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<b>let </b><font color="Maroon">c<sub>1</sub></font> be  non <a href="funct_1.html#V3">constant</a> <a href="goboard5.html#V2">standard</a> <a href="goboard5.html#NM1">special_circular_sequence</a>;<br/>

<b>defpred </b><font color="Maroon">S<sub>1</sub></font>[  <a href="nat_1.html#NM1">Nat</a>] means ( 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">a<sub>1</sub></font> &amp; <font color="Maroon">a<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>1</sub></font> implies  <a href="tops_1.html#K1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K5">left_cell</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">a<sub>1</sub></font></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="goboard9.html#K2" target="_self">LeftComp</a> <font color="Maroon">c<sub>1</sub></font> );<br/>
<a NAME="E1:28"/><i><font color="Green">E28</font></i>: 
<font color="Maroon">S<sub>1</sub></font>[0]
 
;<br/>
<div><i><font color="Green">E29</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="28_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c<sub>2</sub></font> be   <a href="nat_1.html#NM1">Nat</a>;<br/><b>assume </b><a NAME="E1:28_1"/><i><font color="Green">E30</font></i>: 
<font color="Maroon">S<sub>1</sub></font>[<font color="Maroon">c<sub>2</sub></font>]
 ;<br/><b>thus </b><a NAME="E2:28_1"/>
<font color="Maroon">S<sub>1</sub></font>[<font color="Maroon">c<sub>2</sub></font> <a href="nat_1.html#K1">+</a> 1]
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="28_1_1"><b>proof </b></a><div class="add">

<b>assume </b><b>that </b><br/><a NAME="E1:28_1_1"/><i><font color="Green">E31</font></i>: 
1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>2</sub></font> <a href="nat_1.html#K1">+</a> 1
 <b>and </b><br/><a NAME="E2:28_1_1"/><i><font color="Green">E32</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <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>1</sub></font>
 ;<br/>

<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="28_1_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:28_1_1_1"/>
( <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> 0 or <font color="Maroon">c<sub>2</sub></font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 1 )
 </span><b>by </b><i><a class="ref" href="nat_1.html#T39">NAT_1:39</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="28_1_1_1_1"><b>suppose </b></a><a NAME="E1:28_1_1_1_1"/>
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> 0
 ;<br/><div class="add"><b>hence </b><a NAME="E2:28_1_1_1_1"/>
 <a href="tops_1.html#K1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K5">left_cell</a> <font color="Maroon">c<sub>1</sub></font>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="goboard9.html#K2" target="_self">LeftComp</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="ref" href="goboard9.html#D1" target="_self">Def1</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="28_1_1_1_2"><b>suppose </b></a><a NAME="E1:28_1_1_1_2"/><i><font color="Green">E33</font></i>: 
<font color="Maroon">c<sub>2</sub></font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 1
 ;<br/><div class="add"><a NAME="E2:28_1_1_1_2"/><i><font color="Green">E34</font></i>: 
<font color="Maroon">c<sub>2</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>1</sub></font>
 <b>by </b><i><a class="txt" href="goboard9.html#E2:28_1_1"><i><font color="Green">E32</font></i></a>, <a class="ref" href="nat_1.html#T38">NAT_1:38</a></i>;<br/><a NAME="E3:28_1_1_1_2"/><i><font color="Green">E35</font></i>: 
<font color="Maroon">c<sub>2</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>2</sub></font> <a href="nat_1.html#K1">+</a> 1
 <b>by </b><i><a class="ref" href="nat_1.html#T29">NAT_1:29</a></i>;<br/><a NAME="E4:28_1_1_1_2"/><b>then </b>
<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>1</sub></font>
 <b>by </b><i><a class="txt" href="goboard9.html#E2:28_1_1_1_2"><i><font color="Green">E34</font></i></a>, <a class="ref" href="xxreal_0.html#T2">XXREAL_0:2</a></i>;<br/><a NAME="E5:28_1_1_1_2"/><b>then </b><i><font color="Green">E36</font></i>: 
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="goboard9.html#E1:28_1_1_1_2"><i><font color="Green">E33</font></i></a>, <a class="ref" href="finseq_3.html#T27">FINSEQ_3:27</a></i>;<br/><b>then consider </b><font color="Maroon">c<sub>3</sub></font>, <font color="Maroon">c<sub>4</sub></font> being   <a href="nat_1.html#NM1">Nat</a><b> such that </b><br/><a NAME="E7:28_1_1_1_2"/><i><font color="Green">E37</font></i>: 
<span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</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> <span class="p1">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>
 <b>and </b><br/><a NAME="E8:28_1_1_1_2"/><i><font color="Green">E38</font></i>: 
<font color="Maroon">c<sub>1</sub></font> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font>
 <b>by </b><i><a class="ref" href="goboard2.html#T25">GOBOARD2:25</a></i>;<br/><a NAME="E9:28_1_1_1_2"/><i><font color="Green">E39</font></i>: 
<font color="Maroon">c<sub>2</sub></font> <a href="nat_1.html#K1">+</a> 1 <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="goboard9.html#E1:28_1_1"><i><font color="Green">E31</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1_1_2"><i><font color="Green">E34</font></i></a>, <a class="ref" href="finseq_3.html#T27">FINSEQ_3:27</a></i>;<br/><b>then consider </b><font color="Maroon">c<sub>5</sub></font>, <font color="Maroon">c<sub>6</sub></font> being   <a href="nat_1.html#NM1">Nat</a><b> such that </b><br/><a NAME="E11:28_1_1_1_2"/><i><font color="Green">E40</font></i>: 
<span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</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> <span class="p1">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>
 <b>and </b><br/><a NAME="E12:28_1_1_1_2"/><i><font color="Green">E41</font></i>: 
<font color="Maroon">c<sub>1</sub></font> <a href="finseq_4.html#K4">/.</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font>
 <b>by </b><i><a class="ref" href="goboard2.html#T25">GOBOARD2:25</a></i>;<br/><a NAME="E13:28_1_1_1_2"/>
<span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> 1 <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 1
 <b>by </b><i><a class="ref" href="nat_1.html#T29">NAT_1:29</a></i>;<br/><a NAME="E14:28_1_1_1_2"/><b>then </b><i><font color="Green">E42</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> 1 <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="goboard9.html#E2:28_1_1"><i><font color="Green">E32</font></i></a>, <a class="ref" href="finseq_3.html#T27">FINSEQ_3:27</a></i>;<br/><b>then consider </b><font color="Maroon">c<sub>7</sub></font>, <font color="Maroon">c<sub>8</sub></font> being   <a href="nat_1.html#NM1">Nat</a><b> such that </b><br/><a NAME="E16:28_1_1_1_2"/><i><font color="Green">E43</font></i>: 
<span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>8</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> <span class="p1">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>
 <b>and </b><br/><a NAME="E17:28_1_1_1_2"/><i><font color="Green">E44</font></i>: 
<font color="Maroon">c<sub>1</sub></font> <a href="finseq_4.html#K4">/.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>8</sub></font>
 <b>by </b><i><a class="ref" href="goboard2.html#T25">GOBOARD2:25</a></i>;<br/><a NAME="E18:28_1_1_1_2"/><i><font color="Green">E45</font></i>: 
( 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>3</sub></font> &amp; <font color="Maroon">c<sub>3</sub></font> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> )
 <b>by </b><i><a class="txt" href="goboard9.html#E7:28_1_1_1_2"><i><font color="Green">E37</font></i></a>, <a class="ref" href="goboard5.html#T1">GOBOARD5:1</a></i>;<br/><a NAME="E19:28_1_1_1_2"/><i><font color="Green">E46</font></i>: 
( 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>5</sub></font> &amp; <font color="Maroon">c<sub>5</sub></font> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> )
 <b>by </b><i><a class="txt" href="goboard9.html#E11:28_1_1_1_2"><i><font color="Green">E40</font></i></a>, <a class="ref" href="goboard5.html#T1">GOBOARD5:1</a></i>;<br/><a NAME="E20:28_1_1_1_2"/><i><font color="Green">E47</font></i>: 
( 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>7</sub></font> &amp; <font color="Maroon">c<sub>7</sub></font> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> )
 <b>by </b><i><a class="txt" href="goboard9.html#E16:28_1_1_1_2"><i><font color="Green">E43</font></i></a>, <a class="ref" href="goboard5.html#T1">GOBOARD5:1</a></i>;<br/><a NAME="E21:28_1_1_1_2"/><i><font color="Green">E48</font></i>: 
( 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>4</sub></font> &amp; <font color="Maroon">c<sub>4</sub></font> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="matrix_1.html#K1">width</a> <span class="p1">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> )
 <b>by </b><i><a class="txt" href="goboard9.html#E7:28_1_1_1_2"><i><font color="Green">E37</font></i></a>, <a class="ref" href="goboard5.html#T1">GOBOARD5:1</a></i>;<br/><a NAME="E22:28_1_1_1_2"/><i><font color="Green">E49</font></i>: 
( 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>6</sub></font> &amp; <font color="Maroon">c<sub>6</sub></font> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="matrix_1.html#K1">width</a> <span class="p1">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> )
 <b>by </b><i><a class="txt" href="goboard9.html#E11:28_1_1_1_2"><i><font color="Green">E40</font></i></a>, <a class="ref" href="goboard5.html#T1">GOBOARD5:1</a></i>;<br/><a NAME="E23:28_1_1_1_2"/><i><font color="Green">E50</font></i>: 
( 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>8</sub></font> &amp; <font color="Maroon">c<sub>8</sub></font> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="matrix_1.html#K1">width</a> <span class="p1">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> )
 <b>by </b><i><a class="txt" href="goboard9.html#E16:28_1_1_1_2"><i><font color="Green">E43</font></i></a>, <a class="ref" href="goboard5.html#T1">GOBOARD5:1</a></i>;<br/><a NAME="E24:28_1_1_1_2"/><i><font color="Green">E51</font></i>: 
( <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>5</sub></font> or <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>6</sub></font> )
 <b>by </b><i><a class="txt" href="goboard9.html#E5:28_1_1_1_2"><i><font color="Green">E36</font></i></a>, <a class="txt" href="goboard9.html#E7:28_1_1_1_2"><i><font color="Green">E37</font></i></a>, <a class="txt" href="goboard9.html#E8:28_1_1_1_2"><i><font color="Green">E38</font></i></a>, <a class="txt" href="goboard9.html#E9:28_1_1_1_2"><i><font color="Green">E39</font></i></a>, <a class="txt" href="goboard9.html#E11:28_1_1_1_2"><i><font color="Green">E40</font></i></a>, <a class="txt" href="goboard9.html#E12:28_1_1_1_2"><i><font color="Green">E41</font></i></a>, <a class="ref" href="goboard2.html#T16">GOBOARD2:16</a></i>;<br/><a NAME="E25:28_1_1_1_2"/><i><font color="Green">E52</font></i>: 
( <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>7</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> )
 <b>by </b><i><a class="txt" href="goboard9.html#E9:28_1_1_1_2"><i><font color="Green">E39</font></i></a>, <a class="txt" href="goboard9.html#E11:28_1_1_1_2"><i><font color="Green">E40</font></i></a>, <a class="txt" href="goboard9.html#E12:28_1_1_1_2"><i><font color="Green">E41</font></i></a>, <a class="txt" href="goboard9.html#E14:28_1_1_1_2"><i><font color="Green">E42</font></i></a>, <a class="txt" href="goboard9.html#E16:28_1_1_1_2"><i><font color="Green">E43</font></i></a>, <a class="txt" href="goboard9.html#E17:28_1_1_1_2"><i><font color="Green">E44</font></i></a>, <a class="ref" href="goboard2.html#T16">GOBOARD2:16</a></i>;<br/><a NAME="E26:28_1_1_1_2"/><i><font color="Green">E53</font></i>: 
<font color="Maroon">c<sub>1</sub></font> <a href="goboard1.html#R1">is_sequence_on</a>  <a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="ref" href="goboard5.html#D5">GOBOARD5:def 5</a></i>;<br/><a NAME="E27:28_1_1_1_2"/><b>then </b>
<span class="p1">(<span class="default"><a href="complex1.html#K18">abs</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="real_1.html#K5">-</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span> <a href="real_1.html#K3">+</a> <span class="p1">(<span class="default"><a href="complex1.html#K18">abs</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="real_1.html#K5">-</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> 1
 <b>by </b><i><a class="txt" href="goboard9.html#E5:28_1_1_1_2"><i><font color="Green">E36</font></i></a>, <a class="txt" href="goboard9.html#E7:28_1_1_1_2"><i><font color="Green">E37</font></i></a>, <a class="txt" href="goboard9.html#E8:28_1_1_1_2"><i><font color="Green">E38</font></i></a>, <a class="txt" href="goboard9.html#E9:28_1_1_1_2"><i><font color="Green">E39</font></i></a>, <a class="txt" href="goboard9.html#E11:28_1_1_1_2"><i><font color="Green">E40</font></i></a>, <a class="txt" href="goboard9.html#E12:28_1_1_1_2"><i><font color="Green">E41</font></i></a>, <a class="ref" href="goboard1.html#D11">GOBOARD1:def 11</a></i>;<br/><a NAME="E28:28_1_1_1_2"/><b>then </b><i><font color="Green">E54</font></i>: 
( (  <a href="complex1.html#K18">abs</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="real_1.html#K5">-</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="hidden.html#R1">=</a> 1 &amp; <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>6</sub></font> ) or (  <a href="complex1.html#K18">abs</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="real_1.html#K5">-</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="hidden.html#R1">=</a> 1 &amp; <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>5</sub></font> ) )
 <b>by </b><i><a class="ref" href="goboard1.html#T2">GOBOARD1:2</a></i>;<br/><a NAME="E29:28_1_1_1_2"/><b>then </b><i><font color="Green">E55</font></i>: 
( <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>5</sub></font> or <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>5</sub></font> <a href="nat_1.html#K1">+</a> 1 or <font color="Maroon">c<sub>3</sub></font> <a href="nat_1.html#K1">+</a> 1 <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>5</sub></font> )
 <b>by </b><i><a class="ref" href="goboard1.html#T1">GOBOARD1:1</a></i>;<br/><a NAME="E30:28_1_1_1_2"/>
<span class="p1">(<span class="default"><a href="complex1.html#K18">abs</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="real_1.html#K5">-</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span>)</span> <a href="real_1.html#K3">+</a> <span class="p1">(<span class="default"><a href="complex1.html#K18">abs</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="real_1.html#K5">-</a> <font color="Maroon">c<sub>8</sub></font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> 1
 <b>by </b><i><a class="txt" href="goboard9.html#E9:28_1_1_1_2"><i><font color="Green">E39</font></i></a>, <a class="txt" href="goboard9.html#E11:28_1_1_1_2"><i><font color="Green">E40</font></i></a>, <a class="txt" href="goboard9.html#E12:28_1_1_1_2"><i><font color="Green">E41</font></i></a>, <a class="txt" href="goboard9.html#E14:28_1_1_1_2"><i><font color="Green">E42</font></i></a>, <a class="txt" href="goboard9.html#E16:28_1_1_1_2"><i><font color="Green">E43</font></i></a>, <a class="txt" href="goboard9.html#E17:28_1_1_1_2"><i><font color="Green">E44</font></i></a>, <a class="txt" href="goboard9.html#E26:28_1_1_1_2"><i><font color="Green">E53</font></i></a>, <a class="ref" href="goboard1.html#D11">GOBOARD1:def 11</a></i>;<br/><a NAME="E31:28_1_1_1_2"/><b>then </b><i><font color="Green">E56</font></i>: 
( (  <a href="complex1.html#K18">abs</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="real_1.html#K5">-</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="hidden.html#R1">=</a> 1 &amp; <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>8</sub></font> ) or (  <a href="complex1.html#K18">abs</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="real_1.html#K5">-</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="hidden.html#R1">=</a> 1 &amp; <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>7</sub></font> ) )
 <b>by </b><i><a class="ref" href="goboard1.html#T2">GOBOARD1:2</a></i>;<br/><a NAME="E32:28_1_1_1_2"/><b>then </b><i><font color="Green">E57</font></i>: 
( <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>7</sub></font> or <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>7</sub></font> <a href="nat_1.html#K1">+</a> 1 or <font color="Maroon">c<sub>5</sub></font> <a href="nat_1.html#K1">+</a> 1 <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>7</sub></font> )
 <b>by </b><i><a class="ref" href="goboard1.html#T1">GOBOARD1:1</a></i>;<br/><a NAME="E33:28_1_1_1_2"/><i><font color="Green">E58</font></i>: 
( <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>6</sub></font> or <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>6</sub></font> <a href="nat_1.html#K1">+</a> 1 or <font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K1">+</a> 1 <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>6</sub></font> )
 <b>by </b><i><a class="txt" href="goboard9.html#E28:28_1_1_1_2"><i><font color="Green">E54</font></i></a>, <a class="ref" href="goboard1.html#T1">GOBOARD1:1</a></i>;<br/><a NAME="E34:28_1_1_1_2"/><i><font color="Green">E59</font></i>: 
( <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>8</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 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> )
 <b>by </b><i><a class="txt" href="goboard9.html#E31:28_1_1_1_2"><i><font color="Green">E56</font></i></a>, <a class="ref" href="goboard1.html#T1">GOBOARD1:1</a></i>;<br/><div><i><font color="Green">E60</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="28_1_1_1_2_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:28_1_1_1_2_1"/><i><font color="Green">E61</font></i>: 
( <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>7</sub></font> &amp; <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>8</sub></font> )
 ;<br/><div><i><font color="Green">E62</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="28_1_1_1_2_1_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:28_1_1_1_2_1_1"/>
<font color="Maroon">c<sub>2</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> 1
 ;<br/><a NAME="E2:28_1_1_1_2_1_1"/><b>then </b><i><font color="Green">E63</font></i>: 
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> 1
 <b>by </b><i><a class="txt" href="goboard9.html#E1:28_1_1_1_2"><i><font color="Green">E33</font></i></a>, <a class="ref" href="xxreal_0.html#T1">XXREAL_0:1</a></i>;<br/><b>assume </b><a NAME="E3:28_1_1_1_2_1_1"/>
<span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> 1 <a href="xxreal_0.html#NR2" target="_self">&gt;=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>1</sub></font>
 ;<br/><a NAME="E4:28_1_1_1_2_1_1"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> 1 <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="goboard9.html#E2:28_1_1"><i><font color="Green">E32</font></i></a>, <a class="ref" href="xxreal_0.html#T1">XXREAL_0:1</a></i>;<br/><b>hence </b><a NAME="E5:28_1_1_1_2_1_1"/>
contradiction
 <b>by </b><i><a class="txt" href="goboard9.html#E2:28_1_1_1_2_1_1"><i><font color="Green">E63</font></i></a>, <a class="ref" href="goboard7.html#T36">GOBOARD7:36</a></i>;<br/></div><b>end;</b></div><a NAME="E3:28_1_1_1_2_1"/><i><font color="Green">E63</font></i>: 
<font color="Maroon">c<sub>2</sub></font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> 1
 <b>by </b><i><a class="txt" href="goboard9.html#E3:28_1_1_1_2"><i><font color="Green">E35</font></i></a>, <a class="ref" href="nat_1.html#T38">NAT_1:38</a></i>;<br/><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="28_1_1_1_2_1_2"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:28_1_1_1_2_1_2"/>
( <font color="Maroon">c<sub>2</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 1 or <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> 1 <a href="xxreal_0.html#NR3" target="_self">&lt;</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>1</sub></font> )
 </span><b>by </b><i><a class="txt" href="goboard9.html#E2:28_1_1_1_2_1"><i><font color="Green">E62</font></i></a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="28_1_1_1_2_1_2_1"><b>suppose </b></a><a NAME="E1:28_1_1_1_2_1_2_1"/>
<font color="Maroon">c<sub>2</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 1
 ;<br/><div class="add"><b>hence </b><a NAME="E2:28_1_1_1_2_1_2_1"/>
contradiction
 <b>by </b><i><a class="txt" href="goboard9.html#E2:28_1_1"><i><font color="Green">E32</font></i></a>, <a class="txt" href="goboard9.html#E8:28_1_1_1_2"><i><font color="Green">E38</font></i></a>, <a class="txt" href="goboard9.html#E17:28_1_1_1_2"><i><font color="Green">E44</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2_1"><i><font color="Green">E61</font></i></a>, <a class="txt" href="goboard9.html#E3:28_1_1_1_2_1"><i><font color="Green">E63</font></i></a>, <a class="ref" href="goboard7.html#T39">GOBOARD7:39</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="28_1_1_1_2_1_2_2"><b>suppose </b></a><a NAME="E1:28_1_1_1_2_1_2_2"/>
<span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> 1 <a href="xxreal_0.html#NR3" target="_self">&lt;</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>1</sub></font>
 ;<br/><div class="add"><b>hence </b><a NAME="E2:28_1_1_1_2_1_2_2"/>
contradiction
 <b>by </b><i><a class="txt" href="goboard9.html#E1:28_1_1_1_2"><i><font color="Green">E33</font></i></a>, <a class="txt" href="goboard9.html#E8:28_1_1_1_2"><i><font color="Green">E38</font></i></a>, <a class="txt" href="goboard9.html#E17:28_1_1_1_2"><i><font color="Green">E44</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2_1"><i><font color="Green">E61</font></i></a>, <a class="txt" href="goboard9.html#E3:28_1_1_1_2_1"><i><font color="Green">E63</font></i></a>, <a class="ref" href="goboard7.html#T38">GOBOARD7:38</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div><a NAME="E36:28_1_1_1_2"/>
<font color="Maroon">c<sub>5</sub></font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 1
 <b>by </b><i><a class="txt" href="goboard9.html#E11:28_1_1_1_2"><i><font color="Green">E40</font></i></a>, <a class="ref" href="goboard5.html#T1">GOBOARD5:1</a></i>;<br/><a NAME="E37:28_1_1_1_2"/><b>then </b><i><font color="Green">E61</font></i>: 
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>5</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="ref" href="binarith.html#T53">BINARITH:53</a></i>;<br/><a NAME="E38:28_1_1_1_2"/>
<font color="Maroon">c<sub>6</sub></font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 1
 <b>by </b><i><a class="txt" href="goboard9.html#E11:28_1_1_1_2"><i><font color="Green">E40</font></i></a>, <a class="ref" href="goboard5.html#T1">GOBOARD5:1</a></i>;<br/><a NAME="E39:28_1_1_1_2"/><b>then </b><i><font color="Green">E62</font></i>: 
<font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>6</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="ref" href="binarith.html#T53">BINARITH:53</a></i>;<br/><a NAME="E40:28_1_1_1_2"/><b>then </b>
<font color="Maroon">c<sub>6</sub></font> <a href="binarith.html#K5">-'</a> 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>6</sub></font>
 <b>by </b><i><a class="ref" href="nat_1.html#T29">NAT_1:29</a></i>;<br/><a NAME="E41:28_1_1_1_2"/><b>then </b><i><font color="Green">E63</font></i>: 
<font color="Maroon">c<sub>6</sub></font> <a href="binarith.html#K5">-'</a> 1 <a href="xxreal_0.html#R1">&lt;=</a>  <a href="matrix_1.html#K1">width</a> <span class="p1">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="goboard9.html#E22:28_1_1_1_2"><i><font color="Green">E49</font></i></a>, <a class="ref" href="xxreal_0.html#T2">XXREAL_0:2</a></i>;<br/><a NAME="E42:28_1_1_1_2"/>
 <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 1
 <b>by </b><i><a class="ref" href="goboard7.html#T34">GOBOARD7:34</a></i>;<br/><a NAME="E43:28_1_1_1_2"/><b>then </b><i><font color="Green">E64</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p3">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="binarith.html#K5">-'</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> 1 <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>
 <b>by </b><i><a class="ref" href="binarith.html#T53">BINARITH:53</a></i>;<br/><a NAME="E44:28_1_1_1_2"/>
 <a href="matrix_1.html#K1">width</a> <span class="p1">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 1
 <b>by </b><i><a class="ref" href="goboard7.html#T35">GOBOARD7:35</a></i>;<br/><a NAME="E45:28_1_1_1_2"/><b>then </b><i><font color="Green">E65</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="matrix_1.html#K1">width</a> <span class="p3">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="binarith.html#K5">-'</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> 1 <a href="hidden.html#R1">=</a>  <a href="matrix_1.html#K1">width</a> <span class="p1">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>
 <b>by </b><i><a class="ref" href="binarith.html#T53">BINARITH:53</a></i>;<br/><a NAME="E46:28_1_1_1_2"/><i><font color="Green">E66</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> 1 <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>2</sub></font> <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span>
 ;<br/><a NAME="E47:28_1_1_1_2"/><i><font color="Green">E67</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> 1 <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font> <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span>
 ;<br/><a NAME="E48:28_1_1_1_2"/><i><font color="Green">E68</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> 1 <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>7</sub></font> <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span>
 ;<br/><a NAME="E49:28_1_1_1_2"/><i><font color="Green">E69</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> 1 <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span>
 ;<br/><a NAME="E50:28_1_1_1_2"/><i><font color="Green">E70</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> 1 <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>8</sub></font> <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span>
 ;<br/><a NAME="E51:28_1_1_1_2"/><i><font color="Green">E71</font></i>: 
 <a href="goboard9.html#K2" target="_self">LeftComp</a> <font color="Maroon">c<sub>1</sub></font> <a href="connsp_1.html#R4">is_a_component_of</a> <span class="p1">(<span class="default"><a href="topreal1.html#K5">L~</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="subset_1.html#K3">`</a> 
 <b>by </b><i><a class="ref" href="goboard9.html#D1" target="_self">Def1</a></i>;<br/><a NAME="E52:28_1_1_1_2"/><i><font color="Green">E72</font></i>: 
 <a href="tops_1.html#K1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K5">left_cell</a> <font color="Maroon">c<sub>1</sub></font>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> is <a href="connsp_1.html#V2">connected</a>
 <b>by </b><i><a class="txt" href="goboard9.html#E1:28_1_1"><i><font color="Green">E31</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1"><i><font color="Green">E32</font></i></a>, <a class="ref" href="goboard9.html#T22" target="_self">Th22</a></i>;<br/><a NAME="E53:28_1_1_1_2"/><i><font color="Green">E73</font></i>: 
0 <a href="nat_1.html#K1">+</a> 1 <a href="hidden.html#R1">=</a> 1
 ;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="28_1_1_1_2_2"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="28_1_1_1_2_2_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:28_1_1_1_2_2_1"/>
( ( <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>5</sub></font> <a href="nat_1.html#K1">+</a> 1 &amp; <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>7</sub></font> <a href="nat_1.html#K1">+</a> 1 &amp; <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> 1 ) or ( <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>5</sub></font> <a href="nat_1.html#K1">+</a> 1 &amp; <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>7</sub></font> <a href="nat_1.html#K1">+</a> 1 &amp; <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 1 ) or ( <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>5</sub></font> <a href="nat_1.html#K1">+</a> 1 &amp; <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 ) or ( <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>6</sub></font> <a href="nat_1.html#K1">+</a> 1 &amp; <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>7</sub></font> <a href="nat_1.html#K1">+</a> 1 &amp; <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> &amp; <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R1">=</a> 1 ) or ( <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>6</sub></font> <a href="nat_1.html#K1">+</a> 1 &amp; <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>7</sub></font> <a href="nat_1.html#K1">+</a> 1 &amp; <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> &amp; <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R1">=</a> 1 ) or ( <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>6</sub></font> <a href="nat_1.html#K1">+</a> 1 &amp; <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>7</sub></font> <a href="nat_1.html#K1">+</a> 1 &amp; <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> &amp; <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 1 ) or ( <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>6</sub></font> <a href="nat_1.html#K1">+</a> 1 &amp; <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>7</sub></font> <a href="nat_1.html#K1">+</a> 1 &amp; <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> &amp; <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 1 ) or ( <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>6</sub></font> <a href="nat_1.html#K1">+</a> 1 &amp; <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>3</sub></font> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> ) or ( <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>6</sub></font> <a href="nat_1.html#K1">+</a> 1 &amp; <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>3</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> ) or ( <font color="Maroon">c<sub>3</sub></font> <a href="nat_1.html#K1">+</a> 1 <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>5</sub></font> &amp; <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>5</sub></font> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> &amp; <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a>  <a href="matrix_1.html#K1">width</a> <span class="p1">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> ) or ( <font color="Maroon">c<sub>3</sub></font> <a href="nat_1.html#K1">+</a> 1 <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>5</sub></font> &amp; <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>5</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> &amp; <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a>  <a href="matrix_1.html#K1">width</a> <span class="p1">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> ) or ( <font color="Maroon">c<sub>3</sub></font> <a href="nat_1.html#K1">+</a> 1 <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>5</sub></font> &amp; <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>5</sub></font> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> &amp; <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="matrix_1.html#K1">width</a> <span class="p1">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> ) or ( <font color="Maroon">c<sub>3</sub></font> <a href="nat_1.html#K1">+</a> 1 <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>5</sub></font> &amp; <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>5</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> &amp; <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="matrix_1.html#K1">width</a> <span class="p1">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> ) or ( <font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K1">+</a> 1 <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>6</sub></font> &amp; <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>7</sub></font> <a href="nat_1.html#K1">+</a> 1 ) or ( <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>5</sub></font> <a href="nat_1.html#K1">+</a> 1 &amp; <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>5</sub></font> <a href="hidden.html#R1">=</a> 1 &amp; <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R1">=</a> 1 ) or ( <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>5</sub></font> <a href="nat_1.html#K1">+</a> 1 &amp; <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>5</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 1 &amp; <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R1">=</a> 1 ) or ( <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>5</sub></font> <a href="nat_1.html#K1">+</a> 1 &amp; <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>5</sub></font> <a href="hidden.html#R1">=</a> 1 &amp; <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 1 ) or ( <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>5</sub></font> <a href="nat_1.html#K1">+</a> 1 &amp; <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>5</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 1 &amp; <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 1 ) or ( <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>6</sub></font> <a href="nat_1.html#K1">+</a> 1 &amp; <font color="Maroon">c<sub>5</sub></font> <a href="nat_1.html#K1">+</a> 1 <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>7</sub></font> ) or ( <font color="Maroon">c<sub>3</sub></font> <a href="nat_1.html#K1">+</a> 1 <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>5</sub></font> &amp; <font color="Maroon">c<sub>5</sub></font> <a href="nat_1.html#K1">+</a> 1 <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>7</sub></font> &amp; <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a>  <a href="matrix_1.html#K1">width</a> <span class="p1">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> ) or ( <font color="Maroon">c<sub>3</sub></font> <a href="nat_1.html#K1">+</a> 1 <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>5</sub></font> &amp; <font color="Maroon">c<sub>5</sub></font> <a href="nat_1.html#K1">+</a> 1 <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>7</sub></font> &amp; <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="matrix_1.html#K1">width</a> <span class="p1">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> ) or ( <font color="Maroon">c<sub>3</sub></font> <a href="nat_1.html#K1">+</a> 1 <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>5</sub></font> &amp; <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> ) or ( <font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K1">+</a> 1 <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>6</sub></font> &amp; <font color="Maroon">c<sub>5</sub></font> <a href="nat_1.html#K1">+</a> 1 <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>7</sub></font> &amp; <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> 1 &amp; <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R1">=</a>  <a href="matrix_1.html#K1">width</a> <span class="p1">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> ) or ( <font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K1">+</a> 1 <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>6</sub></font> &amp; <font color="Maroon">c<sub>5</sub></font> <a href="nat_1.html#K1">+</a> 1 <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>7</sub></font> &amp; <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 1 &amp; <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R1">=</a>  <a href="matrix_1.html#K1">width</a> <span class="p1">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> ) or ( <font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K1">+</a> 1 <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>6</sub></font> &amp; <font color="Maroon">c<sub>5</sub></font> <a href="nat_1.html#K1">+</a> 1 <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>7</sub></font> &amp; <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> 1 &amp; <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="matrix_1.html#K1">width</a> <span class="p1">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> ) or ( <font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K1">+</a> 1 <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>6</sub></font> &amp; <font color="Maroon">c<sub>5</sub></font> <a href="nat_1.html#K1">+</a> 1 <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>7</sub></font> &amp; <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 1 &amp; <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="matrix_1.html#K1">width</a> <span class="p1">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> ) or ( <font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K1">+</a> 1 <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>6</sub></font> &amp; <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>3</sub></font> <a href="hidden.html#R1">=</a> 1 ) or ( <font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K1">+</a> 1 <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>6</sub></font> &amp; <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>3</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 1 ) )
 </span><b>by </b><i><a class="txt" href="goboard9.html#E5:28_1_1_1_2"><i><font color="Green">E36</font></i></a>, <a class="txt" href="goboard9.html#E8:28_1_1_1_2"><i><font color="Green">E38</font></i></a>, <a class="txt" href="goboard9.html#E9:28_1_1_1_2"><i><font color="Green">E39</font></i></a>, <a class="txt" href="goboard9.html#E12:28_1_1_1_2"><i><font color="Green">E41</font></i></a>, <a class="txt" href="goboard9.html#E14:28_1_1_1_2"><i><font color="Green">E42</font></i></a>, <a class="txt" href="goboard9.html#E17:28_1_1_1_2"><i><font color="Green">E44</font></i></a>, <a class="txt" href="goboard9.html#E29:28_1_1_1_2"><i><font color="Green">E55</font></i></a>, <a class="txt" href="goboard9.html#E32:28_1_1_1_2"><i><font color="Green">E57</font></i></a>, <a class="txt" href="goboard9.html#E33:28_1_1_1_2"><i><font color="Green">E58</font></i></a>, <a class="txt" href="goboard9.html#E34:28_1_1_1_2"><i><font color="Green">E59</font></i></a>, <a class="txt" href="goboard9.html#E35:28_1_1_1_2"><i><font color="Green">E60</font></i></a>, <a class="ref" href="goboard7.html#T31">GOBOARD7:31</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="28_1_1_1_2_2_1_1"><b>suppose </b></a><b>that </b><a NAME="E1:28_1_1_1_2_2_1_1"/><i><font color="Green">E74</font></i>: 
<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>5</sub></font> <a href="nat_1.html#K1">+</a> 1
 <b>and </b><br/><a NAME="E2:28_1_1_1_2_2_1_1"/><i><font color="Green">E75</font></i>: 
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>7</sub></font> <a href="nat_1.html#K1">+</a> 1
 <b>and </b><br/><a NAME="E3:28_1_1_1_2_2_1_1"/><i><font color="Green">E76</font></i>: 
<font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> 1
 ;<br/><div class="add"><a NAME="E4:28_1_1_1_2_2_1_1"/><i><font color="Green">E77</font></i>: 
 <a href="goboard5.html#K5">left_cell</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a>  <a href="goboard5.html#K3">cell</a> <span class="p1">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<font color="Maroon">c<sub>5</sub></font>,0
 <b>by </b><i><a class="txt" href="goboard9.html#E1:28_1_1_1_2"><i><font color="Green">E33</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1_1_2"><i><font color="Green">E34</font></i></a>, <a class="txt" href="goboard9.html#E7:28_1_1_1_2"><i><font color="Green">E37</font></i></a>, <a class="txt" href="goboard9.html#E8:28_1_1_1_2"><i><font color="Green">E38</font></i></a>, <a class="txt" href="goboard9.html#E11:28_1_1_1_2"><i><font color="Green">E40</font></i></a>, <a class="txt" href="goboard9.html#E12:28_1_1_1_2"><i><font color="Green">E41</font></i></a>, <a class="txt" href="goboard9.html#E24:28_1_1_1_2"><i><font color="Green">E51</font></i></a>, <a class="txt" href="goboard9.html#E53:28_1_1_1_2"><i><font color="Green">E73</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2_2_1_1"><i><font color="Green">E74</font></i></a>, <a class="txt" href="goboard9.html#E3:28_1_1_1_2_2_1_1"><i><font color="Green">E76</font></i></a>, <a class="ref" href="goboard5.html#T30">GOBOARD5:30</a></i>;<br/><a NAME="E5:28_1_1_1_2_2_1_1"/>
0 <a href="nat_1.html#K1">+</a> 1 <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>8</sub></font>
 <b>by </b><i><a class="txt" href="goboard9.html#E24:28_1_1_1_2"><i><font color="Green">E51</font></i></a>, <a class="txt" href="goboard9.html#E25:28_1_1_1_2"><i><font color="Green">E52</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2_2_1_1"><i><font color="Green">E74</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1_1_2_2_1_1"><i><font color="Green">E75</font></i></a>, <a class="txt" href="goboard9.html#E3:28_1_1_1_2_2_1_1"><i><font color="Green">E76</font></i></a></i>;<br/><a NAME="E6:28_1_1_1_2_2_1_1"/><b>then </b><i><font color="Green">E78</font></i>: 
 <a href="goboard5.html#K5">left_cell</a> <font color="Maroon">c<sub>1</sub></font>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="hidden.html#R1">=</a>  <a href="goboard5.html#K3">cell</a> <span class="p1">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<font color="Maroon">c<sub>7</sub></font>,0
 <b>by </b><i><a class="txt" href="goboard9.html#E1:28_1_1"><i><font color="Green">E31</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1"><i><font color="Green">E32</font></i></a>, <a class="txt" href="goboard9.html#E11:28_1_1_1_2"><i><font color="Green">E40</font></i></a>, <a class="txt" href="goboard9.html#E12:28_1_1_1_2"><i><font color="Green">E41</font></i></a>, <a class="txt" href="goboard9.html#E16:28_1_1_1_2"><i><font color="Green">E43</font></i></a>, <a class="txt" href="goboard9.html#E17:28_1_1_1_2"><i><font color="Green">E44</font></i></a>, <a class="txt" href="goboard9.html#E24:28_1_1_1_2"><i><font color="Green">E51</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2_2_1_1"><i><font color="Green">E74</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1_1_2_2_1_1"><i><font color="Green">E75</font></i></a>, <a class="txt" href="goboard9.html#E3:28_1_1_1_2_2_1_1"><i><font color="Green">E76</font></i></a>, <a class="ref" href="goboard5.html#T30">GOBOARD5:30</a></i>;<br/><a NAME="E7:28_1_1_1_2_2_1_1"/><i><font color="Green">E79</font></i>: 
 <a href="topreal1.html#K3">LSeg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>5</sub></font>,1</span>)</span> <a href="euclid.html#K17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>3</sub></font>,1</span>)</span></span>)</span></span>)</span> <a href="euclid.html#K20">-</a> <span class="p2"><a href="euclid.html#K23">|[</a><span class="default">0,1</span><a href="euclid.html#K23">]|</a></span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>7</sub></font>,1</span>)</span> <a href="euclid.html#K17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>5</sub></font>,1</span>)</span></span>)</span></span>)</span> <a href="euclid.html#K20">-</a> <span class="p2"><a href="euclid.html#K23">|[</a><span class="default">0,1</span><a href="euclid.html#K23">]|</a></span></span>)</span> is <a href="connsp_1.html#V2">connected</a>
 <b>by </b><i><a class="ref" href="goboard9.html#T8" target="_self">Th8</a></i>;<br/><a NAME="E8:28_1_1_1_2_2_1_1"/><i><font color="Green">E80</font></i>: 
 <a href="topreal1.html#K3">LSeg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>5</sub></font>,1</span>)</span> <a href="euclid.html#K17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>3</sub></font>,1</span>)</span></span>)</span></span>)</span> <a href="euclid.html#K20">-</a> <span class="p2"><a href="euclid.html#K23">|[</a><span class="default">0,1</span><a href="euclid.html#K23">]|</a></span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>7</sub></font>,1</span>)</span> <a href="euclid.html#K17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>5</sub></font>,1</span>)</span></span>)</span></span>)</span> <a href="euclid.html#K20">-</a> <span class="p2"><a href="euclid.html#K23">|[</a><span class="default">0,1</span><a href="euclid.html#K23">]|</a></span></span>)</span> <a href="xboole_0.html#NR5" target="_self">meets</a>  <a href="tops_1.html#K1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K3">cell</a> <span class="p2">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<font color="Maroon">c<sub>5</sub></font>,0</span>)</span>
 <b>by </b><i><a class="txt" href="goboard9.html#E18:28_1_1_1_2"><i><font color="Green">E45</font></i></a>, <a class="txt" href="goboard9.html#E19:28_1_1_1_2"><i><font color="Green">E46</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2_2_1_1"><i><font color="Green">E74</font></i></a>, <a class="ref" href="goboard6.html#T87">GOBOARD6:87</a></i>;<br/><a NAME="E9:28_1_1_1_2_2_1_1"/>
 <a href="topreal1.html#K3">LSeg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>5</sub></font>,1</span>)</span> <a href="euclid.html#K17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>3</sub></font>,1</span>)</span></span>)</span></span>)</span> <a href="euclid.html#K20">-</a> <span class="p2"><a href="euclid.html#K23">|[</a><span class="default">0,1</span><a href="euclid.html#K23">]|</a></span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>7</sub></font>,1</span>)</span> <a href="euclid.html#K17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>5</sub></font>,1</span>)</span></span>)</span></span>)</span> <a href="euclid.html#K20">-</a> <span class="p2"><a href="euclid.html#K23">|[</a><span class="default">0,1</span><a href="euclid.html#K23">]|</a></span></span>)</span> <a href="xboole_0.html#R1">misses</a>  <a href="topreal1.html#K5">L~</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="goboard9.html#E18:28_1_1_1_2"><i><font color="Green">E45</font></i></a>, <a class="txt" href="goboard9.html#E20:28_1_1_1_2"><i><font color="Green">E47</font></i></a>, <a class="txt" href="goboard9.html#E48:28_1_1_1_2"><i><font color="Green">E68</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2_2_1_1"><i><font color="Green">E74</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1_1_2_2_1_1"><i><font color="Green">E75</font></i></a>, <a class="ref" href="goboard8.html#T25">GOBOARD8:25</a></i>;<br/><a NAME="E10:28_1_1_1_2_2_1_1"/><b>then </b>
 <a href="topreal1.html#K3">LSeg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>5</sub></font>,1</span>)</span> <a href="euclid.html#K17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>3</sub></font>,1</span>)</span></span>)</span></span>)</span> <a href="euclid.html#K20">-</a> <span class="p2"><a href="euclid.html#K23">|[</a><span class="default">0,1</span><a href="euclid.html#K23">]|</a></span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>7</sub></font>,1</span>)</span> <a href="euclid.html#K17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>5</sub></font>,1</span>)</span></span>)</span></span>)</span> <a href="euclid.html#K20">-</a> <span class="p2"><a href="euclid.html#K23">|[</a><span class="default">0,1</span><a href="euclid.html#K23">]|</a></span></span>)</span> <a href="tarski.html#R1">c=</a> <span class="p1">(<span class="default"><a href="topreal1.html#K5">L~</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="subset_1.html#K3">`</a> 
 <b>by </b><i><a class="ref" href="subset_1.html#T43">SUBSET_1:43</a></i>;<br/><a NAME="E11:28_1_1_1_2_2_1_1"/><b>then </b><i><font color="Green">E81</font></i>: 
 <a href="topreal1.html#K3">LSeg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>5</sub></font>,1</span>)</span> <a href="euclid.html#K17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>3</sub></font>,1</span>)</span></span>)</span></span>)</span> <a href="euclid.html#K20">-</a> <span class="p2"><a href="euclid.html#K23">|[</a><span class="default">0,1</span><a href="euclid.html#K23">]|</a></span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>7</sub></font>,1</span>)</span> <a href="euclid.html#K17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>5</sub></font>,1</span>)</span></span>)</span></span>)</span> <a href="euclid.html#K20">-</a> <span class="p2"><a href="euclid.html#K23">|[</a><span class="default">0,1</span><a href="euclid.html#K23">]|</a></span></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="goboard9.html#K2" target="_self">LeftComp</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="goboard9.html#E1:28_1"><i><font color="Green">E30</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1"><i><font color="Green">E32</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2"><i><font color="Green">E33</font></i></a>, <a class="txt" href="goboard9.html#E51:28_1_1_1_2"><i><font color="Green">E71</font></i></a>, <a class="txt" href="goboard9.html#E4:28_1_1_1_2_2_1_1"><i><font color="Green">E77</font></i></a>, <a class="txt" href="goboard9.html#E7:28_1_1_1_2_2_1_1"><i><font color="Green">E79</font></i></a>, <a class="txt" href="goboard9.html#E8:28_1_1_1_2_2_1_1"><i><font color="Green">E80</font></i></a>, <a class="ref" href="goboard9.html#T6" target="_self">Th6</a>, <a class="ref" href="nat_1.html#T38">NAT_1:38</a></i>;<br/><a NAME="E12:28_1_1_1_2_2_1_1"/><i><font color="Green">E82</font></i>: 
 <a href="topreal1.html#K3">LSeg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>5</sub></font>,1</span>)</span> <a href="euclid.html#K17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>3</sub></font>,1</span>)</span></span>)</span></span>)</span> <a href="euclid.html#K20">-</a> <span class="p2"><a href="euclid.html#K23">|[</a><span class="default">0,1</span><a href="euclid.html#K23">]|</a></span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>7</sub></font>,1</span>)</span> <a href="euclid.html#K17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>5</sub></font>,1</span>)</span></span>)</span></span>)</span> <a href="euclid.html#K20">-</a> <span class="p2"><a href="euclid.html#K23">|[</a><span class="default">0,1</span><a href="euclid.html#K23">]|</a></span></span>)</span> <a href="xboole_0.html#NR5" target="_self">meets</a>  <a href="tops_1.html#K1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K3">cell</a> <span class="p2">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<font color="Maroon">c<sub>7</sub></font>,0</span>)</span>
 <b>by </b><i><a class="txt" href="goboard9.html#E19:28_1_1_1_2"><i><font color="Green">E46</font></i></a>, <a class="txt" href="goboard9.html#E20:28_1_1_1_2"><i><font color="Green">E47</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1_1_2_2_1_1"><i><font color="Green">E75</font></i></a>, <a class="ref" href="goboard6.html#T87">GOBOARD6:87</a></i>;<br/><a NAME="E13:28_1_1_1_2_2_1_1"/>
 <a href="tops_1.html#K1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K5">left_cell</a> <font color="Maroon">c<sub>1</sub></font>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="xboole_0.html#R1">misses</a>  <a href="topreal1.html#K5">L~</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="goboard9.html#E1:28_1_1"><i><font color="Green">E31</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1"><i><font color="Green">E32</font></i></a>, <a class="ref" href="goboard8.html#T37">GOBOARD8:37</a></i>;<br/><a NAME="E14:28_1_1_1_2_2_1_1"/><b>then </b>
 <a href="tops_1.html#K1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K5">left_cell</a> <font color="Maroon">c<sub>1</sub></font>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="tarski.html#R1">c=</a> <span class="p1">(<span class="default"><a href="topreal1.html#K5">L~</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="subset_1.html#K3">`</a> 
 <b>by </b><i><a class="ref" href="subset_1.html#T43">SUBSET_1:43</a></i>;<br/><b>hence </b><a NAME="E15:28_1_1_1_2_2_1_1"/>
 <a href="tops_1.html#K1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K5">left_cell</a> <font color="Maroon">c<sub>1</sub></font>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="goboard9.html#K2" target="_self">LeftComp</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="goboard9.html#E51:28_1_1_1_2"><i><font color="Green">E71</font></i></a>, <a class="txt" href="goboard9.html#E52:28_1_1_1_2"><i><font color="Green">E72</font></i></a>, <a class="txt" href="goboard9.html#E6:28_1_1_1_2_2_1_1"><i><font color="Green">E78</font></i></a>, <a class="txt" href="goboard9.html#E11:28_1_1_1_2_2_1_1"><i><font color="Green">E81</font></i></a>, <a class="txt" href="goboard9.html#E12:28_1_1_1_2_2_1_1"><i><font color="Green">E82</font></i></a>, <a class="ref" href="goboard9.html#T6" target="_self">Th6</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="28_1_1_1_2_2_1_2"><b>suppose </b></a><b>that </b><a NAME="E1:28_1_1_1_2_2_1_2"/><i><font color="Green">E74</font></i>: 
<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>5</sub></font> <a href="nat_1.html#K1">+</a> 1
 <b>and </b><br/><a NAME="E2:28_1_1_1_2_2_1_2"/><i><font color="Green">E75</font></i>: 
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>7</sub></font> <a href="nat_1.html#K1">+</a> 1
 <b>and </b><br/><a NAME="E3:28_1_1_1_2_2_1_2"/><i><font color="Green">E76</font></i>: 
<font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 1
 ;<br/><div class="add"><a NAME="E4:28_1_1_1_2_2_1_2"/><i><font color="Green">E77</font></i>: 
 <a href="goboard5.html#K5">left_cell</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a>  <a href="goboard5.html#K3">cell</a> <span class="p1">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<font color="Maroon">c<sub>5</sub></font>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span>
 <b>by </b><i><a class="txt" href="goboard9.html#E1:28_1_1_1_2"><i><font color="Green">E33</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1_1_2"><i><font color="Green">E34</font></i></a>, <a class="txt" href="goboard9.html#E7:28_1_1_1_2"><i><font color="Green">E37</font></i></a>, <a class="txt" href="goboard9.html#E8:28_1_1_1_2"><i><font color="Green">E38</font></i></a>, <a class="txt" href="goboard9.html#E11:28_1_1_1_2"><i><font color="Green">E40</font></i></a>, <a class="txt" href="goboard9.html#E12:28_1_1_1_2"><i><font color="Green">E41</font></i></a>, <a class="txt" href="goboard9.html#E24:28_1_1_1_2"><i><font color="Green">E51</font></i></a>, <a class="txt" href="goboard9.html#E39:28_1_1_1_2"><i><font color="Green">E62</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2_2_1_2"><i><font color="Green">E74</font></i></a>, <a class="ref" href="goboard5.html#T30">GOBOARD5:30</a></i>;<br/><a NAME="E5:28_1_1_1_2_2_1_2"/>
1 <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">c<sub>4</sub></font>
 <b>by </b><i><a class="txt" href="goboard9.html#E21:28_1_1_1_2"><i><font color="Green">E48</font></i></a>, <a class="txt" href="goboard9.html#E3:28_1_1_1_2_2_1_2"><i><font color="Green">E76</font></i></a>, <a class="ref" href="xxreal_0.html#T1">XXREAL_0:1</a></i>;<br/><a NAME="E6:28_1_1_1_2_2_1_2"/><b>then </b><i><font color="Green">E78</font></i>: 
1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>4</sub></font> <a href="binarith.html#K5">-'</a> 1
 <b>by </b><i><a class="txt" href="goboard9.html#E24:28_1_1_1_2"><i><font color="Green">E51</font></i></a>, <a class="txt" href="goboard9.html#E39:28_1_1_1_2"><i><font color="Green">E62</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2_2_1_2"><i><font color="Green">E74</font></i></a>, <a class="ref" href="nat_1.html#T38">NAT_1:38</a></i>;<br/><a NAME="E7:28_1_1_1_2_2_1_2"/><i><font color="Green">E79</font></i>: 
 <a href="goboard5.html#K5">left_cell</a> <font color="Maroon">c<sub>1</sub></font>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="hidden.html#R1">=</a>  <a href="goboard5.html#K3">cell</a> <span class="p1">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<font color="Maroon">c<sub>7</sub></font>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span>
 <b>by </b><i><a class="txt" href="goboard9.html#E1:28_1_1"><i><font color="Green">E31</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1"><i><font color="Green">E32</font></i></a>, <a class="txt" href="goboard9.html#E11:28_1_1_1_2"><i><font color="Green">E40</font></i></a>, <a class="txt" href="goboard9.html#E12:28_1_1_1_2"><i><font color="Green">E41</font></i></a>, <a class="txt" href="goboard9.html#E16:28_1_1_1_2"><i><font color="Green">E43</font></i></a>, <a class="txt" href="goboard9.html#E17:28_1_1_1_2"><i><font color="Green">E44</font></i></a>, <a class="txt" href="goboard9.html#E25:28_1_1_1_2"><i><font color="Green">E52</font></i></a>, <a class="txt" href="goboard9.html#E39:28_1_1_1_2"><i><font color="Green">E62</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1_1_2_2_1_2"><i><font color="Green">E75</font></i></a>, <a class="ref" href="goboard5.html#T30">GOBOARD5:30</a></i>;<br/><a NAME="E8:28_1_1_1_2_2_1_2"/><i><font color="Green">E80</font></i>: 
 <a href="topreal1.html#K3">LSeg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>5</sub></font>,<span class="p4">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span></span>)</span> <a href="euclid.html#K17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>7</sub></font>,<span class="p4">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span></span>)</span> <a href="euclid.html#K17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span></span>)</span> is <a href="connsp_1.html#V2">connected</a>
 <b>by </b><i><a class="ref" href="goboard9.html#T8" target="_self">Th8</a></i>;<br/><a NAME="E9:28_1_1_1_2_2_1_2"/><i><font color="Green">E81</font></i>: 
 <a href="topreal1.html#K3">LSeg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>5</sub></font>,<span class="p4">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span></span>)</span> <a href="euclid.html#K17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>7</sub></font>,<span class="p4">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span></span>)</span> <a href="euclid.html#K17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span></span>)</span> <a href="xboole_0.html#NR5" target="_self">meets</a>  <a href="tops_1.html#K1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K3">cell</a> <span class="p2">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<font color="Maroon">c<sub>5</sub></font>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="goboard9.html#E18:28_1_1_1_2"><i><font color="Green">E45</font></i></a>, <a class="txt" href="goboard9.html#E19:28_1_1_1_2"><i><font color="Green">E46</font></i></a>, <a class="txt" href="goboard9.html#E22:28_1_1_1_2"><i><font color="Green">E49</font></i></a>, <a class="txt" href="goboard9.html#E24:28_1_1_1_2"><i><font color="Green">E51</font></i></a>, <a class="txt" href="goboard9.html#E39:28_1_1_1_2"><i><font color="Green">E62</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2_2_1_2"><i><font color="Green">E74</font></i></a>, <a class="txt" href="goboard9.html#E6:28_1_1_1_2_2_1_2"><i><font color="Green">E78</font></i></a>, <a class="ref" href="goboard6.html#T85">GOBOARD6:85</a></i>;<br/><a NAME="E10:28_1_1_1_2_2_1_2"/>
 <a href="topreal1.html#K3">LSeg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>5</sub></font>,<span class="p4">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span></span>)</span> <a href="euclid.html#K17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>7</sub></font>,<span class="p4">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span></span>)</span> <a href="euclid.html#K17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span></span>)</span> <a href="xboole_0.html#R1">misses</a>  <a href="topreal1.html#K5">L~</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="goboard9.html#E2:28_1_1"><i><font color="Green">E32</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2"><i><font color="Green">E33</font></i></a>, <a class="txt" href="goboard9.html#E8:28_1_1_1_2"><i><font color="Green">E38</font></i></a>, <a class="txt" href="goboard9.html#E12:28_1_1_1_2"><i><font color="Green">E41</font></i></a>, <a class="txt" href="goboard9.html#E17:28_1_1_1_2"><i><font color="Green">E44</font></i></a>, <a class="txt" href="goboard9.html#E18:28_1_1_1_2"><i><font color="Green">E45</font></i></a>, <a class="txt" href="goboard9.html#E20:28_1_1_1_2"><i><font color="Green">E47</font></i></a>, <a class="txt" href="goboard9.html#E21:28_1_1_1_2"><i><font color="Green">E48</font></i></a>, <a class="txt" href="goboard9.html#E24:28_1_1_1_2"><i><font color="Green">E51</font></i></a>, <a class="txt" href="goboard9.html#E25:28_1_1_1_2"><i><font color="Green">E52</font></i></a>, <a class="txt" href="goboard9.html#E39:28_1_1_1_2"><i><font color="Green">E62</font></i></a>, <a class="txt" href="goboard9.html#E46:28_1_1_1_2"><i><font color="Green">E66</font></i></a>, <a class="txt" href="goboard9.html#E48:28_1_1_1_2"><i><font color="Green">E68</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2_2_1_2"><i><font color="Green">E74</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1_1_2_2_1_2"><i><font color="Green">E75</font></i></a>, <a class="txt" href="goboard9.html#E6:28_1_1_1_2_2_1_2"><i><font color="Green">E78</font></i></a>, <a class="ref" href="goboard8.html#T11">GOBOARD8:11</a></i>;<br/><a NAME="E11:28_1_1_1_2_2_1_2"/><b>then </b>
 <a href="topreal1.html#K3">LSeg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>5</sub></font>,<span class="p4">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span></span>)</span> <a href="euclid.html#K17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>7</sub></font>,<span class="p4">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span></span>)</span> <a href="euclid.html#K17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span></span>)</span> <a href="tarski.html#R1">c=</a> <span class="p1">(<span class="default"><a href="topreal1.html#K5">L~</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="subset_1.html#K3">`</a> 
 <b>by </b><i><a class="ref" href="subset_1.html#T43">SUBSET_1:43</a></i>;<br/><a NAME="E12:28_1_1_1_2_2_1_2"/><b>then </b><i><font color="Green">E82</font></i>: 
 <a href="topreal1.html#K3">LSeg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>5</sub></font>,<span class="p4">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span></span>)</span> <a href="euclid.html#K17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>7</sub></font>,<span class="p4">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span></span>)</span> <a href="euclid.html#K17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="goboard9.html#K2" target="_self">LeftComp</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="goboard9.html#E1:28_1"><i><font color="Green">E30</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1"><i><font color="Green">E32</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2"><i><font color="Green">E33</font></i></a>, <a class="txt" href="goboard9.html#E51:28_1_1_1_2"><i><font color="Green">E71</font></i></a>, <a class="txt" href="goboard9.html#E4:28_1_1_1_2_2_1_2"><i><font color="Green">E77</font></i></a>, <a class="txt" href="goboard9.html#E8:28_1_1_1_2_2_1_2"><i><font color="Green">E80</font></i></a>, <a class="txt" href="goboard9.html#E9:28_1_1_1_2_2_1_2"><i><font color="Green">E81</font></i></a>, <a class="ref" href="goboard9.html#T6" target="_self">Th6</a>, <a class="ref" href="nat_1.html#T38">NAT_1:38</a></i>;<br/><a NAME="E13:28_1_1_1_2_2_1_2"/><i><font color="Green">E83</font></i>: 
 <a href="topreal1.html#K3">LSeg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>5</sub></font>,<span class="p4">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span></span>)</span> <a href="euclid.html#K17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>7</sub></font>,<span class="p4">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span></span>)</span> <a href="euclid.html#K17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span></span>)</span> <a href="xboole_0.html#NR5" target="_self">meets</a>  <a href="tops_1.html#K1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K3">cell</a> <span class="p2">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<font color="Maroon">c<sub>7</sub></font>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="goboard9.html#E19:28_1_1_1_2"><i><font color="Green">E46</font></i></a>, <a class="txt" href="goboard9.html#E20:28_1_1_1_2"><i><font color="Green">E47</font></i></a>, <a class="txt" href="goboard9.html#E21:28_1_1_1_2"><i><font color="Green">E48</font></i></a>, <a class="txt" href="goboard9.html#E24:28_1_1_1_2"><i><font color="Green">E51</font></i></a>, <a class="txt" href="goboard9.html#E39:28_1_1_1_2"><i><font color="Green">E62</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2_2_1_2"><i><font color="Green">E74</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1_1_2_2_1_2"><i><font color="Green">E75</font></i></a>, <a class="txt" href="goboard9.html#E6:28_1_1_1_2_2_1_2"><i><font color="Green">E78</font></i></a>, <a class="ref" href="goboard6.html#T85">GOBOARD6:85</a></i>;<br/><a NAME="E14:28_1_1_1_2_2_1_2"/>
 <a href="tops_1.html#K1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K5">left_cell</a> <font color="Maroon">c<sub>1</sub></font>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="xboole_0.html#R1">misses</a>  <a href="topreal1.html#K5">L~</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="goboard9.html#E1:28_1_1"><i><font color="Green">E31</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1"><i><font color="Green">E32</font></i></a>, <a class="ref" href="goboard8.html#T37">GOBOARD8:37</a></i>;<br/><a NAME="E15:28_1_1_1_2_2_1_2"/><b>then </b>
 <a href="tops_1.html#K1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K5">left_cell</a> <font color="Maroon">c<sub>1</sub></font>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="tarski.html#R1">c=</a> <span class="p1">(<span class="default"><a href="topreal1.html#K5">L~</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="subset_1.html#K3">`</a> 
 <b>by </b><i><a class="ref" href="subset_1.html#T43">SUBSET_1:43</a></i>;<br/><b>hence </b><a NAME="E16:28_1_1_1_2_2_1_2"/>
 <a href="tops_1.html#K1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K5">left_cell</a> <font color="Maroon">c<sub>1</sub></font>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="goboard9.html#K2" target="_self">LeftComp</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="goboard9.html#E24:28_1_1_1_2"><i><font color="Green">E51</font></i></a>, <a class="txt" href="goboard9.html#E51:28_1_1_1_2"><i><font color="Green">E71</font></i></a>, <a class="txt" href="goboard9.html#E52:28_1_1_1_2"><i><font color="Green">E72</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2_2_1_2"><i><font color="Green">E74</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1_1_2_2_1_2"><i><font color="Green">E75</font></i></a>, <a class="txt" href="goboard9.html#E7:28_1_1_1_2_2_1_2"><i><font color="Green">E79</font></i></a>, <a class="txt" href="goboard9.html#E12:28_1_1_1_2_2_1_2"><i><font color="Green">E82</font></i></a>, <a class="txt" href="goboard9.html#E13:28_1_1_1_2_2_1_2"><i><font color="Green">E83</font></i></a>, <a class="ref" href="goboard9.html#T6" target="_self">Th6</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="28_1_1_1_2_2_1_3"><b>suppose </b></a><b>that </b><a NAME="E1:28_1_1_1_2_2_1_3"/><i><font color="Green">E74</font></i>: 
<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>5</sub></font> <a href="nat_1.html#K1">+</a> 1
 <b>and </b><br/><a NAME="E2:28_1_1_1_2_2_1_3"/><i><font color="Green">E75</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
 ;<br/><div class="add"> <a href="goboard5.html#K5">left_cell</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font> = 
 <a href="goboard5.html#K3">cell</a> <span class="p1">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>8</sub></font>
<b>by </b><i><a class="txt" href="goboard9.html#E1:28_1_1_1_2"><i><font color="Green">E33</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1_1_2"><i><font color="Green">E34</font></i></a>, <a class="txt" href="goboard9.html#E7:28_1_1_1_2"><i><font color="Green">E37</font></i></a>, <a class="txt" href="goboard9.html#E8:28_1_1_1_2"><i><font color="Green">E38</font></i></a>, <a class="txt" href="goboard9.html#E11:28_1_1_1_2"><i><font color="Green">E40</font></i></a>, <a class="txt" href="goboard9.html#E12:28_1_1_1_2"><i><font color="Green">E41</font></i></a>, <a class="txt" href="goboard9.html#E24:28_1_1_1_2"><i><font color="Green">E51</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2_2_1_3"><i><font color="Green">E74</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1_1_2_2_1_3"><i><font color="Green">E75</font></i></a>, <a class="ref" href="goboard5.html#T30">GOBOARD5:30</a></i>
<br/>.= 
 <a href="goboard5.html#K5">left_cell</a> <font color="Maroon">c<sub>1</sub></font>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>
<b>by </b><i><a class="txt" href="goboard9.html#E1:28_1_1"><i><font color="Green">E31</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1"><i><font color="Green">E32</font></i></a>, <a class="txt" href="goboard9.html#E11:28_1_1_1_2"><i><font color="Green">E40</font></i></a>, <a class="txt" href="goboard9.html#E12:28_1_1_1_2"><i><font color="Green">E41</font></i></a>, <a class="txt" href="goboard9.html#E16:28_1_1_1_2"><i><font color="Green">E43</font></i></a>, <a class="txt" href="goboard9.html#E17:28_1_1_1_2"><i><font color="Green">E44</font></i></a>, <a class="txt" href="goboard9.html#E25:28_1_1_1_2"><i><font color="Green">E52</font></i></a>, <a class="txt" href="goboard9.html#E37:28_1_1_1_2"><i><font color="Green">E61</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1_1_2_2_1_3"><i><font color="Green">E75</font></i></a>, <a class="ref" href="goboard5.html#T31">GOBOARD5:31</a></i>
;<br/><b>hence </b><a NAME="E4:28_1_1_1_2_2_1_3"/>
