"><i><font color="Green">E41</font></i></a>, <a class="txt" href="gobrd13.html#E8:57"><i><font color="Green">E44</font></i></a>, <a class="txt" href="gobrd13.html#E17:57"><i><font color="Green">E50</font></i></a>, <a class="txt" href="gobrd13.html#E19:57"><i><font color="Green">E51</font></i></a>, <a class="txt" href="gobrd13.html#E20:57"><i><font color="Green">E52</font></i></a>, <a class="txt" href="gobrd13.html#E22:57"><i><font color="Green">E54</font></i></a>, <a class="ref" href="gobrd13.html#D6" target="_self">Def6</a></i>
<br/>.= 
<font color="Maroon">c<sub>4</sub></font> <a href="finseq_4.html#K4">/.</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>
<b>by </b><i><a class="txt" href="gobrd13.html#E4:57"><i><font color="Green">E40</font></i></a>, <a class="txt" href="gobrd13.html#E6:57"><i><font color="Green">E42</font></i></a>, <a class="txt" href="gobrd13.html#E8:57"><i><font color="Green">E44</font></i></a>, <a class="txt" href="gobrd13.html#E15:57"><i><font color="Green">E48</font></i></a>, <a class="txt" href="gobrd13.html#E16:57"><i><font color="Green">E49</font></i></a>, <a class="txt" href="gobrd13.html#E17:57"><i><font color="Green">E50</font></i></a>, <a class="txt" href="gobrd13.html#E19:57"><i><font color="Green">E51</font></i></a>, <a class="txt" href="gobrd13.html#E20:57"><i><font color="Green">E52</font></i></a>, <a class="txt" href="gobrd13.html#E22:57"><i><font color="Green">E54</font></i></a>, <a class="txt" href="gobrd13.html#E1:57_1_1_1"><i><font color="Green">E55</font></i></a>, <a class="ref" href="gobrd13.html#D6" target="_self">Def6</a></i>
;<br/><br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="57_1_1_2"><b>suppose </b></a><a NAME="E1:57_1_1_2"/><i><font color="Green">E55</font></i>: 
( <font color="Maroon">c<sub>6</sub></font> <a href="nat_1.html#K1">+</a> 1 <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>8</sub></font> &amp; <font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>9</sub></font> )
 ;<br/><div class="add"><b>hence </b><font color="Maroon">c<sub>3</sub></font> <a href="finseq_4.html#K4">/.</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> = 
<font color="Maroon">c<sub>5</sub></font> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>8</sub></font>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>9</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span>
<b>by </b><i><a class="txt" href="gobrd13.html#E5:57"><i><font color="Green">E41</font></i></a>, <a class="txt" href="gobrd13.html#E8:57"><i><font color="Green">E44</font></i></a>, <a class="txt" href="gobrd13.html#E17:57"><i><font color="Green">E50</font></i></a>, <a class="txt" href="gobrd13.html#E19:57"><i><font color="Green">E51</font></i></a>, <a class="txt" href="gobrd13.html#E20:57"><i><font color="Green">E52</font></i></a>, <a class="txt" href="gobrd13.html#E22:57"><i><font color="Green">E54</font></i></a>, <a class="ref" href="gobrd13.html#D6" target="_self">Def6</a></i>
<br/>.= 
<font color="Maroon">c<sub>4</sub></font> <a href="finseq_4.html#K4">/.</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>
<b>by </b><i><a class="txt" href="gobrd13.html#E4:57"><i><font color="Green">E40</font></i></a>, <a class="txt" href="gobrd13.html#E6:57"><i><font color="Green">E42</font></i></a>, <a class="txt" href="gobrd13.html#E8:57"><i><font color="Green">E44</font></i></a>, <a class="txt" href="gobrd13.html#E15:57"><i><font color="Green">E48</font></i></a>, <a class="txt" href="gobrd13.html#E16:57"><i><font color="Green">E49</font></i></a>, <a class="txt" href="gobrd13.html#E17:57"><i><font color="Green">E50</font></i></a>, <a class="txt" href="gobrd13.html#E19:57"><i><font color="Green">E51</font></i></a>, <a class="txt" href="gobrd13.html#E20:57"><i><font color="Green">E52</font></i></a>, <a class="txt" href="gobrd13.html#E22:57"><i><font color="Green">E54</font></i></a>, <a class="txt" href="gobrd13.html#E1:57_1_1_2"><i><font color="Green">E55</font></i></a>, <a class="ref" href="gobrd13.html#D6" target="_self">Def6</a></i>
;<br/><br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="57_1_1_3"><b>suppose </b></a><a NAME="E1:57_1_1_3"/><i><font color="Green">E55</font></i>: 
( <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>8</sub></font> <a href="nat_1.html#K1">+</a> 1 &amp; <font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>9</sub></font> )
 ;<br/><div class="add"><b>hence </b><font color="Maroon">c<sub>3</sub></font> <a href="finseq_4.html#K4">/.</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> = 
<font color="Maroon">c<sub>5</sub></font> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>8</sub></font>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>9</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>
