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<b>let </b><font color="Maroon">c<sub>1</sub></font> be   <a href="goboard1.html#NM1">Go-board</a>;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font> be   <a href="sppol_2.html#NM1">S-Sequence_in_R2</a>;<br/><b>let </b><font color="Maroon">c<sub>3</sub></font> be   <a href="pre_topc.html#NM2">Point</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 2</span>)</span>;<br/><b>let </b><font color="Maroon">c<sub>4</sub></font> be   <a href="nat_1.html#NM1">Nat</a>;<br/>







<b>assume </b><b>that </b><br/><a NAME="E1:54"/><i><font color="Green">E34</font></i>: 
1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>4</sub></font>
 <b>and </b><br/><a NAME="E2:54"/><i><font color="Green">E35</font></i>: 
<font color="Maroon">c<sub>4</sub></font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">c<sub>3</sub></font> <a href="finseq_4.html#K5">..</a> <font color="Maroon">c<sub>2</sub></font>
 <b>and </b><br/><a NAME="E3:54"/><i><font color="Green">E36</font></i>: 
<font color="Maroon">c<sub>2</sub></font> <a href="goboard1.html#R1">is_sequence_on</a> <font color="Maroon">c<sub>1</sub></font>
 <b>and </b><br/><a NAME="E4:54"/><i><font color="Green">E37</font></i>: 
<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K2">rng</a> <font color="Maroon">c<sub>2</sub></font>
 ;<br/>

<a NAME="E5:54"/>
<font color="Maroon">c<sub>3</sub></font> <a href="finseq_4.html#K5">..</a> <font color="Maroon">c<sub>2</sub></font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 1
 
<b>by </b><i><a class="txt" href="jordan1j.html#E1:54"><i><font color="Green">E34</font></i></a>, <a class="txt" href="jordan1j.html#E2:54"><i><font color="Green">E35</font></i></a>, <a class="ref" href="xxreal_0.html#T2">XXREAL_0:2</a></i>;<br/>
<b>then </b><i><font color="Green">E38</font></i>: <font color="Maroon">c<sub>2</sub></font> <a href="finseq_1.html#K17">|</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="finseq_4.html#K5">..</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> = 
 <a href="jordan3.html#K1">mid</a> <font color="Maroon">c<sub>2</sub></font>,1,<span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="finseq_4.html#K5">..</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="jordan3.html#T25">JORDAN3:25</a></i>
<br/>.= 
 <a href="jordan3.html#K4">R_Cut</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>
<b>by </b><i><a class="txt" href="jordan1j.html#E4:54"><i><font color="Green">E37</font></i></a>, <a class="ref" href="jordan1g.html#T57">JORDAN1G:57</a></i>
;<br/>
<a NAME="E7:54"/><i><font color="Green">E39</font></i>: 
<font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K1">+</a> 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>3</sub></font> <a href="finseq_4.html#K5">..</a> <font color="Maroon">c<sub>2</sub></font>
 
<b>by </b><i><a class="txt" href="jordan1j.html#E2:54"><i><font color="Green">E35</font></i></a>, <a class="ref" href="nat_1.html#T38">NAT_1:38</a></i>;<br/>
<a NAME="E8:54"/>
<font color="Maroon">c<sub>3</sub></font> <a href="finseq_4.html#K5">..</a> <font color="Maroon">c<sub>2</sub></font> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>2</sub></font>
 
<b>by </b><i><a class="txt" href="jordan1j.html#E4:54"><i><font color="Green">E37</font></i></a>, <a class="ref" href="finseq_4.html#T31">FINSEQ_4:31</a></i>;<br/>
<a NAME="E9:54"/><b>then </b>
<font color="Maroon">c<sub>4</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>2</sub></font>
 
<b>by </b><i><a class="txt" href="jordan1j.html#E7:54"><i><font color="Green">E39</font></i></a>, <a class="ref" href="xxreal_0.html#T2">XXREAL_0:2</a></i>;<br/>
<b>hence </b><a NAME="E10:54"/>
(  <a href="gobrd13.html#K4">left_cell</a> <span class="p1">(<span class="default"><a href="jordan3.html#K4">R_Cut</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a>  <a href="gobrd13.html#K4">left_cell</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>1</sub></font> &amp;  <a href="gobrd13.html#K3">right_cell</a> <span class="p1">(<span class="default"><a href="jordan3.html#K4">R_Cut</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a>  <a href="gobrd13.html#K3">right_cell</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>1</sub></font> )
 <b>by </b><i><a class="txt" href="jordan1j.html#E1:54"><i><font color="Green">E34</font></i></a>, <a class="txt" href="jordan1j.html#E3:54"><i><font color="Green">E36</font></i></a>, <a class="txt" href="jordan1j.html#E6:54"><i><font color="Green">E38</font></i></a>, <a class="txt" href="jordan1j.html#E7:54"><i><font color="Green">E39</font></i></a>, <a class="ref" href="gobrd13.html#T32">GOBRD13:32</a></i>;<br/>


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