 <a href="tops_1.html#K1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K5">left_cell</a> <font color="Maroon">c<sub>1</sub></font>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="goboard9.html#K2" target="_self">LeftComp</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="goboard9.html#E1:28_1"><i><font color="Green">E30</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1"><i><font color="Green">E32</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2"><i><font color="Green">E33</font></i></a>, <a class="ref" href="nat_1.html#T38">NAT_1:38</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="28_1_1_1_2_2_1_4"><b>suppose </b></a><b>that </b><a NAME="E1:28_1_1_1_2_2_1_4"/><i><font color="Green">E74</font></i>: 
<font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>6</sub></font> <a href="nat_1.html#K1">+</a> 1
 <b>and </b><br/><a NAME="E2:28_1_1_1_2_2_1_4"/><i><font color="Green">E75</font></i>: 
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>7</sub></font> <a href="nat_1.html#K1">+</a> 1
 <b>and </b><br/><a NAME="E3:28_1_1_1_2_2_1_4"/><i><font color="Green">E76</font></i>: 
<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>
 <b>and </b><br/><a NAME="E4:28_1_1_1_2_2_1_4"/><i><font color="Green">E77</font></i>: 
<font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R1">=</a> 1
 ;<br/><div class="add"><a NAME="E5:28_1_1_1_2_2_1_4"/><i><font color="Green">E78</font></i>: 
 <a href="goboard5.html#K5">left_cell</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a>  <a href="goboard5.html#K3">cell</a> <span class="p1">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>6</sub></font>
 <b>by </b><i><a class="txt" href="goboard9.html#E1:28_1_1_1_2"><i><font color="Green">E33</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1_1_2"><i><font color="Green">E34</font></i></a>, <a class="txt" href="goboard9.html#E7:28_1_1_1_2"><i><font color="Green">E37</font></i></a>, <a class="txt" href="goboard9.html#E8:28_1_1_1_2"><i><font color="Green">E38</font></i></a>, <a class="txt" href="goboard9.html#E11:28_1_1_1_2"><i><font color="Green">E40</font></i></a>, <a class="txt" href="goboard9.html#E12:28_1_1_1_2"><i><font color="Green">E41</font></i></a>, <a class="txt" href="goboard9.html#E24:28_1_1_1_2"><i><font color="Green">E51</font></i></a>, <a class="txt" href="goboard9.html#E37:28_1_1_1_2"><i><font color="Green">E61</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2_2_1_4"><i><font color="Green">E74</font></i></a>, <a class="ref" href="goboard5.html#T31">GOBOARD5:31</a></i>;<br/><a NAME="E6:28_1_1_1_2_2_1_4"/><i><font color="Green">E79</font></i>: 
 <a href="topreal1.html#K3">LSeg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p3">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>,1</span>)</span> <a href="euclid.html#K17">+</a> <span class="p2"><a href="euclid.html#K23">|[</a><span class="default">1,<span class="p3">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span></span><a href="euclid.html#K23">]|</a></span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p5">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p0">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>,1</span>)</span> <a href="euclid.html#K17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p5">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p0">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>,2</span>)</span></span>)</span></span>)</span> <a href="euclid.html#K17">+</a> <span class="p2"><a href="euclid.html#K23">|[</a><span class="default">1,0</span><a href="euclid.html#K23">]|</a></span></span>)</span> is <a href="connsp_1.html#V2">connected</a>
 <b>by </b><i><a class="ref" href="goboard9.html#T8" target="_self">Th8</a></i>;<br/><a NAME="E7:28_1_1_1_2_2_1_4"/><i><font color="Green">E80</font></i>: 
 <a href="topreal1.html#K3">LSeg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p3">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>,1</span>)</span> <a href="euclid.html#K17">+</a> <span class="p2"><a href="euclid.html#K23">|[</a><span class="default">1,<span class="p3">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span></span><a href="euclid.html#K23">]|</a></span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p5">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p0">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>,1</span>)</span> <a href="euclid.html#K17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p5">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p0">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>,2</span>)</span></span>)</span></span>)</span> <a href="euclid.html#K17">+</a> <span class="p2"><a href="euclid.html#K23">|[</a><span class="default">1,0</span><a href="euclid.html#K23">]|</a></span></span>)</span> <a href="xboole_0.html#NR5" target="_self">meets</a>  <a href="tops_1.html#K1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K3">cell</a> <span class="p2">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="goboard9.html#E21:28_1_1_1_2"><i><font color="Green">E48</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2_2_1_4"><i><font color="Green">E74</font></i></a>, <a class="txt" href="goboard9.html#E3:28_1_1_1_2_2_1_4"><i><font color="Green">E76</font></i></a>, <a class="txt" href="goboard9.html#E4:28_1_1_1_2_2_1_4"><i><font color="Green">E77</font></i></a>, <a class="ref" href="goboard6.html#T89">GOBOARD6:89</a></i>;<br/><a NAME="E8:28_1_1_1_2_2_1_4"/>
 <a href="topreal1.html#K3">LSeg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p3">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>,1</span>)</span> <a href="euclid.html#K17">+</a> <span class="p2"><a href="euclid.html#K23">|[</a><span class="default">1,<span class="p3">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span></span><a href="euclid.html#K23">]|</a></span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p5">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p0">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>,1</span>)</span> <a href="euclid.html#K17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p5">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p0">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>,2</span>)</span></span>)</span></span>)</span> <a href="euclid.html#K17">+</a> <span class="p2"><a href="euclid.html#K23">|[</a><span class="default">1,0</span><a href="euclid.html#K23">]|</a></span></span>)</span> <a href="xboole_0.html#R1">misses</a>  <a href="topreal1.html#K5">L~</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="ref" href="goboard8.html#T35">GOBOARD8:35</a></i>;<br/><a NAME="E9:28_1_1_1_2_2_1_4"/><b>then </b>
 <a href="topreal1.html#K3">LSeg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p3">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>,1</span>)</span> <a href="euclid.html#K17">+</a> <span class="p2"><a href="euclid.html#K23">|[</a><span class="default">1,<span class="p3">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span></span><a href="euclid.html#K23">]|</a></span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p5">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p0">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>,1</span>)</span> <a href="euclid.html#K17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p5">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p0">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>,2</span>)</span></span>)</span></span>)</span> <a href="euclid.html#K17">+</a> <span class="p2"><a href="euclid.html#K23">|[</a><span class="default">1,0</span><a href="euclid.html#K23">]|</a></span></span>)</span> <a href="tarski.html#R1">c=</a> <span class="p1">(<span class="default"><a href="topreal1.html#K5">L~</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="subset_1.html#K3">`</a> 
 <b>by </b><i><a class="ref" href="subset_1.html#T43">SUBSET_1:43</a></i>;<br/><a NAME="E10:28_1_1_1_2_2_1_4"/><b>then </b><i><font color="Green">E81</font></i>: 
 <a href="topreal1.html#K3">LSeg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p3">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>,1</span>)</span> <a href="euclid.html#K17">+</a> <span class="p2"><a href="euclid.html#K23">|[</a><span class="default">1,<span class="p3">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span></span><a href="euclid.html#K23">]|</a></span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p5">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p0">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>,1</span>)</span> <a href="euclid.html#K17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p5">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p0">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>,2</span>)</span></span>)</span></span>)</span> <a href="euclid.html#K17">+</a> <span class="p2"><a href="euclid.html#K23">|[</a><span class="default">1,0</span><a href="euclid.html#K23">]|</a></span></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="goboard9.html#K2" target="_self">LeftComp</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="goboard9.html#E1:28_1"><i><font color="Green">E30</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1"><i><font color="Green">E32</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2"><i><font color="Green">E33</font></i></a>, <a class="txt" href="goboard9.html#E51:28_1_1_1_2"><i><font color="Green">E71</font></i></a>, <a class="txt" href="goboard9.html#E5:28_1_1_1_2_2_1_4"><i><font color="Green">E78</font></i></a>, <a class="txt" href="goboard9.html#E6:28_1_1_1_2_2_1_4"><i><font color="Green">E79</font></i></a>, <a class="txt" href="goboard9.html#E7:28_1_1_1_2_2_1_4"><i><font color="Green">E80</font></i></a>, <a class="ref" href="goboard9.html#T6" target="_self">Th6</a>, <a class="ref" href="nat_1.html#T38">NAT_1:38</a></i>;<br/><a NAME="E11:28_1_1_1_2_2_1_4"/><i><font color="Green">E82</font></i>: 
<font color="Maroon">c<sub>6</sub></font> <a href="binarith.html#K5">-'</a> 1 <a href="hidden.html#R1">=</a> 0
 <b>by </b><i><a class="txt" href="goboard9.html#E4:28_1_1_1_2_2_1_4"><i><font color="Green">E77</font></i></a>, <a class="txt" href="goboard9.html#E1"><i><font color="Green">Lemma1</font></i></a></i>;<br/><a NAME="E12:28_1_1_1_2_2_1_4"/><i><font color="Green">E83</font></i>: 
 <a href="tops_1.html#K1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K3">cell</a> <span class="p2">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<font color="Maroon">c<sub>5</sub></font>,0</span>)</span> is <a href="connsp_1.html#V2">connected</a>
 <b>by </b><i><a class="txt" href="goboard9.html#E19:28_1_1_1_2"><i><font color="Green">E46</font></i></a>, <a class="txt" href="goboard9.html#E22:28_1_1_1_2"><i><font color="Green">E49</font></i></a>, <a class="ref" href="goboard9.html#T21" target="_self">Th21</a></i>;<br/><a NAME="E13:28_1_1_1_2_2_1_4"/><i><font color="Green">E84</font></i>: 
 <a href="topreal1.html#K3">LSeg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p3">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>,1</span>)</span> <a href="euclid.html#K17">+</a> <span class="p2"><a href="euclid.html#K23">|[</a><span class="default">1,<span class="p3">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span></span><a href="euclid.html#K23">]|</a></span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p5">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p0">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>,1</span>)</span> <a href="euclid.html#K17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p5">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p0">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>,2</span>)</span></span>)</span></span>)</span> <a href="euclid.html#K17">+</a> <span class="p2"><a href="euclid.html#K23">|[</a><span class="default">1,0</span><a href="euclid.html#K23">]|</a></span></span>)</span> <a href="xboole_0.html#NR5" target="_self">meets</a>  <a href="tops_1.html#K1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K3">cell</a> <span class="p2">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<font color="Maroon">c<sub>5</sub></font>,0</span>)</span>
 <b>by </b><i><a class="txt" href="goboard9.html#E24:28_1_1_1_2"><i><font color="Green">E51</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2_2_1_4"><i><font color="Green">E74</font></i></a>, <a class="txt" href="goboard9.html#E3:28_1_1_1_2_2_1_4"><i><font color="Green">E76</font></i></a>, <a class="ref" href="goboard6.html#T93">GOBOARD6:93</a></i>;<br/><a NAME="E14:28_1_1_1_2_2_1_4"/>
 <a href="tops_1.html#K1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K3">cell</a> <span class="p2">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<font color="Maroon">c<sub>5</sub></font>,0</span>)</span> <a href="xboole_0.html#R1">misses</a>  <a href="topreal1.html#K5">L~</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="goboard9.html#E19:28_1_1_1_2"><i><font color="Green">E46</font></i></a>, <a class="txt" href="goboard9.html#E22:28_1_1_1_2"><i><font color="Green">E49</font></i></a>, <a class="ref" href="goboard7.html#T14">GOBOARD7:14</a></i>;<br/><a NAME="E15:28_1_1_1_2_2_1_4"/><b>then </b>
 <a href="tops_1.html#K1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K3">cell</a> <span class="p2">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<font color="Maroon">c<sub>5</sub></font>,0</span>)</span> <a href="tarski.html#R1">c=</a> <span class="p1">(<span class="default"><a href="topreal1.html#K5">L~</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="subset_1.html#K3">`</a> 
 <b>by </b><i><a class="ref" href="subset_1.html#T43">SUBSET_1:43</a></i>;<br/><a NAME="E16:28_1_1_1_2_2_1_4"/><b>then </b><i><font color="Green">E85</font></i>: 
 <a href="tops_1.html#K1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K3">cell</a> <span class="p2">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<font color="Maroon">c<sub>5</sub></font>,0</span>)</span> <a href="tarski.html#R1">c=</a>  <a href="goboard9.html#K2" target="_self">LeftComp</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="goboard9.html#E51:28_1_1_1_2"><i><font color="Green">E71</font></i></a>, <a class="txt" href="goboard9.html#E10:28_1_1_1_2_2_1_4"><i><font color="Green">E81</font></i></a>, <a class="txt" href="goboard9.html#E12:28_1_1_1_2_2_1_4"><i><font color="Green">E83</font></i></a>, <a class="txt" href="goboard9.html#E13:28_1_1_1_2_2_1_4"><i><font color="Green">E84</font></i></a>, <a class="ref" href="goboard9.html#T6" target="_self">Th6</a></i>;<br/><a NAME="E17:28_1_1_1_2_2_1_4"/><i><font color="Green">E86</font></i>: 
 <a href="goboard5.html#K5">left_cell</a> <font color="Maroon">c<sub>1</sub></font>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="hidden.html#R1">=</a>  <a href="goboard5.html#K3">cell</a> <span class="p1">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<font color="Maroon">c<sub>7</sub></font>,0
 <b>by </b><i><a class="txt" href="goboard9.html#E1:28_1_1"><i><font color="Green">E31</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1"><i><font color="Green">E32</font></i></a>, <a class="txt" href="goboard9.html#E11:28_1_1_1_2"><i><font color="Green">E40</font></i></a>, <a class="txt" href="goboard9.html#E12:28_1_1_1_2"><i><font color="Green">E41</font></i></a>, <a class="txt" href="goboard9.html#E16:28_1_1_1_2"><i><font color="Green">E43</font></i></a>, <a class="txt" href="goboard9.html#E17:28_1_1_1_2"><i><font color="Green">E44</font></i></a>, <a class="txt" href="goboard9.html#E25:28_1_1_1_2"><i><font color="Green">E52</font></i></a>, <a class="txt" href="goboard9.html#E39:28_1_1_1_2"><i><font color="Green">E62</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1_1_2_2_1_4"><i><font color="Green">E75</font></i></a>, <a class="txt" href="goboard9.html#E11:28_1_1_1_2_2_1_4"><i><font color="Green">E82</font></i></a>, <a class="ref" href="goboard5.html#T30">GOBOARD5:30</a></i>;<br/><a NAME="E18:28_1_1_1_2_2_1_4"/><i><font color="Green">E87</font></i>: 
 <a href="topreal1.html#K3">LSeg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="binarith.html#K5">-'</a> 1</span>)</span>,1</span>)</span> <a href="euclid.html#K17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p5">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p0">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>,1</span>)</span></span>)</span></span>)</span> <a href="euclid.html#K20">-</a> <span class="p2"><a href="euclid.html#K23">|[</a><span class="default">0,1</span><a href="euclid.html#K23">]|</a></span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p3">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>,1</span>)</span> <a href="euclid.html#K17">+</a> <span class="p2"><a href="euclid.html#K23">|[</a><span class="default">1,<span class="p3">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span></span><a href="euclid.html#K23">]|</a></span></span>)</span> is <a href="connsp_1.html#V2">connected</a>
 <b>by </b><i><a class="ref" href="goboard9.html#T8" target="_self">Th8</a></i>;<br/><a NAME="E19:28_1_1_1_2_2_1_4"/><i><font color="Green">E88</font></i>: 
 <a href="topreal1.html#K3">LSeg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="binarith.html#K5">-'</a> 1</span>)</span>,1</span>)</span> <a href="euclid.html#K17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p5">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p0">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>,1</span>)</span></span>)</span></span>)</span> <a href="euclid.html#K20">-</a> <span class="p2"><a href="euclid.html#K23">|[</a><span class="default">0,1</span><a href="euclid.html#K23">]|</a></span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p3">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>,1</span>)</span> <a href="euclid.html#K17">+</a> <span class="p2"><a href="euclid.html#K23">|[</a><span class="default">1,<span class="p3">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span></span><a href="euclid.html#K23">]|</a></span></span>)</span> <a href="xboole_0.html#NR5" target="_self">meets</a>  <a href="tops_1.html#K1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K3">cell</a> <span class="p2">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<font color="Maroon">c<sub>5</sub></font>,0</span>)</span>
 <b>by </b><i><a class="txt" href="goboard9.html#E24:28_1_1_1_2"><i><font color="Green">E51</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2_2_1_4"><i><font color="Green">E74</font></i></a>, <a class="txt" href="goboard9.html#E3:28_1_1_1_2_2_1_4"><i><font color="Green">E76</font></i></a>, <a class="ref" href="goboard6.html#T93">GOBOARD6:93</a></i>;<br/><a NAME="E20:28_1_1_1_2_2_1_4"/>
 <a href="topreal1.html#K3">LSeg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="binarith.html#K5">-'</a> 1</span>)</span>,1</span>)</span> <a href="euclid.html#K17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p5">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p0">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>,1</span>)</span></span>)</span></span>)</span> <a href="euclid.html#K20">-</a> <span class="p2"><a href="euclid.html#K23">|[</a><span class="default">0,1</span><a href="euclid.html#K23">]|</a></span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p3">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>,1</span>)</span> <a href="euclid.html#K17">+</a> <span class="p2"><a href="euclid.html#K23">|[</a><span class="default">1,<span class="p3">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span></span><a href="euclid.html#K23">]|</a></span></span>)</span> <a href="xboole_0.html#R1">misses</a>  <a href="topreal1.html#K5">L~</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="ref" href="goboard8.html#T27">GOBOARD8:27</a></i>;<br/><a NAME="E21:28_1_1_1_2_2_1_4"/><b>then </b>
 <a href="topreal1.html#K3">LSeg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="binarith.html#K5">-'</a> 1</span>)</span>,1</span>)</span> <a href="euclid.html#K17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p5">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p0">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>,1</span>)</span></span>)</span></span>)</span> <a href="euclid.html#K20">-</a> <span class="p2"><a href="euclid.html#K23">|[</a><span class="default">0,1</span><a href="euclid.html#K23">]|</a></span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p3">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>,1</span>)</span> <a href="euclid.html#K17">+</a> <span class="p2"><a href="euclid.html#K23">|[</a><span class="default">1,<span class="p3">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span></span><a href="euclid.html#K23">]|</a></span></span>)</span> <a href="tarski.html#R1">c=</a> <span class="p1">(<span class="default"><a href="topreal1.html#K5">L~</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="subset_1.html#K3">`</a> 
 <b>by </b><i><a class="ref" href="subset_1.html#T43">SUBSET_1:43</a></i>;<br/><a NAME="E22:28_1_1_1_2_2_1_4"/><b>then </b><i><font color="Green">E89</font></i>: 
 <a href="topreal1.html#K3">LSeg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="binarith.html#K5">-'</a> 1</span>)</span>,1</span>)</span> <a href="euclid.html#K17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p5">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p0">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>,1</span>)</span></span>)</span></span>)</span> <a href="euclid.html#K20">-</a> <span class="p2"><a href="euclid.html#K23">|[</a><span class="default">0,1</span><a href="euclid.html#K23">]|</a></span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p3">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>,1</span>)</span> <a href="euclid.html#K17">+</a> <span class="p2"><a href="euclid.html#K23">|[</a><span class="default">1,<span class="p3">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span></span><a href="euclid.html#K23">]|</a></span></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="goboard9.html#K2" target="_self">LeftComp</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="goboard9.html#E51:28_1_1_1_2"><i><font color="Green">E71</font></i></a>, <a class="txt" href="goboard9.html#E16:28_1_1_1_2_2_1_4"><i><font color="Green">E85</font></i></a>, <a class="txt" href="goboard9.html#E18:28_1_1_1_2_2_1_4"><i><font color="Green">E87</font></i></a>, <a class="txt" href="goboard9.html#E19:28_1_1_1_2_2_1_4"><i><font color="Green">E88</font></i></a>, <a class="ref" href="goboard9.html#T6" target="_self">Th6</a></i>;<br/><a NAME="E23:28_1_1_1_2_2_1_4"/>
<font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p2">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="binarith.html#K5">-'</a> 1
 <b>by </b><i><a class="txt" href="goboard9.html#E24:28_1_1_1_2"><i><font color="Green">E51</font></i></a>, <a class="txt" href="goboard9.html#E37:28_1_1_1_2"><i><font color="Green">E61</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2_2_1_4"><i><font color="Green">E74</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1_1_2_2_1_4"><i><font color="Green">E75</font></i></a>, <a class="txt" href="goboard9.html#E3:28_1_1_1_2_2_1_4"><i><font color="Green">E76</font></i></a></i>;<br/><a NAME="E24:28_1_1_1_2_2_1_4"/><b>then </b><i><font color="Green">E90</font></i>: 
 <a href="topreal1.html#K3">LSeg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="binarith.html#K5">-'</a> 1</span>)</span>,1</span>)</span> <a href="euclid.html#K17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p5">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p0">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>,1</span>)</span></span>)</span></span>)</span> <a href="euclid.html#K20">-</a> <span class="p2"><a href="euclid.html#K23">|[</a><span class="default">0,1</span><a href="euclid.html#K23">]|</a></span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p3">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>,1</span>)</span> <a href="euclid.html#K17">+</a> <span class="p2"><a href="euclid.html#K23">|[</a><span class="default">1,<span class="p3">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span></span><a href="euclid.html#K23">]|</a></span></span>)</span> <a href="xboole_0.html#NR5" target="_self">meets</a>  <a href="tops_1.html#K1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K3">cell</a> <span class="p2">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<font color="Maroon">c<sub>7</sub></font>,0</span>)</span>
 <b>by </b><i><a class="txt" href="goboard9.html#E20:28_1_1_1_2"><i><font color="Green">E47</font></i></a>, <a class="txt" href="goboard9.html#E24:28_1_1_1_2"><i><font color="Green">E51</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2_2_1_4"><i><font color="Green">E74</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1_1_2_2_1_4"><i><font color="Green">E75</font></i></a>, <a class="txt" href="goboard9.html#E3:28_1_1_1_2_2_1_4"><i><font color="Green">E76</font></i></a>, <a class="ref" href="goboard6.html#T87">GOBOARD6:87</a></i>;<br/><a NAME="E25:28_1_1_1_2_2_1_4"/>
 <a href="tops_1.html#K1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K5">left_cell</a> <font color="Maroon">c<sub>1</sub></font>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="xboole_0.html#R1">misses</a>  <a href="topreal1.html#K5">L~</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="goboard9.html#E1:28_1_1"><i><font color="Green">E31</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1"><i><font color="Green">E32</font></i></a>, <a class="ref" href="goboard8.html#T37">GOBOARD8:37</a></i>;<br/><a NAME="E26:28_1_1_1_2_2_1_4"/><b>then </b>
 <a href="tops_1.html#K1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K5">left_cell</a> <font color="Maroon">c<sub>1</sub></font>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="tarski.html#R1">c=</a> <span class="p1">(<span class="default"><a href="topreal1.html#K5">L~</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="subset_1.html#K3">`</a> 
 <b>by </b><i><a class="ref" href="subset_1.html#T43">SUBSET_1:43</a></i>;<br/><b>hence </b><a NAME="E27:28_1_1_1_2_2_1_4"/>
 <a href="tops_1.html#K1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K5">left_cell</a> <font color="Maroon">c<sub>1</sub></font>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="goboard9.html#K2" target="_self">LeftComp</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="goboard9.html#E51:28_1_1_1_2"><i><font color="Green">E71</font></i></a>, <a class="txt" href="goboard9.html#E52:28_1_1_1_2"><i><font color="Green">E72</font></i></a>, <a class="txt" href="goboard9.html#E17:28_1_1_1_2_2_1_4"><i><font color="Green">E86</font></i></a>, <a class="txt" href="goboard9.html#E22:28_1_1_1_2_2_1_4"><i><font color="Green">E89</font></i></a>, <a class="txt" href="goboard9.html#E24:28_1_1_1_2_2_1_4"><i><font color="Green">E90</font></i></a>, <a class="ref" href="goboard9.html#T6" target="_self">Th6</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="28_1_1_1_2_2_1_5"><b>suppose </b></a><b>that </b><a NAME="E1:28_1_1_1_2_2_1_5"/><i><font color="Green">E74</font></i>: 
<font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>6</sub></font> <a href="nat_1.html#K1">+</a> 1
 <b>and </b><br/><a NAME="E2:28_1_1_1_2_2_1_5"/><i><font color="Green">E75</font></i>: 
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>7</sub></font> <a href="nat_1.html#K1">+</a> 1
 <b>and </b><br/><a NAME="E3:28_1_1_1_2_2_1_5"/><i><font color="Green">E76</font></i>: 
<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>
 <b>and </b><br/><a NAME="E4:28_1_1_1_2_2_1_5"/><i><font color="Green">E77</font></i>: 
<font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R1">=</a> 1
 ;<br/><div class="add"><a NAME="E5:28_1_1_1_2_2_1_5"/><i><font color="Green">E78</font></i>: 
 <a href="goboard5.html#K5">left_cell</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a>  <a href="goboard5.html#K3">cell</a> <span class="p1">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>6</sub></font>
 <b>by </b><i><a class="txt" href="goboard9.html#E1:28_1_1_1_2"><i><font color="Green">E33</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1_1_2"><i><font color="Green">E34</font></i></a>, <a class="txt" href="goboard9.html#E7:28_1_1_1_2"><i><font color="Green">E37</font></i></a>, <a class="txt" href="goboard9.html#E8:28_1_1_1_2"><i><font color="Green">E38</font></i></a>, <a class="txt" href="goboard9.html#E11:28_1_1_1_2"><i><font color="Green">E40</font></i></a>, <a class="txt" href="goboard9.html#E12:28_1_1_1_2"><i><font color="Green">E41</font></i></a>, <a class="txt" href="goboard9.html#E24:28_1_1_1_2"><i><font color="Green">E51</font></i></a>, <a class="txt" href="goboard9.html#E37:28_1_1_1_2"><i><font color="Green">E61</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2_2_1_5"><i><font color="Green">E74</font></i></a>, <a class="ref" href="goboard5.html#T31">GOBOARD5:31</a></i>;<br/><a NAME="E6:28_1_1_1_2_2_1_5"/>
 <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> <font color="Maroon">c<sub>3</sub></font>
 <b>by </b><i><a class="txt" href="goboard9.html#E18:28_1_1_1_2"><i><font color="Green">E45</font></i></a>, <a class="txt" href="goboard9.html#E3:28_1_1_1_2_2_1_5"><i><font color="Green">E76</font></i></a>, <a class="ref" href="xxreal_0.html#T1">XXREAL_0:1</a></i>;<br/><a NAME="E7:28_1_1_1_2_2_1_5"/><b>then </b><i><font color="Green">E79</font></i>: 
 <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <font color="Maroon">c<sub>3</sub></font> <a href="nat_1.html#K1">+</a> 1
 <b>by </b><i><a class="ref" href="nat_1.html#T38">NAT_1:38</a></i>;<br/><a NAME="E8:28_1_1_1_2_2_1_5"/><i><font color="Green">E80</font></i>: 
 <a href="topreal1.html#K3">LSeg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>3</sub></font>,1</span>)</span> <a href="euclid.html#K17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,1</span>)</span></span>)</span></span>)</span> <a href="euclid.html#K20">-</a> <span class="p2"><a href="euclid.html#K23">|[</a><span class="default">0,1</span><a href="euclid.html#K23">]|</a></span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>5</sub></font>,1</span>)</span> <a href="euclid.html#K17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,2</span>)</span></span>)</span></span>)</span> is <a href="connsp_1.html#V2">connected</a>
 <b>by </b><i><a class="ref" href="goboard9.html#T8" target="_self">Th8</a></i>;<br/><a NAME="E9:28_1_1_1_2_2_1_5"/><i><font color="Green">E81</font></i>: 
 <a href="topreal1.html#K3">LSeg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>3</sub></font>,1</span>)</span> <a href="euclid.html#K17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,1</span>)</span></span>)</span></span>)</span> <a href="euclid.html#K20">-</a> <span class="p2"><a href="euclid.html#K23">|[</a><span class="default">0,1</span><a href="euclid.html#K23">]|</a></span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>5</sub></font>,1</span>)</span> <a href="euclid.html#K17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p4">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xboole_0.html#NR5" target="_self">meets</a>  <a href="tops_1.html#K1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K3">cell</a> <span class="p2">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="goboard9.html#E19:28_1_1_1_2"><i><font color="Green">E46</font></i></a>, <a class="txt" href="goboard9.html#E21:28_1_1_1_2"><i><font color="Green">E48</font></i></a>, <a class="txt" href="goboard9.html#E24:28_1_1_1_2"><i><font color="Green">E51</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2_2_1_5"><i><font color="Green">E74</font></i></a>, <a class="txt" href="goboard9.html#E4:28_1_1_1_2_2_1_5"><i><font color="Green">E77</font></i></a>, <a class="txt" href="goboard9.html#E7:28_1_1_1_2_2_1_5"><i><font color="Green">E79</font></i></a>, <a class="ref" href="goboard6.html#T85">GOBOARD6:85</a></i>;<br/><a NAME="E10:28_1_1_1_2_2_1_5"/>
 <a href="topreal1.html#K3">LSeg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>3</sub></font>,1</span>)</span> <a href="euclid.html#K17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,1</span>)</span></span>)</span></span>)</span> <a href="euclid.html#K20">-</a> <span class="p2"><a href="euclid.html#K23">|[</a><span class="default">0,1</span><a href="euclid.html#K23">]|</a></span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>5</sub></font>,1</span>)</span> <a href="euclid.html#K17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,2</span>)</span></span>)</span></span>)</span> <a href="xboole_0.html#R1">misses</a>  <a href="topreal1.html#K5">L~</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="goboard9.html#E2:28_1_1"><i><font color="Green">E32</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2"><i><font color="Green">E33</font></i></a>, <a class="txt" href="goboard9.html#E8:28_1_1_1_2"><i><font color="Green">E38</font></i></a>, <a class="txt" href="goboard9.html#E12:28_1_1_1_2"><i><font color="Green">E41</font></i></a>, <a class="txt" href="goboard9.html#E17:28_1_1_1_2"><i><font color="Green">E44</font></i></a>, <a class="txt" href="goboard9.html#E20:28_1_1_1_2"><i><font color="Green">E47</font></i></a>, <a class="txt" href="goboard9.html#E24:28_1_1_1_2"><i><font color="Green">E51</font></i></a>, <a class="txt" href="goboard9.html#E25:28_1_1_1_2"><i><font color="Green">E52</font></i></a>, <a class="txt" href="goboard9.html#E46:28_1_1_1_2"><i><font color="Green">E66</font></i></a>, <a class="txt" href="goboard9.html#E48:28_1_1_1_2"><i><font color="Green">E68</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2_2_1_5"><i><font color="Green">E74</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1_1_2_2_1_5"><i><font color="Green">E75</font></i></a>, <a class="txt" href="goboard9.html#E4:28_1_1_1_2_2_1_5"><i><font color="Green">E77</font></i></a>, <a class="txt" href="goboard9.html#E7:28_1_1_1_2_2_1_5"><i><font color="Green">E79</font></i></a>, <a class="ref" href="goboard8.html#T8">GOBOARD8:8</a></i>;<br/><a NAME="E11:28_1_1_1_2_2_1_5"/><b>then </b>
 <a href="topreal1.html#K3">LSeg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>3</sub></font>,1</span>)</span> <a href="euclid.html#K17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,1</span>)</span></span>)</span></span>)</span> <a href="euclid.html#K20">-</a> <span class="p2"><a href="euclid.html#K23">|[</a><span class="default">0,1</span><a href="euclid.html#K23">]|</a></span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>5</sub></font>,1</span>)</span> <a href="euclid.html#K17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,2</span>)</span></span>)</span></span>)</span> <a href="tarski.html#R1">c=</a> <span class="p1">(<span class="default"><a href="topreal1.html#K5">L~</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="subset_1.html#K3">`</a> 
 <b>by </b><i><a class="ref" href="subset_1.html#T43">SUBSET_1:43</a></i>;<br/><a NAME="E12:28_1_1_1_2_2_1_5"/><b>then </b><i><font color="Green">E82</font></i>: 
 <a href="topreal1.html#K3">LSeg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>3</sub></font>,1</span>)</span> <a href="euclid.html#K17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,1</span>)</span></span>)</span></span>)</span> <a href="euclid.html#K20">-</a> <span class="p2"><a href="euclid.html#K23">|[</a><span class="default">0,1</span><a href="euclid.html#K23">]|</a></span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>5</sub></font>,1</span>)</span> <a href="euclid.html#K17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,2</span>)</span></span>)</span></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="goboard9.html#K2" target="_self">LeftComp</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="goboard9.html#E1:28_1"><i><font color="Green">E30</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1"><i><font color="Green">E32</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2"><i><font color="Green">E33</font></i></a>, <a class="txt" href="goboard9.html#E51:28_1_1_1_2"><i><font color="Green">E71</font></i></a>, <a class="txt" href="goboard9.html#E5:28_1_1_1_2_2_1_5"><i><font color="Green">E78</font></i></a>, <a class="txt" href="goboard9.html#E8:28_1_1_1_2_2_1_5"><i><font color="Green">E80</font></i></a>, <a class="txt" href="goboard9.html#E9:28_1_1_1_2_2_1_5"><i><font color="Green">E81</font></i></a>, <a class="ref" href="goboard9.html#T6" target="_self">Th6</a>, <a class="ref" href="nat_1.html#T38">NAT_1:38</a></i>;<br/><a NAME="E13:28_1_1_1_2_2_1_5"/><i><font color="Green">E83</font></i>: 
<font color="Maroon">c<sub>6</sub></font> <a href="binarith.html#K5">-'</a> 1 <a href="hidden.html#R1">=</a> 0
 <b>by </b><i><a class="txt" href="goboard9.html#E4:28_1_1_1_2_2_1_5"><i><font color="Green">E77</font></i></a>, <a class="txt" href="goboard9.html#E1"><i><font color="Green">Lemma1</font></i></a></i>;<br/><a NAME="E14:28_1_1_1_2_2_1_5"/><i><font color="Green">E84</font></i>: 
 <a href="tops_1.html#K1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K3">cell</a> <span class="p2">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<font color="Maroon">c<sub>5</sub></font>,0</span>)</span> is <a href="connsp_1.html#V2">connected</a>
 <b>by </b><i><a class="txt" href="goboard9.html#E19:28_1_1_1_2"><i><font color="Green">E46</font></i></a>, <a class="txt" href="goboard9.html#E22:28_1_1_1_2"><i><font color="Green">E49</font></i></a>, <a class="ref" href="goboard9.html#T21" target="_self">Th21</a></i>;<br/><a NAME="E15:28_1_1_1_2_2_1_5"/><i><font color="Green">E85</font></i>: 
 <a href="topreal1.html#K3">LSeg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>3</sub></font>,1</span>)</span> <a href="euclid.html#K17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,1</span>)</span></span>)</span></span>)</span> <a href="euclid.html#K20">-</a> <span class="p2"><a href="euclid.html#K23">|[</a><span class="default">0,1</span><a href="euclid.html#K23">]|</a></span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>5</sub></font>,1</span>)</span> <a href="euclid.html#K17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,2</span>)</span></span>)</span></span>)</span> <a href="xboole_0.html#NR5" target="_self">meets</a>  <a href="tops_1.html#K1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K3">cell</a> <span class="p2">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<font color="Maroon">c<sub>5</sub></font>,0</span>)</span>
 <b>by </b><i><a class="txt" href="goboard9.html#E19:28_1_1_1_2"><i><font color="Green">E46</font></i></a>, <a class="txt" href="goboard9.html#E24:28_1_1_1_2"><i><font color="Green">E51</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2_2_1_5"><i><font color="Green">E74</font></i></a>, <a class="txt" href="goboard9.html#E7:28_1_1_1_2_2_1_5"><i><font color="Green">E79</font></i></a>, <a class="ref" href="goboard6.html#T87">GOBOARD6:87</a></i>;<br/><a NAME="E16:28_1_1_1_2_2_1_5"/>
 <a href="tops_1.html#K1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K3">cell</a> <span class="p2">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<font color="Maroon">c<sub>5</sub></font>,0</span>)</span> <a href="xboole_0.html#R1">misses</a>  <a href="topreal1.html#K5">L~</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="goboard9.html#E19:28_1_1_1_2"><i><font color="Green">E46</font></i></a>, <a class="txt" href="goboard9.html#E22:28_1_1_1_2"><i><font color="Green">E49</font></i></a>, <a class="ref" href="goboard7.html#T14">GOBOARD7:14</a></i>;<br/><a NAME="E17:28_1_1_1_2_2_1_5"/><b>then </b>
 <a href="tops_1.html#K1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K3">cell</a> <span class="p2">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<font color="Maroon">c<sub>5</sub></font>,0</span>)</span> <a href="tarski.html#R1">c=</a> <span class="p1">(<span class="default"><a href="topreal1.html#K5">L~</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="subset_1.html#K3">`</a> 
 <b>by </b><i><a class="ref" href="subset_1.html#T43">SUBSET_1:43</a></i>;<br/><a NAME="E18:28_1_1_1_2_2_1_5"/><b>then </b><i><font color="Green">E86</font></i>: 
 <a href="tops_1.html#K1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K3">cell</a> <span class="p2">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<font color="Maroon">c<sub>5</sub></font>,0</span>)</span> <a href="tarski.html#R1">c=</a>  <a href="goboard9.html#K2" target="_self">LeftComp</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="goboard9.html#E51:28_1_1_1_2"><i><font color="Green">E71</font></i></a>, <a class="txt" href="goboard9.html#E12:28_1_1_1_2_2_1_5"><i><font color="Green">E82</font></i></a>, <a class="txt" href="goboard9.html#E14:28_1_1_1_2_2_1_5"><i><font color="Green">E84</font></i></a>, <a class="txt" href="goboard9.html#E15:28_1_1_1_2_2_1_5"><i><font color="Green">E85</font></i></a>, <a class="ref" href="goboard9.html#T6" target="_self">Th6</a></i>;<br/><a NAME="E19:28_1_1_1_2_2_1_5"/><i><font color="Green">E87</font></i>: 
 <a href="goboard5.html#K5">left_cell</a> <font color="Maroon">c<sub>1</sub></font>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="hidden.html#R1">=</a>  <a href="goboard5.html#K3">cell</a> <span class="p1">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<font color="Maroon">c<sub>7</sub></font>,0
 <b>by </b><i><a class="txt" href="goboard9.html#E1:28_1_1"><i><font color="Green">E31</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1"><i><font color="Green">E32</font></i></a>, <a class="txt" href="goboard9.html#E11:28_1_1_1_2"><i><font color="Green">E40</font></i></a>, <a class="txt" href="goboard9.html#E12:28_1_1_1_2"><i><font color="Green">E41</font></i></a>, <a class="txt" href="goboard9.html#E16:28_1_1_1_2"><i><font color="Green">E43</font></i></a>, <a class="txt" href="goboard9.html#E17:28_1_1_1_2"><i><font color="Green">E44</font></i></a>, <a class="txt" href="goboard9.html#E25:28_1_1_1_2"><i><font color="Green">E52</font></i></a>, <a class="txt" href="goboard9.html#E39:28_1_1_1_2"><i><font color="Green">E62</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1_1_2_2_1_5"><i><font color="Green">E75</font></i></a>, <a class="txt" href="goboard9.html#E13:28_1_1_1_2_2_1_5"><i><font color="Green">E83</font></i></a>, <a class="ref" href="goboard5.html#T30">GOBOARD5:30</a></i>;<br/><a NAME="E20:28_1_1_1_2_2_1_5"/><i><font color="Green">E88</font></i>: 
 <a href="topreal1.html#K3">LSeg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>7</sub></font>,1</span>)</span> <a href="euclid.html#K17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,1</span>)</span></span>)</span></span>)</span> <a href="euclid.html#K20">-</a> <span class="p2"><a href="euclid.html#K23">|[</a><span class="default">0,1</span><a href="euclid.html#K23">]|</a></span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,1</span>)</span> <a href="euclid.html#K17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span></span>)</span> <a href="euclid.html#K20">-</a> <span class="p2"><a href="euclid.html#K23">|[</a><span class="default">0,1</span><a href="euclid.html#K23">]|</a></span></span>)</span> is <a href="connsp_1.html#V2">connected</a>
 <b>by </b><i><a class="ref" href="goboard9.html#T8" target="_self">Th8</a></i>;<br/><a NAME="E21:28_1_1_1_2_2_1_5"/><i><font color="Green">E89</font></i>: 
 <a href="topreal1.html#K3">LSeg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>7</sub></font>,1</span>)</span> <a href="euclid.html#K17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,1</span>)</span></span>)</span></span>)</span> <a href="euclid.html#K20">-</a> <span class="p2"><a href="euclid.html#K23">|[</a><span class="default">0,1</span><a href="euclid.html#K23">]|</a></span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,1</span>)</span> <a href="euclid.html#K17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span></span>)</span> <a href="euclid.html#K20">-</a> <span class="p2"><a href="euclid.html#K23">|[</a><span class="default">0,1</span><a href="euclid.html#K23">]|</a></span></span>)</span> <a href="xboole_0.html#NR5" target="_self">meets</a>  <a href="tops_1.html#K1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K3">cell</a> <span class="p2">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<font color="Maroon">c<sub>5</sub></font>,0</span>)</span>
 <b>by </b><i><a class="txt" href="goboard9.html#E19:28_1_1_1_2"><i><font color="Green">E46</font></i></a>, <a class="txt" href="goboard9.html#E24:28_1_1_1_2"><i><font color="Green">E51</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2_2_1_5"><i><font color="Green">E74</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1_1_2_2_1_5"><i><font color="Green">E75</font></i></a>, <a class="txt" href="goboard9.html#E7:28_1_1_1_2_2_1_5"><i><font color="Green">E79</font></i></a>, <a class="ref" href="goboard6.html#T87">GOBOARD6:87</a></i>;<br/><a NAME="E22:28_1_1_1_2_2_1_5"/>
 <a href="topreal1.html#K3">LSeg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>7</sub></font>,1</span>)</span> <a href="euclid.html#K17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,1</span>)</span></span>)</span></span>)</span> <a href="euclid.html#K20">-</a> <span class="p2"><a href="euclid.html#K23">|[</a><span class="default">0,1</span><a href="euclid.html#K23">]|</a></span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,1</span>)</span> <a href="euclid.html#K17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span></span>)</span> <a href="euclid.html#K20">-</a> <span class="p2"><a href="euclid.html#K23">|[</a><span class="default">0,1</span><a href="euclid.html#K23">]|</a></span></span>)</span> <a href="xboole_0.html#R1">misses</a>  <a href="topreal1.html#K5">L~</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="goboard9.html#E20:28_1_1_1_2"><i><font color="Green">E47</font></i></a>, <a class="txt" href="goboard9.html#E24:28_1_1_1_2"><i><font color="Green">E51</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2_2_1_5"><i><font color="Green">E74</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1_1_2_2_1_5"><i><font color="Green">E75</font></i></a>, <a class="txt" href="goboard9.html#E7:28_1_1_1_2_2_1_5"><i><font color="Green">E79</font></i></a>, <a class="ref" href="goboard8.html#T25">GOBOARD8:25</a></i>;<br/><a NAME="E23:28_1_1_1_2_2_1_5"/><b>then </b>
 <a href="topreal1.html#K3">LSeg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>7</sub></font>,1</span>)</span> <a href="euclid.html#K17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,1</span>)</span></span>)</span></span>)</span> <a href="euclid.html#K20">-</a> <span class="p2"><a href="euclid.html#K23">|[</a><span class="default">0,1</span><a href="euclid.html#K23">]|</a></span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,1</span>)</span> <a href="euclid.html#K17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span></span>)</span> <a href="euclid.html#K20">-</a> <span class="p2"><a href="euclid.html#K23">|[</a><span class="default">0,1</span><a href="euclid.html#K23">]|</a></span></span>)</span> <a href="tarski.html#R1">c=</a> <span class="p1">(<span class="default"><a href="topreal1.html#K5">L~</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="subset_1.html#K3">`</a> 
 <b>by </b><i><a class="ref" href="subset_1.html#T43">SUBSET_1:43</a></i>;<br/><a NAME="E24:28_1_1_1_2_2_1_5"/><b>then </b><i><font color="Green">E90</font></i>: 
 <a href="topreal1.html#K3">LSeg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>7</sub></font>,1</span>)</span> <a href="euclid.html#K17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,1</span>)</span></span>)</span></span>)</span> <a href="euclid.html#K20">-</a> <span class="p2"><a href="euclid.html#K23">|[</a><span class="default">0,1</span><a href="euclid.html#K23">]|</a></span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,1</span>)</span> <a href="euclid.html#K17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span></span>)</span> <a href="euclid.html#K20">-</a> <span class="p2"><a href="euclid.html#K23">|[</a><span class="default">0,1</span><a href="euclid.html#K23">]|</a></span></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="goboard9.html#K2" target="_self">LeftComp</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="goboard9.html#E51:28_1_1_1_2"><i><font color="Green">E71</font></i></a>, <a class="txt" href="goboard9.html#E18:28_1_1_1_2_2_1_5"><i><font color="Green">E86</font></i></a>, <a class="txt" href="goboard9.html#E20:28_1_1_1_2_2_1_5"><i><font color="Green">E88</font></i></a>, <a class="txt" href="goboard9.html#E21:28_1_1_1_2_2_1_5"><i><font color="Green">E89</font></i></a>, <a class="ref" href="goboard9.html#T6" target="_self">Th6</a></i>;<br/><a NAME="E25:28_1_1_1_2_2_1_5"/><i><font color="Green">E91</font></i>: 
 <a href="topreal1.html#K3">LSeg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>7</sub></font>,1</span>)</span> <a href="euclid.html#K17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,1</span>)</span></span>)</span></span>)</span> <a href="euclid.html#K20">-</a> <span class="p2"><a href="euclid.html#K23">|[</a><span class="default">0,1</span><a href="euclid.html#K23">]|</a></span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,1</span>)</span> <a href="euclid.html#K17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span></span>)</span> <a href="euclid.html#K20">-</a> <span class="p2"><a href="euclid.html#K23">|[</a><span class="default">0,1</span><a href="euclid.html#K23">]|</a></span></span>)</span> <a href="xboole_0.html#NR5" target="_self">meets</a>  <a href="tops_1.html#K1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K3">cell</a> <span class="p2">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<font color="Maroon">c<sub>7</sub></font>,0</span>)</span>
 <b>by </b><i><a class="txt" href="goboard9.html#E19:28_1_1_1_2"><i><font color="Green">E46</font></i></a>, <a class="txt" href="goboard9.html#E20:28_1_1_1_2"><i><font color="Green">E47</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1_1_2_2_1_5"><i><font color="Green">E75</font></i></a>, <a class="ref" href="goboard6.html#T87">GOBOARD6:87</a></i>;<br/><a NAME="E26:28_1_1_1_2_2_1_5"/>
 <a href="tops_1.html#K1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K5">left_cell</a> <font color="Maroon">c<sub>1</sub></font>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="xboole_0.html#R1">misses</a>  <a href="topreal1.html#K5">L~</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="goboard9.html#E1:28_1_1"><i><font color="Green">E31</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1"><i><font color="Green">E32</font></i></a>, <a class="ref" href="goboard8.html#T37">GOBOARD8:37</a></i>;<br/><a NAME="E27:28_1_1_1_2_2_1_5"/><b>then </b>
 <a href="tops_1.html#K1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K5">left_cell</a> <font color="Maroon">c<sub>1</sub></font>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="tarski.html#R1">c=</a> <span class="p1">(<span class="default"><a href="topreal1.html#K5">L~</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="subset_1.html#K3">`</a> 
 <b>by </b><i><a class="ref" href="subset_1.html#T43">SUBSET_1:43</a></i>;<br/><b>hence </b><a NAME="E28:28_1_1_1_2_2_1_5"/>
 <a href="tops_1.html#K1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K5">left_cell</a> <font color="Maroon">c<sub>1</sub></font>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="goboard9.html#K2" target="_self">LeftComp</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="goboard9.html#E51:28_1_1_1_2"><i><font color="Green">E71</font></i></a>, <a class="txt" href="goboard9.html#E52:28_1_1_1_2"><i><font color="Green">E72</font></i></a>, <a class="txt" href="goboard9.html#E19:28_1_1_1_2_2_1_5"><i><font color="Green">E87</font></i></a>, <a class="txt" href="goboard9.html#E24:28_1_1_1_2_2_1_5"><i><font color="Green">E90</font></i></a>, <a class="txt" href="goboard9.html#E25:28_1_1_1_2_2_1_5"><i><font color="Green">E91</font></i></a>, <a class="ref" href="goboard9.html#T6" target="_self">Th6</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="28_1_1_1_2_2_1_6"><b>suppose </b></a><b>that </b><a NAME="E1:28_1_1_1_2_2_1_6"/><i><font color="Green">E74</font></i>: 
<font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>6</sub></font> <a href="nat_1.html#K1">+</a> 1
 <b>and </b><br/><a NAME="E2:28_1_1_1_2_2_1_6"/><i><font color="Green">E75</font></i>: 
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>7</sub></font> <a href="nat_1.html#K1">+</a> 1
 <b>and </b><br/><a NAME="E3:28_1_1_1_2_2_1_6"/><i><font color="Green">E76</font></i>: 
<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>
 <b>and </b><br/><a NAME="E4:28_1_1_1_2_2_1_6"/><i><font color="Green">E77</font></i>: 
<font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 1
 ;<br/><div class="add"><a NAME="E5:28_1_1_1_2_2_1_6"/><i><font color="Green">E78</font></i>: 
 <a href="goboard5.html#K5">left_cell</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a>  <a href="goboard5.html#K3">cell</a> <span class="p1">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>6</sub></font>
 <b>by </b><i><a class="txt" href="goboard9.html#E1:28_1_1_1_2"><i><font color="Green">E33</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1_1_2"><i><font color="Green">E34</font></i></a>, <a class="txt" href="goboard9.html#E7:28_1_1_1_2"><i><font color="Green">E37</font></i></a>, <a class="txt" href="goboard9.html#E8:28_1_1_1_2"><i><font color="Green">E38</font></i></a>, <a class="txt" href="goboard9.html#E11:28_1_1_1_2"><i><font color="Green">E40</font></i></a>, <a class="txt" href="goboard9.html#E12:28_1_1_1_2"><i><font color="Green">E41</font></i></a>, <a class="txt" href="goboard9.html#E24:28_1_1_1_2"><i><font color="Green">E51</font></i></a>, <a class="txt" href="goboard9.html#E37:28_1_1_1_2"><i><font color="Green">E61</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2_2_1_6"><i><font color="Green">E74</font></i></a>, <a class="ref" href="goboard5.html#T31">GOBOARD5:31</a></i>;<br/><a NAME="E6:28_1_1_1_2_2_1_6"/>
1 <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">c<sub>6</sub></font>
 <b>by </b><i><a class="txt" href="goboard9.html#E22:28_1_1_1_2"><i><font color="Green">E49</font></i></a>, <a class="txt" href="goboard9.html#E4:28_1_1_1_2_2_1_6"><i><font color="Green">E77</font></i></a>, <a class="ref" href="xxreal_0.html#T1">XXREAL_0:1</a></i>;<br/><a NAME="E7:28_1_1_1_2_2_1_6"/><b>then </b><i><font color="Green">E79</font></i>: 
1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>6</sub></font> <a href="binarith.html#K5">-'</a> 1
 <b>by </b><i><a class="txt" href="goboard9.html#E39:28_1_1_1_2"><i><font color="Green">E62</font></i></a>, <a class="ref" href="nat_1.html#T38">NAT_1:38</a></i>;<br/><a NAME="E8:28_1_1_1_2_2_1_6"/><i><font color="Green">E80</font></i>: 
<font color="Maroon">c<sub>6</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>6</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="goboard9.html#E39:28_1_1_1_2"><i><font color="Green">E62</font></i></a></i>;<br/><a NAME="E9:28_1_1_1_2_2_1_6"/><i><font color="Green">E81</font></i>: 
 <a href="topreal1.html#K3">LSeg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p5">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p0">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>,<span class="p5">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span></span>)</span> <a href="euclid.html#K17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p5">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p0">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>,<font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K17">+</a> <span class="p2"><a href="euclid.html#K23">|[</a><span class="default">1,0</span><a href="euclid.html#K23">]|</a></span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p5">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p0">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>,<font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="euclid.html#K17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p5">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p0">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>,<span class="p5">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K17">+</a> <span class="p2"><a href="euclid.html#K23">|[</a><span class="default">1,0</span><a href="euclid.html#K23">]|</a></span></span>)</span> is <a href="connsp_1.html#V2">connected</a>
 <b>by </b><i><a class="ref" href="goboard9.html#T8" target="_self">Th8</a></i>;<br/><a NAME="E10:28_1_1_1_2_2_1_6"/><i><font color="Green">E82</font></i>: 
 <a href="topreal1.html#K3">LSeg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p5">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p0">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>,<span class="p5">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span></span>)</span> <a href="euclid.html#K17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p5">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p0">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>,<font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K17">+</a> <span class="p2"><a href="euclid.html#K23">|[</a><span class="default">1,0</span><a href="euclid.html#K23">]|</a></span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p5">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p0">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>,<font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="euclid.html#K17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p5">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p0">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>,<span class="p5">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K17">+</a> <span class="p2"><a href="euclid.html#K23">|[</a><span class="default">1,0</span><a href="euclid.html#K23">]|</a></span></span>)</span> <a href="xboole_0.html#NR5" target="_self">meets</a>  <a href="tops_1.html#K1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K3">cell</a> <span class="p2">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="goboard9.html#E21:28_1_1_1_2"><i><font color="Green">E48</font></i></a>, <a class="txt" href="goboard9.html#E22:28_1_1_1_2"><i><font color="Green">E49</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2_2_1_6"><i><font color="Green">E74</font></i></a>, <a class="txt" href="goboard9.html#E3:28_1_1_1_2_2_1_6"><i><font color="Green">E76</font></i></a>, <a class="ref" href="goboard6.html#T89">GOBOARD6:89</a></i>;<br/><a NAME="E11:28_1_1_1_2_2_1_6"/>
 <a href="topreal1.html#K3">LSeg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p5">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p0">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>,<span class="p5">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span></span>)</span> <a href="euclid.html#K17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p5">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p0">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>,<font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K17">+</a> <span class="p2"><a href="euclid.html#K23">|[</a><span class="default">1,0</span><a href="euclid.html#K23">]|</a></span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p5">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p0">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>,<font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="euclid.html#K17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p5">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p0">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>,<span class="p5">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K17">+</a> <span class="p2"><a href="euclid.html#K23">|[</a><span class="default">1,0</span><a href="euclid.html#K23">]|</a></span></span>)</span> <a href="xboole_0.html#R1">misses</a>  <a href="topreal1.html#K5">L~</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="goboard9.html#E21:28_1_1_1_2"><i><font color="Green">E48</font></i></a>, <a class="txt" href="goboard9.html#E39:28_1_1_1_2"><i><font color="Green">E62</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2_2_1_6"><i><font color="Green">E74</font></i></a>, <a class="txt" href="goboard9.html#E7:28_1_1_1_2_2_1_6"><i><font color="Green">E79</font></i></a>, <a class="txt" href="goboard9.html#E8:28_1_1_1_2_2_1_6"><i><font color="Green">E80</font></i></a>, <a class="ref" href="goboard8.html#T34">GOBOARD8:34</a></i>;<br/><a NAME="E12:28_1_1_1_2_2_1_6"/><b>then </b>
 <a href="topreal1.html#K3">LSeg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p5">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p0">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>,<span class="p5">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span></span>)</span> <a href="euclid.html#K17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p5">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p0">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>,<font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K17">+</a> <span class="p2"><a href="euclid.html#K23">|[</a><span class="default">1,0</span><a href="euclid.html#K23">]|</a></span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p5">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p0">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>,<font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="euclid.html#K17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p5">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p0">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>,<span class="p5">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K17">+</a> <span class="p2"><a href="euclid.html#K23">|[</a><span class="default">1,0</span><a href="euclid.html#K23">]|</a></span></span>)</span> <a href="tarski.html#R1">c=</a> <span class="p1">(<span class="default"><a href="topreal1.html#K5">L~</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="subset_1.html#K3">`</a> 
 <b>by </b><i><a class="ref" href="subset_1.html#T43">SUBSET_1:43</a></i>;<br/><a NAME="E13:28_1_1_1_2_2_1_6"/><b>then </b><i><font color="Green">E83</font></i>: 
 <a href="topreal1.html#K3">LSeg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p5">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p0">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>,<span class="p5">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span></span>)</span> <a href="euclid.html#K17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p5">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p0">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>,<font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K17">+</a> <span class="p2"><a href="euclid.html#K23">|[</a><span class="default">1,0</span><a href="euclid.html#K23">]|</a></span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p5">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p0">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>,<font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="euclid.html#K17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p5">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p0">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>,<span class="p5">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K17">+</a> <span class="p2"><a href="euclid.html#K23">|[</a><span class="default">1,0</span><a href="euclid.html#K23">]|</a></span></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="goboard9.html#K2" target="_self">LeftComp</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="goboard9.html#E1:28_1"><i><font color="Green">E30</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1"><i><font color="Green">E32</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2"><i><font color="Green">E33</font></i></a>, <a class="txt" href="goboard9.html#E51:28_1_1_1_2"><i><font color="Green">E71</font></i></a>, <a class="txt" href="goboard9.html#E5:28_1_1_1_2_2_1_6"><i><font color="Green">E78</font></i></a>, <a class="txt" href="goboard9.html#E9:28_1_1_1_2_2_1_6"><i><font color="Green">E81</font></i></a>, <a class="txt" href="goboard9.html#E10:28_1_1_1_2_2_1_6"><i><font color="Green">E82</font></i></a>, <a class="ref" href="goboard9.html#T6" target="_self">Th6</a>, <a class="ref" href="nat_1.html#T38">NAT_1:38</a></i>;<br/><a NAME="E14:28_1_1_1_2_2_1_6"/><i><font color="Green">E84</font></i>: 
 <a href="tops_1.html#K1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K3">cell</a> <span class="p2">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<font color="Maroon">c<sub>5</sub></font>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span></span>)</span> is <a href="connsp_1.html#V2">connected</a>
 <b>by </b><i><a class="txt" href="goboard9.html#E19:28_1_1_1_2"><i><font color="Green">E46</font></i></a>, <a class="txt" href="goboard9.html#E41:28_1_1_1_2"><i><font color="Green">E63</font></i></a>, <a class="ref" href="goboard9.html#T21" target="_self">Th21</a></i>;<br/><a NAME="E15:28_1_1_1_2_2_1_6"/>
<font color="Maroon">c<sub>6</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 1
 <b>by </b><i><a class="txt" href="goboard9.html#E22:28_1_1_1_2"><i><font color="Green">E49</font></i></a>, <a class="txt" href="goboard9.html#E4:28_1_1_1_2_2_1_6"><i><font color="Green">E77</font></i></a>, <a class="ref" href="xxreal_0.html#T1">XXREAL_0:1</a></i>;<br/><a NAME="E16:28_1_1_1_2_2_1_6"/><b>then </b>
1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>6</sub></font> <a href="binarith.html#K5">-'</a> 1
 <b>by </b><i><a class="txt" href="goboard9.html#E39:28_1_1_1_2"><i><font color="Green">E62</font></i></a>, <a class="ref" href="nat_1.html#T38">NAT_1:38</a></i>;<br/><a NAME="E17:28_1_1_1_2_2_1_6"/><b>then </b><i><font color="Green">E85</font></i>: 
 <a href="topreal1.html#K3">LSeg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p5">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p0">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>,<span class="p5">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span></span>)</span> <a href="euclid.html#K17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p5">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p0">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>,<font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K17">+</a> <span class="p2"><a href="euclid.html#K23">|[</a><span class="default">1,0</span><a href="euclid.html#K23">]|</a></span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p5">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p0">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>,<font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="euclid.html#K17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p5">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p0">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>,<span class="p5">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K17">+</a> <span class="p2"><a href="euclid.html#K23">|[</a><span class="default">1,0</span><a href="euclid.html#K23">]|</a></span></span>)</span> <a href="xboole_0.html#NR5" target="_self">meets</a>  <a href="tops_1.html#K1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K3">cell</a> <span class="p2">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<font color="Maroon">c<sub>5</sub></font>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="goboard9.html#E22:28_1_1_1_2"><i><font color="Green">E49</font></i></a>, <a class="txt" href="goboard9.html#E24:28_1_1_1_2"><i><font color="Green">E51</font></i></a>, <a class="txt" href="goboard9.html#E39:28_1_1_1_2"><i><font color="Green">E62</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2_2_1_6"><i><font color="Green">E74</font></i></a>, <a class="txt" href="goboard9.html#E3:28_1_1_1_2_2_1_6"><i><font color="Green">E76</font></i></a>, <a class="ref" href="goboard6.html#T89">GOBOARD6:89</a></i>;<br/><a NAME="E18:28_1_1_1_2_2_1_6"/>
 <a href="tops_1.html#K1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K3">cell</a> <span class="p2">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<font color="Maroon">c<sub>5</sub></font>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span></span>)</span> <a href="xboole_0.html#R1">misses</a>  <a href="topreal1.html#K5">L~</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="goboard9.html#E19:28_1_1_1_2"><i><font color="Green">E46</font></i></a>, <a class="txt" href="goboard9.html#E41:28_1_1_1_2"><i><font color="Green">E63</font></i></a>, <a class="ref" href="goboard7.html#T14">GOBOARD7:14</a></i>;<br/><a NAME="E19:28_1_1_1_2_2_1_6"/><b>then </b>
 <a href="tops_1.html#K1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K3">cell</a> <span class="p2">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<font color="Maroon">c<sub>5</sub></font>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span></span>)</span> <a href="tarski.html#R1">c=</a> <span class="p1">(<span class="default"><a href="topreal1.html#K5">L~</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="subset_1.html#K3">`</a> 
 <b>by </b><i><a class="ref" href="subset_1.html#T43">SUBSET_1:43</a></i>;<br/><a NAME="E20:28_1_1_1_2_2_1_6"/><b>then </b><i><font color="Green">E86</font></i>: 
 <a href="tops_1.html#K1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K3">cell</a> <span class="p2">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<font color="Maroon">c<sub>5</sub></font>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="goboard9.html#K2" target="_self">LeftComp</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="goboard9.html#E51:28_1_1_1_2"><i><font color="Green">E71</font></i></a>, <a class="txt" href="goboard9.html#E13:28_1_1_1_2_2_1_6"><i><font color="Green">E83</font></i></a>, <a class="txt" href="goboard9.html#E14:28_1_1_1_2_2_1_6"><i><font color="Green">E84</font></i></a>, <a class="txt" href="goboard9.html#E17:28_1_1_1_2_2_1_6"><i><font color="Green">E85</font></i></a>, <a class="ref" href="goboard9.html#T6" target="_self">Th6</a></i>;<br/><a NAME="E21:28_1_1_1_2_2_1_6"/><i><font color="Green">E87</font></i>: 
 <a href="goboard5.html#K5">left_cell</a> <font color="Maroon">c<sub>1</sub></font>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="hidden.html#R1">=</a>  <a href="goboard5.html#K3">cell</a> <span class="p1">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<font color="Maroon">c<sub>7</sub></font>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span>