<b>by </b><i><a class="txt" href="gobrd13.html#E5:57"><i><font color="Green">E41</font></i></a>, <a class="txt" href="gobrd13.html#E8:57"><i><font color="Green">E44</font></i></a>, <a class="txt" href="gobrd13.html#E17:57"><i><font color="Green">E50</font></i></a>, <a class="txt" href="gobrd13.html#E19:57"><i><font color="Green">E51</font></i></a>, <a class="txt" href="gobrd13.html#E20:57"><i><font color="Green">E52</font></i></a>, <a class="txt" href="gobrd13.html#E22:57"><i><font color="Green">E54</font></i></a>, <a class="ref" href="gobrd13.html#D6" target="_self">Def6</a></i>
<br/>.= 
<font color="Maroon">c<sub>4</sub></font> <a href="finseq_4.html#K4">/.</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>
<b>by </b><i><a class="txt" href="gobrd13.html#E4:57"><i><font color="Green">E40</font></i></a>, <a class="txt" href="gobrd13.html#E6:57"><i><font color="Green">E42</font></i></a>, <a class="txt" href="gobrd13.html#E8:57"><i><font color="Green">E44</font></i></a>, <a class="txt" href="gobrd13.html#E15:57"><i><font color="Green">E48</font></i></a>, <a class="txt" href="gobrd13.html#E16:57"><i><font color="Green">E49</font></i></a>, <a class="txt" href="gobrd13.html#E17:57"><i><font color="Green">E50</font></i></a>, <a class="txt" href="gobrd13.html#E19:57"><i><font color="Green">E51</font></i></a>, <a class="txt" href="gobrd13.html#E20:57"><i><font color="Green">E52</font></i></a>, <a class="txt" href="gobrd13.html#E22:57"><i><font color="Green">E54</font></i></a>, <a class="txt" href="gobrd13.html#E1:57_1_1_3"><i><font color="Green">E55</font></i></a>, <a class="ref" href="gobrd13.html#D6" target="_self">Def6</a></i>
;<br/><br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="57_1_1_4"><b>suppose </b></a><a NAME="E1:57_1_1_4"/><i><font color="Green">E55</font></i>: 
( <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>8</sub></font> &amp; <font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>9</sub></font> <a href="nat_1.html#K1">+</a> 1 )
 ;<br/><div class="add"><b>hence </b><font color="Maroon">c<sub>3</sub></font> <a href="finseq_4.html#K4">/.</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> = 
<font color="Maroon">c<sub>5</sub></font> <a href="matrix_1.html#K3">*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span>,<font color="Maroon">c<sub>9</sub></font>
<b>by </b><i><a class="txt" href="gobrd13.html#E5:57"><i><font color="Green">E41</font></i></a>, <a class="txt" href="gobrd13.html#E8:57"><i><font color="Green">E44</font></i></a>, <a class="txt" href="gobrd13.html#E17:57"><i><font color="Green">E50</font></i></a>, <a class="txt" href="gobrd13.html#E19:57"><i><font color="Green">E51</font></i></a>, <a class="txt" href="gobrd13.html#E20:57"><i><font color="Green">E52</font></i></a>, <a class="txt" href="gobrd13.html#E22:57"><i><font color="Green">E54</font></i></a>, <a class="ref" href="gobrd13.html#D6" target="_self">Def6</a></i>
<br/>.= 
<font color="Maroon">c<sub>4</sub></font> <a href="finseq_4.html#K4">/.</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>
<b>by </b><i><a class="txt" href="gobrd13.html#E4:57"><i><font color="Green">E40</font></i></a>, <a class="txt" href="gobrd13.html#E6:57"><i><font color="Green">E42</font></i></a>, <a class="txt" href="gobrd13.html#E8:57"><i><font color="Green">E44</font></i></a>, <a class="txt" href="gobrd13.html#E15:57"><i><font color="Green">E48</font></i></a>, <a class="txt" href="gobrd13.html#E16:57"><i><font color="Green">E49</font></i></a>, <a class="txt" href="gobrd13.html#E17:57"><i><font color="Green">E50</font></i></a>, <a class="txt" href="gobrd13.html#E19:57"><i><font color="Green">E51</font></i></a>, <a class="txt" href="gobrd13.html#E20:57"><i><font color="Green">E52</font></i></a>, <a class="txt" href="gobrd13.html#E22:57"><i><font color="Green">E54</font></i></a>, <a class="txt" href="gobrd13.html#E1:57_1_1_4"><i><font color="Green">E55</font></i></a>, <a class="ref" href="gobrd13.html#D6" target="_self">Def6</a></i>
;<br/><br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div>
<b>hence </b><font color="Maroon">c<sub>3</sub></font> <a href="finseq_1.html#K17">|</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> = 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="finseq_1.html#K17">|</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="finseq_1.html#K7">^</a> <span class="p1"><a href="finseq_1.html#K9">&lt;*</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="finseq_4.html#K4">/.</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span><a href="finseq_1.html#K9">*&gt;</a></span>
<b>by </b><i><a class="txt" href="gobrd13.html#E1:57"><i><font color="Green">E37</font></i></a>, <a class="txt" href="gobrd13.html#E4:57"><i><font color="Green">E40</font></i></a>, <a class="ref" href="jordan8.html#T2">JORDAN8:2</a></i>
<br/>.= 
<font color="Maroon">c<sub>4</sub></font> <a href="finseq_1.html#K17">|</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>
<b>by </b><i><a class="txt" href="gobrd13.html#E2:57"><i><font color="Green">E38</font></i></a>, <a class="ref" href="jordan8.html#T2">JORDAN8:2</a></i>
;<br/><br/>


</div>