 <b>by </b><i><a class="txt" href="goboard9.html#E1:28_1_1"><i><font color="Green">E31</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1"><i><font color="Green">E32</font></i></a>, <a class="txt" href="goboard9.html#E11:28_1_1_1_2"><i><font color="Green">E40</font></i></a>, <a class="txt" href="goboard9.html#E12:28_1_1_1_2"><i><font color="Green">E41</font></i></a>, <a class="txt" href="goboard9.html#E16:28_1_1_1_2"><i><font color="Green">E43</font></i></a>, <a class="txt" href="goboard9.html#E17:28_1_1_1_2"><i><font color="Green">E44</font></i></a>, <a class="txt" href="goboard9.html#E25:28_1_1_1_2"><i><font color="Green">E52</font></i></a>, <a class="txt" href="goboard9.html#E39:28_1_1_1_2"><i><font color="Green">E62</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1_1_2_2_1_6"><i><font color="Green">E75</font></i></a>, <a class="ref" href="goboard5.html#T30">GOBOARD5:30</a></i>;<br/><a NAME="E22:28_1_1_1_2_2_1_6"/><i><font color="Green">E88</font></i>: 
 <a href="topreal1.html#K3">LSeg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span>,<span class="p4">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span></span>)</span> <a href="euclid.html#K17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>5</sub></font>,<span class="p5">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span></span>)</span> <a href="euclid.html#K17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K17">+</a> <span class="p2"><a href="euclid.html#K23">|[</a><span class="default">1,0</span><a href="euclid.html#K23">]|</a></span></span>)</span> is <a href="connsp_1.html#V2">connected</a>
 <b>by </b><i><a class="ref" href="goboard9.html#T8" target="_self">Th8</a></i>;<br/><a NAME="E23:28_1_1_1_2_2_1_6"/><i><font color="Green">E89</font></i>: 
 <a href="topreal1.html#K3">LSeg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span>,<span class="p4">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span></span>)</span> <a href="euclid.html#K17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>5</sub></font>,<span class="p5">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span></span>)</span> <a href="euclid.html#K17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K17">+</a> <span class="p2"><a href="euclid.html#K23">|[</a><span class="default">1,0</span><a href="euclid.html#K23">]|</a></span></span>)</span> <a href="xboole_0.html#NR5" target="_self">meets</a>  <a href="tops_1.html#K1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K3">cell</a> <span class="p2">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<font color="Maroon">c<sub>5</sub></font>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="goboard9.html#E22:28_1_1_1_2"><i><font color="Green">E49</font></i></a>, <a class="txt" href="goboard9.html#E24:28_1_1_1_2"><i><font color="Green">E51</font></i></a>, <a class="txt" href="goboard9.html#E39:28_1_1_1_2"><i><font color="Green">E62</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2_2_1_6"><i><font color="Green">E74</font></i></a>, <a class="txt" href="goboard9.html#E3:28_1_1_1_2_2_1_6"><i><font color="Green">E76</font></i></a>, <a class="txt" href="goboard9.html#E7:28_1_1_1_2_2_1_6"><i><font color="Green">E79</font></i></a>, <a class="ref" href="goboard6.html#T89">GOBOARD6:89</a></i>;<br/><a NAME="E24:28_1_1_1_2_2_1_6"/><i><font color="Green">E90</font></i>: 
<font color="Maroon">c<sub>5</sub></font> <a href="binarith.html#K5">-'</a> 1 <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>7</sub></font>
 <b>by </b><i><a class="txt" href="goboard9.html#E2:28_1_1_1_2_2_1_6"><i><font color="Green">E75</font></i></a>, <a class="ref" href="binarith.html#T39">BINARITH:39</a></i>;<br/><a NAME="E25:28_1_1_1_2_2_1_6"/><b>then </b>
 <a href="topreal1.html#K3">LSeg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span>,<span class="p4">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span></span>)</span> <a href="euclid.html#K17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>5</sub></font>,<span class="p5">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span></span>)</span> <a href="euclid.html#K17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K17">+</a> <span class="p2"><a href="euclid.html#K23">|[</a><span class="default">1,0</span><a href="euclid.html#K23">]|</a></span></span>)</span> <a href="xboole_0.html#R1">misses</a>  <a href="topreal1.html#K5">L~</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="goboard9.html#E2:28_1_1"><i><font color="Green">E32</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2"><i><font color="Green">E33</font></i></a>, <a class="txt" href="goboard9.html#E8:28_1_1_1_2"><i><font color="Green">E38</font></i></a>, <a class="txt" href="goboard9.html#E12:28_1_1_1_2"><i><font color="Green">E41</font></i></a>, <a class="txt" href="goboard9.html#E17:28_1_1_1_2"><i><font color="Green">E44</font></i></a>, <a class="txt" href="goboard9.html#E21:28_1_1_1_2"><i><font color="Green">E48</font></i></a>, <a class="txt" href="goboard9.html#E24:28_1_1_1_2"><i><font color="Green">E51</font></i></a>, <a class="txt" href="goboard9.html#E25:28_1_1_1_2"><i><font color="Green">E52</font></i></a>, <a class="txt" href="goboard9.html#E39:28_1_1_1_2"><i><font color="Green">E62</font></i></a>, <a class="txt" href="goboard9.html#E46:28_1_1_1_2"><i><font color="Green">E66</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2_2_1_6"><i><font color="Green">E74</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1_1_2_2_1_6"><i><font color="Green">E75</font></i></a>, <a class="txt" href="goboard9.html#E3:28_1_1_1_2_2_1_6"><i><font color="Green">E76</font></i></a>, <a class="txt" href="goboard9.html#E7:28_1_1_1_2_2_1_6"><i><font color="Green">E79</font></i></a>, <a class="txt" href="goboard9.html#E8:28_1_1_1_2_2_1_6"><i><font color="Green">E80</font></i></a>, <a class="ref" href="goboard8.html#T19">GOBOARD8:19</a></i>;<br/><a NAME="E26:28_1_1_1_2_2_1_6"/><b>then </b>
 <a href="topreal1.html#K3">LSeg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span>,<span class="p4">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span></span>)</span> <a href="euclid.html#K17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>5</sub></font>,<span class="p5">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span></span>)</span> <a href="euclid.html#K17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K17">+</a> <span class="p2"><a href="euclid.html#K23">|[</a><span class="default">1,0</span><a href="euclid.html#K23">]|</a></span></span>)</span> <a href="tarski.html#R1">c=</a> <span class="p1">(<span class="default"><a href="topreal1.html#K5">L~</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="subset_1.html#K3">`</a> 
 <b>by </b><i><a class="ref" href="subset_1.html#T43">SUBSET_1:43</a></i>;<br/><a NAME="E27:28_1_1_1_2_2_1_6"/><b>then </b><i><font color="Green">E91</font></i>: 
 <a href="topreal1.html#K3">LSeg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span>,<span class="p4">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span></span>)</span> <a href="euclid.html#K17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>5</sub></font>,<span class="p5">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span></span>)</span> <a href="euclid.html#K17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K17">+</a> <span class="p2"><a href="euclid.html#K23">|[</a><span class="default">1,0</span><a href="euclid.html#K23">]|</a></span></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="goboard9.html#K2" target="_self">LeftComp</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="goboard9.html#E51:28_1_1_1_2"><i><font color="Green">E71</font></i></a>, <a class="txt" href="goboard9.html#E20:28_1_1_1_2_2_1_6"><i><font color="Green">E86</font></i></a>, <a class="txt" href="goboard9.html#E22:28_1_1_1_2_2_1_6"><i><font color="Green">E88</font></i></a>, <a class="txt" href="goboard9.html#E23:28_1_1_1_2_2_1_6"><i><font color="Green">E89</font></i></a>, <a class="ref" href="goboard9.html#T6" target="_self">Th6</a></i>;<br/><a NAME="E28:28_1_1_1_2_2_1_6"/><i><font color="Green">E92</font></i>: 
 <a href="topreal1.html#K3">LSeg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span>,<span class="p4">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span></span>)</span> <a href="euclid.html#K17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>5</sub></font>,<span class="p5">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span></span>)</span> <a href="euclid.html#K17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K17">+</a> <span class="p2"><a href="euclid.html#K23">|[</a><span class="default">1,0</span><a href="euclid.html#K23">]|</a></span></span>)</span> <a href="xboole_0.html#NR5" target="_self">meets</a>  <a href="tops_1.html#K1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K3">cell</a> <span class="p2">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<font color="Maroon">c<sub>7</sub></font>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="goboard9.html#E19:28_1_1_1_2"><i><font color="Green">E46</font></i></a>, <a class="txt" href="goboard9.html#E20:28_1_1_1_2"><i><font color="Green">E47</font></i></a>, <a class="txt" href="goboard9.html#E22:28_1_1_1_2"><i><font color="Green">E49</font></i></a>, <a class="txt" href="goboard9.html#E39:28_1_1_1_2"><i><font color="Green">E62</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1_1_2_2_1_6"><i><font color="Green">E75</font></i></a>, <a class="txt" href="goboard9.html#E7:28_1_1_1_2_2_1_6"><i><font color="Green">E79</font></i></a>, <a class="txt" href="goboard9.html#E24:28_1_1_1_2_2_1_6"><i><font color="Green">E90</font></i></a>, <a class="ref" href="goboard6.html#T85">GOBOARD6:85</a></i>;<br/><a NAME="E29:28_1_1_1_2_2_1_6"/>
 <a href="tops_1.html#K1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K5">left_cell</a> <font color="Maroon">c<sub>1</sub></font>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="xboole_0.html#R1">misses</a>  <a href="topreal1.html#K5">L~</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="goboard9.html#E1:28_1_1"><i><font color="Green">E31</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1"><i><font color="Green">E32</font></i></a>, <a class="ref" href="goboard8.html#T37">GOBOARD8:37</a></i>;<br/><a NAME="E30:28_1_1_1_2_2_1_6"/><b>then </b>
 <a href="tops_1.html#K1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K5">left_cell</a> <font color="Maroon">c<sub>1</sub></font>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="tarski.html#R1">c=</a> <span class="p1">(<span class="default"><a href="topreal1.html#K5">L~</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="subset_1.html#K3">`</a> 
 <b>by </b><i><a class="ref" href="subset_1.html#T43">SUBSET_1:43</a></i>;<br/><b>hence </b><a NAME="E31:28_1_1_1_2_2_1_6"/>
 <a href="tops_1.html#K1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K5">left_cell</a> <font color="Maroon">c<sub>1</sub></font>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="goboard9.html#K2" target="_self">LeftComp</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="goboard9.html#E51:28_1_1_1_2"><i><font color="Green">E71</font></i></a>, <a class="txt" href="goboard9.html#E52:28_1_1_1_2"><i><font color="Green">E72</font></i></a>, <a class="txt" href="goboard9.html#E21:28_1_1_1_2_2_1_6"><i><font color="Green">E87</font></i></a>, <a class="txt" href="goboard9.html#E27:28_1_1_1_2_2_1_6"><i><font color="Green">E91</font></i></a>, <a class="txt" href="goboard9.html#E28:28_1_1_1_2_2_1_6"><i><font color="Green">E92</font></i></a>, <a class="ref" href="goboard9.html#T6" target="_self">Th6</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="28_1_1_1_2_2_1_7"><b>suppose </b></a><b>that </b><a NAME="E1:28_1_1_1_2_2_1_7"/><i><font color="Green">E74</font></i>: 
<font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>6</sub></font> <a href="nat_1.html#K1">+</a> 1
 <b>and </b><br/><a NAME="E2:28_1_1_1_2_2_1_7"/><i><font color="Green">E75</font></i>: 
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>7</sub></font> <a href="nat_1.html#K1">+</a> 1
 <b>and </b><br/><a NAME="E3:28_1_1_1_2_2_1_7"/><i><font color="Green">E76</font></i>: 
<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>
 <b>and </b><br/><a NAME="E4:28_1_1_1_2_2_1_7"/><i><font color="Green">E77</font></i>: 
<font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 1
 ;<br/><div class="add"><a NAME="E5:28_1_1_1_2_2_1_7"/><i><font color="Green">E78</font></i>: 
 <a href="goboard5.html#K5">left_cell</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a>  <a href="goboard5.html#K3">cell</a> <span class="p1">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>6</sub></font>
 <b>by </b><i><a class="txt" href="goboard9.html#E1:28_1_1_1_2"><i><font color="Green">E33</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1_1_2"><i><font color="Green">E34</font></i></a>, <a class="txt" href="goboard9.html#E7:28_1_1_1_2"><i><font color="Green">E37</font></i></a>, <a class="txt" href="goboard9.html#E8:28_1_1_1_2"><i><font color="Green">E38</font></i></a>, <a class="txt" href="goboard9.html#E11:28_1_1_1_2"><i><font color="Green">E40</font></i></a>, <a class="txt" href="goboard9.html#E12:28_1_1_1_2"><i><font color="Green">E41</font></i></a>, <a class="txt" href="goboard9.html#E24:28_1_1_1_2"><i><font color="Green">E51</font></i></a>, <a class="txt" href="goboard9.html#E37:28_1_1_1_2"><i><font color="Green">E61</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2_2_1_7"><i><font color="Green">E74</font></i></a>, <a class="ref" href="goboard5.html#T31">GOBOARD5:31</a></i>;<br/><a NAME="E6:28_1_1_1_2_2_1_7"/>
1 <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">c<sub>6</sub></font>
 <b>by </b><i><a class="txt" href="goboard9.html#E22:28_1_1_1_2"><i><font color="Green">E49</font></i></a>, <a class="txt" href="goboard9.html#E4:28_1_1_1_2_2_1_7"><i><font color="Green">E77</font></i></a>, <a class="ref" href="xxreal_0.html#T1">XXREAL_0:1</a></i>;<br/><a NAME="E7:28_1_1_1_2_2_1_7"/><b>then </b><i><font color="Green">E79</font></i>: 
1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>6</sub></font> <a href="binarith.html#K5">-'</a> 1
 <b>by </b><i><a class="txt" href="goboard9.html#E39:28_1_1_1_2"><i><font color="Green">E62</font></i></a>, <a class="ref" href="nat_1.html#T38">NAT_1:38</a></i>;<br/><a NAME="E8:28_1_1_1_2_2_1_7"/>
 <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> <font color="Maroon">c<sub>3</sub></font>
 <b>by </b><i><a class="txt" href="goboard9.html#E18:28_1_1_1_2"><i><font color="Green">E45</font></i></a>, <a class="txt" href="goboard9.html#E3:28_1_1_1_2_2_1_7"><i><font color="Green">E76</font></i></a>, <a class="ref" href="xxreal_0.html#T1">XXREAL_0:1</a></i>;<br/><a NAME="E9:28_1_1_1_2_2_1_7"/><b>then </b><i><font color="Green">E80</font></i>: 
 <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <font color="Maroon">c<sub>3</sub></font> <a href="nat_1.html#K1">+</a> 1
 <b>by </b><i><a class="ref" href="nat_1.html#T38">NAT_1:38</a></i>;<br/><a NAME="E10:28_1_1_1_2_2_1_7"/><i><font color="Green">E81</font></i>: 
<font color="Maroon">c<sub>6</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>6</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="goboard9.html#E39:28_1_1_1_2"><i><font color="Green">E62</font></i></a></i>;<br/><a NAME="E11:28_1_1_1_2_2_1_7"/><i><font color="Green">E82</font></i>: 
 <a href="topreal1.html#K3">LSeg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>3</sub></font>,<span class="p4">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span></span>)</span> <a href="euclid.html#K17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="euclid.html#K17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p4">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> is <a href="connsp_1.html#V2">connected</a>
 <b>by </b><i><a class="ref" href="goboard9.html#T8" target="_self">Th8</a></i>;<br/><a NAME="E12:28_1_1_1_2_2_1_7"/><i><font color="Green">E83</font></i>: 
 <a href="topreal1.html#K3">LSeg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>3</sub></font>,<span class="p4">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span></span>)</span> <a href="euclid.html#K17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="euclid.html#K17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p4">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xboole_0.html#NR5" target="_self">meets</a>  <a href="tops_1.html#K1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K3">cell</a> <span class="p2">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="goboard9.html#E19:28_1_1_1_2"><i><font color="Green">E46</font></i></a>, <a class="txt" href="goboard9.html#E21:28_1_1_1_2"><i><font color="Green">E48</font></i></a>, <a class="txt" href="goboard9.html#E22:28_1_1_1_2"><i><font color="Green">E49</font></i></a>, <a class="txt" href="goboard9.html#E24:28_1_1_1_2"><i><font color="Green">E51</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2_2_1_7"><i><font color="Green">E74</font></i></a>, <a class="txt" href="goboard9.html#E9:28_1_1_1_2_2_1_7"><i><font color="Green">E80</font></i></a>, <a class="ref" href="goboard6.html#T85">GOBOARD6:85</a></i>;<br/><a NAME="E13:28_1_1_1_2_2_1_7"/>
 <a href="topreal1.html#K3">LSeg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>3</sub></font>,<span class="p4">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span></span>)</span> <a href="euclid.html#K17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="euclid.html#K17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p4">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xboole_0.html#R1">misses</a>  <a href="topreal1.html#K5">L~</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="goboard9.html#E2:28_1_1"><i><font color="Green">E32</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2"><i><font color="Green">E33</font></i></a>, <a class="txt" href="goboard9.html#E8:28_1_1_1_2"><i><font color="Green">E38</font></i></a>, <a class="txt" href="goboard9.html#E12:28_1_1_1_2"><i><font color="Green">E41</font></i></a>, <a class="txt" href="goboard9.html#E17:28_1_1_1_2"><i><font color="Green">E44</font></i></a>, <a class="txt" href="goboard9.html#E20:28_1_1_1_2"><i><font color="Green">E47</font></i></a>, <a class="txt" href="goboard9.html#E21:28_1_1_1_2"><i><font color="Green">E48</font></i></a>, <a class="txt" href="goboard9.html#E24:28_1_1_1_2"><i><font color="Green">E51</font></i></a>, <a class="txt" href="goboard9.html#E25:28_1_1_1_2"><i><font color="Green">E52</font></i></a>, <a class="txt" href="goboard9.html#E39:28_1_1_1_2"><i><font color="Green">E62</font></i></a>, <a class="txt" href="goboard9.html#E46:28_1_1_1_2"><i><font color="Green">E66</font></i></a>, <a class="txt" href="goboard9.html#E48:28_1_1_1_2"><i><font color="Green">E68</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2_2_1_7"><i><font color="Green">E74</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1_1_2_2_1_7"><i><font color="Green">E75</font></i></a>, <a class="txt" href="goboard9.html#E7:28_1_1_1_2_2_1_7"><i><font color="Green">E79</font></i></a>, <a class="txt" href="goboard9.html#E9:28_1_1_1_2_2_1_7"><i><font color="Green">E80</font></i></a>, <a class="txt" href="goboard9.html#E10:28_1_1_1_2_2_1_7"><i><font color="Green">E81</font></i></a>, <a class="ref" href="goboard8.html#T5">GOBOARD8:5</a></i>;<br/><a NAME="E14:28_1_1_1_2_2_1_7"/><b>then </b>
 <a href="topreal1.html#K3">LSeg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>3</sub></font>,<span class="p4">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span></span>)</span> <a href="euclid.html#K17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="euclid.html#K17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p4">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="tarski.html#R1">c=</a> <span class="p1">(<span class="default"><a href="topreal1.html#K5">L~</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="subset_1.html#K3">`</a> 
 <b>by </b><i><a class="ref" href="subset_1.html#T43">SUBSET_1:43</a></i>;<br/><a NAME="E15:28_1_1_1_2_2_1_7"/><b>then </b><i><font color="Green">E84</font></i>: 
 <a href="topreal1.html#K3">LSeg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>3</sub></font>,<span class="p4">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span></span>)</span> <a href="euclid.html#K17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="euclid.html#K17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p4">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="goboard9.html#K2" target="_self">LeftComp</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="goboard9.html#E1:28_1"><i><font color="Green">E30</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1"><i><font color="Green">E32</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2"><i><font color="Green">E33</font></i></a>, <a class="txt" href="goboard9.html#E51:28_1_1_1_2"><i><font color="Green">E71</font></i></a>, <a class="txt" href="goboard9.html#E5:28_1_1_1_2_2_1_7"><i><font color="Green">E78</font></i></a>, <a class="txt" href="goboard9.html#E11:28_1_1_1_2_2_1_7"><i><font color="Green">E82</font></i></a>, <a class="txt" href="goboard9.html#E12:28_1_1_1_2_2_1_7"><i><font color="Green">E83</font></i></a>, <a class="ref" href="goboard9.html#T6" target="_self">Th6</a>, <a class="ref" href="nat_1.html#T38">NAT_1:38</a></i>;<br/><a NAME="E16:28_1_1_1_2_2_1_7"/><i><font color="Green">E85</font></i>: 
 <a href="tops_1.html#K1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K3">cell</a> <span class="p2">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<font color="Maroon">c<sub>5</sub></font>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span></span>)</span> is <a href="connsp_1.html#V2">connected</a>
 <b>by </b><i><a class="txt" href="goboard9.html#E19:28_1_1_1_2"><i><font color="Green">E46</font></i></a>, <a class="txt" href="goboard9.html#E41:28_1_1_1_2"><i><font color="Green">E63</font></i></a>, <a class="ref" href="goboard9.html#T21" target="_self">Th21</a></i>;<br/><a NAME="E17:28_1_1_1_2_2_1_7"/>
<font color="Maroon">c<sub>6</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 1
 <b>by </b><i><a class="txt" href="goboard9.html#E22:28_1_1_1_2"><i><font color="Green">E49</font></i></a>, <a class="txt" href="goboard9.html#E4:28_1_1_1_2_2_1_7"><i><font color="Green">E77</font></i></a>, <a class="ref" href="xxreal_0.html#T1">XXREAL_0:1</a></i>;<br/><a NAME="E18:28_1_1_1_2_2_1_7"/><b>then </b>
1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>6</sub></font> <a href="binarith.html#K5">-'</a> 1
 <b>by </b><i><a class="txt" href="goboard9.html#E39:28_1_1_1_2"><i><font color="Green">E62</font></i></a>, <a class="ref" href="nat_1.html#T38">NAT_1:38</a></i>;<br/><a NAME="E19:28_1_1_1_2_2_1_7"/><b>then </b><i><font color="Green">E86</font></i>: 
 <a href="topreal1.html#K3">LSeg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>5</sub></font>,<span class="p4">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span></span>)</span> <a href="euclid.html#K17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="euclid.html#K17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p4">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xboole_0.html#NR5" target="_self">meets</a>  <a href="tops_1.html#K1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K3">cell</a> <span class="p2">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<font color="Maroon">c<sub>5</sub></font>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="goboard9.html#E19:28_1_1_1_2"><i><font color="Green">E46</font></i></a>, <a class="txt" href="goboard9.html#E22:28_1_1_1_2"><i><font color="Green">E49</font></i></a>, <a class="txt" href="goboard9.html#E24:28_1_1_1_2"><i><font color="Green">E51</font></i></a>, <a class="txt" href="goboard9.html#E39:28_1_1_1_2"><i><font color="Green">E62</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2_2_1_7"><i><font color="Green">E74</font></i></a>, <a class="txt" href="goboard9.html#E9:28_1_1_1_2_2_1_7"><i><font color="Green">E80</font></i></a>, <a class="ref" href="goboard6.html#T85">GOBOARD6:85</a></i>;<br/><a NAME="E20:28_1_1_1_2_2_1_7"/>
 <a href="tops_1.html#K1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K3">cell</a> <span class="p2">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<font color="Maroon">c<sub>5</sub></font>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span></span>)</span> <a href="xboole_0.html#R1">misses</a>  <a href="topreal1.html#K5">L~</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="goboard9.html#E19:28_1_1_1_2"><i><font color="Green">E46</font></i></a>, <a class="txt" href="goboard9.html#E41:28_1_1_1_2"><i><font color="Green">E63</font></i></a>, <a class="ref" href="goboard7.html#T14">GOBOARD7:14</a></i>;<br/><a NAME="E21:28_1_1_1_2_2_1_7"/><b>then </b>
 <a href="tops_1.html#K1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K3">cell</a> <span class="p2">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<font color="Maroon">c<sub>5</sub></font>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span></span>)</span> <a href="tarski.html#R1">c=</a> <span class="p1">(<span class="default"><a href="topreal1.html#K5">L~</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="subset_1.html#K3">`</a> 
 <b>by </b><i><a class="ref" href="subset_1.html#T43">SUBSET_1:43</a></i>;<br/><a NAME="E22:28_1_1_1_2_2_1_7"/><b>then </b><i><font color="Green">E87</font></i>: 
 <a href="tops_1.html#K1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K3">cell</a> <span class="p2">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<font color="Maroon">c<sub>5</sub></font>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="goboard9.html#K2" target="_self">LeftComp</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="goboard9.html#E24:28_1_1_1_2"><i><font color="Green">E51</font></i></a>, <a class="txt" href="goboard9.html#E51:28_1_1_1_2"><i><font color="Green">E71</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2_2_1_7"><i><font color="Green">E74</font></i></a>, <a class="txt" href="goboard9.html#E15:28_1_1_1_2_2_1_7"><i><font color="Green">E84</font></i></a>, <a class="txt" href="goboard9.html#E16:28_1_1_1_2_2_1_7"><i><font color="Green">E85</font></i></a>, <a class="txt" href="goboard9.html#E19:28_1_1_1_2_2_1_7"><i><font color="Green">E86</font></i></a>, <a class="ref" href="goboard9.html#T6" target="_self">Th6</a></i>;<br/><a NAME="E23:28_1_1_1_2_2_1_7"/><i><font color="Green">E88</font></i>: 
 <a href="goboard5.html#K5">left_cell</a> <font color="Maroon">c<sub>1</sub></font>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="hidden.html#R1">=</a>  <a href="goboard5.html#K3">cell</a> <span class="p1">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<font color="Maroon">c<sub>7</sub></font>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span>
 <b>by </b><i><a class="txt" href="goboard9.html#E1:28_1_1"><i><font color="Green">E31</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1"><i><font color="Green">E32</font></i></a>, <a class="txt" href="goboard9.html#E11:28_1_1_1_2"><i><font color="Green">E40</font></i></a>, <a class="txt" href="goboard9.html#E12:28_1_1_1_2"><i><font color="Green">E41</font></i></a>, <a class="txt" href="goboard9.html#E16:28_1_1_1_2"><i><font color="Green">E43</font></i></a>, <a class="txt" href="goboard9.html#E17:28_1_1_1_2"><i><font color="Green">E44</font></i></a>, <a class="txt" href="goboard9.html#E25:28_1_1_1_2"><i><font color="Green">E52</font></i></a>, <a class="txt" href="goboard9.html#E39:28_1_1_1_2"><i><font color="Green">E62</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1_1_2_2_1_7"><i><font color="Green">E75</font></i></a>, <a class="ref" href="goboard5.html#T30">GOBOARD5:30</a></i>;<br/><a NAME="E24:28_1_1_1_2_2_1_7"/><i><font color="Green">E89</font></i>: 
 <a href="topreal1.html#K3">LSeg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>5</sub></font>,<span class="p4">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span></span>)</span> <a href="euclid.html#K17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>7</sub></font>,<span class="p4">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span></span>)</span> <a href="euclid.html#K17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span></span>)</span> is <a href="connsp_1.html#V2">connected</a>
 <b>by </b><i><a class="ref" href="goboard9.html#T8" target="_self">Th8</a></i>;<br/><a NAME="E25:28_1_1_1_2_2_1_7"/><i><font color="Green">E90</font></i>: 
 <a href="topreal1.html#K3">LSeg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>5</sub></font>,<span class="p4">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span></span>)</span> <a href="euclid.html#K17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>7</sub></font>,<span class="p4">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span></span>)</span> <a href="euclid.html#K17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span></span>)</span> <a href="xboole_0.html#NR5" target="_self">meets</a>  <a href="tops_1.html#K1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K3">cell</a> <span class="p2">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<font color="Maroon">c<sub>5</sub></font>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="goboard9.html#E19:28_1_1_1_2"><i><font color="Green">E46</font></i></a>, <a class="txt" href="goboard9.html#E22:28_1_1_1_2"><i><font color="Green">E49</font></i></a>, <a class="txt" href="goboard9.html#E24:28_1_1_1_2"><i><font color="Green">E51</font></i></a>, <a class="txt" href="goboard9.html#E39:28_1_1_1_2"><i><font color="Green">E62</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2_2_1_7"><i><font color="Green">E74</font></i></a>, <a class="txt" href="goboard9.html#E7:28_1_1_1_2_2_1_7"><i><font color="Green">E79</font></i></a>, <a class="txt" href="goboard9.html#E9:28_1_1_1_2_2_1_7"><i><font color="Green">E80</font></i></a>, <a class="ref" href="goboard6.html#T85">GOBOARD6:85</a></i>;<br/><a NAME="E26:28_1_1_1_2_2_1_7"/>
<font color="Maroon">c<sub>5</sub></font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a>  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="goboard9.html#E19:28_1_1_1_2"><i><font color="Green">E46</font></i></a>, <a class="txt" href="goboard9.html#E24:28_1_1_1_2"><i><font color="Green">E51</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2_2_1_7"><i><font color="Green">E74</font></i></a>, <a class="txt" href="goboard9.html#E3:28_1_1_1_2_2_1_7"><i><font color="Green">E76</font></i></a>, <a class="ref" href="xxreal_0.html#T1">XXREAL_0:1</a></i>;<br/><a NAME="E27:28_1_1_1_2_2_1_7"/><b>then </b>
<font color="Maroon">c<sub>5</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> <span class="p1">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>
 <b>by </b><i><a class="ref" href="nat_1.html#T38">NAT_1:38</a></i>;<br/><a NAME="E28:28_1_1_1_2_2_1_7"/><b>then </b>
 <a href="topreal1.html#K3">LSeg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>5</sub></font>,<span class="p4">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span></span>)</span> <a href="euclid.html#K17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>7</sub></font>,<span class="p4">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span></span>)</span> <a href="euclid.html#K17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span></span>)</span> <a href="xboole_0.html#R1">misses</a>  <a href="topreal1.html#K5">L~</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="goboard9.html#E2:28_1_1"><i><font color="Green">E32</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2"><i><font color="Green">E33</font></i></a>, <a class="txt" href="goboard9.html#E8:28_1_1_1_2"><i><font color="Green">E38</font></i></a>, <a class="txt" href="goboard9.html#E12:28_1_1_1_2"><i><font color="Green">E41</font></i></a>, <a class="txt" href="goboard9.html#E17:28_1_1_1_2"><i><font color="Green">E44</font></i></a>, <a class="txt" href="goboard9.html#E20:28_1_1_1_2"><i><font color="Green">E47</font></i></a>, <a class="txt" href="goboard9.html#E21:28_1_1_1_2"><i><font color="Green">E48</font></i></a>, <a class="txt" href="goboard9.html#E24:28_1_1_1_2"><i><font color="Green">E51</font></i></a>, <a class="txt" href="goboard9.html#E25:28_1_1_1_2"><i><font color="Green">E52</font></i></a>, <a class="txt" href="goboard9.html#E39:28_1_1_1_2"><i><font color="Green">E62</font></i></a>, <a class="txt" href="goboard9.html#E46:28_1_1_1_2"><i><font color="Green">E66</font></i></a>, <a class="txt" href="goboard9.html#E48:28_1_1_1_2"><i><font color="Green">E68</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2_2_1_7"><i><font color="Green">E74</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1_1_2_2_1_7"><i><font color="Green">E75</font></i></a>, <a class="txt" href="goboard9.html#E7:28_1_1_1_2_2_1_7"><i><font color="Green">E79</font></i></a>, <a class="txt" href="goboard9.html#E10:28_1_1_1_2_2_1_7"><i><font color="Green">E81</font></i></a>, <a class="ref" href="goboard8.html#T13">GOBOARD8:13</a></i>;<br/><a NAME="E29:28_1_1_1_2_2_1_7"/><b>then </b>
 <a href="topreal1.html#K3">LSeg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>5</sub></font>,<span class="p4">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span></span>)</span> <a href="euclid.html#K17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>7</sub></font>,<span class="p4">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span></span>)</span> <a href="euclid.html#K17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span></span>)</span> <a href="tarski.html#R1">c=</a> <span class="p1">(<span class="default"><a href="topreal1.html#K5">L~</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="subset_1.html#K3">`</a> 
 <b>by </b><i><a class="ref" href="subset_1.html#T43">SUBSET_1:43</a></i>;<br/><a NAME="E30:28_1_1_1_2_2_1_7"/><b>then </b><i><font color="Green">E91</font></i>: 
 <a href="topreal1.html#K3">LSeg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>5</sub></font>,<span class="p4">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span></span>)</span> <a href="euclid.html#K17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>7</sub></font>,<span class="p4">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span></span>)</span> <a href="euclid.html#K17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="goboard9.html#K2" target="_self">LeftComp</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="goboard9.html#E51:28_1_1_1_2"><i><font color="Green">E71</font></i></a>, <a class="txt" href="goboard9.html#E22:28_1_1_1_2_2_1_7"><i><font color="Green">E87</font></i></a>, <a class="txt" href="goboard9.html#E24:28_1_1_1_2_2_1_7"><i><font color="Green">E89</font></i></a>, <a class="txt" href="goboard9.html#E25:28_1_1_1_2_2_1_7"><i><font color="Green">E90</font></i></a>, <a class="ref" href="goboard9.html#T6" target="_self">Th6</a></i>;<br/><a NAME="E31:28_1_1_1_2_2_1_7"/><i><font color="Green">E92</font></i>: 
 <a href="topreal1.html#K3">LSeg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>5</sub></font>,<span class="p4">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span></span>)</span> <a href="euclid.html#K17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>7</sub></font>,<span class="p4">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span></span>)</span> <a href="euclid.html#K17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span></span>)</span> <a href="xboole_0.html#NR5" target="_self">meets</a>  <a href="tops_1.html#K1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K3">cell</a> <span class="p2">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<font color="Maroon">c<sub>7</sub></font>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="goboard9.html#E19:28_1_1_1_2"><i><font color="Green">E46</font></i></a>, <a class="txt" href="goboard9.html#E20:28_1_1_1_2"><i><font color="Green">E47</font></i></a>, <a class="txt" href="goboard9.html#E22:28_1_1_1_2"><i><font color="Green">E49</font></i></a>, <a class="txt" href="goboard9.html#E39:28_1_1_1_2"><i><font color="Green">E62</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1_1_2_2_1_7"><i><font color="Green">E75</font></i></a>, <a class="txt" href="goboard9.html#E7:28_1_1_1_2_2_1_7"><i><font color="Green">E79</font></i></a>, <a class="ref" href="goboard6.html#T85">GOBOARD6:85</a></i>;<br/><a NAME="E32:28_1_1_1_2_2_1_7"/>
 <a href="tops_1.html#K1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K5">left_cell</a> <font color="Maroon">c<sub>1</sub></font>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="xboole_0.html#R1">misses</a>  <a href="topreal1.html#K5">L~</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="goboard9.html#E1:28_1_1"><i><font color="Green">E31</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1"><i><font color="Green">E32</font></i></a>, <a class="ref" href="goboard8.html#T37">GOBOARD8:37</a></i>;<br/><a NAME="E33:28_1_1_1_2_2_1_7"/><b>then </b>
 <a href="tops_1.html#K1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K5">left_cell</a> <font color="Maroon">c<sub>1</sub></font>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="tarski.html#R1">c=</a> <span class="p1">(<span class="default"><a href="topreal1.html#K5">L~</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="subset_1.html#K3">`</a> 
 <b>by </b><i><a class="ref" href="subset_1.html#T43">SUBSET_1:43</a></i>;<br/><b>hence </b><a NAME="E34:28_1_1_1_2_2_1_7"/>
 <a href="tops_1.html#K1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K5">left_cell</a> <font color="Maroon">c<sub>1</sub></font>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="goboard9.html#K2" target="_self">LeftComp</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="goboard9.html#E51:28_1_1_1_2"><i><font color="Green">E71</font></i></a>, <a class="txt" href="goboard9.html#E52:28_1_1_1_2"><i><font color="Green">E72</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1_1_2_2_1_7"><i><font color="Green">E75</font></i></a>, <a class="txt" href="goboard9.html#E23:28_1_1_1_2_2_1_7"><i><font color="Green">E88</font></i></a>, <a class="txt" href="goboard9.html#E30:28_1_1_1_2_2_1_7"><i><font color="Green">E91</font></i></a>, <a class="txt" href="goboard9.html#E31:28_1_1_1_2_2_1_7"><i><font color="Green">E92</font></i></a>, <a class="ref" href="goboard9.html#T6" target="_self">Th6</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="28_1_1_1_2_2_1_8"><b>suppose </b></a><b>that </b><a NAME="E1:28_1_1_1_2_2_1_8"/><i><font color="Green">E74</font></i>: 
<font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>6</sub></font> <a href="nat_1.html#K1">+</a> 1
 <b>and </b><br/><a NAME="E2:28_1_1_1_2_2_1_8"/><i><font color="Green">E75</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
 <b>and </b><br/><a NAME="E3:28_1_1_1_2_2_1_8"/><i><font color="Green">E76</font></i>: 
<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>
 ;<br/><div class="add"><a NAME="E4:28_1_1_1_2_2_1_8"/><i><font color="Green">E77</font></i>: 
 <a href="goboard5.html#K5">left_cell</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a>  <a href="goboard5.html#K3">cell</a> <span class="p1">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p2">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>,<font color="Maroon">c<sub>6</sub></font>
 <b>by </b><i><a class="txt" href="goboard9.html#E1:28_1_1_1_2"><i><font color="Green">E33</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1_1_2"><i><font color="Green">E34</font></i></a>, <a class="txt" href="goboard9.html#E7:28_1_1_1_2"><i><font color="Green">E37</font></i></a>, <a class="txt" href="goboard9.html#E8:28_1_1_1_2"><i><font color="Green">E38</font></i></a>, <a class="txt" href="goboard9.html#E11:28_1_1_1_2"><i><font color="Green">E40</font></i></a>, <a class="txt" href="goboard9.html#E12:28_1_1_1_2"><i><font color="Green">E41</font></i></a>, <a class="txt" href="goboard9.html#E24:28_1_1_1_2"><i><font color="Green">E51</font></i></a>, <a class="txt" href="goboard9.html#E43:28_1_1_1_2"><i><font color="Green">E64</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2_2_1_8"><i><font color="Green">E74</font></i></a>, <a class="txt" href="goboard9.html#E3:28_1_1_1_2_2_1_8"><i><font color="Green">E76</font></i></a>, <a class="ref" href="goboard5.html#T31">GOBOARD5:31</a></i>;<br/><a NAME="E5:28_1_1_1_2_2_1_8"/><i><font color="Green">E78</font></i>: 
 <a href="goboard5.html#K5">left_cell</a> <font color="Maroon">c<sub>1</sub></font>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="hidden.html#R1">=</a>  <a href="goboard5.html#K3">cell</a> <span class="p1">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p2">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>,<font color="Maroon">c<sub>8</sub></font>
 <b>by </b><i><a class="txt" href="goboard9.html#E1:28_1_1"><i><font color="Green">E31</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1"><i><font color="Green">E32</font></i></a>, <a class="txt" href="goboard9.html#E11:28_1_1_1_2"><i><font color="Green">E40</font></i></a>, <a class="txt" href="goboard9.html#E12:28_1_1_1_2"><i><font color="Green">E41</font></i></a>, <a class="txt" href="goboard9.html#E16:28_1_1_1_2"><i><font color="Green">E43</font></i></a>, <a class="txt" href="goboard9.html#E17:28_1_1_1_2"><i><font color="Green">E44</font></i></a>, <a class="txt" href="goboard9.html#E24:28_1_1_1_2"><i><font color="Green">E51</font></i></a>, <a class="txt" href="goboard9.html#E25:28_1_1_1_2"><i><font color="Green">E52</font></i></a>, <a class="txt" href="goboard9.html#E43:28_1_1_1_2"><i><font color="Green">E64</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2_2_1_8"><i><font color="Green">E74</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1_1_2_2_1_8"><i><font color="Green">E75</font></i></a>, <a class="txt" href="goboard9.html#E3:28_1_1_1_2_2_1_8"><i><font color="Green">E76</font></i></a>, <a class="ref" href="goboard5.html#T31">GOBOARD5:31</a></i>;<br/><a NAME="E6:28_1_1_1_2_2_1_8"/><i><font color="Green">E79</font></i>: 
 <a href="topreal1.html#K3">LSeg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p5">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p0">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>,<font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="euclid.html#K17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p5">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p0">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>,<span class="p5">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K17">+</a> <span class="p2"><a href="euclid.html#K23">|[</a><span class="default">1,0</span><a href="euclid.html#K23">]|</a></span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p5">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p0">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>,<span class="p5">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="euclid.html#K17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p5">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p0">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>,<span class="p5">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="nat_1.html#K1">+</a> 2</span>)</span></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K17">+</a> <span class="p2"><a href="euclid.html#K23">|[</a><span class="default">1,0</span><a href="euclid.html#K23">]|</a></span></span>)</span> is <a href="connsp_1.html#V2">connected</a>
 <b>by </b><i><a class="ref" href="goboard9.html#T8" target="_self">Th8</a></i>;<br/><a NAME="E7:28_1_1_1_2_2_1_8"/><i><font color="Green">E80</font></i>: 
 <a href="topreal1.html#K3">LSeg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p5">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p0">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>,<font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="euclid.html#K17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p5">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p0">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>,<span class="p5">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K17">+</a> <span class="p2"><a href="euclid.html#K23">|[</a><span class="default">1,0</span><a href="euclid.html#K23">]|</a></span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p5">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p0">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>,<span class="p5">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="euclid.html#K17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p5">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p0">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>,<span class="p5">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="nat_1.html#K1">+</a> 2</span>)</span></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K17">+</a> <span class="p2"><a href="euclid.html#K23">|[</a><span class="default">1,0</span><a href="euclid.html#K23">]|</a></span></span>)</span> <a href="xboole_0.html#NR5" target="_self">meets</a>  <a href="tops_1.html#K1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K3">cell</a> <span class="p2">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p3">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>,<font color="Maroon">c<sub>6</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="goboard9.html#E21:28_1_1_1_2"><i><font color="Green">E48</font></i></a>, <a class="txt" href="goboard9.html#E22:28_1_1_1_2"><i><font color="Green">E49</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2_2_1_8"><i><font color="Green">E74</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1_1_2_2_1_8"><i><font color="Green">E75</font></i></a>, <a class="ref" href="goboard6.html#T89">GOBOARD6:89</a></i>;<br/><a NAME="E8:28_1_1_1_2_2_1_8"/>
 <a href="topreal1.html#K3">LSeg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p5">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p0">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>,<font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="euclid.html#K17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p5">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p0">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>,<span class="p5">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K17">+</a> <span class="p2"><a href="euclid.html#K23">|[</a><span class="default">1,0</span><a href="euclid.html#K23">]|</a></span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p5">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p0">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>,<span class="p5">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="euclid.html#K17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p5">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p0">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>,<span class="p5">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="nat_1.html#K1">+</a> 2</span>)</span></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K17">+</a> <span class="p2"><a href="euclid.html#K23">|[</a><span class="default">1,0</span><a href="euclid.html#K23">]|</a></span></span>)</span> <a href="xboole_0.html#R1">misses</a>  <a href="topreal1.html#K5">L~</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="goboard9.html#E21:28_1_1_1_2"><i><font color="Green">E48</font></i></a>, <a class="txt" href="goboard9.html#E23:28_1_1_1_2"><i><font color="Green">E50</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2_2_1_8"><i><font color="Green">E74</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1_1_2_2_1_8"><i><font color="Green">E75</font></i></a>, <a class="ref" href="goboard8.html#T34">GOBOARD8:34</a></i>;<br/><a NAME="E9:28_1_1_1_2_2_1_8"/><b>then </b>
 <a href="topreal1.html#K3">LSeg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p5">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p0">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>,<font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="euclid.html#K17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p5">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p0">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>,<span class="p5">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K17">+</a> <span class="p2"><a href="euclid.html#K23">|[</a><span class="default">1,0</span><a href="euclid.html#K23">]|</a></span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p5">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p0">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>,<span class="p5">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="euclid.html#K17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p5">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p0">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>,<span class="p5">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="nat_1.html#K1">+</a> 2</span>)</span></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K17">+</a> <span class="p2"><a href="euclid.html#K23">|[</a><span class="default">1,0</span><a href="euclid.html#K23">]|</a></span></span>)</span> <a href="tarski.html#R1">c=</a> <span class="p1">(<span class="default"><a href="topreal1.html#K5">L~</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="subset_1.html#K3">`</a> 
 <b>by </b><i><a class="ref" href="subset_1.html#T43">SUBSET_1:43</a></i>;<br/><a NAME="E10:28_1_1_1_2_2_1_8"/><b>then </b><i><font color="Green">E81</font></i>: 
 <a href="topreal1.html#K3">LSeg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p5">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p0">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>,<font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="euclid.html#K17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p5">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p0">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>,<span class="p5">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K17">+</a> <span class="p2"><a href="euclid.html#K23">|[</a><span class="default">1,0</span><a href="euclid.html#K23">]|</a></span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p5">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p0">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>,<span class="p5">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="euclid.html#K17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p5">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p0">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>,<span class="p5">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="nat_1.html#K1">+</a> 2</span>)</span></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K17">+</a> <span class="p2"><a href="euclid.html#K23">|[</a><span class="default">1,0</span><a href="euclid.html#K23">]|</a></span></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="goboard9.html#K2" target="_self">LeftComp</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="goboard9.html#E1:28_1"><i><font color="Green">E30</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1"><i><font color="Green">E32</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2"><i><font color="Green">E33</font></i></a>, <a class="txt" href="goboard9.html#E51:28_1_1_1_2"><i><font color="Green">E71</font></i></a>, <a class="txt" href="goboard9.html#E4:28_1_1_1_2_2_1_8"><i><font color="Green">E77</font></i></a>, <a class="txt" href="goboard9.html#E6:28_1_1_1_2_2_1_8"><i><font color="Green">E79</font></i></a>, <a class="txt" href="goboard9.html#E7:28_1_1_1_2_2_1_8"><i><font color="Green">E80</font></i></a>, <a class="ref" href="goboard9.html#T6" target="_self">Th6</a>, <a class="ref" href="nat_1.html#T38">NAT_1:38</a></i>;<br/><a NAME="E11:28_1_1_1_2_2_1_8"/><i><font color="Green">E82</font></i>: 
 <a href="topreal1.html#K3">LSeg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p5">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p0">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>,<font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="euclid.html#K17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p5">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p0">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>,<span class="p5">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K17">+</a> <span class="p2"><a href="euclid.html#K23">|[</a><span class="default">1,0</span><a href="euclid.html#K23">]|</a></span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p5">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p0">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>,<span class="p5">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="euclid.html#K17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p5">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p0">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>,<span class="p5">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="nat_1.html#K1">+</a> 2</span>)</span></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K17">+</a> <span class="p2"><a href="euclid.html#K23">|[</a><span class="default">1,0</span><a href="euclid.html#K23">]|</a></span></span>)</span> <a href="xboole_0.html#NR5" target="_self">meets</a>  <a href="tops_1.html#K1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K3">cell</a> <span class="p2">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>8</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="goboard9.html#E22:28_1_1_1_2"><i><font color="Green">E49</font></i></a>, <a class="txt" href="goboard9.html#E23:28_1_1_1_2"><i><font color="Green">E50</font></i></a>, <a class="txt" href="goboard9.html#E24:28_1_1_1_2"><i><font color="Green">E51</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2_2_1_8"><i><font color="Green">E74</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1_1_2_2_1_8"><i><font color="Green">E75</font></i></a>, <a class="txt" href="goboard9.html#E3:28_1_1_1_2_2_1_8"><i><font color="Green">E76</font></i></a>, <a class="ref" href="goboard6.html#T89">GOBOARD6:89</a></i>;<br/><a NAME="E12:28_1_1_1_2_2_1_8"/>
 <a href="tops_1.html#K1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K5">left_cell</a> <font color="Maroon">c<sub>1</sub></font>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="xboole_0.html#R1">misses</a>  <a href="topreal1.html#K5">L~</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="goboard9.html#E1:28_1_1"><i><font color="Green">E31</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1"><i><font color="Green">E32</font></i></a>, <a class="ref" href="goboard8.html#T37">GOBOARD8:37</a></i>;<br/><a NAME="E13:28_1_1_1_2_2_1_8"/><b>then </b>
 <a href="tops_1.html#K1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K5">left_cell</a> <font color="Maroon">c<sub>1</sub></font>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="tarski.html#R1">c=</a> <span class="p1">(<span class="default"><a href="topreal1.html#K5">L~</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="subset_1.html#K3">`</a> 
 <b>by </b><i><a class="ref" href="subset_1.html#T43">SUBSET_1:43</a></i>;<br/><b>hence </b><a NAME="E14:28_1_1_1_2_2_1_8"/>
 <a href="tops_1.html#K1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K5">left_cell</a> <font color="Maroon">c<sub>1</sub></font>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="goboard9.html#K2" target="_self">LeftComp</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="goboard9.html#E24:28_1_1_1_2"><i><font color="Green">E51</font></i></a>, <a class="txt" href="goboard9.html#E51:28_1_1_1_2"><i><font color="Green">E71</font></i></a>, <a class="txt" href="goboard9.html#E52:28_1_1_1_2"><i><font color="Green">E72</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2_2_1_8"><i><font color="Green">E74</font></i></a>, <a class="txt" href="goboard9.html#E3:28_1_1_1_2_2_1_8"><i><font color="Green">E76</font></i></a>, <a class="txt" href="goboard9.html#E5:28_1_1_1_2_2_1_8"><i><font color="Green">E78</font></i></a>, <a class="txt" href="goboard9.html#E10:28_1_1_1_2_2_1_8"><i><font color="Green">E81</font></i></a>, <a class="txt" href="goboard9.html#E11:28_1_1_1_2_2_1_8"><i><font color="Green">E82</font></i></a>, <a class="ref" href="goboard9.html#T6" target="_self">Th6</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="28_1_1_1_2_2_1_9"><b>suppose </b></a><b>that </b><a NAME="E1:28_1_1_1_2_2_1_9"/><i><font color="Green">E74</font></i>: 
<font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>6</sub></font> <a href="nat_1.html#K1">+</a> 1
 <b>and </b><br/><a NAME="E2:28_1_1_1_2_2_1_9"/><i><font color="Green">E75</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
 <b>and </b><br/><a NAME="E3:28_1_1_1_2_2_1_9"/><i><font color="Green">E76</font></i>: 
<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>
 ;<br/><div class="add"><a NAME="E4:28_1_1_1_2_2_1_9"/><i><font color="Green">E77</font></i>: 
 <a href="goboard5.html#K5">left_cell</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a>  <a href="goboard5.html#K3">cell</a> <span class="p1">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>6</sub></font>
 <b>by </b><i><a class="txt" href="goboard9.html#E1:28_1_1_1_2"><i><font color="Green">E33</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1_1_2"><i><font color="Green">E34</font></i></a>, <a class="txt" href="goboard9.html#E7:28_1_1_1_2"><i><font color="Green">E37</font></i></a>, <a class="txt" href="goboard9.html#E8:28_1_1_1_2"><i><font color="Green">E38</font></i></a>, <a class="txt" href="goboard9.html#E11:28_1_1_1_2"><i><font color="Green">E40</font></i></a>, <a class="txt" href="goboard9.html#E12:28_1_1_1_2"><i><font color="Green">E41</font></i></a>, <a class="txt" href="goboard9.html#E24:28_1_1_1_2"><i><font color="Green">E51</font></i></a>, <a class="txt" href="goboard9.html#E37:28_1_1_1_2"><i><font color="Green">E61</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2_2_1_9"><i><font color="Green">E74</font></i></a>, <a class="ref" href="goboard5.html#T31">GOBOARD5:31</a></i>;<br/><a NAME="E5:28_1_1_1_2_2_1_9"/>
 <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> <font color="Maroon">c<sub>3</sub></font>
 <b>by </b><i><a class="txt" href="goboard9.html#E18:28_1_1_1_2"><i><font color="Green">E45</font></i></a>, <a class="txt" href="goboard9.html#E3:28_1_1_1_2_2_1_9"><i><font color="Green">E76</font></i></a>, <a class="ref" href="xxreal_0.html#T1">XXREAL_0:1</a></i>;<br/><a NAME="E6:28_1_1_1_2_2_1_9"/><b>then </b><i><font color="Green">E78</font></i>: 
 <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <font color="Maroon">c<sub>3</sub></font> <a href="nat_1.html#K1">+</a> 1
 <b>by </b><i><a class="ref" href="nat_1.html#T38">NAT_1:38</a></i>;<br/><a NAME="E7:28_1_1_1_2_2_1_9"/><i><font color="Green">E79</font></i>: 
 <a href="goboard5.html#K5">left_cell</a> <font color="Maroon">c<sub>1</sub></font>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="hidden.html#R1">=</a>  <a href="goboard5.html#K3">cell</a> <span class="p1">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>8</sub></font>
 <b>by </b><i><a class="txt" href="goboard9.html#E1:28_1_1"><i><font color="Green">E31</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1"><i><font color="Green">E32</font></i></a>, <a class="txt" href="goboard9.html#E11:28_1_1_1_2"><i><font color="Green">E40</font></i></a>, <a class="txt" href="goboard9.html#E12:28_1_1_1_2"><i><font color="Green">E41</font></i></a>, <a class="txt" href="goboard9.html#E16:28_1_1_1_2"><i><font color="Green">E43</font></i></a>, <a class="txt" href="goboard9.html#E17:28_1_1_1_2"><i><font color="Green">E44</font></i></a>, <a class="txt" href="goboard9.html#E25:28_1_1_1_2"><i><font color="Green">E52</font></i></a>, <a class="txt" href="goboard9.html#E37:28_1_1_1_2"><i><font color="Green">E61</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1_1_2_2_1_9"><i><font color="Green">E75</font></i></a>, <a class="ref" href="goboard5.html#T31">GOBOARD5:31</a></i>;<br/><a NAME="E8:28_1_1_1_2_2_1_9"/><i><font color="Green">E80</font></i>: 
 <a href="topreal1.html#K3">LSeg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="euclid.html#K17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p4">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>5</sub></font>,<span class="p4">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="euclid.html#K17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p4">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="nat_1.html#K1">+</a> 2</span>)</span></span>)</span></span>)</span></span>)</span> is <a href="connsp_1.html#V2">connected</a>
 <b>by </b><i><a class="ref" href="goboard9.html#T8" target="_self">Th8</a></i>;<br/><a NAME="E9:28_1_1_1_2_2_1_9"/><i><font color="Green">E81</font></i>: 
 <a href="topreal1.html#K3">LSeg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="euclid.html#K17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p4">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>5</sub></font>,<span class="p4">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="euclid.html#K17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p4">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="nat_1.html#K1">+</a> 2</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xboole_0.html#NR5" target="_self">meets</a>  <a href="tops_1.html#K1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K3">cell</a> <span class="p2">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="goboard9.html#E19:28_1_1_1_2"><i><font color="Green">E46</font></i></a>, <a class="txt" href="goboard9.html#E21:28_1_1_1_2"><i><font color="Green">E48</font></i></a>, <a class="txt" href="goboard9.html#E22:28_1_1_1_2"><i><font color="Green">E49</font></i></a>, <a class="txt" href="goboard9.html#E24:28_1_1_1_2"><i><font color="Green">E51</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2_2_1_9"><i><font color="Green">E74</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1_1_2_2_1_9"><i><font color="Green">E75</font></i></a>, <a class="txt" href="goboard9.html#E6:28_1_1_1_2_2_1_9"><i><font color="Green">E78</font></i></a>, <a class="ref" href="goboard6.html#T85">GOBOARD6:85</a></i>;<br/><a NAME="E10:28_1_1_1_2_2_1_9"/>
 <a href="topreal1.html#K3">LSeg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="euclid.html#K17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p4">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>5</sub></font>,<span class="p4">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="euclid.html#K17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p4">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="nat_1.html#K1">+</a> 2</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xboole_0.html#R1">misses</a>  <a href="topreal1.html#K5">L~</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="goboard9.html#E2:28_1_1"><i><font color="Green">E32</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2"><i><font color="Green">E33</font></i></a>, <a class="txt" href="goboard9.html#E8:28_1_1_1_2"><i><font color="Green">E38</font></i></a>, <a class="txt" href="goboard9.html#E12:28_1_1_1_2"><i><font color="Green">E41</font></i></a>, <a class="txt" href="goboard9.html#E17:28_1_1_1_2"><i><font color="Green">E44</font></i></a>, <a class="txt" href="goboard9.html#E18:28_1_1_1_2"><i><font color="Green">E45</font></i></a>, <a class="txt" href="goboard9.html#E21:28_1_1_1_2"><i><font color="Green">E48</font></i></a>, <a class="txt" href="goboard9.html#E23:28_1_1_1_2"><i><font color="Green">E50</font></i></a>, <a class="txt" href="goboard9.html#E24:28_1_1_1_2"><i><font color="Green">E51</font></i></a>, <a class="txt" href="goboard9.html#E25:28_1_1_1_2"><i><font color="Green">E52</font></i></a>, <a class="txt" href="goboard9.html#E46:28_1_1_1_2"><i><font color="Green">E66</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2_2_1_9"><i><font color="Green">E74</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1_1_2_2_1_9"><i><font color="Green">E75</font></i></a>, <a class="txt" href="goboard9.html#E6:28_1_1_1_2_2_1_9"><i><font color="Green">E78</font></i></a>, <a class="ref" href="goboard8.html#T4">GOBOARD8:4</a></i>;<br/><a NAME="E11:28_1_1_1_2_2_1_9"/><b>then </b>
 <a href="topreal1.html#K3">LSeg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="euclid.html#K17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p4">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>5</sub></font>,<span class="p4">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="euclid.html#K17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p4">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="nat_1.html#K1">+</a> 2</span>)</span></span>)</span></span>)</span></span>)</span> <a href="tarski.html#R1">c=</a> <span class="p1">(<span class="default"><a href="topreal1.html#K5">L~</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="subset_1.html#K3">`</a> 
 <b>by </b><i><a class="ref" href="subset_1.html#T43">SUBSET_1:43</a></i>;<br/><a NAME="E12:28_1_1_1_2_2_1_9"/><b>then </b><i><font color="Green">E82</font></i>: 
 <a href="topreal1.html#K3">LSeg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="euclid.html#K17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p4">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>5</sub></font>,<span class="p4">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="euclid.html#K17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p4">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="nat_1.html#K1">+</a> 2</span>)</span></span>)</span></span>)</span></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="goboard9.html#K2" target="_self">LeftComp</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="goboard9.html#E1:28_1"><i><font color="Green">E30</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1"><i><font color="Green">E32</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2"><i><font color="Green">E33</font></i></a>, <a class="txt" href="goboard9.html#E51:28_1_1_1_2"><i><font color="Green">E71</font></i></a>, <a class="txt" href="goboard9.html#E4:28_1_1_1_2_2_1_9"><i><font color="Green">E77</font></i></a>, <a class="txt" href="goboard9.html#E8:28_1_1_1_2_2_1_9"><i><font color="Green">E80</font></i></a>, <a class="txt" href="goboard9.html#E9:28_1_1_1_2_2_1_9"><i><font color="Green">E81</font></i></a>, <a class="ref" href="goboard9.html#T6" target="_self">Th6</a>, <a class="ref" href="nat_1.html#T38">NAT_1:38</a></i>;<br/><a NAME="E13:28_1_1_1_2_2_1_9"/><i><font color="Green">E83</font></i>: 
 <a href="topreal1.html#K3">LSeg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="euclid.html#K17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p4">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>5</sub></font>,<span class="p4">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="euclid.html#K17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p4">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="nat_1.html#K1">+</a> 2</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xboole_0.html#NR5" target="_self">meets</a>  <a href="tops_1.html#K1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K3">cell</a> <span class="p2">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>8</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="goboard9.html#E19:28_1_1_1_2"><i><font color="Green">E46</font></i></a>, <a class="txt" href="goboard9.html#E22:28_1_1_1_2"><i><font color="Green">E49</font></i></a>, <a class="txt" href="goboard9.html#E23:28_1_1_1_2"><i><font color="Green">E50</font></i></a>, <a class="txt" href="goboard9.html#E24:28_1_1_1_2"><i><font color="Green">E51</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2_2_1_9"><i><font color="Green">E74</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1_1_2_2_1_9"><i><font color="Green">E75</font></i></a>, <a class="txt" href="goboard9.html#E6:28_1_1_1_2_2_1_9"><i><font color="Green">E78</font></i></a>, <a class="ref" href="goboard6.html#T85">GOBOARD6:85</a></i>;<br/><a NAME="E14:28_1_1_1_2_2_1_9"/>
 <a href="tops_1.html#K1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K5">left_cell</a> <font color="Maroon">c<sub>1</sub></font>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="xboole_0.html#R1">misses</a>  <a href="topreal1.html#K5">L~</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="goboard9.html#E1:28_1_1"><i><font color="Green">E31</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1"><i><font color="Green">E32</font></i></a>, <a class="ref" href="goboard8.html#T37">GOBOARD8:37</a></i>;<br/><a NAME="E15:28_1_1_1_2_2_1_9"/><b>then </b>
 <a href="tops_1.html#K1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K5">left_cell</a> <font color="Maroon">c<sub>1</sub></font>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="tarski.html#R1">c=</a> <span class="p1">(<span class="default"><a href="topreal1.html#K5">L~</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="subset_1.html#K3">`</a> 
 <b>by </b><i><a class="ref" href="subset_1.html#T43">SUBSET_1:43</a></i>;<br/><b>hence </b><a NAME="E16:28_1_1_1_2_2_1_9"/>
 <a href="tops_1.html#K1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K5">left_cell</a> <font color="Maroon">c<sub>1</sub></font>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="goboard9.html#K2" target="_self">LeftComp</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="goboard9.html#E51:28_1_1_1_2"><i><font color="Green">E71</font></i></a>, <a class="txt" href="goboard9.html#E52:28_1_1_1_2"><i><font color="Green">E72</font></i></a>, <a class="txt" href="goboard9.html#E7:28_1_1_1_2_2_1_9"><i><font color="Green">E79</font></i></a>, <a class="txt" href="goboard9.html#E12:28_1_1_1_2_2_1_9"><i><font color="Green">E82</font></i></a>, <a class="txt" href="goboard9.html#E13:28_1_1_1_2_2_1_9"><i><font color="Green">E83</font></i></a>, <a class="ref" href="goboard9.html#T6" target="_self">Th6</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="28_1_1_1_2_2_1_10"><b>suppose </b></a><b>that </b><a NAME="E1:28_1_1_1_2_2_1_10"/><i><font color="Green">E74</font></i>: 
<font color="Maroon">c<sub>3</sub></font> <a href="nat_1.html#K1">+</a> 1 <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>5</sub></font>
 <b>and </b><br/><a NAME="E2:28_1_1_1_2_2_1_10"/><i><font color="Green">E75</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
 <b>and </b><br/><a NAME="E3:28_1_1_1_2_2_1_10"/><i><font color="Green">E76</font></i>: 
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>
 <b>and </b><br/><a NAME="E4:28_1_1_1_2_2_1_10"/><i><font color="Green">E77</font></i>: 
<font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a>  <a href="matrix_1.html#K1">width</a> <span class="p1">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>
 ;<br/><div class="add"><a NAME="E5:28_1_1_1_2_2_1_10"/><i><font color="Green">E78</font></i>: 
 <a href="goboard5.html#K5">left_cell</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a>  <a href="goboard5.html#K3">cell</a> <span class="p1">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>6</sub></font>
 <b>by </b><i><a class="txt" href="goboard9.html#E1:28_1_1_1_2"><i><font color="Green">E33</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1_1_2"><i><font color="Green">E34</font></i></a>, <a class="txt" href="goboard9.html#E7:28_1_1_1_2"><i><font color="Green">E37</font></i></a>, <a class="txt" href="goboard9.html#E8:28_1_1_1_2"><i><font color="Green">E38</font></i></a>, <a class="txt" href="goboard9.html#E11:28_1_1_1_2"><i><font color="Green">E40</font></i></a>, <a class="txt" href="goboard9.html#E12:28_1_1_1_2"><i><font color="Green">E41</font></i></a>, <a class="txt" href="goboard9.html#E24:28_1_1_1_2"><i><font color="Green">E51</font></i></a>, <a class="txt" href="goboard9.html#E39:28_1_1_1_2"><i><font color="Green">E62</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2_2_1_10"><i><font color="Green">E74</font></i></a>, <a class="ref" href="goboard5.html#T29">GOBOARD5:29</a></i>;<br/><a NAME="E6:28_1_1_1_2_2_1_10"/><i><font color="Green">E79</font></i>: 
<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>5</sub></font> <a href="binarith.html#K5">-'</a> 1
 <b>by </b><i><a class="txt" href="goboard9.html#E43:28_1_1_1_2"><i><font color="Green">E64</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2_2_1_10"><i><font color="Green">E74</font></i></a>, <a class="txt" href="goboard9.html#E3:28_1_1_1_2_2_1_10"><i><font color="Green">E76</font></i></a></i>;<br/><a NAME="E7:28_1_1_1_2_2_1_10"/><i><font color="Green">E80</font></i>: 
 <a href="topreal1.html#K3">LSeg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="euclid.html#K17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K17">+</a> <span class="p2"><a href="euclid.html#K23">|[</a><span class="default">0,1</span><a href="euclid.html#K23">]|</a></span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="euclid.html#K17">+</a> <span class="p2"><a href="euclid.html#K23">|[</a><span class="default">1,1</span><a href="euclid.html#K23">]|</a></span></span>)</span> is <a href="connsp_1.html#V2">connected</a>
 <b>by </b><i><a class="ref" href="goboard9.html#T8" target="_self">Th8</a></i>;<br/><a NAME="E8:28_1_1_1_2_2_1_10"/><i><font color="Green">E81</font></i>: 
 <a href="topreal1.html#K3">LSeg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="euclid.html#K17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K17">+</a> <span class="p2"><a href="euclid.html#K23">|[</a><span class="default">0,1</span><a href="euclid.html#K23">]|</a></span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="euclid.html#K17">+</a> <span class="p2"><a href="euclid.html#K23">|[</a><span class="default">1,1</span><a href="euclid.html#K23">]|</a></span></span>)</span> <a href="xboole_0.html#NR5" target="_self">meets</a>  <a href="tops_1.html#K1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K3">cell</a> <span class="p2">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="goboard9.html#E18:28_1_1_1_2"><i><font color="Green">E45</font></i></a>, <a class="txt" href="goboard9.html#E19:28_1_1_1_2"><i><font color="Green">E46</font></i></a>, <a class="txt" href="goboard9.html#E24:28_1_1_1_2"><i><font color="Green">E51</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2_2_1_10"><i><font color="Green">E74</font></i></a>, <a class="txt" href="goboard9.html#E4:28_1_1_1_2_2_1_10"><i><font color="Green">E77</font></i></a>, <a class="ref" href="goboard6.html#T86">GOBOARD6:86</a></i>;<br/><a NAME="E9:28_1_1_1_2_2_1_10"/>
 <a href="topreal1.html#K3">LSeg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="euclid.html#K17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K17">+</a> <span class="p2"><a href="euclid.html#K23">|[</a><span class="default">0,1</span><a href="euclid.html#K23">]|</a></span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="euclid.html#K17">+</a> <span class="p2"><a href="euclid.html#K23">|[</a><span class="default">1,1</span><a href="euclid.html#K23">]|</a></span></span>)</span> <a href="xboole_0.html#R1">misses</a>  <a href="topreal1.html#K5">L~</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="goboard9.html#E3:28_1_1_1_2_2_1_10"><i><font color="Green">E76</font></i></a>, <a class="txt" href="goboard9.html#E4:28_1_1_1_2_2_1_10"><i><font color="Green">E77</font></i></a>, <a class="txt" href="goboard9.html#E6:28_1_1_1_2_2_1_10"><i><font color="Green">E79</font></i></a>, <a class="ref" href="goboard8.html#T30">GOBOARD8:30</a></i>;<br/><a NAME="E10:28_1_1_1_2_2_1_10"/><b>then </b>
 <a href="topreal1.html#K3">LSeg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="euclid.html#K17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K17">+</a> <span class="p2"><a href="euclid.html#K23">|[</a><span class="default">0,1</span><a href="euclid.html#K23">]|</a></span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="euclid.html#K17">+</a> <span class="p2"><a href="euclid.html#K23">|[</a><span class="default">1,1</span><a href="euclid.html#K23">]|</a></span></span>)</span> <a href="tarski.html#R1">c=</a> <span class="p1">(<span class="default"><a href="topreal1.html#K5">L~</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="subset_1.html#K3">`</a> 
 <b>by </b><i><a class="ref" href="subset_1.html#T43">SUBSET_1:43</a></i>;<br/><a NAME="E11:28_1_1_1_2_2_1_10"/><b>then </b><i><font color="Green">E82</font></i>: 
 <a href="topreal1.html#K3">LSeg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="euclid.html#K17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K17">+</a> <span class="p2"><a href="euclid.html#K23">|[</a><span class="default">0,1</span><a href="euclid.html#K23">]|</a></span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="euclid.html#K17">+</a> <span class="p2"><a href="euclid.html#K23">|[</a><span class="default">1,1</span><a href="euclid.html#K23">]|</a></span></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="goboard9.html#K2" target="_self">LeftComp</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="goboard9.html#E1:28_1"><i><font color="Green">E30</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1"><i><font color="Green">E32</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2"><i><font color="Green">E33</font></i></a>, <a class="txt" href="goboard9.html#E51:28_1_1_1_2"><i><font color="Green">E71</font></i></a>, <a class="txt" href="goboard9.html#E5:28_1_1_1_2_2_1_10"><i><font color="Green">E78</font></i></a>, <a class="txt" href="goboard9.html#E7:28_1_1_1_2_2_1_10"><i><font color="Green">E80</font></i></a>, <a class="txt" href="goboard9.html#E8:28_1_1_1_2_2_1_10"><i><font color="Green">E81</font></i></a>, <a class="ref" href="goboard9.html#T6" target="_self">Th6</a>, <a class="ref" href="nat_1.html#T38">NAT_1:38</a></i>;<br/><a NAME="E12:28_1_1_1_2_2_1_10"/><i><font color="Green">E83</font></i>: 
 <a href="tops_1.html#K1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K3">cell</a> <span class="p2">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span> is <a href="connsp_1.html#V2">connected</a>
 <b>by </b><i><a class="txt" href="goboard9.html#E19:28_1_1_1_2"><i><font color="Green">E46</font></i></a>, <a class="txt" href="goboard9.html#E22:28_1_1_1_2"><i><font color="Green">E49</font></i></a>, <a class="ref" href="goboard9.html#T21" target="_self">Th21</a></i>;<br/><a NAME="E13:28_1_1_1_2_2_1_10"/><i><font color="Green">E84</font></i>: 
 <a href="topreal1.html#K3">LSeg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="euclid.html#K17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K17">+</a> <span class="p2"><a href="euclid.html#K23">|[</a><span class="default">0,1</span><a href="euclid.html#K23">]|</a></span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="euclid.html#K17">+</a> <span class="p2"><a href="euclid.html#K23">|[</a><span class="default">1,1</span><a href="euclid.html#K23">]|</a></span></span>)</span> <a href="xboole_0.html#NR5" target="_self">meets</a>  <a href="tops_1.html#K1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K3">cell</a> <span class="p2">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="goboard9.html#E24:28_1_1_1_2"><i><font color="Green">E51</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2_2_1_10"><i><font color="Green">E74</font></i></a>, <a class="txt" href="goboard9.html#E3:28_1_1_1_2_2_1_10"><i><font color="Green">E76</font></i></a>, <a class="txt" href="goboard9.html#E4:28_1_1_1_2_2_1_10"><i><font color="Green">E77</font></i></a>, <a class="ref" href="goboard6.html#T91">GOBOARD6:91</a></i>;<br/><a NAME="E14:28_1_1_1_2_2_1_10"/>
 <a href="tops_1.html#K1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K3">cell</a> <span class="p2">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="xboole_0.html#R1">misses</a>  <a href="topreal1.html#K5">L~</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="goboard9.html#E19:28_1_1_1_2"><i><font color="Green">E46</font></i></a>, <a class="txt" href="goboard9.html#E22:28_1_1_1_2"><i><font color="Green">E49</font></i></a>, <a class="ref" href="goboard7.html#T14">GOBOARD7:14</a></i>;<br/><a NAME="E15:28_1_1_1_2_2_1_10"/><b>then </b>
 <a href="tops_1.html#K1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K3">cell</a> <span class="p2">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="tarski.html#R1">c=</a> <span class="p1">(<span class="default"><a href="topreal1.html#K5">L~</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="subset_1.html#K3">`</a> 
 <b>by </b><i><a class="ref" href="subset_1.html#T43">SUBSET_1:43</a></i>;<br/><a NAME="E16:28_1_1_1_2_2_1_10"/><b>then </b><i><font color="Green">E85</font></i>: 
 <a href="tops_1.html#K1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K3">cell</a> <span class="p2">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="goboard9.html#K2" target="_self">LeftComp</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="goboard9.html#E51:28_1_1_1_2"><i><font color="Green">E71</font></i></a>, <a class="txt" href="goboard9.html#E11:28_1_1_1_2_2_1_10"><i><font color="Green">E82</font></i></a>, <a class="txt" href="goboard9.html#E12:28_1_1_1_2_2_1_10"><i><font color="Green">E83</font></i></a>, <a class="txt" href="goboard9.html#E13:28_1_1_1_2_2_1_10"><i><font color="Green">E84</font></i></a>, <a class="ref" href="goboard9.html#T6" target="_self">Th6</a></i>;<br/><a NAME="E17:28_1_1_1_2_2_1_10"/><i><font color="Green">E86</font></i>: 
 <a href="goboard5.html#K5">left_cell</a> <font color="Maroon">c<sub>1</sub></font>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="hidden.html#R1">=</a>  <a href="goboard5.html#K3">cell</a> <span class="p1">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>8</sub></font>
 <b>by </b><i><a class="txt" href="goboard9.html#E1:28_1_1"><i><font color="Green">E31</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1"><i><font color="Green">E32</font></i></a>, <a class="txt" href="goboard9.html#E11:28_1_1_1_2"><i><font color="Green">E40</font></i></a>, <a class="txt" href="goboard9.html#E12:28_1_1_1_2"><i><font color="Green">E41</font></i></a>, <a class="txt" href="goboard9.html#E16:28_1_1_1_2"><i><font color="Green">E43</font></i></a>, <a class="txt" href="goboard9.html#E17:28_1_1_1_2"><i><font color="Green">E44</font></i></a>, <a class="txt" href="goboard9.html#E25:28_1_1_1_2"><i><font color="Green">E52</font></i></a>, <a class="txt" href="goboard9.html#E37:28_1_1_1_2"><i><font color="Green">E61</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1_1_2_2_1_10"><i><font color="Green">E75</font></i></a>, <a class="ref" href="goboard5.html#T31">GOBOARD5:31</a></i>;<br/><a NAME="E18:28_1_1_1_2_2_1_10"/><i><font color="Green">E87</font></i>: 
 <a href="topreal1.html#K3">LSeg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="euclid.html#K17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K17">+</a> <span class="p2"><a href="euclid.html#K23">|[</a><span class="default">1,0</span><a href="euclid.html#K23">]|</a></span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="euclid.html#K17">+</a> <span class="p2"><a href="euclid.html#K23">|[</a><span class="default">1,1</span><a href="euclid.html#K23">]|</a></span></span>)</span> is <a href="connsp_1.html#V2">connected</a>
 <b>by </b><i><a class="ref" href="goboard9.html#T8" target="_self">Th8</a></i>;<br/><a NAME="E19:28_1_1_1_2_2_1_10"/><i><font color="Green">E88</font></i>: 
<font color="Maroon">c<sub>8</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>6</sub></font> <a href="binarith.html#K5">-'</a> 1
 <b>by </b><i><a class="txt" href="goboard9.html#E24:28_1_1_1_2"><i><font color="Green">E51</font></i></a>, <a class="txt" href="goboard9.html#E45:28_1_1_1_2"><i><font color="Green">E65</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2_2_1_10"><i><font color="Green">E74</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1_1_2_2_1_10"><i><font color="Green">E75</font></i></a>, <a class="txt" href="goboard9.html#E4:28_1_1_1_2_2_1_10"><i><font color="Green">E77</font></i></a></i>;<br/><a NAME="E20:28_1_1_1_2_2_1_10"/><i><font color="Green">E89</font></i>: 
 <a href="topreal1.html#K3">LSeg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="euclid.html#K17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K17">+</a> <span class="p2"><a href="euclid.html#K23">|[</a><span class="default">1,0</span><a href="euclid.html#K23">]|</a></span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="euclid.html#K17">+</a> <span class="p2"><a href="euclid.html#K23">|[</a><span class="default">1,1</span><a href="euclid.html#K23">]|</a></span></span>)</span> <a href="xboole_0.html#NR5" target="_self">meets</a>  <a href="tops_1.html#K1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K3">cell</a> <span class="p2">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="goboard9.html#E24:28_1_1_1_2"><i><font color="Green">E51</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2_2_1_10"><i><font color="Green">E74</font></i></a>, <a class="txt" href="goboard9.html#E3:28_1_1_1_2_2_1_10"><i><font color="Green">E76</font></i></a>, <a class="txt" href="goboard9.html#E4:28_1_1_1_2_2_1_10"><i><font color="Green">E77</font></i></a>, <a class="ref" href="goboard6.html#T91">GOBOARD6:91</a></i>;<br/><a NAME="E21:28_1_1_1_2_2_1_10"/>
 <a href="topreal1.html#K3">LSeg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="euclid.html#K17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K17">+</a> <span class="p2"><a href="euclid.html#K23">|[</a><span class="default">1,0</span><a href="euclid.html#K23">]|</a></span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="euclid.html#K17">+</a> <span class="p2"><a href="euclid.html#K23">|[</a><span class="default">1,1</span><a href="euclid.html#K23">]|</a></span></span>)</span> <a href="xboole_0.html#R1">misses</a>  <a href="topreal1.html#K5">L~</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="goboard9.html#E24:28_1_1_1_2"><i><font color="Green">E51</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2_2_1_10"><i><font color="Green">E74</font></i></a>, <a class="txt" href="goboard9.html#E3:28_1_1_1_2_2_1_10"><i><font color="Green">E76</font></i></a>, <a class="txt" href="goboard9.html#E4:28_1_1_1_2_2_1_10"><i><font color="Green">E77</font></i></a>, <a class="txt" href="goboard9.html#E19:28_1_1_1_2_2_1_10"><i><font color="Green">E88</font></i></a>, <a class="ref" href="goboard8.html#T36">GOBOARD8:36</a></i>;<br/><a NAME="E22:28_1_1_1_2_2_1_10"/><b>then </b>
 <a href="topreal1.html#K3">LSeg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="euclid.html#K17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K17">+</a> <span class="p2"><a href="euclid.html#K23">|[</a><span class="default">1,0</span><a href="euclid.html#K23">]|</a></span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="euclid.html#K17">+</a> <span class="p2"><a href="euclid.html#K23">|[</a><span class="default">1,1</span><a href="euclid.html#K23">]|</a></span></span>)</span> <a href="tarski.html#R1">c=</a> <span class="p1">(<span class="default"><a href="topreal1.html#K5">L~</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="subset_1.html#K3">`</a> 
 <b>by </b><i><a class="ref" href="subset_1.html#T43">SUBSET_1:43</a></i>;<br/><a NAME="E23:28_1_1_1_2_2_1_10"/><b>then </b><i><font color="Green">E90</font></i>: 
 <a href="topreal1.html#K3">LSeg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="euclid.html#K17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K17">+</a> <span class="p2"><a href="euclid.html#K23">|[</a><span class="default">1,0</span><a href="euclid.html#K23">]|</a></span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="euclid.html#K17">+</a> <span class="p2"><a href="euclid.html#K23">|[</a><span class="default">1,1</span><a href="euclid.html#K23">]|</a></span></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="goboard9.html#K2" target="_self">LeftComp</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="goboard9.html#E51:28_1_1_1_2"><i><font color="Green">E71</font></i></a>, <a class="txt" href="goboard9.html#E16:28_1_1_1_2_2_1_10"><i><font color="Green">E85</font></i></a>, <a class="txt" href="goboard9.html#E18:28_1_1_1_2_2_1_10"><i><font color="Green">E87</font></i></a>, <a class="txt" href="goboard9.html#E20:28_1_1_1_2_2_1_10"><i><font color="Green">E89</font></i></a>, <a class="ref" href="goboard9.html#T6" target="_self">Th6</a></i>;<br/><a NAME="E24:28_1_1_1_2_2_1_10"/><i><font color="Green">E91</font></i>: 
 <a href="topreal1.html#K3">LSeg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="euclid.html#K17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K17">+</a> <span class="p2"><a href="euclid.html#K23">|[</a><span class="default">1,0</span><a href="euclid.html#K23">]|</a></span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="euclid.html#K17">+</a> <span class="p2"><a href="euclid.html#K23">|[</a><span class="default">1,1</span><a href="euclid.html#K23">]|</a></span></span>)</span> <a href="xboole_0.html#NR5" target="_self">meets</a>  <a href="tops_1.html#K1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K3">cell</a> <span class="p2">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>8</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="goboard9.html#E22:28_1_1_1_2"><i><font color="Green">E49</font></i></a>, <a class="txt" href="goboard9.html#E23:28_1_1_1_2"><i><font color="Green">E50</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1_1_2_2_1_10"><i><font color="Green">E75</font></i></a>, <a class="txt" href="goboard9.html#E3:28_1_1_1_2_2_1_10"><i><font color="Green">E76</font></i></a>, <a class="ref" href="goboard6.html#T89">GOBOARD6:89</a></i>;<br/><a NAME="E25:28_1_1_1_2_2_1_10"/>
 <a href="tops_1.html#K1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K5">left_cell</a> <font color="Maroon">c<sub>1</sub></font>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="xboole_0.html#R1">misses</a>  <a href="topreal1.html#K5">L~</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="goboard9.html#E1:28_1_1"><i><font color="Green">E31</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1"><i><font color="Green">E32</font></i></a>, <a class="ref" href="goboard8.html#T37">GOBOARD8:37</a></i>;<br/><a NAME="E26:28_1_1_1_2_2_1_10"/><b>then </b>
 <a href="tops_1.html#K1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K5">left_cell</a> <font color="Maroon">c<sub>1</sub></font>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="tarski.html#R1">c=</a> <span class="p1">(<span class="default"><a href="topreal1.html#K5">L~</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="subset_1.html#K3">`</a> 
 <b>by </b><i><a class="ref" href="subset_1.html#T43">SUBSET_1:43</a></i>;<br/><b>hence </b><a NAME="E27:28_1_1_1_2_2_1_10"/>
 <a href="tops_1.html#K1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K5">left_cell</a> <font color="Maroon">c<sub>1</sub></font>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="goboard9.html#K2" target="_self">LeftComp</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="goboard9.html#E51:28_1_1_1_2"><i><font color="Green">E71</font></i></a>, <a class="txt" href="goboard9.html#E52:28_1_1_1_2"><i><font color="Green">E72</font></i></a>, <a class="txt" href="goboard9.html#E17:28_1_1_1_2_2_1_10"><i><font color="Green">E86</font></i></a>, <a class="txt" href="goboard9.html#E23:28_1_1_1_2_2_1_10"><i><font color="Green">E90</font></i></a>, <a class="txt" href="goboard9.html#E24:28_1_1_1_2_2_1_10"><i><font color="Green">E91</font></i></a>, <a class="ref" href="goboard9.html#T6" target="_self">Th6</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="28_1_1_1_2_2_1_11"><b>suppose </b></a><b>that </b><a NAME="E1:28_1_1_1_2_2_1_11"/><i><font color="Green">E74</font></i>: 
<font color="Maroon">c<sub>3</sub></font> <a href="nat_1.html#K1">+</a> 1 <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>5</sub></font>
 <b>and </b><br/><a NAME="E2:28_1_1_1_2_2_1_11"/><i><font color="Green">E75</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
 <b>and </b><br/><a NAME="E3:28_1_1_1_2_2_1_11"/><i><font color="Green">E76</font></i>: 
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>
 <b>and </b><br/><a NAME="E4:28_1_1_1_2_2_1_11"/><i><font color="Green">E77</font></i>: 
<font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a>  <a href="matrix_1.html#K1">width</a> <span class="p1">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>
 ;<br/><div class="add"><a NAME="E5:28_1_1_1_2_2_1_11"/><i><font color="Green">E78</font></i>: 
 <a href="goboard5.html#K5">left_cell</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a>  <a href="goboard5.html#K3">cell</a> <span class="p1">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>6</sub></font>
 <b>by </b><i><a class="txt" href="goboard9.html#E1:28_1_1_1_2"><i><font color="Green">E33</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1_1_2"><i><font color="Green">E34</font></i></a>, <a class="txt" href="goboard9.html#E7:28_1_1_1_2"><i><font color="Green">E37</font></i></a>, <a class="txt" href="goboard9.html#E8:28_1_1_1_2"><i><font color="Green">E38</font></i></a>, <a class="txt" href="goboard9.html#E11:28_1_1_1_2"><i><font color="Green">E40</font></i></a>, <a class="txt" href="goboard9.html#E12:28_1_1_1_2"><i><font color="Green">E41</font></i></a>, <a class="txt" href="goboard9.html#E24:28_1_1_1_2"><i><font color="Green">E51</font></i></a>, <a class="txt" href="goboard9.html#E39:28_1_1_1_2"><i><font color="Green">E62</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2_2_1_11"><i><font color="Green">E74</font></i></a>, <a class="ref" href="goboard5.html#T29">GOBOARD5:29</a></i>;<br/><a NAME="E6:28_1_1_1_2_2_1_11"/>
 <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> <font color="Maroon">c<sub>5</sub></font>
 <b>by </b><i><a class="txt" href="goboard9.html#E19:28_1_1_1_2"><i><font color="Green">E46</font></i></a>, <a class="txt" href="goboard9.html#E3:28_1_1_1_2_2_1_11"><i><font color="Green">E76</font></i></a>, <a class="ref" href="xxreal_0.html#T1">XXREAL_0:1</a></i>;<br/><a NAME="E7:28_1_1_1_2_2_1_11"/><b>then </b><i><font color="Green">E79</font></i>: 
<font color="Maroon">c<sub>5</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> <span class="p1">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>
 <b>by </b><i><a class="ref" href="nat_1.html#T38">NAT_1:38</a></i>;<br/><a NAME="E8:28_1_1_1_2_2_1_11"/><i><font color="Green">E80</font></i>: 
 <a href="topreal1.html#K3">LSeg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="euclid.html#K17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K17">+</a> <span class="p2"><a href="euclid.html#K23">|[</a><span class="default">0,1</span><a href="euclid.html#K23">]|</a></span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="euclid.html#K17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="nat_1.html#K1">+</a> 2</span>)</span>,<font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K17">+</a> <span class="p2"><a href="euclid.html#K23">|[</a><span class="default">0,1</span><a href="euclid.html#K23">]|</a></span></span>)</span> is <a href="connsp_1.html#V2">connected</a>
 <b>by </b><i><a class="ref" href="goboard9.html#T8" target="_self">Th8</a></i>;<br/><a NAME="E9:28_1_1_1_2_2_1_11"/><i><font color="Green">E81</font></i>: 
 <a href="topreal1.html#K3">LSeg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="euclid.html#K17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K17">+</a> <span class="p2"><a href="euclid.html#K23">|[</a><span class="default">0,1</span><a href="euclid.html#K23">]|</a></span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="euclid.html#K17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="nat_1.html#K1">+</a> 2</span>)</span>,<font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K17">+</a> <span class="p2"><a href="euclid.html#K23">|[</a><span class="default">0,1</span><a href="euclid.html#K23">]|</a></span></span>)</span> <a href="xboole_0.html#NR5" target="_self">meets</a>  <a href="tops_1.html#K1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K3">cell</a> <span class="p2">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="goboard9.html#E18:28_1_1_1_2"><i><font color="Green">E45</font></i></a>, <a class="txt" href="goboard9.html#E19:28_1_1_1_2"><i><font color="Green">E46</font></i></a>, <a class="txt" href="goboard9.html#E24:28_1_1_1_2"><i><font color="Green">E51</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2_2_1_11"><i><font color="Green">E74</font></i></a>, <a class="txt" href="goboard9.html#E4:28_1_1_1_2_2_1_11"><i><font color="Green">E77</font></i></a>, <a class="ref" href="goboard6.html#T86">GOBOARD6:86</a></i>;<br/><a NAME="E10:28_1_1_1_2_2_1_11"/>
 <a href="topreal1.html#K3">LSeg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="euclid.html#K17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K17">+</a> <span class="p2"><a href="euclid.html#K23">|[</a><span class="default">0,1</span><a href="euclid.html#K23">]|</a></span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="euclid.html#K17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="nat_1.html#K1">+</a> 2</span>)</span>,<font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K17">+</a> <span class="p2"><a href="euclid.html#K23">|[</a><span class="default">0,1</span><a href="euclid.html#K23">]|</a></span></span>)</span> <a href="xboole_0.html#R1">misses</a>  <a href="topreal1.html#K5">L~</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="goboard9.html#E18:28_1_1_1_2"><i><font color="Green">E45</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2_2_1_11"><i><font color="Green">E74</font></i></a>, <a class="txt" href="goboard9.html#E4:28_1_1_1_2_2_1_11"><i><font color="Green">E77</font></i></a>, <a class="txt" href="goboard9.html#E7:28_1_1_1_2_2_1_11"><i><font color="Green">E79</font></i></a>, <a class="ref" href="goboard8.html#T28">GOBOARD8:28</a></i>;<br/><a NAME="E11:28_1_1_1_2_2_1_11"/><b>then </b>
 <a href="topreal1.html#K3">LSeg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="euclid.html#K17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K17">+</a> <span class="p2"><a href="euclid.html#K23">|[</a><span class="default">0,1</span><a href="euclid.html#K23">]|</a></span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="euclid.html#K17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="nat_1.html#K1">+</a> 2</span>)</span>,<font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K17">+</a> <span class="p2"><a href="euclid.html#K23">|[</a><span class="default">0,1</span><a href="euclid.html#K23">]|</a></span></span>)</span> <a href="tarski.html#R1">c=</a> <span class="p1">(<span class="default"><a href="topreal1.html#K5">L~</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="subset_1.html#K3">`</a> 
 <b>by </b><i><a class="ref" href="subset_1.html#T43">SUBSET_1:43</a></i>;<br/><a NAME="E12:28_1_1_1_2_2_1_11"/><b>then </b><i><font color="Green">E82</font></i>: 
 <a href="topreal1.html#K3">LSeg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="euclid.html#K17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K17">+</a> <span class="p2"><a href="euclid.html#K23">|[</a><span class="default">0,1</span><a href="euclid.html#K23">]|</a></span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="euclid.html#K17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="nat_1.html#K1">+</a> 2</span>)</span>,<font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K17">+</a> <span class="p2"><a href="euclid.html#K23">|[</a><span class="default">0,1</span><a href="euclid.html#K23">]|</a></span></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="goboard9.html#K2" target="_self">LeftComp</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="goboard9.html#E1:28_1"><i><font color="Green">E30</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1"><i><font color="Green">E32</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2"><i><font color="Green">E33</font></i></a>, <a class="txt" href="goboard9.html#E51:28_1_1_1_2"><i><font color="Green">E71</font></i></a>, <a class="txt" href="goboard9.html#E5:28_1_1_1_2_2_1_11"><i><font color="Green">E78</font></i></a>, <a class="txt" href="goboard9.html#E8:28_1_1_1_2_2_1_11"><i><font color="Green">E80</font></i></a>, <a class="txt" href="goboard9.html#E9:28_1_1_1_2_2_1_11"><i><font color="Green">E81</font></i></a>, <a class="ref" href="goboard9.html#T6" target="_self">Th6</a>, <a class="ref" href="nat_1.html#T38">NAT_1:38</a></i>;<br/><a NAME="E13:28_1_1_1_2_2_1_11"/><i><font color="Green">E83</font></i>: 
 <a href="tops_1.html#K1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K3">cell</a> <span class="p2">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span> is <a href="connsp_1.html#V2">connected</a>
 <b>by </b><i><a class="txt" href="goboard9.html#E19:28_1_1_1_2"><i><font color="Green">E46</font></i></a>, <a class="txt" href="goboard9.html#E22:28_1_1_1_2"><i><font color="Green">E49</font></i></a>, <a class="ref" href="goboard9.html#T21" target="_self">Th21</a></i>;<br/><a NAME="E14:28_1_1_1_2_2_1_11"/><i><font color="Green">E84</font></i>: 
 <a href="topreal1.html#K3">LSeg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="euclid.html#K17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K17">+</a> <span class="p2"><a href="euclid.html#K23">|[</a><span class="default">0,1</span><a href="euclid.html#K23">]|</a></span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="euclid.html#K17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="nat_1.html#K1">+</a> 2</span>)</span>,<font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K17">+</a> <span class="p2"><a href="euclid.html#K23">|[</a><span class="default">0,1</span><a href="euclid.html#K23">]|</a></span></span>)</span> <a href="xboole_0.html#NR5" target="_self">meets</a>  <a href="tops_1.html#K1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K3">cell</a> <span class="p2">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="goboard9.html#E19:28_1_1_1_2"><i><font color="Green">E46</font></i></a>, <a class="txt" href="goboard9.html#E24:28_1_1_1_2"><i><font color="Green">E51</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2_2_1_11"><i><font color="Green">E74</font></i></a>, <a class="txt" href="goboard9.html#E4:28_1_1_1_2_2_1_11"><i><font color="Green">E77</font></i></a>, <a class="txt" href="goboard9.html#E7:28_1_1_1_2_2_1_11"><i><font color="Green">E79</font></i></a>, <a class="ref" href="goboard6.html#T86">GOBOARD6:86</a></i>;<br/><a NAME="E15:28_1_1_1_2_2_1_11"/>
 <a href="tops_1.html#K1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K3">cell</a> <span class="p2">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="xboole_0.html#R1">misses</a>  <a href="topreal1.html#K5">L~</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="goboard9.html#E19:28_1_1_1_2"><i><font color="Green">E46</font></i></a>, <a class="txt" href="goboard9.html#E22:28_1_1_1_2"><i><font color="Green">E49</font></i></a>, <a class="ref" href="goboard7.html#T14">GOBOARD7:14</a></i>;<br/><a NAME="E16:28_1_1_1_2_2_1_11"/><b>then </b>
 <a href="tops_1.html#K1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K3">cell</a> <span class="p2">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="tarski.html#R1">c=</a> <span class="p1">(<span class="default"><a href="topreal1.html#K5">L~</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="subset_1.html#K3">`</a> 
 <b>by </b><i><a class="ref" href="subset_1.html#T43">SUBSET_1:43</a></i>;<br/><a NAME="E17:28_1_1_1_2_2_1_11"/><b>then </b><i><font color="Green">E85</font></i>: 
 <a href="tops_1.html#K1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K3">cell</a> <span class="p2">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="goboard9.html#K2" target="_self">LeftComp</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="goboard9.html#E51:28_1_1_1_2"><i><font color="Green">E71</font></i></a>, <a class="txt" href="goboard9.html#E12:28_1_1_1_2_2_1_11"><i><font color="Green">E82</font></i></a>, <a class="txt" href="goboard9.html#E13:28_1_1_1_2_2_1_11"><i><font color="Green">E83</font></i></a>, <a class="txt" href="goboard9.html#E14:28_1_1_1_2_2_1_11"><i><font color="Green">E84</font></i></a>, <a class="ref" href="goboard9.html#T6" target="_self">Th6</a></i>;<br/><a NAME="E18:28_1_1_1_2_2_1_11"/><i><font color="Green">E86</font></i>: 
 <a href="goboard5.html#K5">left_cell</a> <font color="Maroon">c<sub>1</sub></font>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="hidden.html#R1">=</a>  <a href="goboard5.html#K3">cell</a> <span class="p1">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>8</sub></font>
 <b>by </b><i><a class="txt" href="goboard9.html#E1:28_1_1"><i><font color="Green">E31</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1"><i><font color="Green">E32</font></i></a>, <a class="txt" href="goboard9.html#E11:28_1_1_1_2"><i><font color="Green">E40</font></i></a>, <a class="txt" href="goboard9.html#E12:28_1_1_1_2"><i><font color="Green">E41</font></i></a>, <a class="txt" href="goboard9.html#E16:28_1_1_1_2"><i><font color="Green">E43</font></i></a>, <a class="txt" href="goboard9.html#E17:28_1_1_1_2"><i><font color="Green">E44</font></i></a>, <a class="txt" href="goboard9.html#E25:28_1_1_1_2"><i><font color="Green">E52</font></i></a>, <a class="txt" href="goboard9.html#E37:28_1_1_1_2"><i><font color="Green">E61</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1_1_2_2_1_11"><i><font color="Green">E75</font></i></a>, <a class="ref" href="goboard5.html#T31">GOBOARD5:31</a></i>;<br/><a NAME="E19:28_1_1_1_2_2_1_11"/><i><font color="Green">E87</font></i>: 
 <a href="topreal1.html#K3">LSeg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="euclid.html#K17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="euclid.html#K17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K17">+</a> <span class="p2"><a href="euclid.html#K23">|[</a><span class="default">0,1</span><a href="euclid.html#K23">]|</a></span></span>)</span> is <a href="connsp_1.html#V2">connected</a>
 <b>by </b><i><a class="ref" href="goboard9.html#T8" target="_self">Th8</a></i>;<br/><a NAME="E20:28_1_1_1_2_2_1_11"/><i><font color="Green">E88</font></i>: 
<font color="Maroon">c<sub>8</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>6</sub></font> <a href="binarith.html#K5">-'</a> 1
 <b>by </b><i><a class="txt" href="goboard9.html#E24:28_1_1_1_2"><i><font color="Green">E51</font></i></a>, <a class="txt" href="goboard9.html#E45:28_1_1_1_2"><i><font color="Green">E65</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2_2_1_11"><i><font color="Green">E74</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1_1_2_2_1_11"><i><font color="Green">E75</font></i></a>, <a class="txt" href="goboard9.html#E4:28_1_1_1_2_2_1_11"><i><font color="Green">E77</font></i></a></i>;<br/><a NAME="E21:28_1_1_1_2_2_1_11"/><i><font color="Green">E89</font></i>: 
 <a href="topreal1.html#K3">LSeg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="euclid.html#K17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="euclid.html#K17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K17">+</a> <span class="p2"><a href="euclid.html#K23">|[</a><span class="default">0,1</span><a href="euclid.html#K23">]|</a></span></span>)</span> <a href="xboole_0.html#NR5" target="_self">meets</a>  <a href="tops_1.html#K1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K3">cell</a> <span class="p2">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="goboard9.html#E19:28_1_1_1_2"><i><font color="Green">E46</font></i></a>, <a class="txt" href="goboard9.html#E24:28_1_1_1_2"><i><font color="Green">E51</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2_2_1_11"><i><font color="Green">E74</font></i></a>, <a class="txt" href="goboard9.html#E4:28_1_1_1_2_2_1_11"><i><font color="Green">E77</font></i></a>, <a class="txt" href="goboard9.html#E7:28_1_1_1_2_2_1_11"><i><font color="Green">E79</font></i></a>, <a class="ref" href="goboard6.html#T86">GOBOARD6:86</a></i>;<br/><a NAME="E22:28_1_1_1_2_2_1_11"/>
 <a href="topreal1.html#K3">LSeg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="euclid.html#K17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="euclid.html#K17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K17">+</a> <span class="p2"><a href="euclid.html#K23">|[</a><span class="default">0,1</span><a href="euclid.html#K23">]|</a></span></span>)</span> <a href="xboole_0.html#R1">misses</a>  <a href="topreal1.html#K5">L~</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="goboard9.html#E2:28_1_1"><i><font color="Green">E32</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2"><i><font color="Green">E33</font></i></a>, <a class="txt" href="goboard9.html#E8:28_1_1_1_2"><i><font color="Green">E38</font></i></a>, <a class="txt" href="goboard9.html#E12:28_1_1_1_2"><i><font color="Green">E41</font></i></a>, <a class="txt" href="goboard9.html#E17:28_1_1_1_2"><i><font color="Green">E44</font></i></a>, <a class="txt" href="goboard9.html#E18:28_1_1_1_2"><i><font color="Green">E45</font></i></a>, <a class="txt" href="goboard9.html#E24:28_1_1_1_2"><i><font color="Green">E51</font></i></a>, <a class="txt" href="goboard9.html#E25:28_1_1_1_2"><i><font color="Green">E52</font></i></a>, <a class="txt" href="goboard9.html#E46:28_1_1_1_2"><i><font color="Green">E66</font></i></a>, <a class="txt" href="goboard9.html#E47:28_1_1_1_2"><i><font color="Green">E67</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2_2_1_11"><i><font color="Green">E74</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1_1_2_2_1_11"><i><font color="Green">E75</font></i></a>, <a class="txt" href="goboard9.html#E4:28_1_1_1_2_2_1_11"><i><font color="Green">E77</font></i></a>, <a class="txt" href="goboard9.html#E7:28_1_1_1_2_2_1_11"><i><font color="Green">E79</font></i></a>, <a class="txt" href="goboard9.html#E20:28_1_1_1_2_2_1_11"><i><font color="Green">E88</font></i></a>, <a class="ref" href="goboard8.html#T10">GOBOARD8:10</a></i>;<br/><a NAME="E23:28_1_1_1_2_2_1_11"/><b>then </b>
 <a href="topreal1.html#K3">LSeg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="euclid.html#K17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="euclid.html#K17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K17">+</a> <span class="p2"><a href="euclid.html#K23">|[</a><span class="default">0,1</span><a href="euclid.html#K23">]|</a></span></span>)</span> <a href="tarski.html#R1">c=</a> <span class="p1">(<span class="default"><a href="topreal1.html#K5">L~</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="subset_1.html#K3">`</a> 
 <b>by </b><i><a class="ref" href="subset_1.html#T43">SUBSET_1:43</a></i>;<br/><a NAME="E24:28_1_1_1_2_2_1_11"/><b>then </b><i><font color="Green">E90</font></i>: 
 <a href="topreal1.html#K3">LSeg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="euclid.html#K17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="euclid.html#K17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K17">+</a> <span class="p2"><a href="euclid.html#K23">|[</a><span class="default">0,1</span><a href="euclid.html#K23">]|</a></span></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="goboard9.html#K2" target="_self">LeftComp</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="goboard9.html#E51:28_1_1_1_2"><i><font color="Green">E71</font></i></a>, <a class="txt" href="goboard9.html#E17:28_1_1_1_2_2_1_11"><i><font color="Green">E85</font></i></a>, <a class="txt" href="goboard9.html#E19:28_1_1_1_2_2_1_11"><i><font color="Green">E87</font></i></a>, <a class="txt" href="goboard9.html#E21:28_1_1_1_2_2_1_11"><i><font color="Green">E89</font></i></a>, <a class="ref" href="goboard9.html#T6" target="_self">Th6</a></i>;<br/><a NAME="E25:28_1_1_1_2_2_1_11"/><i><font color="Green">E91</font></i>: 
 <a href="topreal1.html#K3">LSeg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="euclid.html#K17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="euclid.html#K17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K17">+</a> <span class="p2"><a href="euclid.html#K23">|[</a><span class="default">0,1</span><a href="euclid.html#K23">]|</a></span></span>)</span> <a href="xboole_0.html#NR5" target="_self">meets</a>  <a href="tops_1.html#K1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K3">cell</a> <span class="p2">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>8</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="goboard9.html#E19:28_1_1_1_2"><i><font color="Green">E46</font></i></a>, <a class="txt" href="goboard9.html#E23:28_1_1_1_2"><i><font color="Green">E50</font></i></a>, <a class="txt" href="goboard9.html#E24:28_1_1_1_2"><i><font color="Green">E51</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2_2_1_11"><i><font color="Green">E74</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1_1_2_2_1_11"><i><font color="Green">E75</font></i></a>, <a class="txt" href="goboard9.html#E4:28_1_1_1_2_2_1_11"><i><font color="Green">E77</font></i></a>, <a class="txt" href="goboard9.html#E7:28_1_1_1_2_2_1_11"><i><font color="Green">E79</font></i></a>, <a class="ref" href="goboard6.html#T85">GOBOARD6:85</a></i>;<br/><a NAME="E26:28_1_1_1_2_2_1_11"/>
 <a href="tops_1.html#K1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K5">left_cell</a> <font color="Maroon">c<sub>1</sub></font>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="xboole_0.html#R1">misses</a>  <a href="topreal1.html#K5">L~</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="goboard9.html#E1:28_1_1"><i><font color="Green">E31</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1"><i><font color="Green">E32</font></i></a>, <a class="ref" href="goboard8.html#T37">GOBOARD8:37</a></i>;<br/><a NAME="E27:28_1_1_1_2_2_1_11"/><b>then </b>
 <a href="tops_1.html#K1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K5">left_cell</a> <font color="Maroon">c<sub>1</sub></font>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="tarski.html#R1">c=</a> <span class="p1">(<span class="default"><a href="topreal1.html#K5">L~</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="subset_1.html#K3">`</a> 
 <b>by </b><i><a class="ref" href="subset_1.html#T43">SUBSET_1:43</a></i>;<br/><b>hence </b><a NAME="E28:28_1_1_1_2_2_1_11"/>
 <a href="tops_1.html#K1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K5">left_cell</a> <font color="Maroon">c<sub>1</sub></font>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="goboard9.html#K2" target="_self">LeftComp</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="goboard9.html#E51:28_1_1_1_2"><i><font color="Green">E71</font></i></a>, <a class="txt" href="goboard9.html#E52:28_1_1_1_2"><i><font color="Green">E72</font></i></a>, <a class="txt" href="goboard9.html#E18:28_1_1_1_2_2_1_11"><i><font color="Green">E86</font></i></a>, <a class="txt" href="goboard9.html#E24:28_1_1_1_2_2_1_11"><i><font color="Green">E90</font></i></a>, <a class="txt" href="goboard9.html#E25:28_1_1_1_2_2_1_11"><i><font color="Green">E91</font></i></a>, <a class="ref" href="goboard9.html#T6" target="_self">Th6</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="28_1_1_1_2_2_1_12"><b>suppose </b></a><b>that </b><a NAME="E1:28_1_1_1_2_2_1_12"/><i><font color="Green">E74</font></i>: 
<font color="Maroon">c<sub>3</sub></font> <a href="nat_1.html#K1">+</a> 1 <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>5</sub></font>
 <b>and </b><br/><a NAME="E2:28_1_1_1_2_2_1_12"/><i><font color="Green">E75</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
 <b>and </b><br/><a NAME="E3:28_1_1_1_2_2_1_12"/><i><font color="Green">E76</font></i>: 
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>
 <b>and </b><br/><a NAME="E4:28_1_1_1_2_2_1_12"/><i><font color="Green">E77</font></i>: 
<font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="matrix_1.html#K1">width</a> <span class="p1">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>
 ;<br/><div class="add"><a NAME="E5:28_1_1_1_2_2_1_12"/><i><font color="Green">E78</font></i>: 
 <a href="goboard5.html#K5">left_cell</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a>  <a href="goboard5.html#K3">cell</a> <span class="p1">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>6</sub></font>
 <b>by </b><i><a class="txt" href="goboard9.html#E1:28_1_1_1_2"><i><font color="Green">E33</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1_1_2"><i><font color="Green">E34</font></i></a>, <a class="txt" href="goboard9.html#E7:28_1_1_1_2"><i><font color="Green">E37</font></i></a>, <a class="txt" href="goboard9.html#E8:28_1_1_1_2"><i><font color="Green">E38</font></i></a>, <a class="txt" href="goboard9.html#E11:28_1_1_1_2"><i><font color="Green">E40</font></i></a>, <a class="txt" href="goboard9.html#E12:28_1_1_1_2"><i><font color="Green">E41</font></i></a>, <a class="txt" href="goboard9.html#E24:28_1_1_1_2"><i><font color="Green">E51</font></i></a>, <a class="txt" href="goboard9.html#E39:28_1_1_1_2"><i><font color="Green">E62</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2_2_1_12"><i><font color="Green">E74</font></i></a>, <a class="ref" href="goboard5.html#T29">GOBOARD5:29</a></i>;<br/><a NAME="E6:28_1_1_1_2_2_1_12"/>
 <a href="matrix_1.html#K1">width</a> <span class="p1">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> <font color="Maroon">c<sub>4</sub></font>
 <b>by </b><i><a class="txt" href="goboard9.html#E21:28_1_1_1_2"><i><font color="Green">E48</font></i></a>, <a class="txt" href="goboard9.html#E4:28_1_1_1_2_2_1_12"><i><font color="Green">E77</font></i></a>, <a class="ref" href="xxreal_0.html#T1">XXREAL_0:1</a></i>;<br/><a NAME="E7:28_1_1_1_2_2_1_12"/><b>then </b><i><font color="Green">E79</font></i>: 
 <a href="matrix_1.html#K1">width</a> <span class="p1">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K1">+</a> 1
 <b>by </b><i><a class="ref" href="nat_1.html#T38">NAT_1:38</a></i>;<br/><a NAME="E8:28_1_1_1_2_2_1_12"/><i><font color="Green">E80</font></i>: 
<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>5</sub></font> <a href="binarith.html#K5">-'</a> 1
 <b>by </b><i><a class="txt" href="goboard9.html#E43:28_1_1_1_2"><i><font color="Green">E64</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2_2_1_12"><i><font color="Green">E74</font></i></a>, <a class="txt" href="goboard9.html#E3:28_1_1_1_2_2_1_12"><i><font color="Green">E76</font></i></a></i>;<br/><a NAME="E9:28_1_1_1_2_2_1_12"/><i><font color="Green">E81</font></i>: 
 <a href="topreal1.html#K3">LSeg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="euclid.html#K17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>5</sub></font>,<span class="p4">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="euclid.html#K17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>5</sub></font>,<span class="p5">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K17">+</a> <span class="p2"><a href="euclid.html#K23">|[</a><span class="default">1,0</span><a href="euclid.html#K23">]|</a></span></span>)</span> is <a href="connsp_1.html#V2">connected</a>
 <b>by </b><i><a class="ref" href="goboard9.html#T8" target="_self">Th8</a></i>;<br/><a NAME="E10:28_1_1_1_2_2_1_12"/><i><font color="Green">E82</font></i>: 
 <a href="topreal1.html#K3">LSeg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="euclid.html#K17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>5</sub></font>,<span class="p4">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="euclid.html#K17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>5</sub></font>,<span class="p5">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K17">+</a> <span class="p2"><a href="euclid.html#K23">|[</a><span class="default">1,0</span><a href="euclid.html#K23">]|</a></span></span>)</span> <a href="xboole_0.html#NR5" target="_self">meets</a>  <a href="tops_1.html#K1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K3">cell</a> <span class="p2">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="goboard9.html#E18:28_1_1_1_2"><i><font color="Green">E45</font></i></a>, <a class="txt" href="goboard9.html#E19:28_1_1_1_2"><i><font color="Green">E46</font></i></a>, <a class="txt" href="goboard9.html#E22:28_1_1_1_2"><i><font color="Green">E49</font></i></a>, <a class="txt" href="goboard9.html#E24:28_1_1_1_2"><i><font color="Green">E51</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2_2_1_12"><i><font color="Green">E74</font></i></a>, <a class="txt" href="goboard9.html#E7:28_1_1_1_2_2_1_12"><i><font color="Green">E79</font></i></a>, <a class="ref" href="goboard6.html#T85">GOBOARD6:85</a></i>;<br/><a NAME="E11:28_1_1_1_2_2_1_12"/>
 <a href="topreal1.html#K3">LSeg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="euclid.html#K17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>5</sub></font>,<span class="p4">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="euclid.html#K17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>5</sub></font>,<span class="p5">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K17">+</a> <span class="p2"><a href="euclid.html#K23">|[</a><span class="default">1,0</span><a href="euclid.html#K23">]|</a></span></span>)</span> <a href="xboole_0.html#R1">misses</a>  <a href="topreal1.html#K5">L~</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="goboard9.html#E2:28_1_1"><i><font color="Green">E32</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2"><i><font color="Green">E33</font></i></a>, <a class="txt" href="goboard9.html#E8:28_1_1_1_2"><i><font color="Green">E38</font></i></a>, <a class="txt" href="goboard9.html#E12:28_1_1_1_2"><i><font color="Green">E41</font></i></a>, <a class="txt" href="goboard9.html#E17:28_1_1_1_2"><i><font color="Green">E44</font></i></a>, <a class="txt" href="goboard9.html#E23:28_1_1_1_2"><i><font color="Green">E50</font></i></a>, <a class="txt" href="goboard9.html#E24:28_1_1_1_2"><i><font color="Green">E51</font></i></a>, <a class="txt" href="goboard9.html#E25:28_1_1_1_2"><i><font color="Green">E52</font></i></a>, <a class="txt" href="goboard9.html#E46:28_1_1_1_2"><i><font color="Green">E66</font></i></a>, <a class="txt" href="goboard9.html#E50:28_1_1_1_2"><i><font color="Green">E70</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2_2_1_12"><i><font color="Green">E74</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1_1_2_2_1_12"><i><font color="Green">E75</font></i></a>, <a class="txt" href="goboard9.html#E3:28_1_1_1_2_2_1_12"><i><font color="Green">E76</font></i></a>, <a class="txt" href="goboard9.html#E7:28_1_1_1_2_2_1_12"><i><font color="Green">E79</font></i></a>, <a class="txt" href="goboard9.html#E8:28_1_1_1_2_2_1_12"><i><font color="Green">E80</font></i></a>, <a class="ref" href="goboard8.html#T20">GOBOARD8:20</a></i>;<br/><a NAME="E12:28_1_1_1_2_2_1_12"/><b>then </b>
 <a href="topreal1.html#K3">LSeg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="euclid.html#K17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>5</sub></font>,<span class="p4">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="euclid.html#K17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>5</sub></font>,<span class="p5">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K17">+</a> <span class="p2"><a href="euclid.html#K23">|[</a><span class="default">1,0</span><a href="euclid.html#K23">]|</a></span></span>)</span> <a href="tarski.html#R1">c=</a> <span class="p1">(<span class="default"><a href="topreal1.html#K5">L~</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="subset_1.html#K3">`</a> 
 <b>by </b><i><a class="ref" href="subset_1.html#T43">SUBSET_1:43</a></i>;<br/><a NAME="E13:28_1_1_1_2_2_1_12"/><b>then </b><i><font color="Green">E83</font></i>: 
 <a href="topreal1.html#K3">LSeg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="euclid.html#K17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>5</sub></font>,<span class="p4">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="euclid.html#K17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>5</sub></font>,<span class="p5">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K17">+</a> <span class="p2"><a href="euclid.html#K23">|[</a><span class="default">1,0</span><a href="euclid.html#K23">]|</a></span></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="goboard9.html#K2" target="_self">LeftComp</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="goboard9.html#E1:28_1"><i><font color="Green">E30</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1"><i><font color="Green">E32</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2"><i><font color="Green">E33</font></i></a>, <a class="txt" href="goboard9.html#E51:28_1_1_1_2"><i><font color="Green">E71</font></i></a>, <a class="txt" href="goboard9.html#E5:28_1_1_1_2_2_1_12"><i><font color="Green">E78</font></i></a>, <a class="txt" href="goboard9.html#E9:28_1_1_1_2_2_1_12"><i><font color="Green">E81</font></i></a>, <a class="txt" href="goboard9.html#E10:28_1_1_1_2_2_1_12"><i><font color="Green">E82</font></i></a>, <a class="ref" href="goboard9.html#T6" target="_self">Th6</a>, <a class="ref" href="nat_1.html#T38">NAT_1:38</a></i>;<br/><a NAME="E14:28_1_1_1_2_2_1_12"/><i><font color="Green">E84</font></i>: 
 <a href="tops_1.html#K1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K3">cell</a> <span class="p2">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span> is <a href="connsp_1.html#V2">connected</a>
 <b>by </b><i><a class="txt" href="goboard9.html#E19:28_1_1_1_2"><i><font color="Green">E46</font></i></a>, <a class="txt" href="goboard9.html#E22:28_1_1_1_2"><i><font color="Green">E49</font></i></a>, <a class="ref" href="goboard9.html#T21" target="_self">Th21</a></i>;<br/><a NAME="E15:28_1_1_1_2_2_1_12"/><i><font color="Green">E85</font></i>: 
 <a href="topreal1.html#K3">LSeg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="euclid.html#K17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>5</sub></font>,<span class="p4">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="euclid.html#K17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>5</sub></font>,<span class="p5">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K17">+</a> <span class="p2"><a href="euclid.html#K23">|[</a><span class="default">1,0</span><a href="euclid.html#K23">]|</a></span></span>)</span> <a href="xboole_0.html#NR5" target="_self">meets</a>  <a href="tops_1.html#K1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K3">cell</a> <span class="p2">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="goboard9.html#E22:28_1_1_1_2"><i><font color="Green">E49</font></i></a>, <a class="txt" href="goboard9.html#E24:28_1_1_1_2"><i><font color="Green">E51</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2_2_1_12"><i><font color="Green">E74</font></i></a>, <a class="txt" href="goboard9.html#E3:28_1_1_1_2_2_1_12"><i><font color="Green">E76</font></i></a>, <a class="txt" href="goboard9.html#E7:28_1_1_1_2_2_1_12"><i><font color="Green">E79</font></i></a>, <a class="ref" href="goboard6.html#T89">GOBOARD6:89</a></i>;<br/><a NAME="E16:28_1_1_1_2_2_1_12"/>
 <a href="tops_1.html#K1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K3">cell</a> <span class="p2">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="xboole_0.html#R1">misses</a>  <a href="topreal1.html#K5">L~</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="goboard9.html#E19:28_1_1_1_2"><i><font color="Green">E46</font></i></a>, <a class="txt" href="goboard9.html#E22:28_1_1_1_2"><i><font color="Green">E49</font></i></a>, <a class="ref" href="goboard7.html#T14">GOBOARD7:14</a></i>;<br/><a NAME="E17:28_1_1_1_2_2_1_12"/><b>then </b>
 <a href="tops_1.html#K1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K3">cell</a> <span class="p2">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="tarski.html#R1">c=</a> <span class="p1">(<span class="default"><a href="topreal1.html#K5">L~</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="subset_1.html#K3">`</a> 
 <b>by </b><i><a class="ref" href="subset_1.html#T43">SUBSET_1:43</a></i>;<br/><a NAME="E18:28_1_1_1_2_2_1_12"/><b>then </b><i><font color="Green">E86</font></i>: 
 <a href="tops_1.html#K1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K3">cell</a> <span class="p2">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="goboard9.html#K2" target="_self">LeftComp</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="goboard9.html#E51:28_1_1_1_2"><i><font color="Green">E71</font></i></a>, <a class="txt" href="goboard9.html#E13:28_1_1_1_2_2_1_12"><i><font color="Green">E83</font></i></a>, <a class="txt" href="goboard9.html#E14:28_1_1_1_2_2_1_12"><i><font color="Green">E84</font></i></a>, <a class="txt" href="goboard9.html#E15:28_1_1_1_2_2_1_12"><i><font color="Green">E85</font></i></a>, <a class="ref" href="goboard9.html#T6" target="_self">Th6</a></i>;<br/><a NAME="E19:28_1_1_1_2_2_1_12"/><i><font color="Green">E87</font></i>: 
 <a href="goboard5.html#K5">left_cell</a> <font color="Maroon">c<sub>1</sub></font>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="hidden.html#R1">=</a>  <a href="goboard5.html#K3">cell</a> <span class="p1">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>8</sub></font>
 <b>by </b><i><a class="txt" href="goboard9.html#E1:28_1_1"><i><font color="Green">E31</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1"><i><font color="Green">E32</font></i></a>, <a class="txt" href="goboard9.html#E11:28_1_1_1_2"><i><font color="Green">E40</font></i></a>, <a class="txt" href="goboard9.html#E12:28_1_1_1_2"><i><font color="Green">E41</font></i></a>, <a class="txt" href="goboard9.html#E16:28_1_1_1_2"><i><font color="Green">E43</font></i></a>, <a class="txt" href="goboard9.html#E17:28_1_1_1_2"><i><font color="Green">E44</font></i></a>, <a class="txt" href="goboard9.html#E25:28_1_1_1_2"><i><font color="Green">E52</font></i></a>, <a class="txt" href="goboard9.html#E37:28_1_1_1_2"><i><font color="Green">E61</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1_1_2_2_1_12"><i><font color="Green">E75</font></i></a>, <a class="ref" href="goboard5.html#T31">GOBOARD5:31</a></i>;<br/><a NAME="E20:28_1_1_1_2_2_1_12"/><i><font color="Green">E88</font></i>: 
 <a href="topreal1.html#K3">LSeg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p5">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p0">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>,<font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="euclid.html#K17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p5">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p0">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>,<font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K17">+</a> <span class="p2"><a href="euclid.html#K23">|[</a><span class="default">1,0</span><a href="euclid.html#K23">]|</a></span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p5">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p0">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>,<font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="euclid.html#K17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p5">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p0">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>,<span class="p5">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K17">+</a> <span class="p2"><a href="euclid.html#K23">|[</a><span class="default">1,0</span><a href="euclid.html#K23">]|</a></span></span>)</span> is <a href="connsp_1.html#V2">connected</a>
 <b>by </b><i><a class="ref" href="goboard9.html#T8" target="_self">Th8</a></i>;<br/><a NAME="E21:28_1_1_1_2_2_1_12"/><i><font color="Green">E89</font></i>: 
 <a href="topreal1.html#K3">LSeg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p5">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p0">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>,<font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="euclid.html#K17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p5">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p0">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>,<font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K17">+</a> <span class="p2"><a href="euclid.html#K23">|[</a><span class="default">1,0</span><a href="euclid.html#K23">]|</a></span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p5">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p0">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>,<font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="euclid.html#K17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p5">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p0">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>,<span class="p5">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K17">+</a> <span class="p2"><a href="euclid.html#K23">|[</a><span class="default">1,0</span><a href="euclid.html#K23">]|</a></span></span>)</span> <a href="xboole_0.html#NR5" target="_self">meets</a>  <a href="tops_1.html#K1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K3">cell</a> <span class="p2">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="goboard9.html#E22:28_1_1_1_2"><i><font color="Green">E49</font></i></a>, <a class="txt" href="goboard9.html#E24:28_1_1_1_2"><i><font color="Green">E51</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2_2_1_12"><i><font color="Green">E74</font></i></a>, <a class="txt" href="goboard9.html#E3:28_1_1_1_2_2_1_12"><i><font color="Green">E76</font></i></a>, <a class="txt" href="goboard9.html#E7:28_1_1_1_2_2_1_12"><i><font color="Green">E79</font></i></a>, <a class="ref" href="goboard6.html#T89">GOBOARD6:89</a></i>;<br/><a NAME="E22:28_1_1_1_2_2_1_12"/>
 <a href="topreal1.html#K3">LSeg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p5">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p0">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>,<font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="euclid.html#K17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p5">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p0">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>,<font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K17">+</a> <span class="p2"><a href="euclid.html#K23">|[</a><span class="default">1,0</span><a href="euclid.html#K23">]|</a></span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p5">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p0">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>,<font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="euclid.html#K17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p5">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p0">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>,<span class="p5">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K17">+</a> <span class="p2"><a href="euclid.html#K23">|[</a><span class="default">1,0</span><a href="euclid.html#K23">]|</a></span></span>)</span> <a href="xboole_0.html#R1">misses</a>  <a href="topreal1.html#K5">L~</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="goboard9.html#E23:28_1_1_1_2"><i><font color="Green">E50</font></i></a>, <a class="txt" href="goboard9.html#E24:28_1_1_1_2"><i><font color="Green">E51</font></i></a>, <a class="txt" href="goboard9.html#E50:28_1_1_1_2"><i><font color="Green">E70</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2_2_1_12"><i><font color="Green">E74</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1_1_2_2_1_12"><i><font color="Green">E75</font></i></a>, <a class="txt" href="goboard9.html#E7:28_1_1_1_2_2_1_12"><i><font color="Green">E79</font></i></a>, <a class="ref" href="goboard8.html#T34">GOBOARD8:34</a></i>;<br/><a NAME="E23:28_1_1_1_2_2_1_12"/><b>then </b>
 <a href="topreal1.html#K3">LSeg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p5">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p0">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>,<font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="euclid.html#K17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p5">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p0">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>,<font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K17">+</a> <span class="p2"><a href="euclid.html#K23">|[</a><span class="default">1,0</span><a href="euclid.html#K23">]|</a></span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p5">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p0">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>,<font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="euclid.html#K17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p5">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p0">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>,<span class="p5">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K17">+</a> <span class="p2"><a href="euclid.html#K23">|[</a><span class="default">1,0</span><a href="euclid.html#K23">]|</a></span></span>)</span> <a href="tarski.html#R1">c=</a> <span class="p1">(<span class="default"><a href="topreal1.html#K5">L~</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="subset_1.html#K3">`</a> 
 <b>by </b><i><a class="ref" href="subset_1.html#T43">SUBSET_1:43</a></i>;<br/><a NAME="E24:28_1_1_1_2_2_1_12"/><b>then </b><i><font color="Green">E90</font></i>: 
 <a href="topreal1.html#K3">LSeg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p5">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p0">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>,<font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="euclid.html#K17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p5">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p0">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>,<font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K17">+</a> <span class="p2"><a href="euclid.html#K23">|[</a><span class="default">1,0</span><a href="euclid.html#K23">]|</a></span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p5">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p0">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>,<font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="euclid.html#K17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p5">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p0">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>,<span class="p5">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K17">+</a> <span class="p2"><a href="euclid.html#K23">|[</a><span class="default">1,0</span><a href="euclid.html#K23">]|</a></span></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="goboard9.html#K2" target="_self">LeftComp</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="goboard9.html#E51:28_1_1_1_2"><i><font color="Green">E71</font></i></a>, <a class="txt" href="goboard9.html#E18:28_1_1_1_2_2_1_12"><i><font color="Green">E86</font></i></a>, <a class="txt" href="goboard9.html#E20:28_1_1_1_2_2_1_12"><i><font color="Green">E88</font></i></a>, <a class="txt" href="goboard9.html#E21:28_1_1_1_2_2_1_12"><i><font color="Green">E89</font></i></a>, <a class="ref" href="goboard9.html#T6" target="_self">Th6</a></i>;<br/><a NAME="E25:28_1_1_1_2_2_1_12"/><i><font color="Green">E91</font></i>: 
 <a href="topreal1.html#K3">LSeg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p5">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p0">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>,<font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="euclid.html#K17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p5">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p0">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>,<font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K17">+</a> <span class="p2"><a href="euclid.html#K23">|[</a><span class="default">1,0</span><a href="euclid.html#K23">]|</a></span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p5">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p0">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>,<font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="euclid.html#K17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p5">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p0">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>,<span class="p5">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K17">+</a> <span class="p2"><a href="euclid.html#K23">|[</a><span class="default">1,0</span><a href="euclid.html#K23">]|</a></span></span>)</span> <a href="xboole_0.html#NR5" target="_self">meets</a>  <a href="tops_1.html#K1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K3">cell</a> <span class="p2">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>8</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="goboard9.html#E22:28_1_1_1_2"><i><font color="Green">E49</font></i></a>, <a class="txt" href="goboard9.html#E23:28_1_1_1_2"><i><font color="Green">E50</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1_1_2_2_1_12"><i><font color="Green">E75</font></i></a>, <a class="txt" href="goboard9.html#E3:28_1_1_1_2_2_1_12"><i><font color="Green">E76</font></i></a>, <a class="ref" href="goboard6.html#T89">GOBOARD6:89</a></i>;<br/><a NAME="E26:28_1_1_1_2_2_1_12"/>
 <a href="tops_1.html#K1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K5">left_cell</a> <font color="Maroon">c<sub>1</sub></font>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="xboole_0.html#R1">misses</a>  <a href="topreal1.html#K5">L~</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="goboard9.html#E1:28_1_1"><i><font color="Green">E31</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1"><i><font color="Green">E32</font></i></a>, <a class="ref" href="goboard8.html#T37">GOBOARD8:37</a></i>;<br/><a NAME="E27:28_1_1_1_2_2_1_12"/><b>then </b>
 <a href="tops_1.html#K1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K5">left_cell</a> <font color="Maroon">c<sub>1</sub></font>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="tarski.html#R1">c=</a> <span class="p1">(<span class="default"><a href="topreal1.html#K5">L~</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="subset_1.html#K3">`</a> 
 <b>by </b><i><a class="ref" href="subset_1.html#T43">SUBSET_1:43</a></i>;<br/><b>hence </b><a NAME="E28:28_1_1_1_2_2_1_12"/>
 <a href="tops_1.html#K1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K5">left_cell</a> <font color="Maroon">c<sub>1</sub></font>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="goboard9.html#K2" target="_self">LeftComp</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="goboard9.html#E51:28_1_1_1_2"><i><font color="Green">E71</font></i></a>, <a class="txt" href="goboard9.html#E52:28_1_1_1_2"><i><font color="Green">E72</font></i></a>, <a class="txt" href="goboard9.html#E19:28_1_1_1_2_2_1_12"><i><font color="Green">E87</font></i></a>, <a class="txt" href="goboard9.html#E24:28_1_1_1_2_2_1_12"><i><font color="Green">E90</font></i></a>, <a class="txt" href="goboard9.html#E25:28_1_1_1_2_2_1_12"><i><font color="Green">E91</font></i></a>, <a class="ref" href="goboard9.html#T6" target="_self">Th6</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="28_1_1_1_2_2_1_13"><b>suppose </b></a><b>that </b><a NAME="E1:28_1_1_1_2_2_1_13"/><i><font color="Green">E74</font></i>: 
<font color="Maroon">c<sub>3</sub></font> <a href="nat_1.html#K1">+</a> 1 <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>5</sub></font>
 <b>and </b><br/><a NAME="E2:28_1_1_1_2_2_1_13"/><i><font color="Green">E75</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
 <b>and </b><br/><a NAME="E3:28_1_1_1_2_2_1_13"/><i><font color="Green">E76</font></i>: 
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>
 <b>and </b><br/><a NAME="E4:28_1_1_1_2_2_1_13"/><i><font color="Green">E77</font></i>: 
<font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="matrix_1.html#K1">width</a> <span class="p1">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>
 ;<br/><div class="add"><a NAME="E5:28_1_1_1_2_2_1_13"/><i><font color="Green">E78</font></i>: 
 <a href="goboard5.html#K5">left_cell</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a>  <a href="goboard5.html#K3">cell</a> <span class="p1">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>6</sub></font>
 <b>by </b><i><a class="txt" href="goboard9.html#E1:28_1_1_1_2"><i><font color="Green">E33</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1_1_2"><i><font color="Green">E34</font></i></a>, <a class="txt" href="goboard9.html#E7:28_1_1_1_2"><i><font color="Green">E37</font></i></a>, <a class="txt" href="goboard9.html#E8:28_1_1_1_2"><i><font color="Green">E38</font></i></a>, <a class="txt" href="goboard9.html#E11:28_1_1_1_2"><i><font color="Green">E40</font></i></a>, <a class="txt" href="goboard9.html#E12:28_1_1_1_2"><i><font color="Green">E41</font></i></a>, <a class="txt" href="goboard9.html#E24:28_1_1_1_2"><i><font color="Green">E51</font></i></a>, <a class="txt" href="goboard9.html#E39:28_1_1_1_2"><i><font color="Green">E62</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2_2_1_13"><i><font color="Green">E74</font></i></a>, <a class="ref" href="goboard5.html#T29">GOBOARD5:29</a></i>;<br/><a NAME="E6:28_1_1_1_2_2_1_13"/>
 <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> <font color="Maroon">c<sub>5</sub></font>
 <b>by </b><i><a class="txt" href="goboard9.html#E19:28_1_1_1_2"><i><font color="Green">E46</font></i></a>, <a class="txt" href="goboard9.html#E3:28_1_1_1_2_2_1_13"><i><font color="Green">E76</font></i></a>, <a class="ref" href="xxreal_0.html#T1">XXREAL_0:1</a></i>;<br/><a NAME="E7:28_1_1_1_2_2_1_13"/><b>then </b><i><font color="Green">E79</font></i>: 
<font color="Maroon">c<sub>5</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> <span class="p1">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>
 <b>by </b><i><a class="ref" href="nat_1.html#T38">NAT_1:38</a></i>;<br/><a NAME="E8:28_1_1_1_2_2_1_13"/>
 <a href="matrix_1.html#K1">width</a> <span class="p1">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> <font color="Maroon">c<sub>4</sub></font>
 <b>by </b><i><a class="txt" href="goboard9.html#E21:28_1_1_1_2"><i><font color="Green">E48</font></i></a>, <a class="txt" href="goboard9.html#E4:28_1_1_1_2_2_1_13"><i><font color="Green">E77</font></i></a>, <a class="ref" href="xxreal_0.html#T1">XXREAL_0:1</a></i>;<br/><a NAME="E9:28_1_1_1_2_2_1_13"/><b>then </b><i><font color="Green">E80</font></i>: 
 <a href="matrix_1.html#K1">width</a> <span class="p1">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K1">+</a> 1
 <b>by </b><i><a class="ref" href="nat_1.html#T38">NAT_1:38</a></i>;<br/><a NAME="E10:28_1_1_1_2_2_1_13"/><i><font color="Green">E81</font></i>: 
 <a href="topreal1.html#K3">LSeg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>3</sub></font>,<span class="p4">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="euclid.html#K17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p4">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p4">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="euclid.html#K17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p4">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> is <a href="connsp_1.html#V2">connected</a>
 <b>by </b><i><a class="ref" href="goboard9.html#T8" target="_self">Th8</a></i>;<br/><a NAME="E11:28_1_1_1_2_2_1_13"/><i><font color="Green">E82</font></i>: 
 <a href="topreal1.html#K3">LSeg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>3</sub></font>,<span class="p4">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="euclid.html#K17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p4">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p4">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="euclid.html#K17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p4">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xboole_0.html#NR5" target="_self">meets</a>  <a href="tops_1.html#K1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K3">cell</a> <span class="p2">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="goboard9.html#E18:28_1_1_1_2"><i><font color="Green">E45</font></i></a>, <a class="txt" href="goboard9.html#E19:28_1_1_1_2"><i><font color="Green">E46</font></i></a>, <a class="txt" href="goboard9.html#E22:28_1_1_1_2"><i><font color="Green">E49</font></i></a>, <a class="txt" href="goboard9.html#E24:28_1_1_1_2"><i><font color="Green">E51</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2_2_1_13"><i><font color="Green">E74</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1_1_2_2_1_13"><i><font color="Green">E75</font></i></a>, <a class="txt" href="goboard9.html#E9:28_1_1_1_2_2_1_13"><i><font color="Green">E80</font></i></a>, <a class="ref" href="goboard6.html#T85">GOBOARD6:85</a></i>;<br/><a NAME="E12:28_1_1_1_2_2_1_13"/>
 <a href="topreal1.html#K3">LSeg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>3</sub></font>,<span class="p4">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="euclid.html#K17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p4">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p4">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="euclid.html#K17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p4">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xboole_0.html#R1">misses</a>  <a href="topreal1.html#K5">L~</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="goboard9.html#E2:28_1_1"><i><font color="Green">E32</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2"><i><font color="Green">E33</font></i></a>, <a class="txt" href="goboard9.html#E8:28_1_1_1_2"><i><font color="Green">E38</font></i></a>, <a class="txt" href="goboard9.html#E12:28_1_1_1_2"><i><font color="Green">E41</font></i></a>, <a class="txt" href="goboard9.html#E17:28_1_1_1_2"><i><font color="Green">E44</font></i></a>, <a class="txt" href="goboard9.html#E18:28_1_1_1_2"><i><font color="Green">E45</font></i></a>, <a class="txt" href="goboard9.html#E23:28_1_1_1_2"><i><font color="Green">E50</font></i></a>, <a class="txt" href="goboard9.html#E24:28_1_1_1_2"><i><font color="Green">E51</font></i></a>, <a class="txt" href="goboard9.html#E25:28_1_1_1_2"><i><font color="Green">E52</font></i></a>, <a class="txt" href="goboard9.html#E46:28_1_1_1_2"><i><font color="Green">E66</font></i></a>, <a class="txt" href="goboard9.html#E47:28_1_1_1_2"><i><font color="Green">E67</font></i></a>, <a class="txt" href="goboard9.html#E50:28_1_1_1_2"><i><font color="Green">E70</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2_2_1_13"><i><font color="Green">E74</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1_1_2_2_1_13"><i><font color="Green">E75</font></i></a>, <a class="txt" href="goboard9.html#E7:28_1_1_1_2_2_1_13"><i><font color="Green">E79</font></i></a>, <a class="txt" href="goboard9.html#E9:28_1_1_1_2_2_1_13"><i><font color="Green">E80</font></i></a>, <a class="ref" href="goboard8.html#T16">GOBOARD8:16</a></i>;<br/><a NAME="E13:28_1_1_1_2_2_1_13"/><b>then </b>
 <a href="topreal1.html#K3">LSeg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>3</sub></font>,<span class="p4">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="euclid.html#K17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p4">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p4">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="euclid.html#K17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p4">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="tarski.html#R1">c=</a> <span class="p1">(<span class="default"><a href="topreal1.html#K5">L~</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="subset_1.html#K3">`</a> 
 <b>by </b><i><a class="ref" href="subset_1.html#T43">SUBSET_1:43</a></i>;<br/><a NAME="E14:28_1_1_1_2_2_1_13"/><b>then </b><i><font color="Green">E83</font></i>: 
 <a href="topreal1.html#K3">LSeg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>3</sub></font>,<span class="p4">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="euclid.html#K17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p4">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p4">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="euclid.html#K17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p4">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="goboard9.html#K2" target="_self">LeftComp</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="goboard9.html#E1:28_1"><i><font color="Green">E30</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1"><i><font color="Green">E32</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2"><i><font color="Green">E33</font></i></a>, <a class="txt" href="goboard9.html#E51:28_1_1_1_2"><i><font color="Green">E71</font></i></a>, <a class="txt" href="goboard9.html#E5:28_1_1_1_2_2_1_13"><i><font color="Green">E78</font></i></a>, <a class="txt" href="goboard9.html#E10:28_1_1_1_2_2_1_13"><i><font color="Green">E81</font></i></a>, <a class="txt" href="goboard9.html#E11:28_1_1_1_2_2_1_13"><i><font color="Green">E82</font></i></a>, <a class="ref" href="goboard9.html#T6" target="_self">Th6</a>, <a class="ref" href="nat_1.html#T38">NAT_1:38</a></i>;<br/><a NAME="E15:28_1_1_1_2_2_1_13"/><i><font color="Green">E84</font></i>: 
 <a href="tops_1.html#K1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K3">cell</a> <span class="p2">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span> is <a href="connsp_1.html#V2">connected</a>
 <b>by </b><i><a class="txt" href="goboard9.html#E19:28_1_1_1_2"><i><font color="Green">E46</font></i></a>, <a class="txt" href="goboard9.html#E22:28_1_1_1_2"><i><font color="Green">E49</font></i></a>, <a class="ref" href="goboard9.html#T21" target="_self">Th21</a></i>;<br/><a NAME="E16:28_1_1_1_2_2_1_13"/><i><font color="Green">E85</font></i>: 
 <a href="topreal1.html#K3">LSeg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>3</sub></font>,<span class="p4">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="euclid.html#K17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p4">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p4">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="euclid.html#K17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p4">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xboole_0.html#NR5" target="_self">meets</a>  <a href="tops_1.html#K1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K3">cell</a> <span class="p2">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="goboard9.html#E19:28_1_1_1_2"><i><font color="Green">E46</font></i></a>, <a class="txt" href="goboard9.html#E22:28_1_1_1_2"><i><font color="Green">E49</font></i></a>, <a class="txt" href="goboard9.html#E24:28_1_1_1_2"><i><font color="Green">E51</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2_2_1_13"><i><font color="Green">E74</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1_1_2_2_1_13"><i><font color="Green">E75</font></i></a>, <a class="txt" href="goboard9.html#E7:28_1_1_1_2_2_1_13"><i><font color="Green">E79</font></i></a>, <a class="txt" href="goboard9.html#E9:28_1_1_1_2_2_1_13"><i><font color="Green">E80</font></i></a>, <a class="ref" href="goboard6.html#T85">GOBOARD6:85</a></i>;<br/><a NAME="E17:28_1_1_1_2_2_1_13"/>
 <a href="tops_1.html#K1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K3">cell</a> <span class="p2">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="xboole_0.html#R1">misses</a>  <a href="topreal1.html#K5">L~</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="goboard9.html#E19:28_1_1_1_2"><i><font color="Green">E46</font></i></a>, <a class="txt" href="goboard9.html#E22:28_1_1_1_2"><i><font color="Green">E49</font></i></a>, <a class="ref" href="goboard7.html#T14">GOBOARD7:14</a></i>;<br/><a NAME="E18:28_1_1_1_2_2_1_13"/><b>then </b>
 <a href="tops_1.html#K1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K3">cell</a> <span class="p2">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="tarski.html#R1">c=</a> <span class="p1">(<span class="default"><a href="topreal1.html#K5">L~</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="subset_1.html#K3">`</a> 
 <b>by </b><i><a class="ref" href="subset_1.html#T43">SUBSET_1:43</a></i>;<br/><a NAME="E19:28_1_1_1_2_2_1_13"/><b>then </b><i><font color="Green">E86</font></i>: 
 <a href="tops_1.html#K1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K3">cell</a> <span class="p2">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="goboard9.html#K2" target="_self">LeftComp</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="goboard9.html#E51:28_1_1_1_2"><i><font color="Green">E71</font></i></a>, <a class="txt" href="goboard9.html#E14:28_1_1_1_2_2_1_13"><i><font color="Green">E83</font></i></a>, <a class="txt" href="goboard9.html#E15:28_1_1_1_2_2_1_13"><i><font color="Green">E84</font></i></a>, <a class="txt" href="goboard9.html#E16:28_1_1_1_2_2_1_13"><i><font color="Green">E85</font></i></a>, <a class="ref" href="goboard9.html#T6" target="_self">Th6</a></i>;<br/><a NAME="E20:28_1_1_1_2_2_1_13"/><i><font color="Green">E87</font></i>: 
 <a href="goboard5.html#K5">left_cell</a> <font color="Maroon">c<sub>1</sub></font>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="hidden.html#R1">=</a>  <a href="goboard5.html#K3">cell</a> <span class="p1">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>8</sub></font>
 <b>by </b><i><a class="txt" href="goboard9.html#E1:28_1_1"><i><font color="Green">E31</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1"><i><font color="Green">E32</font></i></a>, <a class="txt" href="goboard9.html#E11:28_1_1_1_2"><i><font color="Green">E40</font></i></a>, <a class="txt" href="goboard9.html#E12:28_1_1_1_2"><i><font color="Green">E41</font></i></a>, <a class="txt" href="goboard9.html#E16:28_1_1_1_2"><i><font color="Green">E43</font></i></a>, <a class="txt" href="goboard9.html#E17:28_1_1_1_2"><i><font color="Green">E44</font></i></a>, <a class="txt" href="goboard9.html#E25:28_1_1_1_2"><i><font color="Green">E52</font></i></a>, <a class="txt" href="goboard9.html#E37:28_1_1_1_2"><i><font color="Green">E61</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1_1_2_2_1_13"><i><font color="Green">E75</font></i></a>, <a class="ref" href="goboard5.html#T31">GOBOARD5:31</a></i>;<br/><a NAME="E21:28_1_1_1_2_2_1_13"/><i><font color="Green">E88</font></i>: 
 <a href="topreal1.html#K3">LSeg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="euclid.html#K17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p4">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p4">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="euclid.html#K17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p4">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> is <a href="connsp_1.html#V2">connected</a>
 <b>by </b><i><a class="ref" href="goboard9.html#T8" target="_self">Th8</a></i>;<br/><a NAME="E22:28_1_1_1_2_2_1_13"/><i><font color="Green">E89</font></i>: 
 <a href="topreal1.html#K3">LSeg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="euclid.html#K17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p4">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p4">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="euclid.html#K17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p4">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xboole_0.html#NR5" target="_self">meets</a>  <a href="tops_1.html#K1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K3">cell</a> <span class="p2">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="goboard9.html#E19:28_1_1_1_2"><i><font color="Green">E46</font></i></a>, <a class="txt" href="goboard9.html#E22:28_1_1_1_2"><i><font color="Green">E49</font></i></a>, <a class="txt" href="goboard9.html#E24:28_1_1_1_2"><i><font color="Green">E51</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2_2_1_13"><i><font color="Green">E74</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1_1_2_2_1_13"><i><font color="Green">E75</font></i></a>, <a class="txt" href="goboard9.html#E7:28_1_1_1_2_2_1_13"><i><font color="Green">E79</font></i></a>, <a class="txt" href="goboard9.html#E9:28_1_1_1_2_2_1_13"><i><font color="Green">E80</font></i></a>, <a class="ref" href="goboard6.html#T85">GOBOARD6:85</a></i>;<br/><a NAME="E23:28_1_1_1_2_2_1_13"/>
 <a href="topreal1.html#K3">LSeg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="euclid.html#K17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p4">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p4">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="euclid.html#K17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p4">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xboole_0.html#R1">misses</a>  <a href="topreal1.html#K5">L~</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="goboard9.html#E2:28_1_1"><i><font color="Green">E32</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2"><i><font color="Green">E33</font></i></a>, <a class="txt" href="goboard9.html#E8:28_1_1_1_2"><i><font color="Green">E38</font></i></a>, <a class="txt" href="goboard9.html#E12:28_1_1_1_2"><i><font color="Green">E41</font></i></a>, <a class="txt" href="goboard9.html#E17:28_1_1_1_2"><i><font color="Green">E44</font></i></a>, <a class="txt" href="goboard9.html#E18:28_1_1_1_2"><i><font color="Green">E45</font></i></a>, <a class="txt" href="goboard9.html#E23:28_1_1_1_2"><i><font color="Green">E50</font></i></a>, <a class="txt" href="goboard9.html#E24:28_1_1_1_2"><i><font color="Green">E51</font></i></a>, <a class="txt" href="goboard9.html#E25:28_1_1_1_2"><i><font color="Green">E52</font></i></a>, <a class="txt" href="goboard9.html#E46:28_1_1_1_2"><i><font color="Green">E66</font></i></a>, <a class="txt" href="goboard9.html#E47:28_1_1_1_2"><i><font color="Green">E67</font></i></a>, <a class="txt" href="goboard9.html#E50:28_1_1_1_2"><i><font color="Green">E70</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2_2_1_13"><i><font color="Green">E74</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1_1_2_2_1_13"><i><font color="Green">E75</font></i></a>, <a class="txt" href="goboard9.html#E7:28_1_1_1_2_2_1_13"><i><font color="Green">E79</font></i></a>, <a class="txt" href="goboard9.html#E9:28_1_1_1_2_2_1_13"><i><font color="Green">E80</font></i></a>, <a class="ref" href="goboard8.html#T6">GOBOARD8:6</a></i>;<br/><a NAME="E24:28_1_1_1_2_2_1_13"/><b>then </b>
 <a href="topreal1.html#K3">LSeg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="euclid.html#K17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p4">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p4">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="euclid.html#K17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p4">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="tarski.html#R1">c=</a> <span class="p1">(<span class="default"><a href="topreal1.html#K5">L~</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="subset_1.html#K3">`</a> 
 <b>by </b><i><a class="ref" href="subset_1.html#T43">SUBSET_1:43</a></i>;<br/><a NAME="E25:28_1_1_1_2_2_1_13"/><b>then </b><i><font color="Green">E90</font></i>: 
 <a href="topreal1.html#K3">LSeg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="euclid.html#K17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p4">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p4">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="euclid.html#K17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p4">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="goboard9.html#K2" target="_self">LeftComp</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="goboard9.html#E51:28_1_1_1_2"><i><font color="Green">E71</font></i></a>, <a class="txt" href="goboard9.html#E19:28_1_1_1_2_2_1_13"><i><font color="Green">E86</font></i></a>, <a class="txt" href="goboard9.html#E21:28_1_1_1_2_2_1_13"><i><font color="Green">E88</font></i></a>, <a class="txt" href="goboard9.html#E22:28_1_1_1_2_2_1_13"><i><font color="Green">E89</font></i></a>, <a class="ref" href="goboard9.html#T6" target="_self">Th6</a></i>;<br/><a NAME="E26:28_1_1_1_2_2_1_13"/><i><font color="Green">E91</font></i>: 
 <a href="topreal1.html#K3">LSeg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="euclid.html#K17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p4">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p4">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="euclid.html#K17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p4">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xboole_0.html#NR5" target="_self">meets</a>  <a href="tops_1.html#K1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K3">cell</a> <span class="p2">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>8</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="goboard9.html#E19:28_1_1_1_2"><i><font color="Green">E46</font></i></a>, <a class="txt" href="goboard9.html#E22:28_1_1_1_2"><i><font color="Green">E49</font></i></a>, <a class="txt" href="goboard9.html#E23:28_1_1_1_2"><i><font color="Green">E50</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2_2_1_13"><i><font color="Green">E74</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1_1_2_2_1_13"><i><font color="Green">E75</font></i></a>, <a class="txt" href="goboard9.html#E7:28_1_1_1_2_2_1_13"><i><font color="Green">E79</font></i></a>, <a class="ref" href="goboard6.html#T85">GOBOARD6:85</a></i>;<br/><a NAME="E27:28_1_1_1_2_2_1_13"/>
 <a href="tops_1.html#K1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K5">left_cell</a> <font color="Maroon">c<sub>1</sub></font>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="xboole_0.html#R1">misses</a>  <a href="topreal1.html#K5">L~</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="goboard9.html#E1:28_1_1"><i><font color="Green">E31</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1"><i><font color="Green">E32</font></i></a>, <a class="ref" href="goboard8.html#T37">GOBOARD8:37</a></i>;<br/><a NAME="E28:28_1_1_1_2_2_1_13"/><b>then </b>
 <a href="tops_1.html#K1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K5">left_cell</a> <font color="Maroon">c<sub>1</sub></font>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="tarski.html#R1">c=</a> <span class="p1">(<span class="default"><a href="topreal1.html#K5">L~</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="subset_1.html#K3">`</a> 
 <b>by </b><i><a class="ref" href="subset_1.html#T43">SUBSET_1:43</a></i>;<br/><b>hence </b><a NAME="E29:28_1_1_1_2_2_1_13"/>
 <a href="tops_1.html#K1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K5">left_cell</a> <font color="Maroon">c<sub>1</sub></font>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="goboard9.html#K2" target="_self">LeftComp</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="goboard9.html#E51:28_1_1_1_2"><i><font color="Green">E71</font></i></a>, <a class="txt" href="goboard9.html#E52:28_1_1_1_2"><i><font color="Green">E72</font></i></a>, <a class="txt" href="goboard9.html#E20:28_1_1_1_2_2_1_13"><i><font color="Green">E87</font></i></a>, <a class="txt" href="goboard9.html#E25:28_1_1_1_2_2_1_13"><i><font color="Green">E90</font></i></a>, <a class="txt" href="goboard9.html#E26:28_1_1_1_2_2_1_13"><i><font color="Green">E91</font></i></a>, <a class="ref" href="goboard9.html#T6" target="_self">Th6</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="28_1_1_1_2_2_1_14"><b>suppose </b></a><b>that </b><a NAME="E1:28_1_1_1_2_2_1_14"/><i><font color="Green">E74</font></i>: 
<font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K1">+</a> 1 <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>6</sub></font>
 <b>and </b><br/><a NAME="E2:28_1_1_1_2_2_1_14"/><i><font color="Green">E75</font></i>: 
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>7</sub></font> <a href="nat_1.html#K1">+</a> 1
 ;<br/><div class="add"> <a href="goboard5.html#K5">left_cell</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font> = 
 <a href="goboard5.html#K3">cell</a> <span class="p1">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>4</sub></font>
<b>by </b><i><a class="txt" href="goboard9.html#E1:28_1_1_1_2"><i><font color="Green">E33</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1_1_2"><i><font color="Green">E34</font></i></a>, <a class="txt" href="goboard9.html#E7:28_1_1_1_2"><i><font color="Green">E37</font></i></a>, <a class="txt" href="goboard9.html#E8:28_1_1_1_2"><i><font color="Green">E38</font></i></a>, <a class="txt" href="goboard9.html#E11:28_1_1_1_2"><i><font color="Green">E40</font></i></a>, <a class="txt" href="goboard9.html#E12:28_1_1_1_2"><i><font color="Green">E41</font></i></a>, <a class="txt" href="goboard9.html#E24:28_1_1_1_2"><i><font color="Green">E51</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2_2_1_14"><i><font color="Green">E74</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1_1_2_2_1_14"><i><font color="Green">E75</font></i></a>, <a class="ref" href="goboard5.html#T28">GOBOARD5:28</a></i>
<br/>.= 
 <a href="goboard5.html#K5">left_cell</a> <font color="Maroon">c<sub>1</sub></font>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>
<b>by </b><i><a class="txt" href="goboard9.html#E1:28_1_1"><i><font color="Green">E31</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1"><i><font color="Green">E32</font></i></a>, <a class="txt" href="goboard9.html#E11:28_1_1_1_2"><i><font color="Green">E40</font></i></a>, <a class="txt" href="goboard9.html#E12:28_1_1_1_2"><i><font color="Green">E41</font></i></a>, <a class="txt" href="goboard9.html#E16:28_1_1_1_2"><i><font color="Green">E43</font></i></a>, <a class="txt" href="goboard9.html#E17:28_1_1_1_2"><i><font color="Green">E44</font></i></a>, <a class="txt" href="goboard9.html#E25:28_1_1_1_2"><i><font color="Green">E52</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2_2_1_14"><i><font color="Green">E74</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1_1_2_2_1_14"><i><font color="Green">E75</font></i></a>, <a class="ref" href="goboard5.html#T30">GOBOARD5:30</a></i>
;<br/><b>hence </b><a NAME="E4:28_1_1_1_2_2_1_14"/>
 <a href="tops_1.html#K1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K5">left_cell</a> <font color="Maroon">c<sub>1</sub></font>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="goboard9.html#K2" target="_self">LeftComp</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="goboard9.html#E1:28_1"><i><font color="Green">E30</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1"><i><font color="Green">E32</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2"><i><font color="Green">E33</font></i></a>, <a class="ref" href="nat_1.html#T38">NAT_1:38</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="28_1_1_1_2_2_1_15"><b>suppose </b></a><b>that </b><a NAME="E1:28_1_1_1_2_2_1_15"/><i><font color="Green">E74</font></i>: 
<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>5</sub></font> <a href="nat_1.html#K1">+</a> 1
 <b>and </b><br/><a NAME="E2:28_1_1_1_2_2_1_15"/><i><font color="Green">E75</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>
 <b>and </b><br/><a NAME="E3:28_1_1_1_2_2_1_15"/><i><font color="Green">E76</font></i>: 
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> 1
 <b>and </b><br/><a NAME="E4:28_1_1_1_2_2_1_15"/><i><font color="Green">E77</font></i>: 
<font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R1">=</a> 1
 ;<br/><div class="add"><a NAME="E5:28_1_1_1_2_2_1_15"/><i><font color="Green">E78</font></i>: 
 <a href="goboard5.html#K5">left_cell</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a>  <a href="goboard5.html#K3">cell</a> <span class="p1">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<font color="Maroon">c<sub>5</sub></font>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span>
 <b>by </b><i><a class="txt" href="goboard9.html#E1:28_1_1_1_2"><i><font color="Green">E33</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1_1_2"><i><font color="Green">E34</font></i></a>, <a class="txt" href="goboard9.html#E7:28_1_1_1_2"><i><font color="Green">E37</font></i></a>, <a class="txt" href="goboard9.html#E8:28_1_1_1_2"><i><font color="Green">E38</font></i></a>, <a class="txt" href="goboard9.html#E11:28_1_1_1_2"><i><font color="Green">E40</font></i></a>, <a class="txt" href="goboard9.html#E12:28_1_1_1_2"><i><font color="Green">E41</font></i></a>, <a class="txt" href="goboard9.html#E24:28_1_1_1_2"><i><font color="Green">E51</font></i></a>, <a class="txt" href="goboard9.html#E39:28_1_1_1_2"><i><font color="Green">E62</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2_2_1_15"><i><font color="Green">E74</font></i></a>, <a class="ref" href="goboard5.html#T30">GOBOARD5:30</a></i>;<br/><a NAME="E6:28_1_1_1_2_2_1_15"/><i><font color="Green">E79</font></i>: 
 <a href="topreal1.html#K3">LSeg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="euclid.html#K20">-</a> <span class="p2"><a href="euclid.html#K23">|[</a><span class="default">1,1</span><a href="euclid.html#K23">]|</a></span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="euclid.html#K17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K20">-</a> <span class="p2"><a href="euclid.html#K23">|[</a><span class="default">0,1</span><a href="euclid.html#K23">]|</a></span></span>)</span> is <a href="connsp_1.html#V2">connected</a>
 <b>by </b><i><a class="ref" href="goboard9.html#T8" target="_self">Th8</a></i>;<br/><a NAME="E7:28_1_1_1_2_2_1_15"/>
<font color="Maroon">c<sub>5</sub></font> <a href="binarith.html#K5">-'</a> 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>5</sub></font>
 <b>by </b><i><a class="txt" href="goboard9.html#E2"><i><font color="Green">Lemma2</font></i></a></i>;<br/><a NAME="E8:28_1_1_1_2_2_1_15"/><b>then </b><i><font color="Green">E80</font></i>: 
<font color="Maroon">c<sub>5</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"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="goboard9.html#E19:28_1_1_1_2"><i><font color="Green">E46</font></i></a>, <a class="ref" href="xxreal_0.html#T2">XXREAL_0:2</a></i>;<br/><a NAME="E9:28_1_1_1_2_2_1_15"/><i><font color="Green">E81</font></i>: 
<font color="Maroon">c<sub>6</sub></font> <a href="binarith.html#K5">-'</a> 1 <a href="hidden.html#R1">=</a> 0
 <b>by </b><i><a class="txt" href="goboard9.html#E4:28_1_1_1_2_2_1_15"><i><font color="Green">E77</font></i></a>, <a class="txt" href="goboard9.html#E1"><i><font color="Green">Lemma1</font></i></a></i>;<br/><a NAME="E10:28_1_1_1_2_2_1_15"/><i><font color="Green">E82</font></i>: 
<font color="Maroon">c<sub>5</sub></font> <a href="binarith.html#K5">-'</a> 1 <a href="hidden.html#R1">=</a> 0
 <b>by </b><i><a class="txt" href="goboard9.html#E3:28_1_1_1_2_2_1_15"><i><font color="Green">E76</font></i></a>, <a class="txt" href="goboard9.html#E1"><i><font color="Green">Lemma1</font></i></a></i>;<br/><a NAME="E11:28_1_1_1_2_2_1_15"/>
<font color="Maroon">c<sub>6</sub></font> <a href="binarith.html#K5">-'</a> 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>6</sub></font>
 <b>by </b><i><a class="txt" href="goboard9.html#E2"><i><font color="Green">Lemma2</font></i></a></i>;<br/><a NAME="E12:28_1_1_1_2_2_1_15"/><b>then </b><i><font color="Green">E83</font></i>: 
<font color="Maroon">c<sub>6</sub></font> <a href="binarith.html#K5">-'</a> 1 <a href="xxreal_0.html#R1">&lt;=</a>  <a href="matrix_1.html#K1">width</a> <span class="p1">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="goboard9.html#E22:28_1_1_1_2"><i><font color="Green">E49</font></i></a>, <a class="ref" href="xxreal_0.html#T2">XXREAL_0:2</a></i>;<br/><a NAME="E13:28_1_1_1_2_2_1_15"/><i><font color="Green">E84</font></i>: 
 <a href="topreal1.html#K3">LSeg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="euclid.html#K20">-</a> <span class="p2"><a href="euclid.html#K23">|[</a><span class="default">1,1</span><a href="euclid.html#K23">]|</a></span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="euclid.html#K17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K20">-</a> <span class="p2"><a href="euclid.html#K23">|[</a><span class="default">0,1</span><a href="euclid.html#K23">]|</a></span></span>)</span> <a href="xboole_0.html#NR5" target="_self">meets</a>  <a href="tops_1.html#K1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K3">cell</a> <span class="p2">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<font color="Maroon">c<sub>5</sub></font>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="goboard9.html#E18:28_1_1_1_2"><i><font color="Green">E45</font></i></a>, <a class="txt" href="goboard9.html#E19:28_1_1_1_2"><i><font color="Green">E46</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2_2_1_15"><i><font color="Green">E74</font></i></a>, <a class="txt" href="goboard9.html#E4:28_1_1_1_2_2_1_15"><i><font color="Green">E77</font></i></a>, <a class="txt" href="goboard9.html#E9:28_1_1_1_2_2_1_15"><i><font color="Green">E81</font></i></a>, <a class="ref" href="goboard6.html#T87">GOBOARD6:87</a></i>;<br/><a NAME="E14:28_1_1_1_2_2_1_15"/>
 <a href="topreal1.html#K3">LSeg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="euclid.html#K20">-</a> <span class="p2"><a href="euclid.html#K23">|[</a><span class="default">1,1</span><a href="euclid.html#K23">]|</a></span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="euclid.html#K17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K20">-</a> <span class="p2"><a href="euclid.html#K23">|[</a><span class="default">0,1</span><a href="euclid.html#K23">]|</a></span></span>)</span> <a href="xboole_0.html#R1">misses</a>  <a href="topreal1.html#K5">L~</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="goboard9.html#E1:28_1_1_1_2_2_1_15"><i><font color="Green">E74</font></i></a>, <a class="txt" href="goboard9.html#E3:28_1_1_1_2_2_1_15"><i><font color="Green">E76</font></i></a>, <a class="txt" href="goboard9.html#E4:28_1_1_1_2_2_1_15"><i><font color="Green">E77</font></i></a>, <a class="ref" href="goboard8.html#T26">GOBOARD8:26</a></i>;<br/><a NAME="E15:28_1_1_1_2_2_1_15"/><b>then </b>
 <a href="topreal1.html#K3">LSeg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="euclid.html#K20">-</a> <span class="p2"><a href="euclid.html#K23">|[</a><span class="default">1,1</span><a href="euclid.html#K23">]|</a></span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="euclid.html#K17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K20">-</a> <span class="p2"><a href="euclid.html#K23">|[</a><span class="default">0,1</span><a href="euclid.html#K23">]|</a></span></span>)</span> <a href="tarski.html#R1">c=</a> <span class="p1">(<span class="default"><a href="topreal1.html#K5">L~</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="subset_1.html#K3">`</a> 
 <b>by </b><i><a class="ref" href="subset_1.html#T43">SUBSET_1:43</a></i>;<br/><a NAME="E16:28_1_1_1_2_2_1_15"/><b>then </b><i><font color="Green">E85</font></i>: 
 <a href="topreal1.html#K3">LSeg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="euclid.html#K20">-</a> <span class="p2"><a href="euclid.html#K23">|[</a><span class="default">1,1</span><a href="euclid.html#K23">]|</a></span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="euclid.html#K17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K20">-</a> <span class="p2"><a href="euclid.html#K23">|[</a><span class="default">0,1</span><a href="euclid.html#K23">]|</a></span></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="goboard9.html#K2" target="_self">LeftComp</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="goboard9.html#E1:28_1"><i><font color="Green">E30</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1"><i><font color="Green">E32</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2"><i><font color="Green">E33</font></i></a>, <a class="txt" href="goboard9.html#E51:28_1_1_1_2"><i><font color="Green">E71</font></i></a>, <a class="txt" href="goboard9.html#E5:28_1_1_1_2_2_1_15"><i><font color="Green">E78</font></i></a>, <a class="txt" href="goboard9.html#E6:28_1_1_1_2_2_1_15"><i><font color="Green">E79</font></i></a>, <a class="txt" href="goboard9.html#E13:28_1_1_1_2_2_1_15"><i><font color="Green">E84</font></i></a>, <a class="ref" href="goboard9.html#T6" target="_self">Th6</a>, <a class="ref" href="nat_1.html#T38">NAT_1:38</a></i>;<br/><a NAME="E17:28_1_1_1_2_2_1_15"/><i><font color="Green">E86</font></i>: 
 <a href="tops_1.html#K1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K3">cell</a> <span class="p2">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span></span>)</span> is <a href="connsp_1.html#V2">connected</a>
 <b>by </b><i><a class="txt" href="goboard9.html#E8:28_1_1_1_2_2_1_15"><i><font color="Green">E80</font></i></a>, <a class="txt" href="goboard9.html#E12:28_1_1_1_2_2_1_15"><i><font color="Green">E83</font></i></a>, <a class="ref" href="goboard9.html#T21" target="_self">Th21</a></i>;<br/><a NAME="E18:28_1_1_1_2_2_1_15"/><i><font color="Green">E87</font></i>: 
 <a href="topreal1.html#K3">LSeg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="euclid.html#K20">-</a> <span class="p2"><a href="euclid.html#K23">|[</a><span class="default">1,1</span><a href="euclid.html#K23">]|</a></span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="euclid.html#K17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K20">-</a> <span class="p2"><a href="euclid.html#K23">|[</a><span class="default">0,1</span><a href="euclid.html#K23">]|</a></span></span>)</span> <a href="xboole_0.html#NR5" target="_self">meets</a>  <a href="tops_1.html#K1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K3">cell</a> <span class="p2">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="goboard9.html#E24:28_1_1_1_2"><i><font color="Green">E51</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2_2_1_15"><i><font color="Green">E74</font></i></a>, <a class="txt" href="goboard9.html#E3:28_1_1_1_2_2_1_15"><i><font color="Green">E76</font></i></a>, <a class="txt" href="goboard9.html#E4:28_1_1_1_2_2_1_15"><i><font color="Green">E77</font></i></a>, <a class="txt" href="goboard9.html#E9:28_1_1_1_2_2_1_15"><i><font color="Green">E81</font></i></a>, <a class="ref" href="goboard6.html#T90">GOBOARD6:90</a></i>;<br/><a NAME="E19:28_1_1_1_2_2_1_15"/>
 <a href="tops_1.html#K1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K3">cell</a> <span class="p2">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span></span>)</span> <a href="xboole_0.html#R1">misses</a>  <a href="topreal1.html#K5">L~</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="goboard9.html#E8:28_1_1_1_2_2_1_15"><i><font color="Green">E80</font></i></a>, <a class="txt" href="goboard9.html#E12:28_1_1_1_2_2_1_15"><i><font color="Green">E83</font></i></a>, <a class="ref" href="goboard7.html#T14">GOBOARD7:14</a></i>;<br/><a NAME="E20:28_1_1_1_2_2_1_15"/><b>then </b>
 <a href="tops_1.html#K1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K3">cell</a> <span class="p2">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span></span>)</span> <a href="tarski.html#R1">c=</a> <span class="p1">(<span class="default"><a href="topreal1.html#K5">L~</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="subset_1.html#K3">`</a> 
 <b>by </b><i><a class="ref" href="subset_1.html#T43">SUBSET_1:43</a></i>;<br/><a NAME="E21:28_1_1_1_2_2_1_15"/><b>then </b><i><font color="Green">E88</font></i>: 
 <a href="tops_1.html#K1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K3">cell</a> <span class="p2">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="goboard9.html#K2" target="_self">LeftComp</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="goboard9.html#E24:28_1_1_1_2"><i><font color="Green">E51</font></i></a>, <a class="txt" href="goboard9.html#E51:28_1_1_1_2"><i><font color="Green">E71</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2_2_1_15"><i><font color="Green">E74</font></i></a>, <a class="txt" href="goboard9.html#E16:28_1_1_1_2_2_1_15"><i><font color="Green">E85</font></i></a>, <a class="txt" href="goboard9.html#E17:28_1_1_1_2_2_1_15"><i><font color="Green">E86</font></i></a>, <a class="txt" href="goboard9.html#E18:28_1_1_1_2_2_1_15"><i><font color="Green">E87</font></i></a>, <a class="ref" href="goboard9.html#T6" target="_self">Th6</a></i>;<br/><a NAME="E22:28_1_1_1_2_2_1_15"/><i><font color="Green">E89</font></i>: 
 <a href="goboard5.html#K5">left_cell</a> <font color="Maroon">c<sub>1</sub></font>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="hidden.html#R1">=</a>  <a href="goboard5.html#K3">cell</a> <span class="p1">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span>,<font color="Maroon">c<sub>6</sub></font>
 <b>by </b><i><a class="txt" href="goboard9.html#E1:28_1_1"><i><font color="Green">E31</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1"><i><font color="Green">E32</font></i></a>, <a class="txt" href="goboard9.html#E11:28_1_1_1_2"><i><font color="Green">E40</font></i></a>, <a class="txt" href="goboard9.html#E12:28_1_1_1_2"><i><font color="Green">E41</font></i></a>, <a class="txt" href="goboard9.html#E16:28_1_1_1_2"><i><font color="Green">E43</font></i></a>, <a class="txt" href="goboard9.html#E17:28_1_1_1_2"><i><font color="Green">E44</font></i></a>, <a class="txt" href="goboard9.html#E25:28_1_1_1_2"><i><font color="Green">E52</font></i></a>, <a class="txt" href="goboard9.html#E37:28_1_1_1_2"><i><font color="Green">E61</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1_1_2_2_1_15"><i><font color="Green">E75</font></i></a>, <a class="ref" href="goboard5.html#T28">GOBOARD5:28</a></i>;<br/><a NAME="E23:28_1_1_1_2_2_1_15"/><i><font color="Green">E90</font></i>: 
 <a href="topreal1.html#K3">LSeg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="euclid.html#K20">-</a> <span class="p2"><a href="euclid.html#K23">|[</a><span class="default">1,1</span><a href="euclid.html#K23">]|</a></span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="euclid.html#K17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>8</sub></font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K20">-</a> <span class="p2"><a href="euclid.html#K23">|[</a><span class="default">1,0</span><a href="euclid.html#K23">]|</a></span></span>)</span> is <a href="connsp_1.html#V2">connected</a>
 <b>by </b><i><a class="ref" href="goboard9.html#T8" target="_self">Th8</a></i>;<br/><a NAME="E24:28_1_1_1_2_2_1_15"/><i><font color="Green">E91</font></i>: 
 <a href="topreal1.html#K3">LSeg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="euclid.html#K20">-</a> <span class="p2"><a href="euclid.html#K23">|[</a><span class="default">1,1</span><a href="euclid.html#K23">]|</a></span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="euclid.html#K17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>8</sub></font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K20">-</a> <span class="p2"><a href="euclid.html#K23">|[</a><span class="default">1,0</span><a href="euclid.html#K23">]|</a></span></span>)</span> <a href="xboole_0.html#NR5" target="_self">meets</a>  <a href="tops_1.html#K1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K3">cell</a> <span class="p2">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="goboard9.html#E3:28_1_1_1_2_2_1_15"><i><font color="Green">E76</font></i></a>, <a class="txt" href="goboard9.html#E4:28_1_1_1_2_2_1_15"><i><font color="Green">E77</font></i></a>, <a class="txt" href="goboard9.html#E9:28_1_1_1_2_2_1_15"><i><font color="Green">E81</font></i></a>, <a class="ref" href="goboard6.html#T90">GOBOARD6:90</a></i>;<br/><a NAME="E25:28_1_1_1_2_2_1_15"/>
 <a href="topreal1.html#K3">LSeg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="euclid.html#K20">-</a> <span class="p2"><a href="euclid.html#K23">|[</a><span class="default">1,1</span><a href="euclid.html#K23">]|</a></span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="euclid.html#K17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>8</sub></font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K20">-</a> <span class="p2"><a href="euclid.html#K23">|[</a><span class="default">1,0</span><a href="euclid.html#K23">]|</a></span></span>)</span> <a href="xboole_0.html#R1">misses</a>  <a href="topreal1.html#K5">L~</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="goboard9.html#E2:28_1_1_1_2_2_1_15"><i><font color="Green">E75</font></i></a>, <a class="txt" href="goboard9.html#E3:28_1_1_1_2_2_1_15"><i><font color="Green">E76</font></i></a>, <a class="txt" href="goboard9.html#E4:28_1_1_1_2_2_1_15"><i><font color="Green">E77</font></i></a>, <a class="ref" href="goboard8.html#T32">GOBOARD8:32</a></i>;<br/><a NAME="E26:28_1_1_1_2_2_1_15"/><b>then </b>
 <a href="topreal1.html#K3">LSeg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="euclid.html#K20">-</a> <span class="p2"><a href="euclid.html#K23">|[</a><span class="default">1,1</span><a href="euclid.html#K23">]|</a></span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="euclid.html#K17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>8</sub></font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K20">-</a> <span class="p2"><a href="euclid.html#K23">|[</a><span class="default">1,0</span><a href="euclid.html#K23">]|</a></span></span>)</span> <a href="tarski.html#R1">c=</a> <span class="p1">(<span class="default"><a href="topreal1.html#K5">L~</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="subset_1.html#K3">`</a> 
 <b>by </b><i><a class="ref" href="subset_1.html#T43">SUBSET_1:43</a></i>;<br/><a NAME="E27:28_1_1_1_2_2_1_15"/><b>then </b><i><font color="Green">E92</font></i>: 
 <a href="topreal1.html#K3">LSeg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="euclid.html#K20">-</a> <span class="p2"><a href="euclid.html#K23">|[</a><span class="default">1,1</span><a href="euclid.html#K23">]|</a></span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="euclid.html#K17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>8</sub></font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K20">-</a> <span class="p2"><a href="euclid.html#K23">|[</a><span class="default">1,0</span><a href="euclid.html#K23">]|</a></span></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="goboard9.html#K2" target="_self">LeftComp</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="goboard9.html#E51:28_1_1_1_2"><i><font color="Green">E71</font></i></a>, <a class="txt" href="goboard9.html#E21:28_1_1_1_2_2_1_15"><i><font color="Green">E88</font></i></a>, <a class="txt" href="goboard9.html#E23:28_1_1_1_2_2_1_15"><i><font color="Green">E90</font></i></a>, <a class="txt" href="goboard9.html#E24:28_1_1_1_2_2_1_15"><i><font color="Green">E91</font></i></a>, <a class="ref" href="goboard9.html#T6" target="_self">Th6</a></i>;<br/><a NAME="E28:28_1_1_1_2_2_1_15"/><i><font color="Green">E93</font></i>: 
 <a href="topreal1.html#K3">LSeg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="euclid.html#K20">-</a> <span class="p2"><a href="euclid.html#K23">|[</a><span class="default">1,1</span><a href="euclid.html#K23">]|</a></span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="euclid.html#K17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>8</sub></font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K20">-</a> <span class="p2"><a href="euclid.html#K23">|[</a><span class="default">1,0</span><a href="euclid.html#K23">]|</a></span></span>)</span> <a href="xboole_0.html#NR5" target="_self">meets</a>  <a href="tops_1.html#K1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K3">cell</a> <span class="p2">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span>,<font color="Maroon">c<sub>6</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="goboard9.html#E22:28_1_1_1_2"><i><font color="Green">E49</font></i></a>, <a class="txt" href="goboard9.html#E23:28_1_1_1_2"><i><font color="Green">E50</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1_1_2_2_1_15"><i><font color="Green">E75</font></i></a>, <a class="txt" href="goboard9.html#E3:28_1_1_1_2_2_1_15"><i><font color="Green">E76</font></i></a>, <a class="txt" href="goboard9.html#E10:28_1_1_1_2_2_1_15"><i><font color="Green">E82</font></i></a>, <a class="ref" href="goboard6.html#T88">GOBOARD6:88</a></i>;<br/><a NAME="E29:28_1_1_1_2_2_1_15"/>
 <a href="tops_1.html#K1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K5">left_cell</a> <font color="Maroon">c<sub>1</sub></font>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="xboole_0.html#R1">misses</a>  <a href="topreal1.html#K5">L~</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="goboard9.html#E1:28_1_1"><i><font color="Green">E31</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1"><i><font color="Green">E32</font></i></a>, <a class="ref" href="goboard8.html#T37">GOBOARD8:37</a></i>;<br/><a NAME="E30:28_1_1_1_2_2_1_15"/><b>then </b>
 <a href="tops_1.html#K1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K5">left_cell</a> <font color="Maroon">c<sub>1</sub></font>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="tarski.html#R1">c=</a> <span class="p1">(<span class="default"><a href="topreal1.html#K5">L~</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="subset_1.html#K3">`</a> 
 <b>by </b><i><a class="ref" href="subset_1.html#T43">SUBSET_1:43</a></i>;<br/><b>hence </b><a NAME="E31:28_1_1_1_2_2_1_15"/>
 <a href="tops_1.html#K1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K5">left_cell</a> <font color="Maroon">c<sub>1</sub></font>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="goboard9.html#K2" target="_self">LeftComp</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="goboard9.html#E51:28_1_1_1_2"><i><font color="Green">E71</font></i></a>, <a class="txt" href="goboard9.html#E52:28_1_1_1_2"><i><font color="Green">E72</font></i></a>, <a class="txt" href="goboard9.html#E22:28_1_1_1_2_2_1_15"><i><font color="Green">E89</font></i></a>, <a class="txt" href="goboard9.html#E27:28_1_1_1_2_2_1_15"><i><font color="Green">E92</font></i></a>, <a class="txt" href="goboard9.html#E28:28_1_1_1_2_2_1_15"><i><font color="Green">E93</font></i></a>, <a class="ref" href="goboard9.html#T6" target="_self">Th6</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="28_1_1_1_2_2_1_16"><b>suppose </b></a><b>that </b><a NAME="E1:28_1_1_1_2_2_1_16"/><i><font color="Green">E74</font></i>: 
<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>5</sub></font> <a href="nat_1.html#K1">+</a> 1
 <b>and </b><br/><a NAME="E2:28_1_1_1_2_2_1_16"/><i><font color="Green">E75</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>
 <b>and </b><br/><a NAME="E3:28_1_1_1_2_2_1_16"/><i><font color="Green">E76</font></i>: 
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 1
 <b>and </b><br/><a NAME="E4:28_1_1_1_2_2_1_16"/><i><font color="Green">E77</font></i>: 
<font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R1">=</a> 1
 ;<br/><div class="add"><a NAME="E5:28_1_1_1_2_2_1_16"/><i><font color="Green">E78</font></i>: 
 <a href="goboard5.html#K5">left_cell</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a>  <a href="goboard5.html#K3">cell</a> <span class="p1">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<font color="Maroon">c<sub>5</sub></font>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span>
 <b>by </b><i><a class="txt" href="goboard9.html#E1:28_1_1_1_2"><i><font color="Green">E33</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1_1_2"><i><font color="Green">E34</font></i></a>, <a class="txt" href="goboard9.html#E7:28_1_1_1_2"><i><font color="Green">E37</font></i></a>, <a class="txt" href="goboard9.html#E8:28_1_1_1_2"><i><font color="Green">E38</font></i></a>, <a class="txt" href="goboard9.html#E11:28_1_1_1_2"><i><font color="Green">E40</font></i></a>, <a class="txt" href="goboard9.html#E12:28_1_1_1_2"><i><font color="Green">E41</font></i></a>, <a class="txt" href="goboard9.html#E24:28_1_1_1_2"><i><font color="Green">E51</font></i></a>, <a class="txt" href="goboard9.html#E39:28_1_1_1_2"><i><font color="Green">E62</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2_2_1_16"><i><font color="Green">E74</font></i></a>, <a class="ref" href="goboard5.html#T30">GOBOARD5:30</a></i>;<br/><a NAME="E6:28_1_1_1_2_2_1_16"/>
1 <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">c<sub>5</sub></font>
 <b>by </b><i><a class="txt" href="goboard9.html#E19:28_1_1_1_2"><i><font color="Green">E46</font></i></a>, <a class="txt" href="goboard9.html#E3:28_1_1_1_2_2_1_16"><i><font color="Green">E76</font></i></a>, <a class="ref" href="xxreal_0.html#T1">XXREAL_0:1</a></i>;<br/><a NAME="E7:28_1_1_1_2_2_1_16"/><b>then </b><i><font color="Green">E79</font></i>: 
1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>5</sub></font> <a href="binarith.html#K5">-'</a> 1
 <b>by </b><i><a class="txt" href="goboard9.html#E37:28_1_1_1_2"><i><font color="Green">E61</font></i></a>, <a class="ref" href="nat_1.html#T38">NAT_1:38</a></i>;<br/><a NAME="E8:28_1_1_1_2_2_1_16"/><i><font color="Green">E80</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>5</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> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font>
 <b>by </b><i><a class="txt" href="goboard9.html#E37:28_1_1_1_2"><i><font color="Green">E61</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2_2_1_16"><i><font color="Green">E74</font></i></a></i>;<br/><a NAME="E9:28_1_1_1_2_2_1_16"/><i><font color="Green">E81</font></i>: 
 <a href="topreal1.html#K3">LSeg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span>,1</span>)</span> <a href="euclid.html#K17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>5</sub></font>,1</span>)</span></span>)</span></span>)</span> <a href="euclid.html#K20">-</a> <span class="p2"><a href="euclid.html#K23">|[</a><span class="default">0,1</span><a href="euclid.html#K23">]|</a></span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>5</sub></font>,1</span>)</span> <a href="euclid.html#K17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>3</sub></font>,1</span>)</span></span>)</span></span>)</span> <a href="euclid.html#K20">-</a> <span class="p2"><a href="euclid.html#K23">|[</a><span class="default">0,1</span><a href="euclid.html#K23">]|</a></span></span>)</span> is <a href="connsp_1.html#V2">connected</a>
 <b>by </b><i><a class="ref" href="goboard9.html#T8" target="_self">Th8</a></i>;<br/><a NAME="E10:28_1_1_1_2_2_1_16"/>
<font color="Maroon">c<sub>5</sub></font> <a href="binarith.html#K5">-'</a> 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>5</sub></font>
 <b>by </b><i><a class="txt" href="goboard9.html#E2"><i><font color="Green">Lemma2</font></i></a></i>;<br/><a NAME="E11:28_1_1_1_2_2_1_16"/><b>then </b><i><font color="Green">E82</font></i>: 
<font color="Maroon">c<sub>5</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"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="goboard9.html#E19:28_1_1_1_2"><i><font color="Green">E46</font></i></a>, <a class="ref" href="xxreal_0.html#T2">XXREAL_0:2</a></i>;<br/><a NAME="E12:28_1_1_1_2_2_1_16"/><i><font color="Green">E83</font></i>: 
<font color="Maroon">c<sub>6</sub></font> <a href="binarith.html#K5">-'</a> 1 <a href="hidden.html#R1">=</a> 0
 <b>by </b><i><a class="txt" href="goboard9.html#E4:28_1_1_1_2_2_1_16"><i><font color="Green">E77</font></i></a>, <a class="txt" href="goboard9.html#E1"><i><font color="Green">Lemma1</font></i></a></i>;<br/><a NAME="E13:28_1_1_1_2_2_1_16"/>
<font color="Maroon">c<sub>6</sub></font> <a href="binarith.html#K5">-'</a> 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>6</sub></font>
 <b>by </b><i><a class="txt" href="goboard9.html#E2"><i><font color="Green">Lemma2</font></i></a></i>;<br/><a NAME="E14:28_1_1_1_2_2_1_16"/><b>then </b><i><font color="Green">E84</font></i>: 
<font color="Maroon">c<sub>6</sub></font> <a href="binarith.html#K5">-'</a> 1 <a href="xxreal_0.html#R1">&lt;=</a>  <a href="matrix_1.html#K1">width</a> <span class="p1">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="goboard9.html#E22:28_1_1_1_2"><i><font color="Green">E49</font></i></a>, <a class="ref" href="xxreal_0.html#T2">XXREAL_0:2</a></i>;<br/><a NAME="E15:28_1_1_1_2_2_1_16"/><i><font color="Green">E85</font></i>: 
 <a href="topreal1.html#K3">LSeg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span>,1</span>)</span> <a href="euclid.html#K17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>5</sub></font>,1</span>)</span></span>)</span></span>)</span> <a href="euclid.html#K20">-</a> <span class="p2"><a href="euclid.html#K23">|[</a><span class="default">0,1</span><a href="euclid.html#K23">]|</a></span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>5</sub></font>,1</span>)</span> <a href="euclid.html#K17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>3</sub></font>,1</span>)</span></span>)</span></span>)</span> <a href="euclid.html#K20">-</a> <span class="p2"><a href="euclid.html#K23">|[</a><span class="default">0,1</span><a href="euclid.html#K23">]|</a></span></span>)</span> <a href="xboole_0.html#NR5" target="_self">meets</a>  <a href="tops_1.html#K1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K3">cell</a> <span class="p2">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<font color="Maroon">c<sub>5</sub></font>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="goboard9.html#E18:28_1_1_1_2"><i><font color="Green">E45</font></i></a>, <a class="txt" href="goboard9.html#E19:28_1_1_1_2"><i><font color="Green">E46</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2_2_1_16"><i><font color="Green">E74</font></i></a>, <a class="txt" href="goboard9.html#E12:28_1_1_1_2_2_1_16"><i><font color="Green">E83</font></i></a>, <a class="ref" href="goboard6.html#T87">GOBOARD6:87</a></i>;<br/><a NAME="E16:28_1_1_1_2_2_1_16"/>
 <a href="topreal1.html#K3">LSeg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span>,1</span>)</span> <a href="euclid.html#K17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>5</sub></font>,1</span>)</span></span>)</span></span>)</span> <a href="euclid.html#K20">-</a> <span class="p2"><a href="euclid.html#K23">|[</a><span class="default">0,1</span><a href="euclid.html#K23">]|</a></span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>5</sub></font>,1</span>)</span> <a href="euclid.html#K17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>3</sub></font>,1</span>)</span></span>)</span></span>)</span> <a href="euclid.html#K20">-</a> <span class="p2"><a href="euclid.html#K23">|[</a><span class="default">0,1</span><a href="euclid.html#K23">]|</a></span></span>)</span> <a href="xboole_0.html#R1">misses</a>  <a href="topreal1.html#K5">L~</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="goboard9.html#E18:28_1_1_1_2"><i><font color="Green">E45</font></i></a>, <a class="txt" href="goboard9.html#E37:28_1_1_1_2"><i><font color="Green">E61</font></i></a>, <a class="txt" href="goboard9.html#E7:28_1_1_1_2_2_1_16"><i><font color="Green">E79</font></i></a>, <a class="txt" href="goboard9.html#E8:28_1_1_1_2_2_1_16"><i><font color="Green">E80</font></i></a>, <a class="ref" href="goboard8.html#T25">GOBOARD8:25</a></i>;<br/><a NAME="E17:28_1_1_1_2_2_1_16"/><b>then </b>
 <a href="topreal1.html#K3">LSeg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span>,1</span>)</span> <a href="euclid.html#K17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>5</sub></font>,1</span>)</span></span>)</span></span>)</span> <a href="euclid.html#K20">-</a> <span class="p2"><a href="euclid.html#K23">|[</a><span class="default">0,1</span><a href="euclid.html#K23">]|</a></span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>5</sub></font>,1</span>)</span> <a href="euclid.html#K17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>3</sub></font>,1</span>)</span></span>)</span></span>)</span> <a href="euclid.html#K20">-</a> <span class="p2"><a href="euclid.html#K23">|[</a><span class="default">0,1</span><a href="euclid.html#K23">]|</a></span></span>)</span> <a href="tarski.html#R1">c=</a> <span class="p1">(<span class="default"><a href="topreal1.html#K5">L~</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="subset_1.html#K3">`</a> 
 <b>by </b><i><a class="ref" href="subset_1.html#T43">SUBSET_1:43</a></i>;<br/><a NAME="E18:28_1_1_1_2_2_1_16"/><b>then </b><i><font color="Green">E86</font></i>: 
 <a href="topreal1.html#K3">LSeg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span>,1</span>)</span> <a href="euclid.html#K17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>5</sub></font>,1</span>)</span></span>)</span></span>)</span> <a href="euclid.html#K20">-</a> <span class="p2"><a href="euclid.html#K23">|[</a><span class="default">0,1</span><a href="euclid.html#K23">]|</a></span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>5</sub></font>,1</span>)</span> <a href="euclid.html#K17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>3</sub></font>,1</span>)</span></span>)</span></span>)</span> <a href="euclid.html#K20">-</a> <span class="p2"><a href="euclid.html#K23">|[</a><span class="default">0,1</span><a href="euclid.html#K23">]|</a></span></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="goboard9.html#K2" target="_self">LeftComp</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="goboard9.html#E1:28_1"><i><font color="Green">E30</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1"><i><font color="Green">E32</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2"><i><font color="Green">E33</font></i></a>, <a class="txt" href="goboard9.html#E51:28_1_1_1_2"><i><font color="Green">E71</font></i></a>, <a class="txt" href="goboard9.html#E5:28_1_1_1_2_2_1_16"><i><font color="Green">E78</font></i></a>, <a class="txt" href="goboard9.html#E9:28_1_1_1_2_2_1_16"><i><font color="Green">E81</font></i></a>, <a class="txt" href="goboard9.html#E15:28_1_1_1_2_2_1_16"><i><font color="Green">E85</font></i></a>, <a class="ref" href="goboard9.html#T6" target="_self">Th6</a>, <a class="ref" href="nat_1.html#T38">NAT_1:38</a></i>;<br/><a NAME="E19:28_1_1_1_2_2_1_16"/><i><font color="Green">E87</font></i>: 
 <a href="tops_1.html#K1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K3">cell</a> <span class="p2">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span></span>)</span> is <a href="connsp_1.html#V2">connected</a>
 <b>by </b><i><a class="txt" href="goboard9.html#E11:28_1_1_1_2_2_1_16"><i><font color="Green">E82</font></i></a>, <a class="txt" href="goboard9.html#E14:28_1_1_1_2_2_1_16"><i><font color="Green">E84</font></i></a>, <a class="ref" href="goboard9.html#T21" target="_self">Th21</a></i>;<br/><a NAME="E20:28_1_1_1_2_2_1_16"/><i><font color="Green">E88</font></i>: 
 <a href="topreal1.html#K3">LSeg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span>,1</span>)</span> <a href="euclid.html#K17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>5</sub></font>,1</span>)</span></span>)</span></span>)</span> <a href="euclid.html#K20">-</a> <span class="p2"><a href="euclid.html#K23">|[</a><span class="default">0,1</span><a href="euclid.html#K23">]|</a></span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>5</sub></font>,1</span>)</span> <a href="euclid.html#K17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>3</sub></font>,1</span>)</span></span>)</span></span>)</span> <a href="euclid.html#K20">-</a> <span class="p2"><a href="euclid.html#K23">|[</a><span class="default">0,1</span><a href="euclid.html#K23">]|</a></span></span>)</span> <a href="xboole_0.html#NR5" target="_self">meets</a>  <a href="tops_1.html#K1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K3">cell</a> <span class="p2">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="goboard9.html#E19:28_1_1_1_2"><i><font color="Green">E46</font></i></a>, <a class="txt" href="goboard9.html#E24:28_1_1_1_2"><i><font color="Green">E51</font></i></a>, <a class="txt" href="goboard9.html#E37:28_1_1_1_2"><i><font color="Green">E61</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2_2_1_16"><i><font color="Green">E74</font></i></a>, <a class="txt" href="goboard9.html#E7:28_1_1_1_2_2_1_16"><i><font color="Green">E79</font></i></a>, <a class="txt" href="goboard9.html#E12:28_1_1_1_2_2_1_16"><i><font color="Green">E83</font></i></a>, <a class="ref" href="goboard6.html#T87">GOBOARD6:87</a></i>;<br/><a NAME="E21:28_1_1_1_2_2_1_16"/>
 <a href="tops_1.html#K1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K3">cell</a> <span class="p2">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span></span>)</span> <a href="xboole_0.html#R1">misses</a>  <a href="topreal1.html#K5">L~</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="goboard9.html#E11:28_1_1_1_2_2_1_16"><i><font color="Green">E82</font></i></a>, <a class="txt" href="goboard9.html#E14:28_1_1_1_2_2_1_16"><i><font color="Green">E84</font></i></a>, <a class="ref" href="goboard7.html#T14">GOBOARD7:14</a></i>;<br/><a NAME="E22:28_1_1_1_2_2_1_16"/><b>then </b>
 <a href="tops_1.html#K1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K3">cell</a> <span class="p2">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span></span>)</span> <a href="tarski.html#R1">c=</a> <span class="p1">(<span class="default"><a href="topreal1.html#K5">L~</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="subset_1.html#K3">`</a> 
 <b>by </b><i><a class="ref" href="subset_1.html#T43">SUBSET_1:43</a></i>;<br/><a NAME="E23:28_1_1_1_2_2_1_16"/><b>then </b><i><font color="Green">E89</font></i>: 
 <a href="tops_1.html#K1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K3">cell</a> <span class="p2">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="goboard9.html#K2" target="_self">LeftComp</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="goboard9.html#E24:28_1_1_1_2"><i><font color="Green">E51</font></i></a>, <a class="txt" href="goboard9.html#E51:28_1_1_1_2"><i><font color="Green">E71</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2_2_1_16"><i><font color="Green">E74</font></i></a>, <a class="txt" href="goboard9.html#E18:28_1_1_1_2_2_1_16"><i><font color="Green">E86</font></i></a>, <a class="txt" href="goboard9.html#E19:28_1_1_1_2_2_1_16"><i><font color="Green">E87</font></i></a>, <a class="txt" href="goboard9.html#E20:28_1_1_1_2_2_1_16"><i><font color="Green">E88</font></i></a>, <a class="ref" href="goboard9.html#T6" target="_self">Th6</a></i>;<br/><a NAME="E24:28_1_1_1_2_2_1_16"/><i><font color="Green">E90</font></i>: 
 <a href="goboard5.html#K5">left_cell</a> <font color="Maroon">c<sub>1</sub></font>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="hidden.html#R1">=</a>  <a href="goboard5.html#K3">cell</a> <span class="p1">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span>,<font color="Maroon">c<sub>6</sub></font>
 <b>by </b><i><a class="txt" href="goboard9.html#E1:28_1_1"><i><font color="Green">E31</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1"><i><font color="Green">E32</font></i></a>, <a class="txt" href="goboard9.html#E11:28_1_1_1_2"><i><font color="Green">E40</font></i></a>, <a class="txt" href="goboard9.html#E12:28_1_1_1_2"><i><font color="Green">E41</font></i></a>, <a class="txt" href="goboard9.html#E16:28_1_1_1_2"><i><font color="Green">E43</font></i></a>, <a class="txt" href="goboard9.html#E17:28_1_1_1_2"><i><font color="Green">E44</font></i></a>, <a class="txt" href="goboard9.html#E25:28_1_1_1_2"><i><font color="Green">E52</font></i></a>, <a class="txt" href="goboard9.html#E37:28_1_1_1_2"><i><font color="Green">E61</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1_1_2_2_1_16"><i><font color="Green">E75</font></i></a>, <a class="ref" href="goboard5.html#T28">GOBOARD5:28</a></i>;<br/><a NAME="E25:28_1_1_1_2_2_1_16"/><i><font color="Green">E91</font></i>: 
 <a href="topreal1.html#K3">LSeg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span>,1</span>)</span> <a href="euclid.html#K17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>5</sub></font>,1</span>)</span></span>)</span></span>)</span> <a href="euclid.html#K20">-</a> <span class="p2"><a href="euclid.html#K23">|[</a><span class="default">0,1</span><a href="euclid.html#K23">]|</a></span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span>,1</span>)</span> <a href="euclid.html#K17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>5</sub></font>,2</span>)</span></span>)</span></span>)</span> is <a href="connsp_1.html#V2">connected</a>
 <b>by </b><i><a class="ref" href="goboard9.html#T8" target="_self">Th8</a></i>;<br/><a NAME="E26:28_1_1_1_2_2_1_16"/><i><font color="Green">E92</font></i>: 
 <a href="topreal1.html#K3">LSeg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span>,1</span>)</span> <a href="euclid.html#K17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>5</sub></font>,1</span>)</span></span>)</span></span>)</span> <a href="euclid.html#K20">-</a> <span class="p2"><a href="euclid.html#K23">|[</a><span class="default">0,1</span><a href="euclid.html#K23">]|</a></span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span>,1</span>)</span> <a href="euclid.html#K17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>5</sub></font>,2</span>)</span></span>)</span></span>)</span> <a href="xboole_0.html#NR5" target="_self">meets</a>  <a href="tops_1.html#K1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K3">cell</a> <span class="p2">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="goboard9.html#E19:28_1_1_1_2"><i><font color="Green">E46</font></i></a>, <a class="txt" href="goboard9.html#E37:28_1_1_1_2"><i><font color="Green">E61</font></i></a>, <a class="txt" href="goboard9.html#E7:28_1_1_1_2_2_1_16"><i><font color="Green">E79</font></i></a>, <a class="txt" href="goboard9.html#E12:28_1_1_1_2_2_1_16"><i><font color="Green">E83</font></i></a>, <a class="ref" href="goboard6.html#T87">GOBOARD6:87</a></i>;<br/><a NAME="E27:28_1_1_1_2_2_1_16"/>
 <a href="topreal1.html#K3">LSeg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span>,1</span>)</span> <a href="euclid.html#K17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>5</sub></font>,1</span>)</span></span>)</span></span>)</span> <a href="euclid.html#K20">-</a> <span class="p2"><a href="euclid.html#K23">|[</a><span class="default">0,1</span><a href="euclid.html#K23">]|</a></span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span>,1</span>)</span> <a href="euclid.html#K17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>5</sub></font>,2</span>)</span></span>)</span></span>)</span> <a href="xboole_0.html#R1">misses</a>  <a href="topreal1.html#K5">L~</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="goboard9.html#E2:28_1_1"><i><font color="Green">E32</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2"><i><font color="Green">E33</font></i></a>, <a class="txt" href="goboard9.html#E8:28_1_1_1_2"><i><font color="Green">E38</font></i></a>, <a class="txt" href="goboard9.html#E12:28_1_1_1_2"><i><font color="Green">E41</font></i></a>, <a class="txt" href="goboard9.html#E17:28_1_1_1_2"><i><font color="Green">E44</font></i></a>, <a class="txt" href="goboard9.html#E18:28_1_1_1_2"><i><font color="Green">E45</font></i></a>, <a class="txt" href="goboard9.html#E24:28_1_1_1_2"><i><font color="Green">E51</font></i></a>, <a class="txt" href="goboard9.html#E25:28_1_1_1_2"><i><font color="Green">E52</font></i></a>, <a class="txt" href="goboard9.html#E37:28_1_1_1_2"><i><font color="Green">E61</font></i></a>, <a class="txt" href="goboard9.html#E46:28_1_1_1_2"><i><font color="Green">E66</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1_1_2_2_1_16"><i><font color="Green">E75</font></i></a>, <a class="txt" href="goboard9.html#E4:28_1_1_1_2_2_1_16"><i><font color="Green">E77</font></i></a>, <a class="txt" href="goboard9.html#E7:28_1_1_1_2_2_1_16"><i><font color="Green">E79</font></i></a>, <a class="txt" href="goboard9.html#E8:28_1_1_1_2_2_1_16"><i><font color="Green">E80</font></i></a>, <a class="ref" href="goboard8.html#T7">GOBOARD8:7</a></i>;<br/><a NAME="E28:28_1_1_1_2_2_1_16"/><b>then </b>
 <a href="topreal1.html#K3">LSeg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span>,1</span>)</span> <a href="euclid.html#K17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>5</sub></font>,1</span>)</span></span>)</span></span>)</span> <a href="euclid.html#K20">-</a> <span class="p2"><a href="euclid.html#K23">|[</a><span class="default">0,1</span><a href="euclid.html#K23">]|</a></span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span>,1</span>)</span> <a href="euclid.html#K17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>5</sub></font>,2</span>)</span></span>)</span></span>)</span> <a href="tarski.html#R1">c=</a> <span class="p1">(<span class="default"><a href="topreal1.html#K5">L~</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="subset_1.html#K3">`</a> 
 <b>by </b><i><a class="ref" href="subset_1.html#T43">SUBSET_1:43</a></i>;<br/><a NAME="E29:28_1_1_1_2_2_1_16"/><b>then </b><i><font color="Green">E93</font></i>: 
 <a href="topreal1.html#K3">LSeg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span>,1</span>)</span> <a href="euclid.html#K17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>5</sub></font>,1</span>)</span></span>)</span></span>)</span> <a href="euclid.html#K20">-</a> <span class="p2"><a href="euclid.html#K23">|[</a><span class="default">0,1</span><a href="euclid.html#K23">]|</a></span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span>,1</span>)</span> <a href="euclid.html#K17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>5</sub></font>,2</span>)</span></span>)</span></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="goboard9.html#K2" target="_self">LeftComp</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="goboard9.html#E51:28_1_1_1_2"><i><font color="Green">E71</font></i></a>, <a class="txt" href="goboard9.html#E23:28_1_1_1_2_2_1_16"><i><font color="Green">E89</font></i></a>, <a class="txt" href="goboard9.html#E25:28_1_1_1_2_2_1_16"><i><font color="Green">E91</font></i></a>, <a class="txt" href="goboard9.html#E26:28_1_1_1_2_2_1_16"><i><font color="Green">E92</font></i></a>, <a class="ref" href="goboard9.html#T6" target="_self">Th6</a></i>;<br/><a NAME="E30:28_1_1_1_2_2_1_16"/><i><font color="Green">E94</font></i>: 
 <a href="topreal1.html#K3">LSeg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span>,1</span>)</span> <a href="euclid.html#K17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>5</sub></font>,1</span>)</span></span>)</span></span>)</span> <a href="euclid.html#K20">-</a> <span class="p2"><a href="euclid.html#K23">|[</a><span class="default">0,1</span><a href="euclid.html#K23">]|</a></span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span>,1</span>)</span> <a href="euclid.html#K17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>5</sub></font>,2</span>)</span></span>)</span></span>)</span> <a href="xboole_0.html#NR5" target="_self">meets</a>  <a href="tops_1.html#K1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K3">cell</a> <span class="p2">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span>,<font color="Maroon">c<sub>6</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="goboard9.html#E19:28_1_1_1_2"><i><font color="Green">E46</font></i></a>, <a class="txt" href="goboard9.html#E23:28_1_1_1_2"><i><font color="Green">E50</font></i></a>, <a class="txt" href="goboard9.html#E37:28_1_1_1_2"><i><font color="Green">E61</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1_1_2_2_1_16"><i><font color="Green">E75</font></i></a>, <a class="txt" href="goboard9.html#E4:28_1_1_1_2_2_1_16"><i><font color="Green">E77</font></i></a>, <a class="txt" href="goboard9.html#E7:28_1_1_1_2_2_1_16"><i><font color="Green">E79</font></i></a>, <a class="ref" href="goboard6.html#T85">GOBOARD6:85</a></i>;<br/><a NAME="E31:28_1_1_1_2_2_1_16"/>
 <a href="tops_1.html#K1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K5">left_cell</a> <font color="Maroon">c<sub>1</sub></font>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="xboole_0.html#R1">misses</a>  <a href="topreal1.html#K5">L~</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="goboard9.html#E1:28_1_1"><i><font color="Green">E31</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1"><i><font color="Green">E32</font></i></a>, <a class="ref" href="goboard8.html#T37">GOBOARD8:37</a></i>;<br/><a NAME="E32:28_1_1_1_2_2_1_16"/><b>then </b>
 <a href="tops_1.html#K1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K5">left_cell</a> <font color="Maroon">c<sub>1</sub></font>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="tarski.html#R1">c=</a> <span class="p1">(<span class="default"><a href="topreal1.html#K5">L~</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="subset_1.html#K3">`</a> 
 <b>by </b><i><a class="ref" href="subset_1.html#T43">SUBSET_1:43</a></i>;<br/><b>hence </b><a NAME="E33:28_1_1_1_2_2_1_16"/>
 <a href="tops_1.html#K1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K5">left_cell</a> <font color="Maroon">c<sub>1</sub></font>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="goboard9.html#K2" target="_self">LeftComp</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="goboard9.html#E51:28_1_1_1_2"><i><font color="Green">E71</font></i></a>, <a class="txt" href="goboard9.html#E52:28_1_1_1_2"><i><font color="Green">E72</font></i></a>, <a class="txt" href="goboard9.html#E24:28_1_1_1_2_2_1_16"><i><font color="Green">E90</font></i></a>, <a class="txt" href="goboard9.html#E29:28_1_1_1_2_2_1_16"><i><font color="Green">E93</font></i></a>, <a class="txt" href="goboard9.html#E30:28_1_1_1_2_2_1_16"><i><font color="Green">E94</font></i></a>, <a class="ref" href="goboard9.html#T6" target="_self">Th6</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="28_1_1_1_2_2_1_17"><b>suppose </b></a><b>that </b><a NAME="E1:28_1_1_1_2_2_1_17"/><i><font color="Green">E74</font></i>: 
<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>5</sub></font> <a href="nat_1.html#K1">+</a> 1
 <b>and </b><br/><a NAME="E2:28_1_1_1_2_2_1_17"/><i><font color="Green">E75</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>
 <b>and </b><br/><a NAME="E3:28_1_1_1_2_2_1_17"/><i><font color="Green">E76</font></i>: 
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> 1
 <b>and </b><br/><a NAME="E4:28_1_1_1_2_2_1_17"/><i><font color="Green">E77</font></i>: 
<font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 1
 ;<br/><div class="add"><a NAME="E5:28_1_1_1_2_2_1_17"/><i><font color="Green">E78</font></i>: 
 <a href="goboard5.html#K5">left_cell</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a>  <a href="goboard5.html#K3">cell</a> <span class="p1">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<font color="Maroon">c<sub>5</sub></font>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span>
 <b>by </b><i><a class="txt" href="goboard9.html#E1:28_1_1_1_2"><i><font color="Green">E33</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1_1_2"><i><font color="Green">E34</font></i></a>, <a class="txt" href="goboard9.html#E7:28_1_1_1_2"><i><font color="Green">E37</font></i></a>, <a class="txt" href="goboard9.html#E8:28_1_1_1_2"><i><font color="Green">E38</font></i></a>, <a class="txt" href="goboard9.html#E11:28_1_1_1_2"><i><font color="Green">E40</font></i></a>, <a class="txt" href="goboard9.html#E12:28_1_1_1_2"><i><font color="Green">E41</font></i></a>, <a class="txt" href="goboard9.html#E24:28_1_1_1_2"><i><font color="Green">E51</font></i></a>, <a class="txt" href="goboard9.html#E39:28_1_1_1_2"><i><font color="Green">E62</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2_2_1_17"><i><font color="Green">E74</font></i></a>, <a class="ref" href="goboard5.html#T30">GOBOARD5:30</a></i>;<br/><a NAME="E6:28_1_1_1_2_2_1_17"/>
1 <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">c<sub>4</sub></font>
 <b>by </b><i><a class="txt" href="goboard9.html#E21:28_1_1_1_2"><i><font color="Green">E48</font></i></a>, <a class="txt" href="goboard9.html#E24:28_1_1_1_2"><i><font color="Green">E51</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2_2_1_17"><i><font color="Green">E74</font></i></a>, <a class="txt" href="goboard9.html#E4:28_1_1_1_2_2_1_17"><i><font color="Green">E77</font></i></a>, <a class="ref" href="xxreal_0.html#T1">XXREAL_0:1</a></i>;<br/><a NAME="E7:28_1_1_1_2_2_1_17"/><b>then </b><i><font color="Green">E79</font></i>: 
1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>4</sub></font> <a href="binarith.html#K5">-'</a> 1
 <b>by </b><i><a class="txt" href="goboard9.html#E24:28_1_1_1_2"><i><font color="Green">E51</font></i></a>, <a class="txt" href="goboard9.html#E39:28_1_1_1_2"><i><font color="Green">E62</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2_2_1_17"><i><font color="Green">E74</font></i></a>, <a class="ref" href="nat_1.html#T38">NAT_1:38</a></i>;<br/><i><font color="Green">E80</font></i>: <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</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> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> 1

<br/>.= 
<font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K1">+</a> 1
<b>by </b><i><a class="txt" href="goboard9.html#E24:28_1_1_1_2"><i><font color="Green">E51</font></i></a>, <a class="txt" href="goboard9.html#E39:28_1_1_1_2"><i><font color="Green">E62</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2_2_1_17"><i><font color="Green">E74</font></i></a></i>
<br/>.= 
<font color="Maroon">c<sub>8</sub></font>
<b>by </b><i><a class="txt" href="goboard9.html#E24:28_1_1_1_2"><i><font color="Green">E51</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2_2_1_17"><i><font color="Green">E74</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1_1_2_2_1_17"><i><font color="Green">E75</font></i></a></i>
;<br/><a NAME="E9:28_1_1_1_2_2_1_17"/><i><font color="Green">E81</font></i>: 
 <a href="topreal1.html#K3">LSeg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> 1,<span class="p5">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span></span>)</span> <a href="euclid.html#K17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> 1,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K20">-</a> <span class="p2"><a href="euclid.html#K23">|[</a><span class="default">1,0</span><a href="euclid.html#K23">]|</a></span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> 1,<span class="p4">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span></span>)</span> <a href="euclid.html#K17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> 2,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> is <a href="connsp_1.html#V2">connected</a>
 <b>by </b><i><a class="ref" href="goboard9.html#T8" target="_self">Th8</a></i>;<br/><a NAME="E10:28_1_1_1_2_2_1_17"/><i><font color="Green">E82</font></i>: 
 <a href="topreal1.html#K3">LSeg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> 1,<span class="p5">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span></span>)</span> <a href="euclid.html#K17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> 1,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K20">-</a> <span class="p2"><a href="euclid.html#K23">|[</a><span class="default">1,0</span><a href="euclid.html#K23">]|</a></span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> 1,<span class="p4">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span></span>)</span> <a href="euclid.html#K17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> 2,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xboole_0.html#NR5" target="_self">meets</a>  <a href="tops_1.html#K1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K3">cell</a> <span class="p2">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<font color="Maroon">c<sub>5</sub></font>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="goboard9.html#E18:28_1_1_1_2"><i><font color="Green">E45</font></i></a>, <a class="txt" href="goboard9.html#E22:28_1_1_1_2"><i><font color="Green">E49</font></i></a>, <a class="txt" href="goboard9.html#E24:28_1_1_1_2"><i><font color="Green">E51</font></i></a>, <a class="txt" href="goboard9.html#E39:28_1_1_1_2"><i><font color="Green">E62</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2_2_1_17"><i><font color="Green">E74</font></i></a>, <a class="txt" href="goboard9.html#E3:28_1_1_1_2_2_1_17"><i><font color="Green">E76</font></i></a>, <a class="txt" href="goboard9.html#E7:28_1_1_1_2_2_1_17"><i><font color="Green">E79</font></i></a>, <a class="ref" href="goboard6.html#T85">GOBOARD6:85</a></i>;<br/><a NAME="E11:28_1_1_1_2_2_1_17"/>
 <a href="topreal1.html#K3">LSeg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> 1,<span class="p5">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span></span>)</span> <a href="euclid.html#K17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> 1,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K20">-</a> <span class="p2"><a href="euclid.html#K23">|[</a><span class="default">1,0</span><a href="euclid.html#K23">]|</a></span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> 1,<span class="p4">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span></span>)</span> <a href="euclid.html#K17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> 2,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xboole_0.html#R1">misses</a>  <a href="topreal1.html#K5">L~</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="goboard9.html#E2:28_1_1"><i><font color="Green">E32</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2"><i><font color="Green">E33</font></i></a>, <a class="txt" href="goboard9.html#E8:28_1_1_1_2"><i><font color="Green">E38</font></i></a>, <a class="txt" href="goboard9.html#E12:28_1_1_1_2"><i><font color="Green">E41</font></i></a>, <a class="txt" href="goboard9.html#E17:28_1_1_1_2"><i><font color="Green">E44</font></i></a>, <a class="txt" href="goboard9.html#E23:28_1_1_1_2"><i><font color="Green">E50</font></i></a>, <a class="txt" href="goboard9.html#E24:28_1_1_1_2"><i><font color="Green">E51</font></i></a>, <a class="txt" href="goboard9.html#E25:28_1_1_1_2"><i><font color="Green">E52</font></i></a>, <a class="txt" href="goboard9.html#E39:28_1_1_1_2"><i><font color="Green">E62</font></i></a>, <a class="txt" href="goboard9.html#E46:28_1_1_1_2"><i><font color="Green">E66</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2_2_1_17"><i><font color="Green">E74</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1_1_2_2_1_17"><i><font color="Green">E75</font></i></a>, <a class="txt" href="goboard9.html#E3:28_1_1_1_2_2_1_17"><i><font color="Green">E76</font></i></a>, <a class="txt" href="goboard9.html#E7:28_1_1_1_2_2_1_17"><i><font color="Green">E79</font></i></a>, <a class="txt" href="goboard9.html#E8:28_1_1_1_2_2_1_17"><i><font color="Green">E80</font></i></a>, <a class="ref" href="goboard8.html#T17">GOBOARD8:17</a></i>;<br/><a NAME="E12:28_1_1_1_2_2_1_17"/><b>then </b>
 <a href="topreal1.html#K3">LSeg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> 1,<span class="p5">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span></span>)</span> <a href="euclid.html#K17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> 1,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K20">-</a> <span class="p2"><a href="euclid.html#K23">|[</a><span class="default">1,0</span><a href="euclid.html#K23">]|</a></span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> 1,<span class="p4">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span></span>)</span> <a href="euclid.html#K17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> 2,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="tarski.html#R1">c=</a> <span class="p1">(<span class="default"><a href="topreal1.html#K5">L~</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="subset_1.html#K3">`</a> 
 <b>by </b><i><a class="ref" href="subset_1.html#T43">SUBSET_1:43</a></i>;<br/><a NAME="E13:28_1_1_1_2_2_1_17"/><b>then </b><i><font color="Green">E83</font></i>: 
 <a href="topreal1.html#K3">LSeg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> 1,<span class="p5">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span></span>)</span> <a href="euclid.html#K17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> 1,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K20">-</a> <span class="p2"><a href="euclid.html#K23">|[</a><span class="default">1,0</span><a href="euclid.html#K23">]|</a></span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> 1,<span class="p4">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span></span>)</span> <a href="euclid.html#K17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> 2,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="goboard9.html#K2" target="_self">LeftComp</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="goboard9.html#E1:28_1"><i><font color="Green">E30</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1"><i><font color="Green">E32</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2"><i><font color="Green">E33</font></i></a>, <a class="txt" href="goboard9.html#E51:28_1_1_1_2"><i><font color="Green">E71</font></i></a>, <a class="txt" href="goboard9.html#E5:28_1_1_1_2_2_1_17"><i><font color="Green">E78</font></i></a>, <a class="txt" href="goboard9.html#E9:28_1_1_1_2_2_1_17"><i><font color="Green">E81</font></i></a>, <a class="txt" href="goboard9.html#E10:28_1_1_1_2_2_1_17"><i><font color="Green">E82</font></i></a>, <a class="ref" href="goboard9.html#T6" target="_self">Th6</a>, <a class="ref" href="nat_1.html#T38">NAT_1:38</a></i>;<br/><a NAME="E14:28_1_1_1_2_2_1_17"/>
<font color="Maroon">c<sub>5</sub></font> <a href="binarith.html#K5">-'</a> 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>5</sub></font>
 <b>by </b><i><a class="txt" href="goboard9.html#E2"><i><font color="Green">Lemma2</font></i></a></i>;<br/><a NAME="E15:28_1_1_1_2_2_1_17"/><b>then </b><i><font color="Green">E84</font></i>: 
<font color="Maroon">c<sub>5</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"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="goboard9.html#E19:28_1_1_1_2"><i><font color="Green">E46</font></i></a>, <a class="ref" href="xxreal_0.html#T2">XXREAL_0:2</a></i>;<br/><a NAME="E16:28_1_1_1_2_2_1_17"/><i><font color="Green">E85</font></i>: 
<font color="Maroon">c<sub>5</sub></font> <a href="binarith.html#K5">-'</a> 1 <a href="hidden.html#R1">=</a> 0
 <b>by </b><i><a class="txt" href="goboard9.html#E3:28_1_1_1_2_2_1_17"><i><font color="Green">E76</font></i></a>, <a class="txt" href="goboard9.html#E1"><i><font color="Green">Lemma1</font></i></a></i>;<br/><a NAME="E17:28_1_1_1_2_2_1_17"/>
<font color="Maroon">c<sub>6</sub></font> <a href="binarith.html#K5">-'</a> 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>6</sub></font>
 <b>by </b><i><a class="txt" href="goboard9.html#E2"><i><font color="Green">Lemma2</font></i></a></i>;<br/><a NAME="E18:28_1_1_1_2_2_1_17"/><b>then </b><i><font color="Green">E86</font></i>: 
<font color="Maroon">c<sub>6</sub></font> <a href="binarith.html#K5">-'</a> 1 <a href="xxreal_0.html#R1">&lt;=</a>  <a href="matrix_1.html#K1">width</a> <span class="p1">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="goboard9.html#E22:28_1_1_1_2"><i><font color="Green">E49</font></i></a>, <a class="ref" href="xxreal_0.html#T2">XXREAL_0:2</a></i>;<br/><a NAME="E19:28_1_1_1_2_2_1_17"/><b>then </b><i><font color="Green">E87</font></i>: 
 <a href="tops_1.html#K1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K3">cell</a> <span class="p2">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span></span>)</span> is <a href="connsp_1.html#V2">connected</a>
 <b>by </b><i><a class="txt" href="goboard9.html#E15:28_1_1_1_2_2_1_17"><i><font color="Green">E84</font></i></a>, <a class="ref" href="goboard9.html#T21" target="_self">Th21</a></i>;<br/><a NAME="E20:28_1_1_1_2_2_1_17"/><i><font color="Green">E88</font></i>: 
 <a href="topreal1.html#K3">LSeg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> 1,<span class="p5">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span></span>)</span> <a href="euclid.html#K17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> 1,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K20">-</a> <span class="p2"><a href="euclid.html#K23">|[</a><span class="default">1,0</span><a href="euclid.html#K23">]|</a></span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> 1,<span class="p4">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span></span>)</span> <a href="euclid.html#K17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> 2,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xboole_0.html#NR5" target="_self">meets</a>  <a href="tops_1.html#K1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K3">cell</a> <span class="p2">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="goboard9.html#E22:28_1_1_1_2"><i><font color="Green">E49</font></i></a>, <a class="txt" href="goboard9.html#E24:28_1_1_1_2"><i><font color="Green">E51</font></i></a>, <a class="txt" href="goboard9.html#E39:28_1_1_1_2"><i><font color="Green">E62</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2_2_1_17"><i><font color="Green">E74</font></i></a>, <a class="txt" href="goboard9.html#E7:28_1_1_1_2_2_1_17"><i><font color="Green">E79</font></i></a>, <a class="txt" href="goboard9.html#E16:28_1_1_1_2_2_1_17"><i><font color="Green">E85</font></i></a>, <a class="ref" href="goboard6.html#T88">GOBOARD6:88</a></i>;<br/><a NAME="E21:28_1_1_1_2_2_1_17"/>
 <a href="tops_1.html#K1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K3">cell</a> <span class="p2">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span></span>)</span> <a href="xboole_0.html#R1">misses</a>  <a href="topreal1.html#K5">L~</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="goboard9.html#E15:28_1_1_1_2_2_1_17"><i><font color="Green">E84</font></i></a>, <a class="txt" href="goboard9.html#E18:28_1_1_1_2_2_1_17"><i><font color="Green">E86</font></i></a>, <a class="ref" href="goboard7.html#T14">GOBOARD7:14</a></i>;<br/><a NAME="E22:28_1_1_1_2_2_1_17"/><b>then </b>
 <a href="tops_1.html#K1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K3">cell</a> <span class="p2">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span></span>)</span> <a href="tarski.html#R1">c=</a> <span class="p1">(<span class="default"><a href="topreal1.html#K5">L~</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="subset_1.html#K3">`</a> 
 <b>by </b><i><a class="ref" href="subset_1.html#T43">SUBSET_1:43</a></i>;<br/><a NAME="E23:28_1_1_1_2_2_1_17"/><b>then </b><i><font color="Green">E89</font></i>: 
 <a href="tops_1.html#K1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K3">cell</a> <span class="p2">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="goboard9.html#K2" target="_self">LeftComp</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="goboard9.html#E24:28_1_1_1_2"><i><font color="Green">E51</font></i></a>, <a class="txt" href="goboard9.html#E51:28_1_1_1_2"><i><font color="Green">E71</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2_2_1_17"><i><font color="Green">E74</font></i></a>, <a class="txt" href="goboard9.html#E13:28_1_1_1_2_2_1_17"><i><font color="Green">E83</font></i></a>, <a class="txt" href="goboard9.html#E19:28_1_1_1_2_2_1_17"><i><font color="Green">E87</font></i></a>, <a class="txt" href="goboard9.html#E20:28_1_1_1_2_2_1_17"><i><font color="Green">E88</font></i></a>, <a class="ref" href="goboard9.html#T6" target="_self">Th6</a></i>;<br/><a NAME="E24:28_1_1_1_2_2_1_17"/><i><font color="Green">E90</font></i>: 
 <a href="goboard5.html#K5">left_cell</a> <font color="Maroon">c<sub>1</sub></font>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="hidden.html#R1">=</a>  <a href="goboard5.html#K3">cell</a> <span class="p1">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span>,<font color="Maroon">c<sub>6</sub></font>
 <b>by </b><i><a class="txt" href="goboard9.html#E1:28_1_1"><i><font color="Green">E31</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1"><i><font color="Green">E32</font></i></a>, <a class="txt" href="goboard9.html#E11:28_1_1_1_2"><i><font color="Green">E40</font></i></a>, <a class="txt" href="goboard9.html#E12:28_1_1_1_2"><i><font color="Green">E41</font></i></a>, <a class="txt" href="goboard9.html#E16:28_1_1_1_2"><i><font color="Green">E43</font></i></a>, <a class="txt" href="goboard9.html#E17:28_1_1_1_2"><i><font color="Green">E44</font></i></a>, <a class="txt" href="goboard9.html#E25:28_1_1_1_2"><i><font color="Green">E52</font></i></a>, <a class="txt" href="goboard9.html#E37:28_1_1_1_2"><i><font color="Green">E61</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1_1_2_2_1_17"><i><font color="Green">E75</font></i></a>, <a class="ref" href="goboard5.html#T28">GOBOARD5:28</a></i>;<br/><a NAME="E25:28_1_1_1_2_2_1_17"/><i><font color="Green">E91</font></i>: 
 <a href="topreal1.html#K3">LSeg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> 1,<span class="p5">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span></span>)</span> <a href="euclid.html#K17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> 1,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K20">-</a> <span class="p2"><a href="euclid.html#K23">|[</a><span class="default">1,0</span><a href="euclid.html#K23">]|</a></span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> 1,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="euclid.html#K17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> 1,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K20">-</a> <span class="p2"><a href="euclid.html#K23">|[</a><span class="default">1,0</span><a href="euclid.html#K23">]|</a></span></span>)</span> is <a href="connsp_1.html#V2">connected</a>
 <b>by </b><i><a class="ref" href="goboard9.html#T8" target="_self">Th8</a></i>;<br/><a NAME="E26:28_1_1_1_2_2_1_17"/><i><font color="Green">E92</font></i>: 
 <a href="topreal1.html#K3">LSeg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> 1,<span class="p5">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span></span>)</span> <a href="euclid.html#K17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> 1,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K20">-</a> <span class="p2"><a href="euclid.html#K23">|[</a><span class="default">1,0</span><a href="euclid.html#K23">]|</a></span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> 1,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="euclid.html#K17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> 1,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K20">-</a> <span class="p2"><a href="euclid.html#K23">|[</a><span class="default">1,0</span><a href="euclid.html#K23">]|</a></span></span>)</span> <a href="xboole_0.html#NR5" target="_self">meets</a>  <a href="tops_1.html#K1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K3">cell</a> <span class="p2">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="goboard9.html#E22:28_1_1_1_2"><i><font color="Green">E49</font></i></a>, <a class="txt" href="goboard9.html#E24:28_1_1_1_2"><i><font color="Green">E51</font></i></a>, <a class="txt" href="goboard9.html#E39:28_1_1_1_2"><i><font color="Green">E62</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2_2_1_17"><i><font color="Green">E74</font></i></a>, <a class="txt" href="goboard9.html#E7:28_1_1_1_2_2_1_17"><i><font color="Green">E79</font></i></a>, <a class="txt" href="goboard9.html#E16:28_1_1_1_2_2_1_17"><i><font color="Green">E85</font></i></a>, <a class="ref" href="goboard6.html#T88">GOBOARD6:88</a></i>;<br/><a NAME="E27:28_1_1_1_2_2_1_17"/>
 <a href="topreal1.html#K3">LSeg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> 1,<span class="p5">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span></span>)</span> <a href="euclid.html#K17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> 1,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K20">-</a> <span class="p2"><a href="euclid.html#K23">|[</a><span class="default">1,0</span><a href="euclid.html#K23">]|</a></span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> 1,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="euclid.html#K17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> 1,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K20">-</a> <span class="p2"><a href="euclid.html#K23">|[</a><span class="default">1,0</span><a href="euclid.html#K23">]|</a></span></span>)</span> <a href="xboole_0.html#R1">misses</a>  <a href="topreal1.html#K5">L~</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="goboard9.html#E23:28_1_1_1_2"><i><font color="Green">E50</font></i></a>, <a class="txt" href="goboard9.html#E24:28_1_1_1_2"><i><font color="Green">E51</font></i></a>, <a class="txt" href="goboard9.html#E39:28_1_1_1_2"><i><font color="Green">E62</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2_2_1_17"><i><font color="Green">E74</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1_1_2_2_1_17"><i><font color="Green">E75</font></i></a>, <a class="txt" href="goboard9.html#E7:28_1_1_1_2_2_1_17"><i><font color="Green">E79</font></i></a>, <a class="ref" href="goboard8.html#T31">GOBOARD8:31</a></i>;<br/><a NAME="E28:28_1_1_1_2_2_1_17"/><b>then </b>
 <a href="topreal1.html#K3">LSeg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> 1,<span class="p5">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span></span>)</span> <a href="euclid.html#K17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> 1,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K20">-</a> <span class="p2"><a href="euclid.html#K23">|[</a><span class="default">1,0</span><a href="euclid.html#K23">]|</a></span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> 1,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="euclid.html#K17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> 1,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K20">-</a> <span class="p2"><a href="euclid.html#K23">|[</a><span class="default">1,0</span><a href="euclid.html#K23">]|</a></span></span>)</span> <a href="tarski.html#R1">c=</a> <span class="p1">(<span class="default"><a href="topreal1.html#K5">L~</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="subset_1.html#K3">`</a> 
 <b>by </b><i><a class="ref" href="subset_1.html#T43">SUBSET_1:43</a></i>;<br/><a NAME="E29:28_1_1_1_2_2_1_17"/><b>then </b><i><font color="Green">E93</font></i>: 
 <a href="topreal1.html#K3">LSeg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> 1,<span class="p5">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span></span>)</span> <a href="euclid.html#K17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> 1,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K20">-</a> <span class="p2"><a href="euclid.html#K23">|[</a><span class="default">1,0</span><a href="euclid.html#K23">]|</a></span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> 1,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="euclid.html#K17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> 1,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K20">-</a> <span class="p2"><a href="euclid.html#K23">|[</a><span class="default">1,0</span><a href="euclid.html#K23">]|</a></span></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="goboard9.html#K2" target="_self">LeftComp</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="goboard9.html#E51:28_1_1_1_2"><i><font color="Green">E71</font></i></a>, <a class="txt" href="goboard9.html#E23:28_1_1_1_2_2_1_17"><i><font color="Green">E89</font></i></a>, <a class="txt" href="goboard9.html#E25:28_1_1_1_2_2_1_17"><i><font color="Green">E91</font></i></a>, <a class="txt" href="goboard9.html#E26:28_1_1_1_2_2_1_17"><i><font color="Green">E92</font></i></a>, <a class="ref" href="goboard9.html#T6" target="_self">Th6</a></i>;<br/><a NAME="E30:28_1_1_1_2_2_1_17"/><i><font color="Green">E94</font></i>: 
 <a href="topreal1.html#K3">LSeg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> 1,<span class="p5">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span></span>)</span> <a href="euclid.html#K17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> 1,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K20">-</a> <span class="p2"><a href="euclid.html#K23">|[</a><span class="default">1,0</span><a href="euclid.html#K23">]|</a></span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> 1,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="euclid.html#K17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> 1,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K20">-</a> <span class="p2"><a href="euclid.html#K23">|[</a><span class="default">1,0</span><a href="euclid.html#K23">]|</a></span></span>)</span> <a href="xboole_0.html#NR5" target="_self">meets</a>  <a href="tops_1.html#K1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K3">cell</a> <span class="p2">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span>,<font color="Maroon">c<sub>6</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="goboard9.html#E22:28_1_1_1_2"><i><font color="Green">E49</font></i></a>, <a class="txt" href="goboard9.html#E23:28_1_1_1_2"><i><font color="Green">E50</font></i></a>, <a class="txt" href="goboard9.html#E39:28_1_1_1_2"><i><font color="Green">E62</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1_1_2_2_1_17"><i><font color="Green">E75</font></i></a>, <a class="txt" href="goboard9.html#E16:28_1_1_1_2_2_1_17"><i><font color="Green">E85</font></i></a>, <a class="ref" href="goboard6.html#T88">GOBOARD6:88</a></i>;<br/><a NAME="E31:28_1_1_1_2_2_1_17"/>
 <a href="tops_1.html#K1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K5">left_cell</a> <font color="Maroon">c<sub>1</sub></font>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="xboole_0.html#R1">misses</a>  <a href="topreal1.html#K5">L~</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="goboard9.html#E1:28_1_1"><i><font color="Green">E31</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1"><i><font color="Green">E32</font></i></a>, <a class="ref" href="goboard8.html#T37">GOBOARD8:37</a></i>;<br/><a NAME="E32:28_1_1_1_2_2_1_17"/><b>then </b>
 <a href="tops_1.html#K1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K5">left_cell</a> <font color="Maroon">c<sub>1</sub></font>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="tarski.html#R1">c=</a> <span class="p1">(<span class="default"><a href="topreal1.html#K5">L~</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="subset_1.html#K3">`</a> 
 <b>by </b><i><a class="ref" href="subset_1.html#T43">SUBSET_1:43</a></i>;<br/><b>hence </b><a NAME="E33:28_1_1_1_2_2_1_17"/>
 <a href="tops_1.html#K1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K5">left_cell</a> <font color="Maroon">c<sub>1</sub></font>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="goboard9.html#K2" target="_self">LeftComp</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="goboard9.html#E51:28_1_1_1_2"><i><font color="Green">E71</font></i></a>, <a class="txt" href="goboard9.html#E52:28_1_1_1_2"><i><font color="Green">E72</font></i></a>, <a class="txt" href="goboard9.html#E24:28_1_1_1_2_2_1_17"><i><font color="Green">E90</font></i></a>, <a class="txt" href="goboard9.html#E29:28_1_1_1_2_2_1_17"><i><font color="Green">E93</font></i></a>, <a class="txt" href="goboard9.html#E30:28_1_1_1_2_2_1_17"><i><font color="Green">E94</font></i></a>, <a class="ref" href="goboard9.html#T6" target="_self">Th6</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="28_1_1_1_2_2_1_18"><b>suppose </b></a><b>that </b><a NAME="E1:28_1_1_1_2_2_1_18"/><i><font color="Green">E74</font></i>: 
<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>5</sub></font> <a href="nat_1.html#K1">+</a> 1
 <b>and </b><br/><a NAME="E2:28_1_1_1_2_2_1_18"/><i><font color="Green">E75</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>
 <b>and </b><br/><a NAME="E3:28_1_1_1_2_2_1_18"/><i><font color="Green">E76</font></i>: 
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 1
 <b>and </b><br/><a NAME="E4:28_1_1_1_2_2_1_18"/><i><font color="Green">E77</font></i>: 
<font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 1
 ;<br/><div class="add"><a NAME="E5:28_1_1_1_2_2_1_18"/><i><font color="Green">E78</font></i>: 
 <a href="goboard5.html#K5">left_cell</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a>  <a href="goboard5.html#K3">cell</a> <span class="p1">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<font color="Maroon">c<sub>5</sub></font>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span>
 <b>by </b><i><a class="txt" href="goboard9.html#E1:28_1_1_1_2"><i><font color="Green">E33</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1_1_2"><i><font color="Green">E34</font></i></a>, <a class="txt" href="goboard9.html#E7:28_1_1_1_2"><i><font color="Green">E37</font></i></a>, <a class="txt" href="goboard9.html#E8:28_1_1_1_2"><i><font color="Green">E38</font></i></a>, <a class="txt" href="goboard9.html#E11:28_1_1_1_2"><i><font color="Green">E40</font></i></a>, <a class="txt" href="goboard9.html#E12:28_1_1_1_2"><i><font color="Green">E41</font></i></a>, <a class="txt" href="goboard9.html#E24:28_1_1_1_2"><i><font color="Green">E51</font></i></a>, <a class="txt" href="goboard9.html#E39:28_1_1_1_2"><i><font color="Green">E62</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2_2_1_18"><i><font color="Green">E74</font></i></a>, <a class="ref" href="goboard5.html#T30">GOBOARD5:30</a></i>;<br/><a NAME="E6:28_1_1_1_2_2_1_18"/>
1 <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">c<sub>4</sub></font>
 <b>by </b><i><a class="txt" href="goboard9.html#E21:28_1_1_1_2"><i><font color="Green">E48</font></i></a>, <a class="txt" href="goboard9.html#E24:28_1_1_1_2"><i><font color="Green">E51</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2_2_1_18"><i><font color="Green">E74</font></i></a>, <a class="txt" href="goboard9.html#E4:28_1_1_1_2_2_1_18"><i><font color="Green">E77</font></i></a>, <a class="ref" href="xxreal_0.html#T1">XXREAL_0:1</a></i>;<br/><a NAME="E7:28_1_1_1_2_2_1_18"/><b>then </b><i><font color="Green">E79</font></i>: 
1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>4</sub></font> <a href="binarith.html#K5">-'</a> 1
 <b>by </b><i><a class="txt" href="goboard9.html#E24:28_1_1_1_2"><i><font color="Green">E51</font></i></a>, <a class="txt" href="goboard9.html#E39:28_1_1_1_2"><i><font color="Green">E62</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2_2_1_18"><i><font color="Green">E74</font></i></a>, <a class="ref" href="nat_1.html#T38">NAT_1:38</a></i>;<br/><a NAME="E8:28_1_1_1_2_2_1_18"/>
1 <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">c<sub>5</sub></font>
 <b>by </b><i><a class="txt" href="goboard9.html#E19:28_1_1_1_2"><i><font color="Green">E46</font></i></a>, <a class="txt" href="goboard9.html#E3:28_1_1_1_2_2_1_18"><i><font color="Green">E76</font></i></a>, <a class="ref" href="xxreal_0.html#T1">XXREAL_0:1</a></i>;<br/><a NAME="E9:28_1_1_1_2_2_1_18"/><b>then </b><i><font color="Green">E80</font></i>: 
1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>5</sub></font> <a href="binarith.html#K5">-'</a> 1
 <b>by </b><i><a class="txt" href="goboard9.html#E37:28_1_1_1_2"><i><font color="Green">E61</font></i></a>, <a class="ref" href="nat_1.html#T38">NAT_1:38</a></i>;<br/><a NAME="E10:28_1_1_1_2_2_1_18"/><i><font color="Green">E81</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>5</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> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font>
 <b>by </b><i><a class="txt" href="goboard9.html#E37:28_1_1_1_2"><i><font color="Green">E61</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2_2_1_18"><i><font color="Green">E74</font></i></a></i>;<br/><i><font color="Green">E82</font></i>: <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</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> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> 1

<br/>.= 
<font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K1">+</a> 1
<b>by </b><i><a class="txt" href="goboard9.html#E24:28_1_1_1_2"><i><font color="Green">E51</font></i></a>, <a class="txt" href="goboard9.html#E39:28_1_1_1_2"><i><font color="Green">E62</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2_2_1_18"><i><font color="Green">E74</font></i></a></i>
<br/>.= 
<font color="Maroon">c<sub>8</sub></font>
<b>by </b><i><a class="txt" href="goboard9.html#E24:28_1_1_1_2"><i><font color="Green">E51</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2_2_1_18"><i><font color="Green">E74</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1_1_2_2_1_18"><i><font color="Green">E75</font></i></a></i>
;<br/><a NAME="E12:28_1_1_1_2_2_1_18"/><i><font color="Green">E83</font></i>: 
 <a href="topreal1.html#K3">LSeg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span>,<span class="p4">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span></span>)</span> <a href="euclid.html#K17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>5</sub></font>,<span class="p4">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span></span>)</span> <a href="euclid.html#K17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span></span>)</span> is <a href="connsp_1.html#V2">connected</a>
 <b>by </b><i><a class="ref" href="goboard9.html#T8" target="_self">Th8</a></i>;<br/><a NAME="E13:28_1_1_1_2_2_1_18"/><i><font color="Green">E84</font></i>: 
 <a href="topreal1.html#K3">LSeg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span>,<span class="p4">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span></span>)</span> <a href="euclid.html#K17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>5</sub></font>,<span class="p4">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span></span>)</span> <a href="euclid.html#K17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span></span>)</span> <a href="xboole_0.html#NR5" target="_self">meets</a>  <a href="tops_1.html#K1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K3">cell</a> <span class="p2">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<font color="Maroon">c<sub>5</sub></font>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="goboard9.html#E18:28_1_1_1_2"><i><font color="Green">E45</font></i></a>, <a class="txt" href="goboard9.html#E19:28_1_1_1_2"><i><font color="Green">E46</font></i></a>, <a class="txt" href="goboard9.html#E22:28_1_1_1_2"><i><font color="Green">E49</font></i></a>, <a class="txt" href="goboard9.html#E24:28_1_1_1_2"><i><font color="Green">E51</font></i></a>, <a class="txt" href="goboard9.html#E39:28_1_1_1_2"><i><font color="Green">E62</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2_2_1_18"><i><font color="Green">E74</font></i></a>, <a class="txt" href="goboard9.html#E7:28_1_1_1_2_2_1_18"><i><font color="Green">E79</font></i></a>, <a class="ref" href="goboard6.html#T85">GOBOARD6:85</a></i>;<br/><a NAME="E14:28_1_1_1_2_2_1_18"/>
 <a href="topreal1.html#K3">LSeg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span>,<span class="p4">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span></span>)</span> <a href="euclid.html#K17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>5</sub></font>,<span class="p4">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span></span>)</span> <a href="euclid.html#K17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span></span>)</span> <a href="xboole_0.html#R1">misses</a>  <a href="topreal1.html#K5">L~</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="goboard9.html#E2:28_1_1"><i><font color="Green">E32</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2"><i><font color="Green">E33</font></i></a>, <a class="txt" href="goboard9.html#E8:28_1_1_1_2"><i><font color="Green">E38</font></i></a>, <a class="txt" href="goboard9.html#E12:28_1_1_1_2"><i><font color="Green">E41</font></i></a>, <a class="txt" href="goboard9.html#E17:28_1_1_1_2"><i><font color="Green">E44</font></i></a>, <a class="txt" href="goboard9.html#E18:28_1_1_1_2"><i><font color="Green">E45</font></i></a>, <a class="txt" href="goboard9.html#E23:28_1_1_1_2"><i><font color="Green">E50</font></i></a>, <a class="txt" href="goboard9.html#E24:28_1_1_1_2"><i><font color="Green">E51</font></i></a>, <a class="txt" href="goboard9.html#E25:28_1_1_1_2"><i><font color="Green">E52</font></i></a>, <a class="txt" href="goboard9.html#E37:28_1_1_1_2"><i><font color="Green">E61</font></i></a>, <a class="txt" href="goboard9.html#E39:28_1_1_1_2"><i><font color="Green">E62</font></i></a>, <a class="txt" href="goboard9.html#E46:28_1_1_1_2"><i><font color="Green">E66</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1_1_2_2_1_18"><i><font color="Green">E75</font></i></a>, <a class="txt" href="goboard9.html#E7:28_1_1_1_2_2_1_18"><i><font color="Green">E79</font></i></a>, <a class="txt" href="goboard9.html#E9:28_1_1_1_2_2_1_18"><i><font color="Green">E80</font></i></a>, <a class="txt" href="goboard9.html#E10:28_1_1_1_2_2_1_18"><i><font color="Green">E81</font></i></a>, <a class="txt" href="goboard9.html#E11:28_1_1_1_2_2_1_18"><i><font color="Green">E82</font></i></a>, <a class="ref" href="goboard8.html#T12">GOBOARD8:12</a></i>;<br/><a NAME="E15:28_1_1_1_2_2_1_18"/><b>then </b>
 <a href="topreal1.html#K3">LSeg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span>,<span class="p4">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span></span>)</span> <a href="euclid.html#K17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>5</sub></font>,<span class="p4">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span></span>)</span> <a href="euclid.html#K17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span></span>)</span> <a href="tarski.html#R1">c=</a> <span class="p1">(<span class="default"><a href="topreal1.html#K5">L~</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="subset_1.html#K3">`</a> 
 <b>by </b><i><a class="ref" href="subset_1.html#T43">SUBSET_1:43</a></i>;<br/><a NAME="E16:28_1_1_1_2_2_1_18"/><b>then </b><i><font color="Green">E85</font></i>: 
 <a href="topreal1.html#K3">LSeg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span>,<span class="p4">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span></span>)</span> <a href="euclid.html#K17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>5</sub></font>,<span class="p4">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span></span>)</span> <a href="euclid.html#K17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="goboard9.html#K2" target="_self">LeftComp</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="goboard9.html#E1:28_1"><i><font color="Green">E30</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1"><i><font color="Green">E32</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2"><i><font color="Green">E33</font></i></a>, <a class="txt" href="goboard9.html#E51:28_1_1_1_2"><i><font color="Green">E71</font></i></a>, <a class="txt" href="goboard9.html#E5:28_1_1_1_2_2_1_18"><i><font color="Green">E78</font></i></a>, <a class="txt" href="goboard9.html#E12:28_1_1_1_2_2_1_18"><i><font color="Green">E83</font></i></a>, <a class="txt" href="goboard9.html#E13:28_1_1_1_2_2_1_18"><i><font color="Green">E84</font></i></a>, <a class="ref" href="goboard9.html#T6" target="_self">Th6</a>, <a class="ref" href="nat_1.html#T38">NAT_1:38</a></i>;<br/><a NAME="E17:28_1_1_1_2_2_1_18"/>
<font color="Maroon">c<sub>5</sub></font> <a href="binarith.html#K5">-'</a> 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>5</sub></font>
 <b>by </b><i><a class="txt" href="goboard9.html#E2"><i><font color="Green">Lemma2</font></i></a></i>;<br/><a NAME="E18:28_1_1_1_2_2_1_18"/><b>then </b><i><font color="Green">E86</font></i>: 
<font color="Maroon">c<sub>5</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"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="goboard9.html#E19:28_1_1_1_2"><i><font color="Green">E46</font></i></a>, <a class="ref" href="xxreal_0.html#T2">XXREAL_0:2</a></i>;<br/><a NAME="E19:28_1_1_1_2_2_1_18"/>
<font color="Maroon">c<sub>6</sub></font> <a href="binarith.html#K5">-'</a> 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>6</sub></font>
 <b>by </b><i><a class="txt" href="goboard9.html#E2"><i><font color="Green">Lemma2</font></i></a></i>;<br/><a NAME="E20:28_1_1_1_2_2_1_18"/><b>then </b><i><font color="Green">E87</font></i>: 
<font color="Maroon">c<sub>6</sub></font> <a href="binarith.html#K5">-'</a> 1 <a href="xxreal_0.html#R1">&lt;=</a>  <a href="matrix_1.html#K1">width</a> <span class="p1">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="goboard9.html#E22:28_1_1_1_2"><i><font color="Green">E49</font></i></a>, <a class="ref" href="xxreal_0.html#T2">XXREAL_0:2</a></i>;<br/><a NAME="E21:28_1_1_1_2_2_1_18"/><b>then </b><i><font color="Green">E88</font></i>: 
 <a href="tops_1.html#K1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K3">cell</a> <span class="p2">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span></span>)</span> is <a href="connsp_1.html#V2">connected</a>
 <b>by </b><i><a class="txt" href="goboard9.html#E18:28_1_1_1_2_2_1_18"><i><font color="Green">E86</font></i></a>, <a class="ref" href="goboard9.html#T21" target="_self">Th21</a></i>;<br/><a NAME="E22:28_1_1_1_2_2_1_18"/><i><font color="Green">E89</font></i>: 
 <a href="topreal1.html#K3">LSeg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span>,<span class="p4">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span></span>)</span> <a href="euclid.html#K17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>5</sub></font>,<span class="p4">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span></span>)</span> <a href="euclid.html#K17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span></span>)</span> <a href="xboole_0.html#NR5" target="_self">meets</a>  <a href="tops_1.html#K1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K3">cell</a> <span class="p2">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="goboard9.html#E19:28_1_1_1_2"><i><font color="Green">E46</font></i></a>, <a class="txt" href="goboard9.html#E22:28_1_1_1_2"><i><font color="Green">E49</font></i></a>, <a class="txt" href="goboard9.html#E24:28_1_1_1_2"><i><font color="Green">E51</font></i></a>, <a class="txt" href="goboard9.html#E37:28_1_1_1_2"><i><font color="Green">E61</font></i></a>, <a class="txt" href="goboard9.html#E39:28_1_1_1_2"><i><font color="Green">E62</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2_2_1_18"><i><font color="Green">E74</font></i></a>, <a class="txt" href="goboard9.html#E7:28_1_1_1_2_2_1_18"><i><font color="Green">E79</font></i></a>, <a class="txt" href="goboard9.html#E9:28_1_1_1_2_2_1_18"><i><font color="Green">E80</font></i></a>, <a class="ref" href="goboard6.html#T85">GOBOARD6:85</a></i>;<br/><a NAME="E23:28_1_1_1_2_2_1_18"/>
 <a href="tops_1.html#K1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K3">cell</a> <span class="p2">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span></span>)</span> <a href="xboole_0.html#R1">misses</a>  <a href="topreal1.html#K5">L~</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="goboard9.html#E18:28_1_1_1_2_2_1_18"><i><font color="Green">E86</font></i></a>, <a class="txt" href="goboard9.html#E20:28_1_1_1_2_2_1_18"><i><font color="Green">E87</font></i></a>, <a class="ref" href="goboard7.html#T14">GOBOARD7:14</a></i>;<br/><a NAME="E24:28_1_1_1_2_2_1_18"/><b>then </b>
 <a href="tops_1.html#K1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K3">cell</a> <span class="p2">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span></span>)</span> <a href="tarski.html#R1">c=</a> <span class="p1">(<span class="default"><a href="topreal1.html#K5">L~</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="subset_1.html#K3">`</a> 
 <b>by </b><i><a class="ref" href="subset_1.html#T43">SUBSET_1:43</a></i>;<br/><a NAME="E25:28_1_1_1_2_2_1_18"/><b>then </b><i><font color="Green">E90</font></i>: 
 <a href="tops_1.html#K1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K3">cell</a> <span class="p2">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="goboard9.html#K2" target="_self">LeftComp</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="goboard9.html#E24:28_1_1_1_2"><i><font color="Green">E51</font></i></a>, <a class="txt" href="goboard9.html#E51:28_1_1_1_2"><i><font color="Green">E71</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2_2_1_18"><i><font color="Green">E74</font></i></a>, <a class="txt" href="goboard9.html#E16:28_1_1_1_2_2_1_18"><i><font color="Green">E85</font></i></a>, <a class="txt" href="goboard9.html#E21:28_1_1_1_2_2_1_18"><i><font color="Green">E88</font></i></a>, <a class="txt" href="goboard9.html#E22:28_1_1_1_2_2_1_18"><i><font color="Green">E89</font></i></a>, <a class="ref" href="goboard9.html#T6" target="_self">Th6</a></i>;<br/><a NAME="E26:28_1_1_1_2_2_1_18"/><i><font color="Green">E91</font></i>: 
 <a href="goboard5.html#K5">left_cell</a> <font color="Maroon">c<sub>1</sub></font>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="hidden.html#R1">=</a>  <a href="goboard5.html#K3">cell</a> <span class="p1">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span>,<font color="Maroon">c<sub>6</sub></font>
 <b>by </b><i><a class="txt" href="goboard9.html#E1:28_1_1"><i><font color="Green">E31</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1"><i><font color="Green">E32</font></i></a>, <a class="txt" href="goboard9.html#E11:28_1_1_1_2"><i><font color="Green">E40</font></i></a>, <a class="txt" href="goboard9.html#E12:28_1_1_1_2"><i><font color="Green">E41</font></i></a>, <a class="txt" href="goboard9.html#E16:28_1_1_1_2"><i><font color="Green">E43</font></i></a>, <a class="txt" href="goboard9.html#E17:28_1_1_1_2"><i><font color="Green">E44</font></i></a>, <a class="txt" href="goboard9.html#E25:28_1_1_1_2"><i><font color="Green">E52</font></i></a>, <a class="txt" href="goboard9.html#E37:28_1_1_1_2"><i><font color="Green">E61</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1_1_2_2_1_18"><i><font color="Green">E75</font></i></a>, <a class="ref" href="goboard5.html#T28">GOBOARD5:28</a></i>;<br/><a NAME="E27:28_1_1_1_2_2_1_18"/><i><font color="Green">E92</font></i>: 
 <a href="topreal1.html#K3">LSeg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span>,<span class="p4">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span></span>)</span> <a href="euclid.html#K17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span>,<font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="euclid.html#K17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>8</sub></font></span>)</span></span>)</span></span>)</span> is <a href="connsp_1.html#V2">connected</a>
 <b>by </b><i><a class="ref" href="goboard9.html#T8" target="_self">Th8</a></i>;<br/><a NAME="E28:28_1_1_1_2_2_1_18"/><i><font color="Green">E93</font></i>: 
 <a href="topreal1.html#K3">LSeg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span>,<span class="p4">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span></span>)</span> <a href="euclid.html#K17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span>,<font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="euclid.html#K17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>8</sub></font></span>)</span></span>)</span></span>)</span> <a href="xboole_0.html#NR5" target="_self">meets</a>  <a href="tops_1.html#K1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K3">cell</a> <span class="p2">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="goboard9.html#E19:28_1_1_1_2"><i><font color="Green">E46</font></i></a>, <a class="txt" href="goboard9.html#E22:28_1_1_1_2"><i><font color="Green">E49</font></i></a>, <a class="txt" href="goboard9.html#E24:28_1_1_1_2"><i><font color="Green">E51</font></i></a>, <a class="txt" href="goboard9.html#E37:28_1_1_1_2"><i><font color="Green">E61</font></i></a>, <a class="txt" href="goboard9.html#E39:28_1_1_1_2"><i><font color="Green">E62</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2_2_1_18"><i><font color="Green">E74</font></i></a>, <a class="txt" href="goboard9.html#E7:28_1_1_1_2_2_1_18"><i><font color="Green">E79</font></i></a>, <a class="txt" href="goboard9.html#E9:28_1_1_1_2_2_1_18"><i><font color="Green">E80</font></i></a>, <a class="ref" href="goboard6.html#T85">GOBOARD6:85</a></i>;<br/><a NAME="E29:28_1_1_1_2_2_1_18"/>
 <a href="topreal1.html#K3">LSeg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span>,<span class="p4">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span></span>)</span> <a href="euclid.html#K17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span>,<font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="euclid.html#K17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>8</sub></font></span>)</span></span>)</span></span>)</span> <a href="xboole_0.html#R1">misses</a>  <a href="topreal1.html#K5">L~</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="goboard9.html#E2:28_1_1"><i><font color="Green">E32</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2"><i><font color="Green">E33</font></i></a>, <a class="txt" href="goboard9.html#E8:28_1_1_1_2"><i><font color="Green">E38</font></i></a>, <a class="txt" href="goboard9.html#E12:28_1_1_1_2"><i><font color="Green">E41</font></i></a>, <a class="txt" href="goboard9.html#E17:28_1_1_1_2"><i><font color="Green">E44</font></i></a>, <a class="txt" href="goboard9.html#E18:28_1_1_1_2"><i><font color="Green">E45</font></i></a>, <a class="txt" href="goboard9.html#E23:28_1_1_1_2"><i><font color="Green">E50</font></i></a>, <a class="txt" href="goboard9.html#E24:28_1_1_1_2"><i><font color="Green">E51</font></i></a>, <a class="txt" href="goboard9.html#E25:28_1_1_1_2"><i><font color="Green">E52</font></i></a>, <a class="txt" href="goboard9.html#E37:28_1_1_1_2"><i><font color="Green">E61</font></i></a>, <a class="txt" href="goboard9.html#E39:28_1_1_1_2"><i><font color="Green">E62</font></i></a>, <a class="txt" href="goboard9.html#E46:28_1_1_1_2"><i><font color="Green">E66</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1_1_2_2_1_18"><i><font color="Green">E75</font></i></a>, <a class="txt" href="goboard9.html#E7:28_1_1_1_2_2_1_18"><i><font color="Green">E79</font></i></a>, <a class="txt" href="goboard9.html#E9:28_1_1_1_2_2_1_18"><i><font color="Green">E80</font></i></a>, <a class="txt" href="goboard9.html#E10:28_1_1_1_2_2_1_18"><i><font color="Green">E81</font></i></a>, <a class="txt" href="goboard9.html#E11:28_1_1_1_2_2_1_18"><i><font color="Green">E82</font></i></a>, <a class="ref" href="goboard8.html#T2">GOBOARD8:2</a></i>;<br/><a NAME="E30:28_1_1_1_2_2_1_18"/><b>then </b>
 <a href="topreal1.html#K3">LSeg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span>,<span class="p4">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span></span>)</span> <a href="euclid.html#K17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span>,<font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="euclid.html#K17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>8</sub></font></span>)</span></span>)</span></span>)</span> <a href="tarski.html#R1">c=</a> <span class="p1">(<span class="default"><a href="topreal1.html#K5">L~</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="subset_1.html#K3">`</a> 
 <b>by </b><i><a class="ref" href="subset_1.html#T43">SUBSET_1:43</a></i>;<br/><a NAME="E31:28_1_1_1_2_2_1_18"/><b>then </b><i><font color="Green">E94</font></i>: 
 <a href="topreal1.html#K3">LSeg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span>,<span class="p4">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span></span>)</span> <a href="euclid.html#K17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span>,<font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="euclid.html#K17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>8</sub></font></span>)</span></span>)</span></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="goboard9.html#K2" target="_self">LeftComp</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="goboard9.html#E51:28_1_1_1_2"><i><font color="Green">E71</font></i></a>, <a class="txt" href="goboard9.html#E25:28_1_1_1_2_2_1_18"><i><font color="Green">E90</font></i></a>, <a class="txt" href="goboard9.html#E27:28_1_1_1_2_2_1_18"><i><font color="Green">E92</font></i></a>, <a class="txt" href="goboard9.html#E28:28_1_1_1_2_2_1_18"><i><font color="Green">E93</font></i></a>, <a class="ref" href="goboard9.html#T6" target="_self">Th6</a></i>;<br/><a NAME="E32:28_1_1_1_2_2_1_18"/><i><font color="Green">E95</font></i>: 
 <a href="topreal1.html#K3">LSeg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span>,<span class="p4">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span></span>)</span> <a href="euclid.html#K17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span>,<font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="euclid.html#K17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>8</sub></font></span>)</span></span>)</span></span>)</span> <a href="xboole_0.html#NR5" target="_self">meets</a>  <a href="tops_1.html#K1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K3">cell</a> <span class="p2">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span>,<font color="Maroon">c<sub>6</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="goboard9.html#E19:28_1_1_1_2"><i><font color="Green">E46</font></i></a>, <a class="txt" href="goboard9.html#E22:28_1_1_1_2"><i><font color="Green">E49</font></i></a>, <a class="txt" href="goboard9.html#E23:28_1_1_1_2"><i><font color="Green">E50</font></i></a>, <a class="txt" href="goboard9.html#E37:28_1_1_1_2"><i><font color="Green">E61</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1_1_2_2_1_18"><i><font color="Green">E75</font></i></a>, <a class="txt" href="goboard9.html#E9:28_1_1_1_2_2_1_18"><i><font color="Green">E80</font></i></a>, <a class="ref" href="goboard6.html#T85">GOBOARD6:85</a></i>;<br/><a NAME="E33:28_1_1_1_2_2_1_18"/>
 <a href="tops_1.html#K1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K5">left_cell</a> <font color="Maroon">c<sub>1</sub></font>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="xboole_0.html#R1">misses</a>  <a href="topreal1.html#K5">L~</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="goboard9.html#E1:28_1_1"><i><font color="Green">E31</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1"><i><font color="Green">E32</font></i></a>, <a class="ref" href="goboard8.html#T37">GOBOARD8:37</a></i>;<br/><a NAME="E34:28_1_1_1_2_2_1_18"/><b>then </b>
 <a href="tops_1.html#K1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K5">left_cell</a> <font color="Maroon">c<sub>1</sub></font>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="tarski.html#R1">c=</a> <span class="p1">(<span class="default"><a href="topreal1.html#K5">L~</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="subset_1.html#K3">`</a> 
 <b>by </b><i><a class="ref" href="subset_1.html#T43">SUBSET_1:43</a></i>;<br/><b>hence </b><a NAME="E35:28_1_1_1_2_2_1_18"/>
 <a href="tops_1.html#K1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K5">left_cell</a> <font color="Maroon">c<sub>1</sub></font>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="goboard9.html#K2" target="_self">LeftComp</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="goboard9.html#E51:28_1_1_1_2"><i><font color="Green">E71</font></i></a>, <a class="txt" href="goboard9.html#E52:28_1_1_1_2"><i><font color="Green">E72</font></i></a>, <a class="txt" href="goboard9.html#E26:28_1_1_1_2_2_1_18"><i><font color="Green">E91</font></i></a>, <a class="txt" href="goboard9.html#E31:28_1_1_1_2_2_1_18"><i><font color="Green">E94</font></i></a>, <a class="txt" href="goboard9.html#E32:28_1_1_1_2_2_1_18"><i><font color="Green">E95</font></i></a>, <a class="ref" href="goboard9.html#T6" target="_self">Th6</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="28_1_1_1_2_2_1_19"><b>suppose </b></a><b>that </b><a NAME="E1:28_1_1_1_2_2_1_19"/><i><font color="Green">E74</font></i>: 
<font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>6</sub></font> <a href="nat_1.html#K1">+</a> 1
 <b>and </b><br/><a NAME="E2:28_1_1_1_2_2_1_19"/><i><font color="Green">E75</font></i>: 
<font color="Maroon">c<sub>5</sub></font> <a href="nat_1.html#K1">+</a> 1 <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>7</sub></font>
 ;<br/><div class="add"> <a href="goboard5.html#K5">left_cell</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font> = 
 <a href="goboard5.html#K3">cell</a> <span class="p1">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>6</sub></font>
<b>by </b><i><a class="txt" href="goboard9.html#E1:28_1_1_1_2"><i><font color="Green">E33</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1_1_2"><i><font color="Green">E34</font></i></a>, <a class="txt" href="goboard9.html#E7:28_1_1_1_2"><i><font color="Green">E37</font></i></a>, <a class="txt" href="goboard9.html#E8:28_1_1_1_2"><i><font color="Green">E38</font></i></a>, <a class="txt" href="goboard9.html#E11:28_1_1_1_2"><i><font color="Green">E40</font></i></a>, <a class="txt" href="goboard9.html#E12:28_1_1_1_2"><i><font color="Green">E41</font></i></a>, <a class="txt" href="goboard9.html#E24:28_1_1_1_2"><i><font color="Green">E51</font></i></a>, <a class="txt" href="goboard9.html#E37:28_1_1_1_2"><i><font color="Green">E61</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2_2_1_19"><i><font color="Green">E74</font></i></a>, <a class="ref" href="goboard5.html#T31">GOBOARD5:31</a></i>
<br/>.= 
 <a href="goboard5.html#K5">left_cell</a> <font color="Maroon">c<sub>1</sub></font>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>
<b>by </b><i><a class="txt" href="goboard9.html#E1:28_1_1"><i><font color="Green">E31</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1"><i><font color="Green">E32</font></i></a>, <a class="txt" href="goboard9.html#E11:28_1_1_1_2"><i><font color="Green">E40</font></i></a>, <a class="txt" href="goboard9.html#E12:28_1_1_1_2"><i><font color="Green">E41</font></i></a>, <a class="txt" href="goboard9.html#E16:28_1_1_1_2"><i><font color="Green">E43</font></i></a>, <a class="txt" href="goboard9.html#E17:28_1_1_1_2"><i><font color="Green">E44</font></i></a>, <a class="txt" href="goboard9.html#E24:28_1_1_1_2"><i><font color="Green">E51</font></i></a>, <a class="txt" href="goboard9.html#E25:28_1_1_1_2"><i><font color="Green">E52</font></i></a>, <a class="txt" href="goboard9.html#E39:28_1_1_1_2"><i><font color="Green">E62</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2_2_1_19"><i><font color="Green">E74</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1_1_2_2_1_19"><i><font color="Green">E75</font></i></a>, <a class="ref" href="goboard5.html#T29">GOBOARD5:29</a></i>
;<br/><b>hence </b><a NAME="E4:28_1_1_1_2_2_1_19"/>
 <a href="tops_1.html#K1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K5">left_cell</a> <font color="Maroon">c<sub>1</sub></font>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="goboard9.html#K2" target="_self">LeftComp</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="goboard9.html#E1:28_1"><i><font color="Green">E30</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1"><i><font color="Green">E32</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2"><i><font color="Green">E33</font></i></a>, <a class="ref" href="nat_1.html#T38">NAT_1:38</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="28_1_1_1_2_2_1_20"><b>suppose </b></a><b>that </b><a NAME="E1:28_1_1_1_2_2_1_20"/><i><font color="Green">E74</font></i>: 
<font color="Maroon">c<sub>3</sub></font> <a href="nat_1.html#K1">+</a> 1 <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>5</sub></font>
 <b>and </b><br/><a NAME="E2:28_1_1_1_2_2_1_20"/><i><font color="Green">E75</font></i>: 
<font color="Maroon">c<sub>5</sub></font> <a href="nat_1.html#K1">+</a> 1 <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>7</sub></font>
 <b>and </b><br/><a NAME="E3:28_1_1_1_2_2_1_20"/><i><font color="Green">E76</font></i>: 
<font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a>  <a href="matrix_1.html#K1">width</a> <span class="p1">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>
 ;<br/><div class="add"><a NAME="E4:28_1_1_1_2_2_1_20"/><i><font color="Green">E77</font></i>: 
 <a href="goboard5.html#K5">left_cell</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a>  <a href="goboard5.html#K3">cell</a> <span class="p1">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<font color="Maroon">c<sub>3</sub></font>,<span class="p1">(<span class="default"><a href="matrix_1.html#K1">width</a> <span class="p2">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="goboard9.html#E1:28_1_1_1_2"><i><font color="Green">E33</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1_1_2"><i><font color="Green">E34</font></i></a>, <a class="txt" href="goboard9.html#E7:28_1_1_1_2"><i><font color="Green">E37</font></i></a>, <a class="txt" href="goboard9.html#E8:28_1_1_1_2"><i><font color="Green">E38</font></i></a>, <a class="txt" href="goboard9.html#E11:28_1_1_1_2"><i><font color="Green">E40</font></i></a>, <a class="txt" href="goboard9.html#E12:28_1_1_1_2"><i><font color="Green">E41</font></i></a>, <a class="txt" href="goboard9.html#E24:28_1_1_1_2"><i><font color="Green">E51</font></i></a>, <a class="txt" href="goboard9.html#E45:28_1_1_1_2"><i><font color="Green">E65</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2_2_1_20"><i><font color="Green">E74</font></i></a>, <a class="txt" href="goboard9.html#E3:28_1_1_1_2_2_1_20"><i><font color="Green">E76</font></i></a>, <a class="ref" href="goboard5.html#T29">GOBOARD5:29</a></i>;<br/><a NAME="E5:28_1_1_1_2_2_1_20"/><i><font color="Green">E78</font></i>: 
 <a href="goboard5.html#K5">left_cell</a> <font color="Maroon">c<sub>1</sub></font>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="hidden.html#R1">=</a>  <a href="goboard5.html#K3">cell</a> <span class="p1">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<font color="Maroon">c<sub>5</sub></font>,<span class="p1">(<span class="default"><a href="matrix_1.html#K1">width</a> <span class="p2">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="goboard9.html#E1:28_1_1"><i><font color="Green">E31</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1"><i><font color="Green">E32</font></i></a>, <a class="txt" href="goboard9.html#E11:28_1_1_1_2"><i><font color="Green">E40</font></i></a>, <a class="txt" href="goboard9.html#E12:28_1_1_1_2"><i><font color="Green">E41</font></i></a>, <a class="txt" href="goboard9.html#E16:28_1_1_1_2"><i><font color="Green">E43</font></i></a>, <a class="txt" href="goboard9.html#E17:28_1_1_1_2"><i><font color="Green">E44</font></i></a>, <a class="txt" href="goboard9.html#E24:28_1_1_1_2"><i><font color="Green">E51</font></i></a>, <a class="txt" href="goboard9.html#E25:28_1_1_1_2"><i><font color="Green">E52</font></i></a>, <a class="txt" href="goboard9.html#E45:28_1_1_1_2"><i><font color="Green">E65</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2_2_1_20"><i><font color="Green">E74</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1_1_2_2_1_20"><i><font color="Green">E75</font></i></a>, <a class="txt" href="goboard9.html#E3:28_1_1_1_2_2_1_20"><i><font color="Green">E76</font></i></a>, <a class="ref" href="goboard5.html#T29">GOBOARD5:29</a></i>;<br/><a NAME="E6:28_1_1_1_2_2_1_20"/><i><font color="Green">E79</font></i>: 
 <a href="topreal1.html#K3">LSeg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>3</sub></font>,<span class="p5">(<span class="default"><a href="matrix_1.html#K1">width</a> <span class="p0">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p5">(<span class="default"><a href="matrix_1.html#K1">width</a> <span class="p0">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K17">+</a> <span class="p2"><a href="euclid.html#K23">|[</a><span class="default">0,1</span><a href="euclid.html#K23">]|</a></span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>5</sub></font>,<span class="p5">(<span class="default"><a href="matrix_1.html#K1">width</a> <span class="p0">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p5">(<span class="default"><a href="matrix_1.html#K1">width</a> <span class="p0">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K17">+</a> <span class="p2"><a href="euclid.html#K23">|[</a><span class="default">0,1</span><a href="euclid.html#K23">]|</a></span></span>)</span> is <a href="connsp_1.html#V2">connected</a>
 <b>by </b><i><a class="ref" href="goboard9.html#T8" target="_self">Th8</a></i>;<br/><a NAME="E7:28_1_1_1_2_2_1_20"/><i><font color="Green">E80</font></i>: 
 <a href="topreal1.html#K3">LSeg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>3</sub></font>,<span class="p5">(<span class="default"><a href="matrix_1.html#K1">width</a> <span class="p0">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p5">(<span class="default"><a href="matrix_1.html#K1">width</a> <span class="p0">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K17">+</a> <span class="p2"><a href="euclid.html#K23">|[</a><span class="default">0,1</span><a href="euclid.html#K23">]|</a></span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>5</sub></font>,<span class="p5">(<span class="default"><a href="matrix_1.html#K1">width</a> <span class="p0">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p5">(<span class="default"><a href="matrix_1.html#K1">width</a> <span class="p0">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K17">+</a> <span class="p2"><a href="euclid.html#K23">|[</a><span class="default">0,1</span><a href="euclid.html#K23">]|</a></span></span>)</span> <a href="xboole_0.html#NR5" target="_self">meets</a>  <a href="tops_1.html#K1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K3">cell</a> <span class="p2">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<font color="Maroon">c<sub>3</sub></font>,<span class="p2">(<span class="default"><a href="matrix_1.html#K1">width</a> <span class="p3">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="goboard9.html#E18:28_1_1_1_2"><i><font color="Green">E45</font></i></a>, <a class="txt" href="goboard9.html#E19:28_1_1_1_2"><i><font color="Green">E46</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2_2_1_20"><i><font color="Green">E74</font></i></a>, <a class="ref" href="goboard6.html#T86">GOBOARD6:86</a></i>;<br/><a NAME="E8:28_1_1_1_2_2_1_20"/>
 <a href="topreal1.html#K3">LSeg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>3</sub></font>,<span class="p5">(<span class="default"><a href="matrix_1.html#K1">width</a> <span class="p0">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p5">(<span class="default"><a href="matrix_1.html#K1">width</a> <span class="p0">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K17">+</a> <span class="p2"><a href="euclid.html#K23">|[</a><span class="default">0,1</span><a href="euclid.html#K23">]|</a></span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>5</sub></font>,<span class="p5">(<span class="default"><a href="matrix_1.html#K1">width</a> <span class="p0">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p5">(<span class="default"><a href="matrix_1.html#K1">width</a> <span class="p0">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K17">+</a> <span class="p2"><a href="euclid.html#K23">|[</a><span class="default">0,1</span><a href="euclid.html#K23">]|</a></span></span>)</span> <a href="xboole_0.html#R1">misses</a>  <a href="topreal1.html#K5">L~</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="goboard9.html#E18:28_1_1_1_2"><i><font color="Green">E45</font></i></a>, <a class="txt" href="goboard9.html#E20:28_1_1_1_2"><i><font color="Green">E47</font></i></a>, <a class="txt" href="goboard9.html#E47:28_1_1_1_2"><i><font color="Green">E67</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2_2_1_20"><i><font color="Green">E74</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1_1_2_2_1_20"><i><font color="Green">E75</font></i></a>, <a class="ref" href="goboard8.html#T28">GOBOARD8:28</a></i>;<br/><a NAME="E9:28_1_1_1_2_2_1_20"/><b>then </b>
 <a href="topreal1.html#K3">LSeg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>3</sub></font>,<span class="p5">(<span class="default"><a href="matrix_1.html#K1">width</a> <span class="p0">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p5">(<span class="default"><a href="matrix_1.html#K1">width</a> <span class="p0">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K17">+</a> <span class="p2"><a href="euclid.html#K23">|[</a><span class="default">0,1</span><a href="euclid.html#K23">]|</a></span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>5</sub></font>,<span class="p5">(<span class="default"><a href="matrix_1.html#K1">width</a> <span class="p0">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p5">(<span class="default"><a href="matrix_1.html#K1">width</a> <span class="p0">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K17">+</a> <span class="p2"><a href="euclid.html#K23">|[</a><span class="default">0,1</span><a href="euclid.html#K23">]|</a></span></span>)</span> <a href="tarski.html#R1">c=</a> <span class="p1">(<span class="default"><a href="topreal1.html#K5">L~</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="subset_1.html#K3">`</a> 
 <b>by </b><i><a class="ref" href="subset_1.html#T43">SUBSET_1:43</a></i>;<br/><a NAME="E10:28_1_1_1_2_2_1_20"/><b>then </b><i><font color="Green">E81</font></i>: 
 <a href="topreal1.html#K3">LSeg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>3</sub></font>,<span class="p5">(<span class="default"><a href="matrix_1.html#K1">width</a> <span class="p0">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p5">(<span class="default"><a href="matrix_1.html#K1">width</a> <span class="p0">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K17">+</a> <span class="p2"><a href="euclid.html#K23">|[</a><span class="default">0,1</span><a href="euclid.html#K23">]|</a></span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>5</sub></font>,<span class="p5">(<span class="default"><a href="matrix_1.html#K1">width</a> <span class="p0">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p5">(<span class="default"><a href="matrix_1.html#K1">width</a> <span class="p0">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K17">+</a> <span class="p2"><a href="euclid.html#K23">|[</a><span class="default">0,1</span><a href="euclid.html#K23">]|</a></span></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="goboard9.html#K2" target="_self">LeftComp</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="goboard9.html#E1:28_1"><i><font color="Green">E30</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1"><i><font color="Green">E32</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2"><i><font color="Green">E33</font></i></a>, <a class="txt" href="goboard9.html#E51:28_1_1_1_2"><i><font color="Green">E71</font></i></a>, <a class="txt" href="goboard9.html#E4:28_1_1_1_2_2_1_20"><i><font color="Green">E77</font></i></a>, <a class="txt" href="goboard9.html#E6:28_1_1_1_2_2_1_20"><i><font color="Green">E79</font></i></a>, <a class="txt" href="goboard9.html#E7:28_1_1_1_2_2_1_20"><i><font color="Green">E80</font></i></a>, <a class="ref" href="goboard9.html#T6" target="_self">Th6</a>, <a class="ref" href="nat_1.html#T38">NAT_1:38</a></i>;<br/><a NAME="E11:28_1_1_1_2_2_1_20"/><i><font color="Green">E82</font></i>: 
 <a href="topreal1.html#K3">LSeg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>3</sub></font>,<span class="p5">(<span class="default"><a href="matrix_1.html#K1">width</a> <span class="p0">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p5">(<span class="default"><a href="matrix_1.html#K1">width</a> <span class="p0">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K17">+</a> <span class="p2"><a href="euclid.html#K23">|[</a><span class="default">0,1</span><a href="euclid.html#K23">]|</a></span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>5</sub></font>,<span class="p5">(<span class="default"><a href="matrix_1.html#K1">width</a> <span class="p0">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p5">(<span class="default"><a href="matrix_1.html#K1">width</a> <span class="p0">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K17">+</a> <span class="p2"><a href="euclid.html#K23">|[</a><span class="default">0,1</span><a href="euclid.html#K23">]|</a></span></span>)</span> <a href="xboole_0.html#NR5" target="_self">meets</a>  <a href="tops_1.html#K1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K3">cell</a> <span class="p2">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<font color="Maroon">c<sub>5</sub></font>,<span class="p2">(<span class="default"><a href="matrix_1.html#K1">width</a> <span class="p3">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="goboard9.html#E19:28_1_1_1_2"><i><font color="Green">E46</font></i></a>, <a class="txt" href="goboard9.html#E20:28_1_1_1_2"><i><font color="Green">E47</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1_1_2_2_1_20"><i><font color="Green">E75</font></i></a>, <a class="ref" href="goboard6.html#T86">GOBOARD6:86</a></i>;<br/><a NAME="E12:28_1_1_1_2_2_1_20"/>
 <a href="tops_1.html#K1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K5">left_cell</a> <font color="Maroon">c<sub>1</sub></font>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="xboole_0.html#R1">misses</a>  <a href="topreal1.html#K5">L~</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="goboard9.html#E1:28_1_1"><i><font color="Green">E31</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1"><i><font color="Green">E32</font></i></a>, <a class="ref" href="goboard8.html#T37">GOBOARD8:37</a></i>;<br/><a NAME="E13:28_1_1_1_2_2_1_20"/><b>then </b>
 <a href="tops_1.html#K1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K5">left_cell</a> <font color="Maroon">c<sub>1</sub></font>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="tarski.html#R1">c=</a> <span class="p1">(<span class="default"><a href="topreal1.html#K5">L~</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="subset_1.html#K3">`</a> 
 <b>by </b><i><a class="ref" href="subset_1.html#T43">SUBSET_1:43</a></i>;<br/><b>hence </b><a NAME="E14:28_1_1_1_2_2_1_20"/>
 <a href="tops_1.html#K1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K5">left_cell</a> <font color="Maroon">c<sub>1</sub></font>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="goboard9.html#K2" target="_self">LeftComp</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="goboard9.html#E51:28_1_1_1_2"><i><font color="Green">E71</font></i></a>, <a class="txt" href="goboard9.html#E52:28_1_1_1_2"><i><font color="Green">E72</font></i></a>, <a class="txt" href="goboard9.html#E5:28_1_1_1_2_2_1_20"><i><font color="Green">E78</font></i></a>, <a class="txt" href="goboard9.html#E10:28_1_1_1_2_2_1_20"><i><font color="Green">E81</font></i></a>, <a class="txt" href="goboard9.html#E11:28_1_1_1_2_2_1_20"><i><font color="Green">E82</font></i></a>, <a class="ref" href="goboard9.html#T6" target="_self">Th6</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="28_1_1_1_2_2_1_21"><b>suppose </b></a><b>that </b><a NAME="E1:28_1_1_1_2_2_1_21"/><i><font color="Green">E74</font></i>: 
<font color="Maroon">c<sub>3</sub></font> <a href="nat_1.html#K1">+</a> 1 <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>5</sub></font>
 <b>and </b><br/><a NAME="E2:28_1_1_1_2_2_1_21"/><i><font color="Green">E75</font></i>: 
<font color="Maroon">c<sub>5</sub></font> <a href="nat_1.html#K1">+</a> 1 <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>7</sub></font>
 <b>and </b><br/><a NAME="E3:28_1_1_1_2_2_1_21"/><i><font color="Green">E76</font></i>: 
<font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="matrix_1.html#K1">width</a> <span class="p1">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>
 ;<br/><div class="add"><a NAME="E4:28_1_1_1_2_2_1_21"/><i><font color="Green">E77</font></i>: 
 <a href="goboard5.html#K5">left_cell</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a>  <a href="goboard5.html#K3">cell</a> <span class="p1">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>6</sub></font>
 <b>by </b><i><a class="txt" href="goboard9.html#E1:28_1_1_1_2"><i><font color="Green">E33</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1_1_2"><i><font color="Green">E34</font></i></a>, <a class="txt" href="goboard9.html#E7:28_1_1_1_2"><i><font color="Green">E37</font></i></a>, <a class="txt" href="goboard9.html#E8:28_1_1_1_2"><i><font color="Green">E38</font></i></a>, <a class="txt" href="goboard9.html#E11:28_1_1_1_2"><i><font color="Green">E40</font></i></a>, <a class="txt" href="goboard9.html#E12:28_1_1_1_2"><i><font color="Green">E41</font></i></a>, <a class="txt" href="goboard9.html#E24:28_1_1_1_2"><i><font color="Green">E51</font></i></a>, <a class="txt" href="goboard9.html#E39:28_1_1_1_2"><i><font color="Green">E62</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2_2_1_21"><i><font color="Green">E74</font></i></a>, <a class="ref" href="goboard5.html#T29">GOBOARD5:29</a></i>;<br/><a NAME="E5:28_1_1_1_2_2_1_21"/>
 <a href="matrix_1.html#K1">width</a> <span class="p1">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> <font color="Maroon">c<sub>4</sub></font>
 <b>by </b><i><a class="txt" href="goboard9.html#E21:28_1_1_1_2"><i><font color="Green">E48</font></i></a>, <a class="txt" href="goboard9.html#E3:28_1_1_1_2_2_1_21"><i><font color="Green">E76</font></i></a>, <a class="ref" href="xxreal_0.html#T1">XXREAL_0:1</a></i>;<br/><a NAME="E6:28_1_1_1_2_2_1_21"/><b>then </b><i><font color="Green">E78</font></i>: 
 <a href="matrix_1.html#K1">width</a> <span class="p1">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K1">+</a> 1
 <b>by </b><i><a class="ref" href="nat_1.html#T38">NAT_1:38</a></i>;<br/><a NAME="E7:28_1_1_1_2_2_1_21"/><i><font color="Green">E79</font></i>: 
 <a href="goboard5.html#K5">left_cell</a> <font color="Maroon">c<sub>1</sub></font>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="hidden.html#R1">=</a>  <a href="goboard5.html#K3">cell</a> <span class="p1">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font>
 <b>by </b><i><a class="txt" href="goboard9.html#E1:28_1_1"><i><font color="Green">E31</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1"><i><font color="Green">E32</font></i></a>, <a class="txt" href="goboard9.html#E11:28_1_1_1_2"><i><font color="Green">E40</font></i></a>, <a class="txt" href="goboard9.html#E12:28_1_1_1_2"><i><font color="Green">E41</font></i></a>, <a class="txt" href="goboard9.html#E16:28_1_1_1_2"><i><font color="Green">E43</font></i></a>, <a class="txt" href="goboard9.html#E17:28_1_1_1_2"><i><font color="Green">E44</font></i></a>, <a class="txt" href="goboard9.html#E25:28_1_1_1_2"><i><font color="Green">E52</font></i></a>, <a class="txt" href="goboard9.html#E39:28_1_1_1_2"><i><font color="Green">E62</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1_1_2_2_1_21"><i><font color="Green">E75</font></i></a>, <a class="ref" href="goboard5.html#T29">GOBOARD5:29</a></i>;<br/><a NAME="E8:28_1_1_1_2_2_1_21"/><i><font color="Green">E80</font></i>: 
 <a href="topreal1.html#K3">LSeg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="euclid.html#K17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p4">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="euclid.html#K17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p4">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> is <a href="connsp_1.html#V2">connected</a>
 <b>by </b><i><a class="ref" href="goboard9.html#T8" target="_self">Th8</a></i>;<br/><a NAME="E9:28_1_1_1_2_2_1_21"/><i><font color="Green">E81</font></i>: 
 <a href="topreal1.html#K3">LSeg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="euclid.html#K17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p4">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="euclid.html#K17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p4">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xboole_0.html#NR5" target="_self">meets</a>  <a href="tops_1.html#K1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K3">cell</a> <span class="p2">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="goboard9.html#E18:28_1_1_1_2"><i><font color="Green">E45</font></i></a>, <a class="txt" href="goboard9.html#E19:28_1_1_1_2"><i><font color="Green">E46</font></i></a>, <a class="txt" href="goboard9.html#E22:28_1_1_1_2"><i><font color="Green">E49</font></i></a>, <a class="txt" href="goboard9.html#E24:28_1_1_1_2"><i><font color="Green">E51</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2_2_1_21"><i><font color="Green">E74</font></i></a>, <a class="txt" href="goboard9.html#E6:28_1_1_1_2_2_1_21"><i><font color="Green">E78</font></i></a>, <a class="ref" href="goboard6.html#T85">GOBOARD6:85</a></i>;<br/><a NAME="E10:28_1_1_1_2_2_1_21"/>
 <a href="topreal1.html#K3">LSeg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="euclid.html#K17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p4">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="euclid.html#K17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p4">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xboole_0.html#R1">misses</a>  <a href="topreal1.html#K5">L~</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="goboard9.html#E2:28_1_1"><i><font color="Green">E32</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2"><i><font color="Green">E33</font></i></a>, <a class="txt" href="goboard9.html#E8:28_1_1_1_2"><i><font color="Green">E38</font></i></a>, <a class="txt" href="goboard9.html#E12:28_1_1_1_2"><i><font color="Green">E41</font></i></a>, <a class="txt" href="goboard9.html#E17:28_1_1_1_2"><i><font color="Green">E44</font></i></a>, <a class="txt" href="goboard9.html#E18:28_1_1_1_2"><i><font color="Green">E45</font></i></a>, <a class="txt" href="goboard9.html#E20:28_1_1_1_2"><i><font color="Green">E47</font></i></a>, <a class="txt" href="goboard9.html#E21:28_1_1_1_2"><i><font color="Green">E48</font></i></a>, <a class="txt" href="goboard9.html#E24:28_1_1_1_2"><i><font color="Green">E51</font></i></a>, <a class="txt" href="goboard9.html#E25:28_1_1_1_2"><i><font color="Green">E52</font></i></a>, <a class="txt" href="goboard9.html#E46:28_1_1_1_2"><i><font color="Green">E66</font></i></a>, <a class="txt" href="goboard9.html#E47:28_1_1_1_2"><i><font color="Green">E67</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2_2_1_21"><i><font color="Green">E74</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1_1_2_2_1_21"><i><font color="Green">E75</font></i></a>, <a class="txt" href="goboard9.html#E6:28_1_1_1_2_2_1_21"><i><font color="Green">E78</font></i></a>, <a class="ref" href="goboard8.html#T14">GOBOARD8:14</a></i>;<br/><a NAME="E11:28_1_1_1_2_2_1_21"/><b>then </b>
 <a href="topreal1.html#K3">LSeg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="euclid.html#K17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p4">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="euclid.html#K17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p4">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="tarski.html#R1">c=</a> <span class="p1">(<span class="default"><a href="topreal1.html#K5">L~</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="subset_1.html#K3">`</a> 
 <b>by </b><i><a class="ref" href="subset_1.html#T43">SUBSET_1:43</a></i>;<br/><a NAME="E12:28_1_1_1_2_2_1_21"/><b>then </b><i><font color="Green">E82</font></i>: 
 <a href="topreal1.html#K3">LSeg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="euclid.html#K17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p4">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="euclid.html#K17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p4">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="goboard9.html#K2" target="_self">LeftComp</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="goboard9.html#E1:28_1"><i><font color="Green">E30</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1"><i><font color="Green">E32</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2"><i><font color="Green">E33</font></i></a>, <a class="txt" href="goboard9.html#E51:28_1_1_1_2"><i><font color="Green">E71</font></i></a>, <a class="txt" href="goboard9.html#E4:28_1_1_1_2_2_1_21"><i><font color="Green">E77</font></i></a>, <a class="txt" href="goboard9.html#E8:28_1_1_1_2_2_1_21"><i><font color="Green">E80</font></i></a>, <a class="txt" href="goboard9.html#E9:28_1_1_1_2_2_1_21"><i><font color="Green">E81</font></i></a>, <a class="ref" href="goboard9.html#T6" target="_self">Th6</a>, <a class="ref" href="nat_1.html#T38">NAT_1:38</a></i>;<br/><a NAME="E13:28_1_1_1_2_2_1_21"/><i><font color="Green">E83</font></i>: 
 <a href="topreal1.html#K3">LSeg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="euclid.html#K17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p4">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="euclid.html#K17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p4">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xboole_0.html#NR5" target="_self">meets</a>  <a href="tops_1.html#K1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K3">cell</a> <span class="p2">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="goboard9.html#E19:28_1_1_1_2"><i><font color="Green">E46</font></i></a>, <a class="txt" href="goboard9.html#E20:28_1_1_1_2"><i><font color="Green">E47</font></i></a>, <a class="txt" href="goboard9.html#E21:28_1_1_1_2"><i><font color="Green">E48</font></i></a>, <a class="txt" href="goboard9.html#E24:28_1_1_1_2"><i><font color="Green">E51</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2_2_1_21"><i><font color="Green">E74</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1_1_2_2_1_21"><i><font color="Green">E75</font></i></a>, <a class="txt" href="goboard9.html#E6:28_1_1_1_2_2_1_21"><i><font color="Green">E78</font></i></a>, <a class="ref" href="goboard6.html#T85">GOBOARD6:85</a></i>;<br/><a NAME="E14:28_1_1_1_2_2_1_21"/>
 <a href="tops_1.html#K1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K5">left_cell</a> <font color="Maroon">c<sub>1</sub></font>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="xboole_0.html#R1">misses</a>  <a href="topreal1.html#K5">L~</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="goboard9.html#E1:28_1_1"><i><font color="Green">E31</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1"><i><font color="Green">E32</font></i></a>, <a class="ref" href="goboard8.html#T37">GOBOARD8:37</a></i>;<br/><a NAME="E15:28_1_1_1_2_2_1_21"/><b>then </b>
 <a href="tops_1.html#K1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K5">left_cell</a> <font color="Maroon">c<sub>1</sub></font>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="tarski.html#R1">c=</a> <span class="p1">(<span class="default"><a href="topreal1.html#K5">L~</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="subset_1.html#K3">`</a> 
 <b>by </b><i><a class="ref" href="subset_1.html#T43">SUBSET_1:43</a></i>;<br/><b>hence </b><a NAME="E16:28_1_1_1_2_2_1_21"/>
 <a href="tops_1.html#K1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K5">left_cell</a> <font color="Maroon">c<sub>1</sub></font>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="goboard9.html#K2" target="_self">LeftComp</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="goboard9.html#E51:28_1_1_1_2"><i><font color="Green">E71</font></i></a>, <a class="txt" href="goboard9.html#E52:28_1_1_1_2"><i><font color="Green">E72</font></i></a>, <a class="txt" href="goboard9.html#E7:28_1_1_1_2_2_1_21"><i><font color="Green">E79</font></i></a>, <a class="txt" href="goboard9.html#E12:28_1_1_1_2_2_1_21"><i><font color="Green">E82</font></i></a>, <a class="txt" href="goboard9.html#E13:28_1_1_1_2_2_1_21"><i><font color="Green">E83</font></i></a>, <a class="ref" href="goboard9.html#T6" target="_self">Th6</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="28_1_1_1_2_2_1_22"><b>suppose </b></a><b>that </b><a NAME="E1:28_1_1_1_2_2_1_22"/><i><font color="Green">E74</font></i>: 
<font color="Maroon">c<sub>3</sub></font> <a href="nat_1.html#K1">+</a> 1 <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>5</sub></font>
 <b>and </b><br/><a NAME="E2:28_1_1_1_2_2_1_22"/><i><font color="Green">E75</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>
 ;<br/><div class="add"> <a href="goboard5.html#K5">left_cell</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font> = 
 <a href="goboard5.html#K3">cell</a> <span class="p1">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>6</sub></font>
<b>by </b><i><a class="txt" href="goboard9.html#E1:28_1_1_1_2"><i><font color="Green">E33</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1_1_2"><i><font color="Green">E34</font></i></a>, <a class="txt" href="goboard9.html#E7:28_1_1_1_2"><i><font color="Green">E37</font></i></a>, <a class="txt" href="goboard9.html#E8:28_1_1_1_2"><i><font color="Green">E38</font></i></a>, <a class="txt" href="goboard9.html#E11:28_1_1_1_2"><i><font color="Green">E40</font></i></a>, <a class="txt" href="goboard9.html#E12:28_1_1_1_2"><i><font color="Green">E41</font></i></a>, <a class="txt" href="goboard9.html#E24:28_1_1_1_2"><i><font color="Green">E51</font></i></a>, <a class="txt" href="goboard9.html#E39:28_1_1_1_2"><i><font color="Green">E62</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2_2_1_22"><i><font color="Green">E74</font></i></a>, <a class="ref" href="goboard5.html#T29">GOBOARD5:29</a></i>
<br/>.= 
 <a href="goboard5.html#K5">left_cell</a> <font color="Maroon">c<sub>1</sub></font>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>
<b>by </b><i><a class="txt" href="goboard9.html#E1:28_1_1"><i><font color="Green">E31</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1"><i><font color="Green">E32</font></i></a>, <a class="txt" href="goboard9.html#E11:28_1_1_1_2"><i><font color="Green">E40</font></i></a>, <a class="txt" href="goboard9.html#E12:28_1_1_1_2"><i><font color="Green">E41</font></i></a>, <a class="txt" href="goboard9.html#E16:28_1_1_1_2"><i><font color="Green">E43</font></i></a>, <a class="txt" href="goboard9.html#E17:28_1_1_1_2"><i><font color="Green">E44</font></i></a>, <a class="txt" href="goboard9.html#E25:28_1_1_1_2"><i><font color="Green">E52</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2_2_1_22"><i><font color="Green">E74</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1_1_2_2_1_22"><i><font color="Green">E75</font></i></a>, <a class="ref" href="goboard5.html#T28">GOBOARD5:28</a></i>
;<br/><b>hence </b><a NAME="E4:28_1_1_1_2_2_1_22"/>
 <a href="tops_1.html#K1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K5">left_cell</a> <font color="Maroon">c<sub>1</sub></font>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="goboard9.html#K2" target="_self">LeftComp</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="goboard9.html#E1:28_1"><i><font color="Green">E30</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1"><i><font color="Green">E32</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2"><i><font color="Green">E33</font></i></a>, <a class="ref" href="nat_1.html#T38">NAT_1:38</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="28_1_1_1_2_2_1_23"><b>suppose </b></a><b>that </b><a NAME="E1:28_1_1_1_2_2_1_23"/><i><font color="Green">E74</font></i>: 
<font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K1">+</a> 1 <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>6</sub></font>
 <b>and </b><br/><a NAME="E2:28_1_1_1_2_2_1_23"/><i><font color="Green">E75</font></i>: 
<font color="Maroon">c<sub>5</sub></font> <a href="nat_1.html#K1">+</a> 1 <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>7</sub></font>
 <b>and </b><br/><a NAME="E3:28_1_1_1_2_2_1_23"/><i><font color="Green">E76</font></i>: 
<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> 1
 <b>and </b><br/><a NAME="E4:28_1_1_1_2_2_1_23"/><i><font color="Green">E77</font></i>: 
<font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R1">=</a>  <a href="matrix_1.html#K1">width</a> <span class="p1">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>
 ;<br/><div class="add"><a NAME="E5:28_1_1_1_2_2_1_23"/><i><font color="Green">E78</font></i>: 
 <a href="goboard5.html#K5">left_cell</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a>  <a href="goboard5.html#K3">cell</a> <span class="p1">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span>,<font color="Maroon">c<sub>4</sub></font>
 <b>by </b><i><a class="txt" href="goboard9.html#E1:28_1_1_1_2"><i><font color="Green">E33</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1_1_2"><i><font color="Green">E34</font></i></a>, <a class="txt" href="goboard9.html#E7:28_1_1_1_2"><i><font color="Green">E37</font></i></a>, <a class="txt" href="goboard9.html#E8:28_1_1_1_2"><i><font color="Green">E38</font></i></a>, <a class="txt" href="goboard9.html#E11:28_1_1_1_2"><i><font color="Green">E40</font></i></a>, <a class="txt" href="goboard9.html#E12:28_1_1_1_2"><i><font color="Green">E41</font></i></a>, <a class="txt" href="goboard9.html#E24:28_1_1_1_2"><i><font color="Green">E51</font></i></a>, <a class="txt" href="goboard9.html#E37:28_1_1_1_2"><i><font color="Green">E61</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2_2_1_23"><i><font color="Green">E74</font></i></a>, <a class="ref" href="goboard5.html#T28">GOBOARD5:28</a></i>;<br/><a NAME="E6:28_1_1_1_2_2_1_23"/><i><font color="Green">E79</font></i>: 
<font color="Maroon">c<sub>3</sub></font> <a href="binarith.html#K5">-'</a> 1 <a href="hidden.html#R1">=</a> 0
 <b>by </b><i><a class="txt" href="goboard9.html#E3:28_1_1_1_2_2_1_23"><i><font color="Green">E76</font></i></a>, <a class="txt" href="goboard9.html#E1"><i><font color="Green">Lemma1</font></i></a></i>;<br/><a NAME="E7:28_1_1_1_2_2_1_23"/><i><font color="Green">E80</font></i>: 
<font color="Maroon">c<sub>6</sub></font> <a href="binarith.html#K5">-'</a> 1 <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>4</sub></font>
 <b>by </b><i><a class="txt" href="goboard9.html#E1:28_1_1_1_2_2_1_23"><i><font color="Green">E74</font></i></a>, <a class="ref" href="binarith.html#T39">BINARITH:39</a></i>;<br/><a NAME="E8:28_1_1_1_2_2_1_23"/><i><font color="Green">E81</font></i>: 
 <a href="topreal1.html#K3">LSeg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> 1,<font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="euclid.html#K17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> 1,<font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K20">-</a> <span class="p2"><a href="euclid.html#K23">|[</a><span class="default">1,0</span><a href="euclid.html#K23">]|</a></span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> 1,<font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="euclid.html#K17">+</a> <span class="p2"><a href="euclid.html#K23">|[</a><span class="default"><span class="p3">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1</span><a href="euclid.html#K23">]|</a></span></span>)</span> is <a href="connsp_1.html#V2">connected</a>
 <b>by </b><i><a class="ref" href="goboard9.html#T8" target="_self">Th8</a></i>;<br/><a NAME="E9:28_1_1_1_2_2_1_23"/><i><font color="Green">E82</font></i>: 
 <a href="topreal1.html#K3">LSeg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> 1,<font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="euclid.html#K17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> 1,<font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K20">-</a> <span class="p2"><a href="euclid.html#K23">|[</a><span class="default">1,0</span><a href="euclid.html#K23">]|</a></span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> 1,<font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="euclid.html#K17">+</a> <span class="p2"><a href="euclid.html#K23">|[</a><span class="default"><span class="p3">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1</span><a href="euclid.html#K23">]|</a></span></span>)</span> <a href="xboole_0.html#NR5" target="_self">meets</a>  <a href="tops_1.html#K1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K3">cell</a> <span class="p2">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span>,<font color="Maroon">c<sub>4</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="goboard9.html#E21:28_1_1_1_2"><i><font color="Green">E48</font></i></a>, <a class="txt" href="goboard9.html#E22:28_1_1_1_2"><i><font color="Green">E49</font></i></a>, <a class="txt" href="goboard9.html#E24:28_1_1_1_2"><i><font color="Green">E51</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2_2_1_23"><i><font color="Green">E74</font></i></a>, <a class="txt" href="goboard9.html#E6:28_1_1_1_2_2_1_23"><i><font color="Green">E79</font></i></a>, <a class="ref" href="goboard6.html#T88">GOBOARD6:88</a></i>;<br/><a NAME="E10:28_1_1_1_2_2_1_23"/>
 <a href="topreal1.html#K3">LSeg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> 1,<font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="euclid.html#K17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> 1,<font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K20">-</a> <span class="p2"><a href="euclid.html#K23">|[</a><span class="default">1,0</span><a href="euclid.html#K23">]|</a></span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> 1,<font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="euclid.html#K17">+</a> <span class="p2"><a href="euclid.html#K23">|[</a><span class="default"><span class="p3">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1</span><a href="euclid.html#K23">]|</a></span></span>)</span> <a href="xboole_0.html#R1">misses</a>  <a href="topreal1.html#K5">L~</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="goboard9.html#E4:28_1_1_1_2_2_1_23"><i><font color="Green">E77</font></i></a>, <a class="txt" href="goboard9.html#E7:28_1_1_1_2_2_1_23"><i><font color="Green">E80</font></i></a>, <a class="ref" href="goboard8.html#T33">GOBOARD8:33</a></i>;<br/><a NAME="E11:28_1_1_1_2_2_1_23"/><b>then </b>
 <a href="topreal1.html#K3">LSeg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> 1,<font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="euclid.html#K17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> 1,<font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K20">-</a> <span class="p2"><a href="euclid.html#K23">|[</a><span class="default">1,0</span><a href="euclid.html#K23">]|</a></span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> 1,<font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="euclid.html#K17">+</a> <span class="p2"><a href="euclid.html#K23">|[</a><span class="default"><span class="p3">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1</span><a href="euclid.html#K23">]|</a></span></span>)</span> <a href="tarski.html#R1">c=</a> <span class="p1">(<span class="default"><a href="topreal1.html#K5">L~</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="subset_1.html#K3">`</a> 
 <b>by </b><i><a class="ref" href="subset_1.html#T43">SUBSET_1:43</a></i>;<br/><a NAME="E12:28_1_1_1_2_2_1_23"/><b>then </b><i><font color="Green">E83</font></i>: 
 <a href="topreal1.html#K3">LSeg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> 1,<font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="euclid.html#K17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> 1,<font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K20">-</a> <span class="p2"><a href="euclid.html#K23">|[</a><span class="default">1,0</span><a href="euclid.html#K23">]|</a></span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> 1,<font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="euclid.html#K17">+</a> <span class="p2"><a href="euclid.html#K23">|[</a><span class="default"><span class="p3">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1</span><a href="euclid.html#K23">]|</a></span></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="goboard9.html#K2" target="_self">LeftComp</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="goboard9.html#E1:28_1"><i><font color="Green">E30</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1"><i><font color="Green">E32</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2"><i><font color="Green">E33</font></i></a>, <a class="txt" href="goboard9.html#E51:28_1_1_1_2"><i><font color="Green">E71</font></i></a>, <a class="txt" href="goboard9.html#E5:28_1_1_1_2_2_1_23"><i><font color="Green">E78</font></i></a>, <a class="txt" href="goboard9.html#E8:28_1_1_1_2_2_1_23"><i><font color="Green">E81</font></i></a>, <a class="txt" href="goboard9.html#E9:28_1_1_1_2_2_1_23"><i><font color="Green">E82</font></i></a>, <a class="ref" href="goboard9.html#T6" target="_self">Th6</a>, <a class="ref" href="nat_1.html#T38">NAT_1:38</a></i>;<br/><a NAME="E13:28_1_1_1_2_2_1_23"/>
<font color="Maroon">c<sub>5</sub></font> <a href="binarith.html#K5">-'</a> 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>5</sub></font>
 <b>by </b><i><a class="txt" href="goboard9.html#E2"><i><font color="Green">Lemma2</font></i></a></i>;<br/><a NAME="E14:28_1_1_1_2_2_1_23"/><b>then </b><i><font color="Green">E84</font></i>: 
<font color="Maroon">c<sub>5</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"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="goboard9.html#E19:28_1_1_1_2"><i><font color="Green">E46</font></i></a>, <a class="ref" href="xxreal_0.html#T2">XXREAL_0:2</a></i>;<br/><a NAME="E15:28_1_1_1_2_2_1_23"/><b>then </b><i><font color="Green">E85</font></i>: 
 <a href="tops_1.html#K1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K3">cell</a> <span class="p2">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span>,<font color="Maroon">c<sub>6</sub></font></span>)</span> is <a href="connsp_1.html#V2">connected</a>
 <b>by </b><i><a class="txt" href="goboard9.html#E22:28_1_1_1_2"><i><font color="Green">E49</font></i></a>, <a class="ref" href="goboard9.html#T21" target="_self">Th21</a></i>;<br/><a NAME="E16:28_1_1_1_2_2_1_23"/><i><font color="Green">E86</font></i>: 
 <a href="topreal1.html#K3">LSeg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> 1,<font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="euclid.html#K17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> 1,<font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K20">-</a> <span class="p2"><a href="euclid.html#K23">|[</a><span class="default">1,0</span><a href="euclid.html#K23">]|</a></span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> 1,<font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="euclid.html#K17">+</a> <span class="p2"><a href="euclid.html#K23">|[</a><span class="default"><span class="p3">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1</span><a href="euclid.html#K23">]|</a></span></span>)</span> <a href="xboole_0.html#NR5" target="_self">meets</a>  <a href="tops_1.html#K1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K3">cell</a> <span class="p2">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span>,<font color="Maroon">c<sub>6</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="goboard9.html#E4:28_1_1_1_2_2_1_23"><i><font color="Green">E77</font></i></a>, <a class="txt" href="goboard9.html#E6:28_1_1_1_2_2_1_23"><i><font color="Green">E79</font></i></a>, <a class="ref" href="goboard6.html#T92">GOBOARD6:92</a></i>;<br/><a NAME="E17:28_1_1_1_2_2_1_23"/>
 <a href="tops_1.html#K1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K3">cell</a> <span class="p2">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span>,<font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="xboole_0.html#R1">misses</a>  <a href="topreal1.html#K5">L~</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="goboard9.html#E22:28_1_1_1_2"><i><font color="Green">E49</font></i></a>, <a class="txt" href="goboard9.html#E14:28_1_1_1_2_2_1_23"><i><font color="Green">E84</font></i></a>, <a class="ref" href="goboard7.html#T14">GOBOARD7:14</a></i>;<br/><a NAME="E18:28_1_1_1_2_2_1_23"/><b>then </b>
 <a href="tops_1.html#K1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K3">cell</a> <span class="p2">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span>,<font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="tarski.html#R1">c=</a> <span class="p1">(<span class="default"><a href="topreal1.html#K5">L~</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="subset_1.html#K3">`</a> 
 <b>by </b><i><a class="ref" href="subset_1.html#T43">SUBSET_1:43</a></i>;<br/><a NAME="E19:28_1_1_1_2_2_1_23"/><b>then </b><i><font color="Green">E87</font></i>: 
 <a href="tops_1.html#K1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K3">cell</a> <span class="p2">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span>,<font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="goboard9.html#K2" target="_self">LeftComp</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="goboard9.html#E24:28_1_1_1_2"><i><font color="Green">E51</font></i></a>, <a class="txt" href="goboard9.html#E51:28_1_1_1_2"><i><font color="Green">E71</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2_2_1_23"><i><font color="Green">E74</font></i></a>, <a class="txt" href="goboard9.html#E12:28_1_1_1_2_2_1_23"><i><font color="Green">E83</font></i></a>, <a class="txt" href="goboard9.html#E15:28_1_1_1_2_2_1_23"><i><font color="Green">E85</font></i></a>, <a class="txt" href="goboard9.html#E16:28_1_1_1_2_2_1_23"><i><font color="Green">E86</font></i></a>, <a class="ref" href="goboard9.html#T6" target="_self">Th6</a></i>;<br/><a NAME="E20:28_1_1_1_2_2_1_23"/><i><font color="Green">E88</font></i>: 
 <a href="goboard5.html#K5">left_cell</a> <font color="Maroon">c<sub>1</sub></font>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="hidden.html#R1">=</a>  <a href="goboard5.html#K3">cell</a> <span class="p1">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font>
 <b>by </b><i><a class="txt" href="goboard9.html#E1:28_1_1"><i><font color="Green">E31</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1"><i><font color="Green">E32</font></i></a>, <a class="txt" href="goboard9.html#E11:28_1_1_1_2"><i><font color="Green">E40</font></i></a>, <a class="txt" href="goboard9.html#E12:28_1_1_1_2"><i><font color="Green">E41</font></i></a>, <a class="txt" href="goboard9.html#E16:28_1_1_1_2"><i><font color="Green">E43</font></i></a>, <a class="txt" href="goboard9.html#E17:28_1_1_1_2"><i><font color="Green">E44</font></i></a>, <a class="txt" href="goboard9.html#E25:28_1_1_1_2"><i><font color="Green">E52</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2_2_1_23"><i><font color="Green">E74</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1_1_2_2_1_23"><i><font color="Green">E75</font></i></a>, <a class="ref" href="goboard5.html#T29">GOBOARD5:29</a></i>;<br/><a NAME="E21:28_1_1_1_2_2_1_23"/><i><font color="Green">E89</font></i>: 
 <a href="topreal1.html#K3">LSeg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> 1,<font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="euclid.html#K17">+</a> <span class="p2"><a href="euclid.html#K23">|[</a><span class="default"><span class="p3">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1</span><a href="euclid.html#K23">]|</a></span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> 1,<font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="euclid.html#K17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> 2,<font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K17">+</a> <span class="p2"><a href="euclid.html#K23">|[</a><span class="default">0,1</span><a href="euclid.html#K23">]|</a></span></span>)</span> is <a href="connsp_1.html#V2">connected</a>
 <b>by </b><i><a class="ref" href="goboard9.html#T8" target="_self">Th8</a></i>;<br/><a NAME="E22:28_1_1_1_2_2_1_23"/><i><font color="Green">E90</font></i>: 
 <a href="topreal1.html#K3">LSeg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> 1,<font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="euclid.html#K17">+</a> <span class="p2"><a href="euclid.html#K23">|[</a><span class="default"><span class="p3">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1</span><a href="euclid.html#K23">]|</a></span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> 1,<font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="euclid.html#K17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> 2,<font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K17">+</a> <span class="p2"><a href="euclid.html#K23">|[</a><span class="default">0,1</span><a href="euclid.html#K23">]|</a></span></span>)</span> <a href="xboole_0.html#NR5" target="_self">meets</a>  <a href="tops_1.html#K1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K3">cell</a> <span class="p2">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span>,<font color="Maroon">c<sub>6</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="goboard9.html#E24:28_1_1_1_2"><i><font color="Green">E51</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2_2_1_23"><i><font color="Green">E74</font></i></a>, <a class="txt" href="goboard9.html#E4:28_1_1_1_2_2_1_23"><i><font color="Green">E77</font></i></a>, <a class="txt" href="goboard9.html#E6:28_1_1_1_2_2_1_23"><i><font color="Green">E79</font></i></a>, <a class="ref" href="goboard6.html#T92">GOBOARD6:92</a></i>;<br/><a NAME="E23:28_1_1_1_2_2_1_23"/>
 <a href="topreal1.html#K3">LSeg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> 1,<font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="euclid.html#K17">+</a> <span class="p2"><a href="euclid.html#K23">|[</a><span class="default"><span class="p3">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1</span><a href="euclid.html#K23">]|</a></span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> 1,<font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="euclid.html#K17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> 2,<font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K17">+</a> <span class="p2"><a href="euclid.html#K23">|[</a><span class="default">0,1</span><a href="euclid.html#K23">]|</a></span></span>)</span> <a href="xboole_0.html#R1">misses</a>  <a href="topreal1.html#K5">L~</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="goboard9.html#E4:28_1_1_1_2_2_1_23"><i><font color="Green">E77</font></i></a>, <a class="ref" href="goboard8.html#T29">GOBOARD8:29</a></i>;<br/><a NAME="E24:28_1_1_1_2_2_1_23"/><b>then </b>
 <a href="topreal1.html#K3">LSeg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> 1,<font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="euclid.html#K17">+</a> <span class="p2"><a href="euclid.html#K23">|[</a><span class="default"><span class="p3">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1</span><a href="euclid.html#K23">]|</a></span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> 1,<font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="euclid.html#K17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> 2,<font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K17">+</a> <span class="p2"><a href="euclid.html#K23">|[</a><span class="default">0,1</span><a href="euclid.html#K23">]|</a></span></span>)</span> <a href="tarski.html#R1">c=</a> <span class="p1">(<span class="default"><a href="topreal1.html#K5">L~</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="subset_1.html#K3">`</a> 
 <b>by </b><i><a class="ref" href="subset_1.html#T43">SUBSET_1:43</a></i>;<br/><a NAME="E25:28_1_1_1_2_2_1_23"/><b>then </b><i><font color="Green">E91</font></i>: 
 <a href="topreal1.html#K3">LSeg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> 1,<font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="euclid.html#K17">+</a> <span class="p2"><a href="euclid.html#K23">|[</a><span class="default"><span class="p3">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1</span><a href="euclid.html#K23">]|</a></span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> 1,<font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="euclid.html#K17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> 2,<font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K17">+</a> <span class="p2"><a href="euclid.html#K23">|[</a><span class="default">0,1</span><a href="euclid.html#K23">]|</a></span></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="goboard9.html#K2" target="_self">LeftComp</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="goboard9.html#E51:28_1_1_1_2"><i><font color="Green">E71</font></i></a>, <a class="txt" href="goboard9.html#E19:28_1_1_1_2_2_1_23"><i><font color="Green">E87</font></i></a>, <a class="txt" href="goboard9.html#E21:28_1_1_1_2_2_1_23"><i><font color="Green">E89</font></i></a>, <a class="txt" href="goboard9.html#E22:28_1_1_1_2_2_1_23"><i><font color="Green">E90</font></i></a>, <a class="ref" href="goboard9.html#T6" target="_self">Th6</a></i>;<br/><a NAME="E26:28_1_1_1_2_2_1_23"/><i><font color="Green">E92</font></i>: 
 <a href="topreal1.html#K3">LSeg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> 1,<font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="euclid.html#K17">+</a> <span class="p2"><a href="euclid.html#K23">|[</a><span class="default"><span class="p3">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,1</span><a href="euclid.html#K23">]|</a></span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> 1,<font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="euclid.html#K17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> 2,<font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K17">+</a> <span class="p2"><a href="euclid.html#K23">|[</a><span class="default">0,1</span><a href="euclid.html#K23">]|</a></span></span>)</span> <a href="xboole_0.html#NR5" target="_self">meets</a>  <a href="tops_1.html#K1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K3">cell</a> <span class="p2">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="goboard9.html#E20:28_1_1_1_2"><i><font color="Green">E47</font></i></a>, <a class="txt" href="goboard9.html#E24:28_1_1_1_2"><i><font color="Green">E51</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2_2_1_23"><i><font color="Green">E74</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1_1_2_2_1_23"><i><font color="Green">E75</font></i></a>, <a class="txt" href="goboard9.html#E3:28_1_1_1_2_2_1_23"><i><font color="Green">E76</font></i></a>, <a class="txt" href="goboard9.html#E4:28_1_1_1_2_2_1_23"><i><font color="Green">E77</font></i></a>, <a class="ref" href="goboard6.html#T86">GOBOARD6:86</a></i>;<br/><a NAME="E27:28_1_1_1_2_2_1_23"/>
 <a href="tops_1.html#K1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K5">left_cell</a> <font color="Maroon">c<sub>1</sub></font>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="xboole_0.html#R1">misses</a>  <a href="topreal1.html#K5">L~</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="goboard9.html#E1:28_1_1"><i><font color="Green">E31</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1"><i><font color="Green">E32</font></i></a>, <a class="ref" href="goboard8.html#T37">GOBOARD8:37</a></i>;<br/><a NAME="E28:28_1_1_1_2_2_1_23"/><b>then </b>
 <a href="tops_1.html#K1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K5">left_cell</a> <font color="Maroon">c<sub>1</sub></font>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="tarski.html#R1">c=</a> <span class="p1">(<span class="default"><a href="topreal1.html#K5">L~</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="subset_1.html#K3">`</a> 
 <b>by </b><i><a class="ref" href="subset_1.html#T43">SUBSET_1:43</a></i>;<br/><b>hence </b><a NAME="E29:28_1_1_1_2_2_1_23"/>
 <a href="tops_1.html#K1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K5">left_cell</a> <font color="Maroon">c<sub>1</sub></font>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="goboard9.html#K2" target="_self">LeftComp</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="goboard9.html#E51:28_1_1_1_2"><i><font color="Green">E71</font></i></a>, <a class="txt" href="goboard9.html#E52:28_1_1_1_2"><i><font color="Green">E72</font></i></a>, <a class="txt" href="goboard9.html#E20:28_1_1_1_2_2_1_23"><i><font color="Green">E88</font></i></a>, <a class="txt" href="goboard9.html#E25:28_1_1_1_2_2_1_23"><i><font color="Green">E91</font></i></a>, <a class="txt" href="goboard9.html#E26:28_1_1_1_2_2_1_23"><i><font color="Green">E92</font></i></a>, <a class="ref" href="goboard9.html#T6" target="_self">Th6</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="28_1_1_1_2_2_1_24"><b>suppose </b></a><b>that </b><a NAME="E1:28_1_1_1_2_2_1_24"/><i><font color="Green">E74</font></i>: 
<font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K1">+</a> 1 <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>6</sub></font>
 <b>and </b><br/><a NAME="E2:28_1_1_1_2_2_1_24"/><i><font color="Green">E75</font></i>: 
<font color="Maroon">c<sub>5</sub></font> <a href="nat_1.html#K1">+</a> 1 <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>7</sub></font>
 <b>and </b><br/><a NAME="E3:28_1_1_1_2_2_1_24"/><i><font color="Green">E76</font></i>: 
<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 1
 <b>and </b><br/><a NAME="E4:28_1_1_1_2_2_1_24"/><i><font color="Green">E77</font></i>: 
<font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R1">=</a>  <a href="matrix_1.html#K1">width</a> <span class="p1">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>
 ;<br/><div class="add"><a NAME="E5:28_1_1_1_2_2_1_24"/><i><font color="Green">E78</font></i>: 
 <a href="goboard5.html#K5">left_cell</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a>  <a href="goboard5.html#K3">cell</a> <span class="p1">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span>,<font color="Maroon">c<sub>4</sub></font>
 <b>by </b><i><a class="txt" href="goboard9.html#E1:28_1_1_1_2"><i><font color="Green">E33</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1_1_2"><i><font color="Green">E34</font></i></a>, <a class="txt" href="goboard9.html#E7:28_1_1_1_2"><i><font color="Green">E37</font></i></a>, <a class="txt" href="goboard9.html#E8:28_1_1_1_2"><i><font color="Green">E38</font></i></a>, <a class="txt" href="goboard9.html#E11:28_1_1_1_2"><i><font color="Green">E40</font></i></a>, <a class="txt" href="goboard9.html#E12:28_1_1_1_2"><i><font color="Green">E41</font></i></a>, <a class="txt" href="goboard9.html#E24:28_1_1_1_2"><i><font color="Green">E51</font></i></a>, <a class="txt" href="goboard9.html#E37:28_1_1_1_2"><i><font color="Green">E61</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2_2_1_24"><i><font color="Green">E74</font></i></a>, <a class="ref" href="goboard5.html#T28">GOBOARD5:28</a></i>;<br/><a NAME="E6:28_1_1_1_2_2_1_24"/>
1 <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">c<sub>3</sub></font>
 <b>by </b><i><a class="txt" href="goboard9.html#E18:28_1_1_1_2"><i><font color="Green">E45</font></i></a>, <a class="txt" href="goboard9.html#E3:28_1_1_1_2_2_1_24"><i><font color="Green">E76</font></i></a>, <a class="ref" href="xxreal_0.html#T1">XXREAL_0:1</a></i>;<br/><a NAME="E7:28_1_1_1_2_2_1_24"/><b>then </b><i><font color="Green">E79</font></i>: 
1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>3</sub></font> <a href="binarith.html#K5">-'</a> 1
 <b>by </b><i><a class="txt" href="goboard9.html#E24:28_1_1_1_2"><i><font color="Green">E51</font></i></a>, <a class="txt" href="goboard9.html#E37:28_1_1_1_2"><i><font color="Green">E61</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2_2_1_24"><i><font color="Green">E74</font></i></a>, <a class="ref" href="nat_1.html#T38">NAT_1:38</a></i>;<br/><a NAME="E8:28_1_1_1_2_2_1_24"/><i><font color="Green">E80</font></i>: 
<font color="Maroon">c<sub>6</sub></font> <a href="binarith.html#K5">-'</a> 1 <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>4</sub></font>
 <b>by </b><i><a class="txt" href="goboard9.html#E1:28_1_1_1_2_2_1_24"><i><font color="Green">E74</font></i></a>, <a class="ref" href="binarith.html#T39">BINARITH:39</a></i>;<br/><a NAME="E9:28_1_1_1_2_2_1_24"/><i><font color="Green">E81</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>5</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> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>7</sub></font>
 <b>by </b><i><a class="txt" href="goboard9.html#E37:28_1_1_1_2"><i><font color="Green">E61</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1_1_2_2_1_24"><i><font color="Green">E75</font></i></a></i>;<br/><a NAME="E10:28_1_1_1_2_2_1_24"/><i><font color="Green">E82</font></i>: 
 <a href="topreal1.html#K3">LSeg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span>,<font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="euclid.html#K17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span>,<font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="euclid.html#K17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K17">+</a> <span class="p2"><a href="euclid.html#K23">|[</a><span class="default">0,1</span><a href="euclid.html#K23">]|</a></span></span>)</span> is <a href="connsp_1.html#V2">connected</a>
 <b>by </b><i><a class="ref" href="goboard9.html#T8" target="_self">Th8</a></i>;<br/><a NAME="E11:28_1_1_1_2_2_1_24"/><i><font color="Green">E83</font></i>: 
 <a href="topreal1.html#K3">LSeg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span>,<font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="euclid.html#K17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span>,<font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="euclid.html#K17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K17">+</a> <span class="p2"><a href="euclid.html#K23">|[</a><span class="default">0,1</span><a href="euclid.html#K23">]|</a></span></span>)</span> <a href="xboole_0.html#NR5" target="_self">meets</a>  <a href="tops_1.html#K1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K3">cell</a> <span class="p2">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span>,<font color="Maroon">c<sub>4</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="goboard9.html#E19:28_1_1_1_2"><i><font color="Green">E46</font></i></a>, <a class="txt" href="goboard9.html#E21:28_1_1_1_2"><i><font color="Green">E48</font></i></a>, <a class="txt" href="goboard9.html#E22:28_1_1_1_2"><i><font color="Green">E49</font></i></a>, <a class="txt" href="goboard9.html#E24:28_1_1_1_2"><i><font color="Green">E51</font></i></a>, <a class="txt" href="goboard9.html#E37:28_1_1_1_2"><i><font color="Green">E61</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2_2_1_24"><i><font color="Green">E74</font></i></a>, <a class="txt" href="goboard9.html#E7:28_1_1_1_2_2_1_24"><i><font color="Green">E79</font></i></a>, <a class="ref" href="goboard6.html#T85">GOBOARD6:85</a></i>;<br/><a NAME="E12:28_1_1_1_2_2_1_24"/>
 <a href="topreal1.html#K3">LSeg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span>,<font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="euclid.html#K17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span>,<font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="euclid.html#K17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K17">+</a> <span class="p2"><a href="euclid.html#K23">|[</a><span class="default">0,1</span><a href="euclid.html#K23">]|</a></span></span>)</span> <a href="xboole_0.html#R1">misses</a>  <a href="topreal1.html#K5">L~</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="goboard9.html#E2:28_1_1"><i><font color="Green">E32</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2"><i><font color="Green">E33</font></i></a>, <a class="txt" href="goboard9.html#E8:28_1_1_1_2"><i><font color="Green">E38</font></i></a>, <a class="txt" href="goboard9.html#E12:28_1_1_1_2"><i><font color="Green">E41</font></i></a>, <a class="txt" href="goboard9.html#E17:28_1_1_1_2"><i><font color="Green">E44</font></i></a>, <a class="txt" href="goboard9.html#E20:28_1_1_1_2"><i><font color="Green">E47</font></i></a>, <a class="txt" href="goboard9.html#E24:28_1_1_1_2"><i><font color="Green">E51</font></i></a>, <a class="txt" href="goboard9.html#E25:28_1_1_1_2"><i><font color="Green">E52</font></i></a>, <a class="txt" href="goboard9.html#E37:28_1_1_1_2"><i><font color="Green">E61</font></i></a>, <a class="txt" href="goboard9.html#E46:28_1_1_1_2"><i><font color="Green">E66</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2_2_1_24"><i><font color="Green">E74</font></i></a>, <a class="txt" href="goboard9.html#E4:28_1_1_1_2_2_1_24"><i><font color="Green">E77</font></i></a>, <a class="txt" href="goboard9.html#E7:28_1_1_1_2_2_1_24"><i><font color="Green">E79</font></i></a>, <a class="txt" href="goboard9.html#E8:28_1_1_1_2_2_1_24"><i><font color="Green">E80</font></i></a>, <a class="txt" href="goboard9.html#E9:28_1_1_1_2_2_1_24"><i><font color="Green">E81</font></i></a>, <a class="ref" href="goboard8.html#T9">GOBOARD8:9</a></i>;<br/><a NAME="E13:28_1_1_1_2_2_1_24"/><b>then </b>
 <a href="topreal1.html#K3">LSeg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span>,<font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="euclid.html#K17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span>,<font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="euclid.html#K17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K17">+</a> <span class="p2"><a href="euclid.html#K23">|[</a><span class="default">0,1</span><a href="euclid.html#K23">]|</a></span></span>)</span> <a href="tarski.html#R1">c=</a> <span class="p1">(<span class="default"><a href="topreal1.html#K5">L~</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="subset_1.html#K3">`</a> 
 <b>by </b><i><a class="ref" href="subset_1.html#T43">SUBSET_1:43</a></i>;<br/><a NAME="E14:28_1_1_1_2_2_1_24"/><b>then </b><i><font color="Green">E84</font></i>: 
 <a href="topreal1.html#K3">LSeg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span>,<font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="euclid.html#K17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span>,<font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="euclid.html#K17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K17">+</a> <span class="p2"><a href="euclid.html#K23">|[</a><span class="default">0,1</span><a href="euclid.html#K23">]|</a></span></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="goboard9.html#K2" target="_self">LeftComp</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="goboard9.html#E1:28_1"><i><font color="Green">E30</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1"><i><font color="Green">E32</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2"><i><font color="Green">E33</font></i></a>, <a class="txt" href="goboard9.html#E51:28_1_1_1_2"><i><font color="Green">E71</font></i></a>, <a class="txt" href="goboard9.html#E5:28_1_1_1_2_2_1_24"><i><font color="Green">E78</font></i></a>, <a class="txt" href="goboard9.html#E10:28_1_1_1_2_2_1_24"><i><font color="Green">E82</font></i></a>, <a class="txt" href="goboard9.html#E11:28_1_1_1_2_2_1_24"><i><font color="Green">E83</font></i></a>, <a class="ref" href="goboard9.html#T6" target="_self">Th6</a>, <a class="ref" href="nat_1.html#T38">NAT_1:38</a></i>;<br/><a NAME="E15:28_1_1_1_2_2_1_24"/>
<font color="Maroon">c<sub>5</sub></font> <a href="binarith.html#K5">-'</a> 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>5</sub></font>
 <b>by </b><i><a class="txt" href="goboard9.html#E2"><i><font color="Green">Lemma2</font></i></a></i>;<br/><a NAME="E16:28_1_1_1_2_2_1_24"/><b>then </b><i><font color="Green">E85</font></i>: 
<font color="Maroon">c<sub>5</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"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="goboard9.html#E19:28_1_1_1_2"><i><font color="Green">E46</font></i></a>, <a class="ref" href="xxreal_0.html#T2">XXREAL_0:2</a></i>;<br/><a NAME="E17:28_1_1_1_2_2_1_24"/><b>then </b><i><font color="Green">E86</font></i>: 
 <a href="tops_1.html#K1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K3">cell</a> <span class="p2">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span>,<font color="Maroon">c<sub>6</sub></font></span>)</span> is <a href="connsp_1.html#V2">connected</a>
 <b>by </b><i><a class="txt" href="goboard9.html#E22:28_1_1_1_2"><i><font color="Green">E49</font></i></a>, <a class="ref" href="goboard9.html#T21" target="_self">Th21</a></i>;<br/><a NAME="E18:28_1_1_1_2_2_1_24"/><i><font color="Green">E87</font></i>: 
 <a href="topreal1.html#K3">LSeg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span>,<font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="euclid.html#K17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span>,<font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="euclid.html#K17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K17">+</a> <span class="p2"><a href="euclid.html#K23">|[</a><span class="default">0,1</span><a href="euclid.html#K23">]|</a></span></span>)</span> <a href="xboole_0.html#NR5" target="_self">meets</a>  <a href="tops_1.html#K1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K3">cell</a> <span class="p2">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span>,<font color="Maroon">c<sub>6</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="goboard9.html#E18:28_1_1_1_2"><i><font color="Green">E45</font></i></a>, <a class="txt" href="goboard9.html#E24:28_1_1_1_2"><i><font color="Green">E51</font></i></a>, <a class="txt" href="goboard9.html#E37:28_1_1_1_2"><i><font color="Green">E61</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2_2_1_24"><i><font color="Green">E74</font></i></a>, <a class="txt" href="goboard9.html#E4:28_1_1_1_2_2_1_24"><i><font color="Green">E77</font></i></a>, <a class="txt" href="goboard9.html#E7:28_1_1_1_2_2_1_24"><i><font color="Green">E79</font></i></a>, <a class="ref" href="goboard6.html#T86">GOBOARD6:86</a></i>;<br/><a NAME="E19:28_1_1_1_2_2_1_24"/>
 <a href="tops_1.html#K1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K3">cell</a> <span class="p2">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span>,<font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="xboole_0.html#R1">misses</a>  <a href="topreal1.html#K5">L~</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="goboard9.html#E22:28_1_1_1_2"><i><font color="Green">E49</font></i></a>, <a class="txt" href="goboard9.html#E16:28_1_1_1_2_2_1_24"><i><font color="Green">E85</font></i></a>, <a class="ref" href="goboard7.html#T14">GOBOARD7:14</a></i>;<br/><a NAME="E20:28_1_1_1_2_2_1_24"/><b>then </b>
 <a href="tops_1.html#K1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K3">cell</a> <span class="p2">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span>,<font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="tarski.html#R1">c=</a> <span class="p1">(<span class="default"><a href="topreal1.html#K5">L~</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="subset_1.html#K3">`</a> 
 <b>by </b><i><a class="ref" href="subset_1.html#T43">SUBSET_1:43</a></i>;<br/><a NAME="E21:28_1_1_1_2_2_1_24"/><b>then </b><i><font color="Green">E88</font></i>: 
 <a href="tops_1.html#K1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K3">cell</a> <span class="p2">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span>,<font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="goboard9.html#K2" target="_self">LeftComp</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="goboard9.html#E24:28_1_1_1_2"><i><font color="Green">E51</font></i></a>, <a class="txt" href="goboard9.html#E51:28_1_1_1_2"><i><font color="Green">E71</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2_2_1_24"><i><font color="Green">E74</font></i></a>, <a class="txt" href="goboard9.html#E14:28_1_1_1_2_2_1_24"><i><font color="Green">E84</font></i></a>, <a class="txt" href="goboard9.html#E17:28_1_1_1_2_2_1_24"><i><font color="Green">E86</font></i></a>, <a class="txt" href="goboard9.html#E18:28_1_1_1_2_2_1_24"><i><font color="Green">E87</font></i></a>, <a class="ref" href="goboard9.html#T6" target="_self">Th6</a></i>;<br/><a NAME="E22:28_1_1_1_2_2_1_24"/><i><font color="Green">E89</font></i>: 
 <a href="goboard5.html#K5">left_cell</a> <font color="Maroon">c<sub>1</sub></font>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="hidden.html#R1">=</a>  <a href="goboard5.html#K3">cell</a> <span class="p1">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font>
 <b>by </b><i><a class="txt" href="goboard9.html#E1:28_1_1"><i><font color="Green">E31</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1"><i><font color="Green">E32</font></i></a>, <a class="txt" href="goboard9.html#E11:28_1_1_1_2"><i><font color="Green">E40</font></i></a>, <a class="txt" href="goboard9.html#E12:28_1_1_1_2"><i><font color="Green">E41</font></i></a>, <a class="txt" href="goboard9.html#E16:28_1_1_1_2"><i><font color="Green">E43</font></i></a>, <a class="txt" href="goboard9.html#E17:28_1_1_1_2"><i><font color="Green">E44</font></i></a>, <a class="txt" href="goboard9.html#E25:28_1_1_1_2"><i><font color="Green">E52</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2_2_1_24"><i><font color="Green">E74</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1_1_2_2_1_24"><i><font color="Green">E75</font></i></a>, <a class="ref" href="goboard5.html#T29">GOBOARD5:29</a></i>;<br/><a NAME="E23:28_1_1_1_2_2_1_24"/><i><font color="Green">E90</font></i>: 
 <a href="topreal1.html#K3">LSeg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span>,<font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="euclid.html#K17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K17">+</a> <span class="p2"><a href="euclid.html#K23">|[</a><span class="default">0,1</span><a href="euclid.html#K23">]|</a></span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="euclid.html#K17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K17">+</a> <span class="p2"><a href="euclid.html#K23">|[</a><span class="default">0,1</span><a href="euclid.html#K23">]|</a></span></span>)</span> is <a href="connsp_1.html#V2">connected</a>
 <b>by </b><i><a class="ref" href="goboard9.html#T8" target="_self">Th8</a></i>;<br/><a NAME="E24:28_1_1_1_2_2_1_24"/><i><font color="Green">E91</font></i>: 
 <a href="topreal1.html#K3">LSeg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span>,<font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="euclid.html#K17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K17">+</a> <span class="p2"><a href="euclid.html#K23">|[</a><span class="default">0,1</span><a href="euclid.html#K23">]|</a></span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="euclid.html#K17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K17">+</a> <span class="p2"><a href="euclid.html#K23">|[</a><span class="default">0,1</span><a href="euclid.html#K23">]|</a></span></span>)</span> <a href="xboole_0.html#NR5" target="_self">meets</a>  <a href="tops_1.html#K1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K3">cell</a> <span class="p2">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span>,<font color="Maroon">c<sub>6</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="goboard9.html#E19:28_1_1_1_2"><i><font color="Green">E46</font></i></a>, <a class="txt" href="goboard9.html#E24:28_1_1_1_2"><i><font color="Green">E51</font></i></a>, <a class="txt" href="goboard9.html#E37:28_1_1_1_2"><i><font color="Green">E61</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2_2_1_24"><i><font color="Green">E74</font></i></a>, <a class="txt" href="goboard9.html#E4:28_1_1_1_2_2_1_24"><i><font color="Green">E77</font></i></a>, <a class="txt" href="goboard9.html#E7:28_1_1_1_2_2_1_24"><i><font color="Green">E79</font></i></a>, <a class="ref" href="goboard6.html#T86">GOBOARD6:86</a></i>;<br/><a NAME="E25:28_1_1_1_2_2_1_24"/>
 <a href="topreal1.html#K3">LSeg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span>,<font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="euclid.html#K17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K17">+</a> <span class="p2"><a href="euclid.html#K23">|[</a><span class="default">0,1</span><a href="euclid.html#K23">]|</a></span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="euclid.html#K17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K17">+</a> <span class="p2"><a href="euclid.html#K23">|[</a><span class="default">0,1</span><a href="euclid.html#K23">]|</a></span></span>)</span> <a href="xboole_0.html#R1">misses</a>  <a href="topreal1.html#K5">L~</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="goboard9.html#E20:28_1_1_1_2"><i><font color="Green">E47</font></i></a>, <a class="txt" href="goboard9.html#E24:28_1_1_1_2"><i><font color="Green">E51</font></i></a>, <a class="txt" href="goboard9.html#E37:28_1_1_1_2"><i><font color="Green">E61</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2_2_1_24"><i><font color="Green">E74</font></i></a>, <a class="txt" href="goboard9.html#E4:28_1_1_1_2_2_1_24"><i><font color="Green">E77</font></i></a>, <a class="txt" href="goboard9.html#E7:28_1_1_1_2_2_1_24"><i><font color="Green">E79</font></i></a>, <a class="txt" href="goboard9.html#E9:28_1_1_1_2_2_1_24"><i><font color="Green">E81</font></i></a>, <a class="ref" href="goboard8.html#T28">GOBOARD8:28</a></i>;<br/><a NAME="E26:28_1_1_1_2_2_1_24"/><b>then </b>
 <a href="topreal1.html#K3">LSeg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span>,<font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="euclid.html#K17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K17">+</a> <span class="p2"><a href="euclid.html#K23">|[</a><span class="default">0,1</span><a href="euclid.html#K23">]|</a></span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="euclid.html#K17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K17">+</a> <span class="p2"><a href="euclid.html#K23">|[</a><span class="default">0,1</span><a href="euclid.html#K23">]|</a></span></span>)</span> <a href="tarski.html#R1">c=</a> <span class="p1">(<span class="default"><a href="topreal1.html#K5">L~</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="subset_1.html#K3">`</a> 
 <b>by </b><i><a class="ref" href="subset_1.html#T43">SUBSET_1:43</a></i>;<br/><a NAME="E27:28_1_1_1_2_2_1_24"/><b>then </b><i><font color="Green">E92</font></i>: 
 <a href="topreal1.html#K3">LSeg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span>,<font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="euclid.html#K17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K17">+</a> <span class="p2"><a href="euclid.html#K23">|[</a><span class="default">0,1</span><a href="euclid.html#K23">]|</a></span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="euclid.html#K17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K17">+</a> <span class="p2"><a href="euclid.html#K23">|[</a><span class="default">0,1</span><a href="euclid.html#K23">]|</a></span></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="goboard9.html#K2" target="_self">LeftComp</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="goboard9.html#E51:28_1_1_1_2"><i><font color="Green">E71</font></i></a>, <a class="txt" href="goboard9.html#E21:28_1_1_1_2_2_1_24"><i><font color="Green">E88</font></i></a>, <a class="txt" href="goboard9.html#E23:28_1_1_1_2_2_1_24"><i><font color="Green">E90</font></i></a>, <a class="txt" href="goboard9.html#E24:28_1_1_1_2_2_1_24"><i><font color="Green">E91</font></i></a>, <a class="ref" href="goboard9.html#T6" target="_self">Th6</a></i>;<br/><a NAME="E28:28_1_1_1_2_2_1_24"/><i><font color="Green">E93</font></i>: 
 <a href="topreal1.html#K3">LSeg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span>,<font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="euclid.html#K17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K17">+</a> <span class="p2"><a href="euclid.html#K23">|[</a><span class="default">0,1</span><a href="euclid.html#K23">]|</a></span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="euclid.html#K17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K17">+</a> <span class="p2"><a href="euclid.html#K23">|[</a><span class="default">0,1</span><a href="euclid.html#K23">]|</a></span></span>)</span> <a href="xboole_0.html#NR5" target="_self">meets</a>  <a href="tops_1.html#K1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K3">cell</a> <span class="p2">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="goboard9.html#E19:28_1_1_1_2"><i><font color="Green">E46</font></i></a>, <a class="txt" href="goboard9.html#E20:28_1_1_1_2"><i><font color="Green">E47</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1_1_2_2_1_24"><i><font color="Green">E75</font></i></a>, <a class="txt" href="goboard9.html#E4:28_1_1_1_2_2_1_24"><i><font color="Green">E77</font></i></a>, <a class="ref" href="goboard6.html#T86">GOBOARD6:86</a></i>;<br/><a NAME="E29:28_1_1_1_2_2_1_24"/>
 <a href="tops_1.html#K1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K5">left_cell</a> <font color="Maroon">c<sub>1</sub></font>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="xboole_0.html#R1">misses</a>  <a href="topreal1.html#K5">L~</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="goboard9.html#E1:28_1_1"><i><font color="Green">E31</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1"><i><font color="Green">E32</font></i></a>, <a class="ref" href="goboard8.html#T37">GOBOARD8:37</a></i>;<br/><a NAME="E30:28_1_1_1_2_2_1_24"/><b>then </b>
 <a href="tops_1.html#K1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K5">left_cell</a> <font color="Maroon">c<sub>1</sub></font>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="tarski.html#R1">c=</a> <span class="p1">(<span class="default"><a href="topreal1.html#K5">L~</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="subset_1.html#K3">`</a> 
 <b>by </b><i><a class="ref" href="subset_1.html#T43">SUBSET_1:43</a></i>;<br/><b>hence </b><a NAME="E31:28_1_1_1_2_2_1_24"/>
 <a href="tops_1.html#K1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K5">left_cell</a> <font color="Maroon">c<sub>1</sub></font>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="goboard9.html#K2" target="_self">LeftComp</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="goboard9.html#E51:28_1_1_1_2"><i><font color="Green">E71</font></i></a>, <a class="txt" href="goboard9.html#E52:28_1_1_1_2"><i><font color="Green">E72</font></i></a>, <a class="txt" href="goboard9.html#E22:28_1_1_1_2_2_1_24"><i><font color="Green">E89</font></i></a>, <a class="txt" href="goboard9.html#E27:28_1_1_1_2_2_1_24"><i><font color="Green">E92</font></i></a>, <a class="txt" href="goboard9.html#E28:28_1_1_1_2_2_1_24"><i><font color="Green">E93</font></i></a>, <a class="ref" href="goboard9.html#T6" target="_self">Th6</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="28_1_1_1_2_2_1_25"><b>suppose </b></a><b>that </b><a NAME="E1:28_1_1_1_2_2_1_25"/><i><font color="Green">E74</font></i>: 
<font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K1">+</a> 1 <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>6</sub></font>
 <b>and </b><br/><a NAME="E2:28_1_1_1_2_2_1_25"/><i><font color="Green">E75</font></i>: 
<font color="Maroon">c<sub>5</sub></font> <a href="nat_1.html#K1">+</a> 1 <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>7</sub></font>
 <b>and </b><br/><a NAME="E3:28_1_1_1_2_2_1_25"/><i><font color="Green">E76</font></i>: 
<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> 1
 <b>and </b><br/><a NAME="E4:28_1_1_1_2_2_1_25"/><i><font color="Green">E77</font></i>: 
<font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="matrix_1.html#K1">width</a> <span class="p1">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>
 ;<br/><div class="add"><a NAME="E5:28_1_1_1_2_2_1_25"/><i><font color="Green">E78</font></i>: 
 <a href="goboard5.html#K5">left_cell</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a>  <a href="goboard5.html#K3">cell</a> <span class="p1">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span>,<font color="Maroon">c<sub>4</sub></font>
 <b>by </b><i><a class="txt" href="goboard9.html#E1:28_1_1_1_2"><i><font color="Green">E33</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1_1_2"><i><font color="Green">E34</font></i></a>, <a class="txt" href="goboard9.html#E7:28_1_1_1_2"><i><font color="Green">E37</font></i></a>, <a class="txt" href="goboard9.html#E8:28_1_1_1_2"><i><font color="Green">E38</font></i></a>, <a class="txt" href="goboard9.html#E11:28_1_1_1_2"><i><font color="Green">E40</font></i></a>, <a class="txt" href="goboard9.html#E12:28_1_1_1_2"><i><font color="Green">E41</font></i></a>, <a class="txt" href="goboard9.html#E24:28_1_1_1_2"><i><font color="Green">E51</font></i></a>, <a class="txt" href="goboard9.html#E37:28_1_1_1_2"><i><font color="Green">E61</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2_2_1_25"><i><font color="Green">E74</font></i></a>, <a class="ref" href="goboard5.html#T28">GOBOARD5:28</a></i>;<br/><a NAME="E6:28_1_1_1_2_2_1_25"/>
 <a href="matrix_1.html#K1">width</a> <span class="p1">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> <font color="Maroon">c<sub>6</sub></font>
 <b>by </b><i><a class="txt" href="goboard9.html#E22:28_1_1_1_2"><i><font color="Green">E49</font></i></a>, <a class="txt" href="goboard9.html#E4:28_1_1_1_2_2_1_25"><i><font color="Green">E77</font></i></a>, <a class="ref" href="xxreal_0.html#T1">XXREAL_0:1</a></i>;<br/><a NAME="E7:28_1_1_1_2_2_1_25"/><b>then </b><i><font color="Green">E79</font></i>: 
 <a href="matrix_1.html#K1">width</a> <span class="p1">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <font color="Maroon">c<sub>6</sub></font> <a href="nat_1.html#K1">+</a> 1
 <b>by </b><i><a class="ref" href="nat_1.html#T38">NAT_1:38</a></i>;<br/><a NAME="E8:28_1_1_1_2_2_1_25"/><i><font color="Green">E80</font></i>: 
<font color="Maroon">c<sub>3</sub></font> <a href="binarith.html#K5">-'</a> 1 <a href="hidden.html#R1">=</a> 0
 <b>by </b><i><a class="txt" href="goboard9.html#E3:28_1_1_1_2_2_1_25"><i><font color="Green">E76</font></i></a>, <a class="txt" href="goboard9.html#E1"><i><font color="Green">Lemma1</font></i></a></i>;<br/><a NAME="E9:28_1_1_1_2_2_1_25"/><i><font color="Green">E81</font></i>: 
 <a href="topreal1.html#K3">LSeg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="euclid.html#K17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K20">-</a> <span class="p2"><a href="euclid.html#K23">|[</a><span class="default">1,0</span><a href="euclid.html#K23">]|</a></span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="euclid.html#K17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>3</sub></font>,<span class="p5">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K20">-</a> <span class="p2"><a href="euclid.html#K23">|[</a><span class="default">1,0</span><a href="euclid.html#K23">]|</a></span></span>)</span> is <a href="connsp_1.html#V2">connected</a>
 <b>by </b><i><a class="ref" href="goboard9.html#T8" target="_self">Th8</a></i>;<br/><a NAME="E10:28_1_1_1_2_2_1_25"/><i><font color="Green">E82</font></i>: 
 <a href="topreal1.html#K3">LSeg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="euclid.html#K17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K20">-</a> <span class="p2"><a href="euclid.html#K23">|[</a><span class="default">1,0</span><a href="euclid.html#K23">]|</a></span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="euclid.html#K17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>3</sub></font>,<span class="p5">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K20">-</a> <span class="p2"><a href="euclid.html#K23">|[</a><span class="default">1,0</span><a href="euclid.html#K23">]|</a></span></span>)</span> <a href="xboole_0.html#NR5" target="_self">meets</a>  <a href="tops_1.html#K1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K3">cell</a> <span class="p2">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span>,<font color="Maroon">c<sub>4</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="goboard9.html#E21:28_1_1_1_2"><i><font color="Green">E48</font></i></a>, <a class="txt" href="goboard9.html#E22:28_1_1_1_2"><i><font color="Green">E49</font></i></a>, <a class="txt" href="goboard9.html#E24:28_1_1_1_2"><i><font color="Green">E51</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2_2_1_25"><i><font color="Green">E74</font></i></a>, <a class="txt" href="goboard9.html#E3:28_1_1_1_2_2_1_25"><i><font color="Green">E76</font></i></a>, <a class="txt" href="goboard9.html#E8:28_1_1_1_2_2_1_25"><i><font color="Green">E80</font></i></a>, <a class="ref" href="goboard6.html#T88">GOBOARD6:88</a></i>;<br/><a NAME="E11:28_1_1_1_2_2_1_25"/>
 <a href="topreal1.html#K3">LSeg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="euclid.html#K17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K20">-</a> <span class="p2"><a href="euclid.html#K23">|[</a><span class="default">1,0</span><a href="euclid.html#K23">]|</a></span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="euclid.html#K17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>3</sub></font>,<span class="p5">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K20">-</a> <span class="p2"><a href="euclid.html#K23">|[</a><span class="default">1,0</span><a href="euclid.html#K23">]|</a></span></span>)</span> <a href="xboole_0.html#R1">misses</a>  <a href="topreal1.html#K5">L~</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="goboard9.html#E21:28_1_1_1_2"><i><font color="Green">E48</font></i></a>, <a class="txt" href="goboard9.html#E49:28_1_1_1_2"><i><font color="Green">E69</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2_2_1_25"><i><font color="Green">E74</font></i></a>, <a class="txt" href="goboard9.html#E3:28_1_1_1_2_2_1_25"><i><font color="Green">E76</font></i></a>, <a class="txt" href="goboard9.html#E7:28_1_1_1_2_2_1_25"><i><font color="Green">E79</font></i></a>, <a class="ref" href="goboard8.html#T31">GOBOARD8:31</a></i>;<br/><a NAME="E12:28_1_1_1_2_2_1_25"/><b>then </b>
 <a href="topreal1.html#K3">LSeg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="euclid.html#K17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K20">-</a> <span class="p2"><a href="euclid.html#K23">|[</a><span class="default">1,0</span><a href="euclid.html#K23">]|</a></span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="euclid.html#K17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>3</sub></font>,<span class="p5">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K20">-</a> <span class="p2"><a href="euclid.html#K23">|[</a><span class="default">1,0</span><a href="euclid.html#K23">]|</a></span></span>)</span> <a href="tarski.html#R1">c=</a> <span class="p1">(<span class="default"><a href="topreal1.html#K5">L~</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="subset_1.html#K3">`</a> 
 <b>by </b><i><a class="ref" href="subset_1.html#T43">SUBSET_1:43</a></i>;<br/><a NAME="E13:28_1_1_1_2_2_1_25"/><b>then </b><i><font color="Green">E83</font></i>: 
 <a href="topreal1.html#K3">LSeg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="euclid.html#K17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K20">-</a> <span class="p2"><a href="euclid.html#K23">|[</a><span class="default">1,0</span><a href="euclid.html#K23">]|</a></span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="euclid.html#K17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>3</sub></font>,<span class="p5">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K20">-</a> <span class="p2"><a href="euclid.html#K23">|[</a><span class="default">1,0</span><a href="euclid.html#K23">]|</a></span></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="goboard9.html#K2" target="_self">LeftComp</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="goboard9.html#E1:28_1"><i><font color="Green">E30</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1"><i><font color="Green">E32</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2"><i><font color="Green">E33</font></i></a>, <a class="txt" href="goboard9.html#E51:28_1_1_1_2"><i><font color="Green">E71</font></i></a>, <a class="txt" href="goboard9.html#E5:28_1_1_1_2_2_1_25"><i><font color="Green">E78</font></i></a>, <a class="txt" href="goboard9.html#E9:28_1_1_1_2_2_1_25"><i><font color="Green">E81</font></i></a>, <a class="txt" href="goboard9.html#E10:28_1_1_1_2_2_1_25"><i><font color="Green">E82</font></i></a>, <a class="ref" href="goboard9.html#T6" target="_self">Th6</a>, <a class="ref" href="nat_1.html#T38">NAT_1:38</a></i>;<br/><a NAME="E14:28_1_1_1_2_2_1_25"/>
<font color="Maroon">c<sub>5</sub></font> <a href="binarith.html#K5">-'</a> 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>5</sub></font>
 <b>by </b><i><a class="txt" href="goboard9.html#E2"><i><font color="Green">Lemma2</font></i></a></i>;<br/><a NAME="E15:28_1_1_1_2_2_1_25"/><b>then </b><i><font color="Green">E84</font></i>: 
<font color="Maroon">c<sub>5</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"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="goboard9.html#E19:28_1_1_1_2"><i><font color="Green">E46</font></i></a>, <a class="ref" href="xxreal_0.html#T2">XXREAL_0:2</a></i>;<br/><a NAME="E16:28_1_1_1_2_2_1_25"/><b>then </b><i><font color="Green">E85</font></i>: 
 <a href="tops_1.html#K1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K3">cell</a> <span class="p2">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span>,<font color="Maroon">c<sub>6</sub></font></span>)</span> is <a href="connsp_1.html#V2">connected</a>
 <b>by </b><i><a class="txt" href="goboard9.html#E22:28_1_1_1_2"><i><font color="Green">E49</font></i></a>, <a class="ref" href="goboard9.html#T21" target="_self">Th21</a></i>;<br/><a NAME="E17:28_1_1_1_2_2_1_25"/><i><font color="Green">E86</font></i>: 
 <a href="topreal1.html#K3">LSeg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="euclid.html#K17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K20">-</a> <span class="p2"><a href="euclid.html#K23">|[</a><span class="default">1,0</span><a href="euclid.html#K23">]|</a></span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="euclid.html#K17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>3</sub></font>,<span class="p5">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K20">-</a> <span class="p2"><a href="euclid.html#K23">|[</a><span class="default">1,0</span><a href="euclid.html#K23">]|</a></span></span>)</span> <a href="xboole_0.html#NR5" target="_self">meets</a>  <a href="tops_1.html#K1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K3">cell</a> <span class="p2">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span>,<font color="Maroon">c<sub>6</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="goboard9.html#E22:28_1_1_1_2"><i><font color="Green">E49</font></i></a>, <a class="txt" href="goboard9.html#E3:28_1_1_1_2_2_1_25"><i><font color="Green">E76</font></i></a>, <a class="txt" href="goboard9.html#E7:28_1_1_1_2_2_1_25"><i><font color="Green">E79</font></i></a>, <a class="txt" href="goboard9.html#E8:28_1_1_1_2_2_1_25"><i><font color="Green">E80</font></i></a>, <a class="ref" href="goboard6.html#T88">GOBOARD6:88</a></i>;<br/><a NAME="E18:28_1_1_1_2_2_1_25"/>
 <a href="tops_1.html#K1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K3">cell</a> <span class="p2">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span>,<font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="xboole_0.html#R1">misses</a>  <a href="topreal1.html#K5">L~</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="goboard9.html#E22:28_1_1_1_2"><i><font color="Green">E49</font></i></a>, <a class="txt" href="goboard9.html#E15:28_1_1_1_2_2_1_25"><i><font color="Green">E84</font></i></a>, <a class="ref" href="goboard7.html#T14">GOBOARD7:14</a></i>;<br/><a NAME="E19:28_1_1_1_2_2_1_25"/><b>then </b>
 <a href="tops_1.html#K1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K3">cell</a> <span class="p2">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span>,<font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="tarski.html#R1">c=</a> <span class="p1">(<span class="default"><a href="topreal1.html#K5">L~</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="subset_1.html#K3">`</a> 
 <b>by </b><i><a class="ref" href="subset_1.html#T43">SUBSET_1:43</a></i>;<br/><a NAME="E20:28_1_1_1_2_2_1_25"/><b>then </b><i><font color="Green">E87</font></i>: 
 <a href="tops_1.html#K1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K3">cell</a> <span class="p2">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span>,<font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="goboard9.html#K2" target="_self">LeftComp</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="goboard9.html#E24:28_1_1_1_2"><i><font color="Green">E51</font></i></a>, <a class="txt" href="goboard9.html#E51:28_1_1_1_2"><i><font color="Green">E71</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2_2_1_25"><i><font color="Green">E74</font></i></a>, <a class="txt" href="goboard9.html#E13:28_1_1_1_2_2_1_25"><i><font color="Green">E83</font></i></a>, <a class="txt" href="goboard9.html#E16:28_1_1_1_2_2_1_25"><i><font color="Green">E85</font></i></a>, <a class="txt" href="goboard9.html#E17:28_1_1_1_2_2_1_25"><i><font color="Green">E86</font></i></a>, <a class="ref" href="goboard9.html#T6" target="_self">Th6</a></i>;<br/><a NAME="E21:28_1_1_1_2_2_1_25"/><i><font color="Green">E88</font></i>: 
 <a href="goboard5.html#K5">left_cell</a> <font color="Maroon">c<sub>1</sub></font>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="hidden.html#R1">=</a>  <a href="goboard5.html#K3">cell</a> <span class="p1">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font>
 <b>by </b><i><a class="txt" href="goboard9.html#E1:28_1_1"><i><font color="Green">E31</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1"><i><font color="Green">E32</font></i></a>, <a class="txt" href="goboard9.html#E11:28_1_1_1_2"><i><font color="Green">E40</font></i></a>, <a class="txt" href="goboard9.html#E12:28_1_1_1_2"><i><font color="Green">E41</font></i></a>, <a class="txt" href="goboard9.html#E16:28_1_1_1_2"><i><font color="Green">E43</font></i></a>, <a class="txt" href="goboard9.html#E17:28_1_1_1_2"><i><font color="Green">E44</font></i></a>, <a class="txt" href="goboard9.html#E25:28_1_1_1_2"><i><font color="Green">E52</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2_2_1_25"><i><font color="Green">E74</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1_1_2_2_1_25"><i><font color="Green">E75</font></i></a>, <a class="ref" href="goboard5.html#T29">GOBOARD5:29</a></i>;<br/><a NAME="E22:28_1_1_1_2_2_1_25"/><i><font color="Green">E89</font></i>: 
 <a href="topreal1.html#K3">LSeg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>5</sub></font>,<span class="p5">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="euclid.html#K17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>5</sub></font>,<span class="p5">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K1">+</a> 2</span>)</span></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K20">-</a> <span class="p2"><a href="euclid.html#K23">|[</a><span class="default">1,0</span><a href="euclid.html#K23">]|</a></span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>5</sub></font>,<span class="p4">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="euclid.html#K17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>7</sub></font>,<span class="p4">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K1">+</a> 2</span>)</span></span>)</span></span>)</span></span>)</span> is <a href="connsp_1.html#V2">connected</a>
 <b>by </b><i><a class="ref" href="goboard9.html#T8" target="_self">Th8</a></i>;<br/><a NAME="E23:28_1_1_1_2_2_1_25"/><i><font color="Green">E90</font></i>: 
 <a href="topreal1.html#K3">LSeg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>5</sub></font>,<span class="p5">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="euclid.html#K17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>5</sub></font>,<span class="p5">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K1">+</a> 2</span>)</span></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K20">-</a> <span class="p2"><a href="euclid.html#K23">|[</a><span class="default">1,0</span><a href="euclid.html#K23">]|</a></span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>5</sub></font>,<span class="p4">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="euclid.html#K17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>7</sub></font>,<span class="p4">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K1">+</a> 2</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xboole_0.html#NR5" target="_self">meets</a>  <a href="tops_1.html#K1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K3">cell</a> <span class="p2">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span>,<font color="Maroon">c<sub>6</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="goboard9.html#E22:28_1_1_1_2"><i><font color="Green">E49</font></i></a>, <a class="txt" href="goboard9.html#E24:28_1_1_1_2"><i><font color="Green">E51</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2_2_1_25"><i><font color="Green">E74</font></i></a>, <a class="txt" href="goboard9.html#E3:28_1_1_1_2_2_1_25"><i><font color="Green">E76</font></i></a>, <a class="txt" href="goboard9.html#E7:28_1_1_1_2_2_1_25"><i><font color="Green">E79</font></i></a>, <a class="txt" href="goboard9.html#E8:28_1_1_1_2_2_1_25"><i><font color="Green">E80</font></i></a>, <a class="ref" href="goboard6.html#T88">GOBOARD6:88</a></i>;<br/><a NAME="E24:28_1_1_1_2_2_1_25"/>
 <a href="topreal1.html#K3">LSeg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>5</sub></font>,<span class="p5">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="euclid.html#K17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>5</sub></font>,<span class="p5">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K1">+</a> 2</span>)</span></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K20">-</a> <span class="p2"><a href="euclid.html#K23">|[</a><span class="default">1,0</span><a href="euclid.html#K23">]|</a></span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>5</sub></font>,<span class="p4">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="euclid.html#K17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>7</sub></font>,<span class="p4">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K1">+</a> 2</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xboole_0.html#R1">misses</a>  <a href="topreal1.html#K5">L~</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="goboard9.html#E2:28_1_1"><i><font color="Green">E32</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2"><i><font color="Green">E33</font></i></a>, <a class="txt" href="goboard9.html#E8:28_1_1_1_2"><i><font color="Green">E38</font></i></a>, <a class="txt" href="goboard9.html#E12:28_1_1_1_2"><i><font color="Green">E41</font></i></a>, <a class="txt" href="goboard9.html#E17:28_1_1_1_2"><i><font color="Green">E44</font></i></a>, <a class="txt" href="goboard9.html#E21:28_1_1_1_2"><i><font color="Green">E48</font></i></a>, <a class="txt" href="goboard9.html#E24:28_1_1_1_2"><i><font color="Green">E51</font></i></a>, <a class="txt" href="goboard9.html#E25:28_1_1_1_2"><i><font color="Green">E52</font></i></a>, <a class="txt" href="goboard9.html#E46:28_1_1_1_2"><i><font color="Green">E66</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2_2_1_25"><i><font color="Green">E74</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1_1_2_2_1_25"><i><font color="Green">E75</font></i></a>, <a class="txt" href="goboard9.html#E3:28_1_1_1_2_2_1_25"><i><font color="Green">E76</font></i></a>, <a class="txt" href="goboard9.html#E7:28_1_1_1_2_2_1_25"><i><font color="Green">E79</font></i></a>, <a class="ref" href="goboard8.html#T18">GOBOARD8:18</a></i>;<br/><a NAME="E25:28_1_1_1_2_2_1_25"/><b>then </b>
 <a href="topreal1.html#K3">LSeg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>5</sub></font>,<span class="p5">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="euclid.html#K17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>5</sub></font>,<span class="p5">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K1">+</a> 2</span>)</span></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K20">-</a> <span class="p2"><a href="euclid.html#K23">|[</a><span class="default">1,0</span><a href="euclid.html#K23">]|</a></span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>5</sub></font>,<span class="p4">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="euclid.html#K17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>7</sub></font>,<span class="p4">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K1">+</a> 2</span>)</span></span>)</span></span>)</span></span>)</span> <a href="tarski.html#R1">c=</a> <span class="p1">(<span class="default"><a href="topreal1.html#K5">L~</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="subset_1.html#K3">`</a> 
 <b>by </b><i><a class="ref" href="subset_1.html#T43">SUBSET_1:43</a></i>;<br/><a NAME="E26:28_1_1_1_2_2_1_25"/><b>then </b><i><font color="Green">E91</font></i>: 
 <a href="topreal1.html#K3">LSeg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>5</sub></font>,<span class="p5">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="euclid.html#K17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>5</sub></font>,<span class="p5">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K1">+</a> 2</span>)</span></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K20">-</a> <span class="p2"><a href="euclid.html#K23">|[</a><span class="default">1,0</span><a href="euclid.html#K23">]|</a></span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>5</sub></font>,<span class="p4">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="euclid.html#K17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>7</sub></font>,<span class="p4">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K1">+</a> 2</span>)</span></span>)</span></span>)</span></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="goboard9.html#K2" target="_self">LeftComp</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="goboard9.html#E51:28_1_1_1_2"><i><font color="Green">E71</font></i></a>, <a class="txt" href="goboard9.html#E20:28_1_1_1_2_2_1_25"><i><font color="Green">E87</font></i></a>, <a class="txt" href="goboard9.html#E22:28_1_1_1_2_2_1_25"><i><font color="Green">E89</font></i></a>, <a class="txt" href="goboard9.html#E23:28_1_1_1_2_2_1_25"><i><font color="Green">E90</font></i></a>, <a class="ref" href="goboard9.html#T6" target="_self">Th6</a></i>;<br/><a NAME="E27:28_1_1_1_2_2_1_25"/><i><font color="Green">E92</font></i>: 
 <a href="topreal1.html#K3">LSeg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>5</sub></font>,<span class="p5">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="euclid.html#K17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>5</sub></font>,<span class="p5">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K1">+</a> 2</span>)</span></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K20">-</a> <span class="p2"><a href="euclid.html#K23">|[</a><span class="default">1,0</span><a href="euclid.html#K23">]|</a></span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>5</sub></font>,<span class="p4">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="euclid.html#K17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>7</sub></font>,<span class="p4">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K1">+</a> 2</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xboole_0.html#NR5" target="_self">meets</a>  <a href="tops_1.html#K1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K3">cell</a> <span class="p2">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="goboard9.html#E19:28_1_1_1_2"><i><font color="Green">E46</font></i></a>, <a class="txt" href="goboard9.html#E20:28_1_1_1_2"><i><font color="Green">E47</font></i></a>, <a class="txt" href="goboard9.html#E22:28_1_1_1_2"><i><font color="Green">E49</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2_2_1_25"><i><font color="Green">E74</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1_1_2_2_1_25"><i><font color="Green">E75</font></i></a>, <a class="txt" href="goboard9.html#E7:28_1_1_1_2_2_1_25"><i><font color="Green">E79</font></i></a>, <a class="ref" href="goboard6.html#T85">GOBOARD6:85</a></i>;<br/><a NAME="E28:28_1_1_1_2_2_1_25"/>
 <a href="tops_1.html#K1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K5">left_cell</a> <font color="Maroon">c<sub>1</sub></font>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="xboole_0.html#R1">misses</a>  <a href="topreal1.html#K5">L~</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="goboard9.html#E1:28_1_1"><i><font color="Green">E31</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1"><i><font color="Green">E32</font></i></a>, <a class="ref" href="goboard8.html#T37">GOBOARD8:37</a></i>;<br/><a NAME="E29:28_1_1_1_2_2_1_25"/><b>then </b>
 <a href="tops_1.html#K1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K5">left_cell</a> <font color="Maroon">c<sub>1</sub></font>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="tarski.html#R1">c=</a> <span class="p1">(<span class="default"><a href="topreal1.html#K5">L~</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="subset_1.html#K3">`</a> 
 <b>by </b><i><a class="ref" href="subset_1.html#T43">SUBSET_1:43</a></i>;<br/><b>hence </b><a NAME="E30:28_1_1_1_2_2_1_25"/>
 <a href="tops_1.html#K1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K5">left_cell</a> <font color="Maroon">c<sub>1</sub></font>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="goboard9.html#K2" target="_self">LeftComp</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="goboard9.html#E51:28_1_1_1_2"><i><font color="Green">E71</font></i></a>, <a class="txt" href="goboard9.html#E52:28_1_1_1_2"><i><font color="Green">E72</font></i></a>, <a class="txt" href="goboard9.html#E21:28_1_1_1_2_2_1_25"><i><font color="Green">E88</font></i></a>, <a class="txt" href="goboard9.html#E26:28_1_1_1_2_2_1_25"><i><font color="Green">E91</font></i></a>, <a class="txt" href="goboard9.html#E27:28_1_1_1_2_2_1_25"><i><font color="Green">E92</font></i></a>, <a class="ref" href="goboard9.html#T6" target="_self">Th6</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="28_1_1_1_2_2_1_26"><b>suppose </b></a><b>that </b><a NAME="E1:28_1_1_1_2_2_1_26"/><i><font color="Green">E74</font></i>: 
<font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K1">+</a> 1 <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>6</sub></font>
 <b>and </b><br/><a NAME="E2:28_1_1_1_2_2_1_26"/><i><font color="Green">E75</font></i>: 
<font color="Maroon">c<sub>5</sub></font> <a href="nat_1.html#K1">+</a> 1 <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>7</sub></font>
 <b>and </b><br/><a NAME="E3:28_1_1_1_2_2_1_26"/><i><font color="Green">E76</font></i>: 
<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 1
 <b>and </b><br/><a NAME="E4:28_1_1_1_2_2_1_26"/><i><font color="Green">E77</font></i>: 
<font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="matrix_1.html#K1">width</a> <span class="p1">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>
 ;<br/><div class="add"><a NAME="E5:28_1_1_1_2_2_1_26"/><i><font color="Green">E78</font></i>: 
 <a href="goboard5.html#K5">left_cell</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a>  <a href="goboard5.html#K3">cell</a> <span class="p1">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span>,<font color="Maroon">c<sub>4</sub></font>
 <b>by </b><i><a class="txt" href="goboard9.html#E1:28_1_1_1_2"><i><font color="Green">E33</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1_1_2"><i><font color="Green">E34</font></i></a>, <a class="txt" href="goboard9.html#E7:28_1_1_1_2"><i><font color="Green">E37</font></i></a>, <a class="txt" href="goboard9.html#E8:28_1_1_1_2"><i><font color="Green">E38</font></i></a>, <a class="txt" href="goboard9.html#E11:28_1_1_1_2"><i><font color="Green">E40</font></i></a>, <a class="txt" href="goboard9.html#E12:28_1_1_1_2"><i><font color="Green">E41</font></i></a>, <a class="txt" href="goboard9.html#E24:28_1_1_1_2"><i><font color="Green">E51</font></i></a>, <a class="txt" href="goboard9.html#E37:28_1_1_1_2"><i><font color="Green">E61</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2_2_1_26"><i><font color="Green">E74</font></i></a>, <a class="ref" href="goboard5.html#T28">GOBOARD5:28</a></i>;<br/><a NAME="E6:28_1_1_1_2_2_1_26"/>
1 <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">c<sub>3</sub></font>
 <b>by </b><i><a class="txt" href="goboard9.html#E18:28_1_1_1_2"><i><font color="Green">E45</font></i></a>, <a class="txt" href="goboard9.html#E3:28_1_1_1_2_2_1_26"><i><font color="Green">E76</font></i></a>, <a class="ref" href="xxreal_0.html#T1">XXREAL_0:1</a></i>;<br/><a NAME="E7:28_1_1_1_2_2_1_26"/><b>then </b><i><font color="Green">E79</font></i>: 
1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>3</sub></font> <a href="binarith.html#K5">-'</a> 1
 <b>by </b><i><a class="txt" href="goboard9.html#E24:28_1_1_1_2"><i><font color="Green">E51</font></i></a>, <a class="txt" href="goboard9.html#E37:28_1_1_1_2"><i><font color="Green">E61</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2_2_1_26"><i><font color="Green">E74</font></i></a>, <a class="ref" href="nat_1.html#T38">NAT_1:38</a></i>;<br/><a NAME="E8:28_1_1_1_2_2_1_26"/>
 <a href="matrix_1.html#K1">width</a> <span class="p1">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> <font color="Maroon">c<sub>6</sub></font>
 <b>by </b><i><a class="txt" href="goboard9.html#E22:28_1_1_1_2"><i><font color="Green">E49</font></i></a>, <a class="txt" href="goboard9.html#E4:28_1_1_1_2_2_1_26"><i><font color="Green">E77</font></i></a>, <a class="ref" href="xxreal_0.html#T1">XXREAL_0:1</a></i>;<br/><a NAME="E9:28_1_1_1_2_2_1_26"/><b>then </b><i><font color="Green">E80</font></i>: 
 <a href="matrix_1.html#K1">width</a> <span class="p1">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <font color="Maroon">c<sub>6</sub></font> <a href="nat_1.html#K1">+</a> 1
 <b>by </b><i><a class="ref" href="nat_1.html#T38">NAT_1:38</a></i>;<br/><a NAME="E10:28_1_1_1_2_2_1_26"/><i><font color="Green">E81</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>5</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> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>7</sub></font>
 <b>by </b><i><a class="txt" href="goboard9.html#E37:28_1_1_1_2"><i><font color="Green">E61</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1_1_2_2_1_26"><i><font color="Green">E75</font></i></a></i>;<br/><a NAME="E11:28_1_1_1_2_2_1_26"/><i><font color="Green">E82</font></i>: 
 <a href="topreal1.html#K3">LSeg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span>,<font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="euclid.html#K17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span>,<font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="euclid.html#K17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>3</sub></font>,<span class="p4">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> is <a href="connsp_1.html#V2">connected</a>
 <b>by </b><i><a class="ref" href="goboard9.html#T8" target="_self">Th8</a></i>;<br/><a NAME="E12:28_1_1_1_2_2_1_26"/><i><font color="Green">E83</font></i>: 
 <a href="topreal1.html#K3">LSeg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span>,<font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="euclid.html#K17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span>,<font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="euclid.html#K17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>3</sub></font>,<span class="p4">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xboole_0.html#NR5" target="_self">meets</a>  <a href="tops_1.html#K1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K3">cell</a> <span class="p2">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span>,<font color="Maroon">c<sub>4</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="goboard9.html#E19:28_1_1_1_2"><i><font color="Green">E46</font></i></a>, <a class="txt" href="goboard9.html#E21:28_1_1_1_2"><i><font color="Green">E48</font></i></a>, <a class="txt" href="goboard9.html#E22:28_1_1_1_2"><i><font color="Green">E49</font></i></a>, <a class="txt" href="goboard9.html#E24:28_1_1_1_2"><i><font color="Green">E51</font></i></a>, <a class="txt" href="goboard9.html#E37:28_1_1_1_2"><i><font color="Green">E61</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2_2_1_26"><i><font color="Green">E74</font></i></a>, <a class="txt" href="goboard9.html#E7:28_1_1_1_2_2_1_26"><i><font color="Green">E79</font></i></a>, <a class="ref" href="goboard6.html#T85">GOBOARD6:85</a></i>;<br/><a NAME="E13:28_1_1_1_2_2_1_26"/>
 <a href="topreal1.html#K3">LSeg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span>,<font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="euclid.html#K17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span>,<font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="euclid.html#K17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>3</sub></font>,<span class="p4">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xboole_0.html#R1">misses</a>  <a href="topreal1.html#K5">L~</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="goboard9.html#E2:28_1_1"><i><font color="Green">E32</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2"><i><font color="Green">E33</font></i></a>, <a class="txt" href="goboard9.html#E8:28_1_1_1_2"><i><font color="Green">E38</font></i></a>, <a class="txt" href="goboard9.html#E12:28_1_1_1_2"><i><font color="Green">E41</font></i></a>, <a class="txt" href="goboard9.html#E17:28_1_1_1_2"><i><font color="Green">E44</font></i></a>, <a class="txt" href="goboard9.html#E20:28_1_1_1_2"><i><font color="Green">E47</font></i></a>, <a class="txt" href="goboard9.html#E21:28_1_1_1_2"><i><font color="Green">E48</font></i></a>, <a class="txt" href="goboard9.html#E24:28_1_1_1_2"><i><font color="Green">E51</font></i></a>, <a class="txt" href="goboard9.html#E25:28_1_1_1_2"><i><font color="Green">E52</font></i></a>, <a class="txt" href="goboard9.html#E37:28_1_1_1_2"><i><font color="Green">E61</font></i></a>, <a class="txt" href="goboard9.html#E46:28_1_1_1_2"><i><font color="Green">E66</font></i></a>, <a class="txt" href="goboard9.html#E49:28_1_1_1_2"><i><font color="Green">E69</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2_2_1_26"><i><font color="Green">E74</font></i></a>, <a class="txt" href="goboard9.html#E7:28_1_1_1_2_2_1_26"><i><font color="Green">E79</font></i></a>, <a class="txt" href="goboard9.html#E9:28_1_1_1_2_2_1_26"><i><font color="Green">E80</font></i></a>, <a class="txt" href="goboard9.html#E10:28_1_1_1_2_2_1_26"><i><font color="Green">E81</font></i></a>, <a class="ref" href="goboard8.html#T3">GOBOARD8:3</a></i>;<br/><a NAME="E14:28_1_1_1_2_2_1_26"/><b>then </b>
 <a href="topreal1.html#K3">LSeg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span>,<font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="euclid.html#K17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span>,<font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="euclid.html#K17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>3</sub></font>,<span class="p4">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="tarski.html#R1">c=</a> <span class="p1">(<span class="default"><a href="topreal1.html#K5">L~</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="subset_1.html#K3">`</a> 
 <b>by </b><i><a class="ref" href="subset_1.html#T43">SUBSET_1:43</a></i>;<br/><a NAME="E15:28_1_1_1_2_2_1_26"/><b>then </b><i><font color="Green">E84</font></i>: 
 <a href="topreal1.html#K3">LSeg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span>,<font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="euclid.html#K17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span>,<font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="euclid.html#K17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>3</sub></font>,<span class="p4">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="goboard9.html#K2" target="_self">LeftComp</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="goboard9.html#E1:28_1"><i><font color="Green">E30</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1"><i><font color="Green">E32</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2"><i><font color="Green">E33</font></i></a>, <a class="txt" href="goboard9.html#E51:28_1_1_1_2"><i><font color="Green">E71</font></i></a>, <a class="txt" href="goboard9.html#E5:28_1_1_1_2_2_1_26"><i><font color="Green">E78</font></i></a>, <a class="txt" href="goboard9.html#E11:28_1_1_1_2_2_1_26"><i><font color="Green">E82</font></i></a>, <a class="txt" href="goboard9.html#E12:28_1_1_1_2_2_1_26"><i><font color="Green">E83</font></i></a>, <a class="ref" href="goboard9.html#T6" target="_self">Th6</a>, <a class="ref" href="nat_1.html#T38">NAT_1:38</a></i>;<br/><a NAME="E16:28_1_1_1_2_2_1_26"/>
<font color="Maroon">c<sub>5</sub></font> <a href="binarith.html#K5">-'</a> 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>5</sub></font>
 <b>by </b><i><a class="txt" href="goboard9.html#E2"><i><font color="Green">Lemma2</font></i></a></i>;<br/><a NAME="E17:28_1_1_1_2_2_1_26"/><b>then </b><i><font color="Green">E85</font></i>: 
<font color="Maroon">c<sub>5</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"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="goboard9.html#E19:28_1_1_1_2"><i><font color="Green">E46</font></i></a>, <a class="ref" href="xxreal_0.html#T2">XXREAL_0:2</a></i>;<br/><a NAME="E18:28_1_1_1_2_2_1_26"/><b>then </b><i><font color="Green">E86</font></i>: 
 <a href="tops_1.html#K1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K3">cell</a> <span class="p2">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span>,<font color="Maroon">c<sub>6</sub></font></span>)</span> is <a href="connsp_1.html#V2">connected</a>
 <b>by </b><i><a class="txt" href="goboard9.html#E22:28_1_1_1_2"><i><font color="Green">E49</font></i></a>, <a class="ref" href="goboard9.html#T21" target="_self">Th21</a></i>;<br/><a NAME="E19:28_1_1_1_2_2_1_26"/><i><font color="Green">E87</font></i>: 
 <a href="topreal1.html#K3">LSeg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span>,<font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="euclid.html#K17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span>,<font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="euclid.html#K17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>3</sub></font>,<span class="p4">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xboole_0.html#NR5" target="_self">meets</a>  <a href="tops_1.html#K1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K3">cell</a> <span class="p2">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span>,<font color="Maroon">c<sub>6</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="goboard9.html#E18:28_1_1_1_2"><i><font color="Green">E45</font></i></a>, <a class="txt" href="goboard9.html#E22:28_1_1_1_2"><i><font color="Green">E49</font></i></a>, <a class="txt" href="goboard9.html#E24:28_1_1_1_2"><i><font color="Green">E51</font></i></a>, <a class="txt" href="goboard9.html#E37:28_1_1_1_2"><i><font color="Green">E61</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2_2_1_26"><i><font color="Green">E74</font></i></a>, <a class="txt" href="goboard9.html#E7:28_1_1_1_2_2_1_26"><i><font color="Green">E79</font></i></a>, <a class="txt" href="goboard9.html#E9:28_1_1_1_2_2_1_26"><i><font color="Green">E80</font></i></a>, <a class="ref" href="goboard6.html#T85">GOBOARD6:85</a></i>;<br/><a NAME="E20:28_1_1_1_2_2_1_26"/>
 <a href="tops_1.html#K1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K3">cell</a> <span class="p2">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span>,<font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="xboole_0.html#R1">misses</a>  <a href="topreal1.html#K5">L~</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="goboard9.html#E22:28_1_1_1_2"><i><font color="Green">E49</font></i></a>, <a class="txt" href="goboard9.html#E17:28_1_1_1_2_2_1_26"><i><font color="Green">E85</font></i></a>, <a class="ref" href="goboard7.html#T14">GOBOARD7:14</a></i>;<br/><a NAME="E21:28_1_1_1_2_2_1_26"/><b>then </b>
 <a href="tops_1.html#K1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K3">cell</a> <span class="p2">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span>,<font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="tarski.html#R1">c=</a> <span class="p1">(<span class="default"><a href="topreal1.html#K5">L~</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="subset_1.html#K3">`</a> 
 <b>by </b><i><a class="ref" href="subset_1.html#T43">SUBSET_1:43</a></i>;<br/><a NAME="E22:28_1_1_1_2_2_1_26"/><b>then </b><i><font color="Green">E88</font></i>: 
 <a href="tops_1.html#K1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K3">cell</a> <span class="p2">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span>,<font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="goboard9.html#K2" target="_self">LeftComp</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="goboard9.html#E24:28_1_1_1_2"><i><font color="Green">E51</font></i></a>, <a class="txt" href="goboard9.html#E51:28_1_1_1_2"><i><font color="Green">E71</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2_2_1_26"><i><font color="Green">E74</font></i></a>, <a class="txt" href="goboard9.html#E15:28_1_1_1_2_2_1_26"><i><font color="Green">E84</font></i></a>, <a class="txt" href="goboard9.html#E18:28_1_1_1_2_2_1_26"><i><font color="Green">E86</font></i></a>, <a class="txt" href="goboard9.html#E19:28_1_1_1_2_2_1_26"><i><font color="Green">E87</font></i></a>, <a class="ref" href="goboard9.html#T6" target="_self">Th6</a></i>;<br/><a NAME="E23:28_1_1_1_2_2_1_26"/><i><font color="Green">E89</font></i>: 
 <a href="goboard5.html#K5">left_cell</a> <font color="Maroon">c<sub>1</sub></font>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="hidden.html#R1">=</a>  <a href="goboard5.html#K3">cell</a> <span class="p1">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font>
 <b>by </b><i><a class="txt" href="goboard9.html#E1:28_1_1"><i><font color="Green">E31</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1"><i><font color="Green">E32</font></i></a>, <a class="txt" href="goboard9.html#E11:28_1_1_1_2"><i><font color="Green">E40</font></i></a>, <a class="txt" href="goboard9.html#E12:28_1_1_1_2"><i><font color="Green">E41</font></i></a>, <a class="txt" href="goboard9.html#E16:28_1_1_1_2"><i><font color="Green">E43</font></i></a>, <a class="txt" href="goboard9.html#E17:28_1_1_1_2"><i><font color="Green">E44</font></i></a>, <a class="txt" href="goboard9.html#E25:28_1_1_1_2"><i><font color="Green">E52</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2_2_1_26"><i><font color="Green">E74</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1_1_2_2_1_26"><i><font color="Green">E75</font></i></a>, <a class="ref" href="goboard5.html#T29">GOBOARD5:29</a></i>;<br/><a NAME="E24:28_1_1_1_2_2_1_26"/><i><font color="Green">E90</font></i>: 
 <a href="topreal1.html#K3">LSeg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span>,<font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="euclid.html#K17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>5</sub></font>,<span class="p4">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="euclid.html#K17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>7</sub></font>,<span class="p4">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> is <a href="connsp_1.html#V2">connected</a>
 <b>by </b><i><a class="ref" href="goboard9.html#T8" target="_self">Th8</a></i>;<br/><a NAME="E25:28_1_1_1_2_2_1_26"/><i><font color="Green">E91</font></i>: 
 <a href="topreal1.html#K3">LSeg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span>,<font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="euclid.html#K17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>5</sub></font>,<span class="p4">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="euclid.html#K17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>7</sub></font>,<span class="p4">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xboole_0.html#NR5" target="_self">meets</a>  <a href="tops_1.html#K1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K3">cell</a> <span class="p2">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span>,<font color="Maroon">c<sub>6</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="goboard9.html#E19:28_1_1_1_2"><i><font color="Green">E46</font></i></a>, <a class="txt" href="goboard9.html#E22:28_1_1_1_2"><i><font color="Green">E49</font></i></a>, <a class="txt" href="goboard9.html#E24:28_1_1_1_2"><i><font color="Green">E51</font></i></a>, <a class="txt" href="goboard9.html#E37:28_1_1_1_2"><i><font color="Green">E61</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2_2_1_26"><i><font color="Green">E74</font></i></a>, <a class="txt" href="goboard9.html#E7:28_1_1_1_2_2_1_26"><i><font color="Green">E79</font></i></a>, <a class="txt" href="goboard9.html#E9:28_1_1_1_2_2_1_26"><i><font color="Green">E80</font></i></a>, <a class="ref" href="goboard6.html#T85">GOBOARD6:85</a></i>;<br/><a NAME="E26:28_1_1_1_2_2_1_26"/>
 <a href="topreal1.html#K3">LSeg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span>,<font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="euclid.html#K17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>5</sub></font>,<span class="p4">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="euclid.html#K17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>7</sub></font>,<span class="p4">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xboole_0.html#R1">misses</a>  <a href="topreal1.html#K5">L~</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="goboard9.html#E2:28_1_1"><i><font color="Green">E32</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2"><i><font color="Green">E33</font></i></a>, <a class="txt" href="goboard9.html#E8:28_1_1_1_2"><i><font color="Green">E38</font></i></a>, <a class="txt" href="goboard9.html#E12:28_1_1_1_2"><i><font color="Green">E41</font></i></a>, <a class="txt" href="goboard9.html#E17:28_1_1_1_2"><i><font color="Green">E44</font></i></a>, <a class="txt" href="goboard9.html#E20:28_1_1_1_2"><i><font color="Green">E47</font></i></a>, <a class="txt" href="goboard9.html#E21:28_1_1_1_2"><i><font color="Green">E48</font></i></a>, <a class="txt" href="goboard9.html#E24:28_1_1_1_2"><i><font color="Green">E51</font></i></a>, <a class="txt" href="goboard9.html#E25:28_1_1_1_2"><i><font color="Green">E52</font></i></a>, <a class="txt" href="goboard9.html#E37:28_1_1_1_2"><i><font color="Green">E61</font></i></a>, <a class="txt" href="goboard9.html#E46:28_1_1_1_2"><i><font color="Green">E66</font></i></a>, <a class="txt" href="goboard9.html#E49:28_1_1_1_2"><i><font color="Green">E69</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2_2_1_26"><i><font color="Green">E74</font></i></a>, <a class="txt" href="goboard9.html#E7:28_1_1_1_2_2_1_26"><i><font color="Green">E79</font></i></a>, <a class="txt" href="goboard9.html#E9:28_1_1_1_2_2_1_26"><i><font color="Green">E80</font></i></a>, <a class="txt" href="goboard9.html#E10:28_1_1_1_2_2_1_26"><i><font color="Green">E81</font></i></a>, <a class="ref" href="goboard8.html#T15">GOBOARD8:15</a></i>;<br/><a NAME="E27:28_1_1_1_2_2_1_26"/><b>then </b>
 <a href="topreal1.html#K3">LSeg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span>,<font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="euclid.html#K17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>5</sub></font>,<span class="p4">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="euclid.html#K17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>7</sub></font>,<span class="p4">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="tarski.html#R1">c=</a> <span class="p1">(<span class="default"><a href="topreal1.html#K5">L~</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="subset_1.html#K3">`</a> 
 <b>by </b><i><a class="ref" href="subset_1.html#T43">SUBSET_1:43</a></i>;<br/><a NAME="E28:28_1_1_1_2_2_1_26"/><b>then </b><i><font color="Green">E92</font></i>: 
 <a href="topreal1.html#K3">LSeg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span>,<font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="euclid.html#K17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>5</sub></font>,<span class="p4">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="euclid.html#K17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>7</sub></font>,<span class="p4">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="goboard9.html#K2" target="_self">LeftComp</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="goboard9.html#E51:28_1_1_1_2"><i><font color="Green">E71</font></i></a>, <a class="txt" href="goboard9.html#E22:28_1_1_1_2_2_1_26"><i><font color="Green">E88</font></i></a>, <a class="txt" href="goboard9.html#E24:28_1_1_1_2_2_1_26"><i><font color="Green">E90</font></i></a>, <a class="txt" href="goboard9.html#E25:28_1_1_1_2_2_1_26"><i><font color="Green">E91</font></i></a>, <a class="ref" href="goboard9.html#T6" target="_self">Th6</a></i>;<br/><a NAME="E29:28_1_1_1_2_2_1_26"/><i><font color="Green">E93</font></i>: 
 <a href="topreal1.html#K3">LSeg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span>,<font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="euclid.html#K17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>5</sub></font>,<span class="p4">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="euclid.html#K17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>7</sub></font>,<span class="p4">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xboole_0.html#NR5" target="_self">meets</a>  <a href="tops_1.html#K1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K3">cell</a> <span class="p2">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="goboard9.html#E19:28_1_1_1_2"><i><font color="Green">E46</font></i></a>, <a class="txt" href="goboard9.html#E20:28_1_1_1_2"><i><font color="Green">E47</font></i></a>, <a class="txt" href="goboard9.html#E22:28_1_1_1_2"><i><font color="Green">E49</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1_1_2_2_1_26"><i><font color="Green">E75</font></i></a>, <a class="txt" href="goboard9.html#E9:28_1_1_1_2_2_1_26"><i><font color="Green">E80</font></i></a>, <a class="ref" href="goboard6.html#T85">GOBOARD6:85</a></i>;<br/><a NAME="E30:28_1_1_1_2_2_1_26"/>
 <a href="tops_1.html#K1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K5">left_cell</a> <font color="Maroon">c<sub>1</sub></font>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="xboole_0.html#R1">misses</a>  <a href="topreal1.html#K5">L~</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="goboard9.html#E1:28_1_1"><i><font color="Green">E31</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1"><i><font color="Green">E32</font></i></a>, <a class="ref" href="goboard8.html#T37">GOBOARD8:37</a></i>;<br/><a NAME="E31:28_1_1_1_2_2_1_26"/><b>then </b>
 <a href="tops_1.html#K1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K5">left_cell</a> <font color="Maroon">c<sub>1</sub></font>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="tarski.html#R1">c=</a> <span class="p1">(<span class="default"><a href="topreal1.html#K5">L~</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="subset_1.html#K3">`</a> 
 <b>by </b><i><a class="ref" href="subset_1.html#T43">SUBSET_1:43</a></i>;<br/><b>hence </b><a NAME="E32:28_1_1_1_2_2_1_26"/>
 <a href="tops_1.html#K1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K5">left_cell</a> <font color="Maroon">c<sub>1</sub></font>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="goboard9.html#K2" target="_self">LeftComp</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="goboard9.html#E51:28_1_1_1_2"><i><font color="Green">E71</font></i></a>, <a class="txt" href="goboard9.html#E52:28_1_1_1_2"><i><font color="Green">E72</font></i></a>, <a class="txt" href="goboard9.html#E23:28_1_1_1_2_2_1_26"><i><font color="Green">E89</font></i></a>, <a class="txt" href="goboard9.html#E28:28_1_1_1_2_2_1_26"><i><font color="Green">E92</font></i></a>, <a class="txt" href="goboard9.html#E29:28_1_1_1_2_2_1_26"><i><font color="Green">E93</font></i></a>, <a class="ref" href="goboard9.html#T6" target="_self">Th6</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="28_1_1_1_2_2_1_27"><b>suppose </b></a><b>that </b><a NAME="E1:28_1_1_1_2_2_1_27"/><i><font color="Green">E74</font></i>: 
<font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K1">+</a> 1 <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>6</sub></font>
 <b>and </b><br/><a NAME="E2:28_1_1_1_2_2_1_27"/><i><font color="Green">E75</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>
 <b>and </b><br/><a NAME="E3:28_1_1_1_2_2_1_27"/><i><font color="Green">E76</font></i>: 
<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> 1
 ;<br/><div class="add"><a NAME="E4:28_1_1_1_2_2_1_27"/><i><font color="Green">E77</font></i>: 
 <a href="goboard5.html#K5">left_cell</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a>  <a href="goboard5.html#K3">cell</a> <span class="p1">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,0,<font color="Maroon">c<sub>4</sub></font>
 <b>by </b><i><a class="txt" href="goboard9.html#E1:28_1_1_1_2"><i><font color="Green">E33</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1_1_2"><i><font color="Green">E34</font></i></a>, <a class="txt" href="goboard9.html#E7:28_1_1_1_2"><i><font color="Green">E37</font></i></a>, <a class="txt" href="goboard9.html#E8:28_1_1_1_2"><i><font color="Green">E38</font></i></a>, <a class="txt" href="goboard9.html#E11:28_1_1_1_2"><i><font color="Green">E40</font></i></a>, <a class="txt" href="goboard9.html#E12:28_1_1_1_2"><i><font color="Green">E41</font></i></a>, <a class="txt" href="goboard9.html#E24:28_1_1_1_2"><i><font color="Green">E51</font></i></a>, <a class="txt" href="goboard9.html#E53:28_1_1_1_2"><i><font color="Green">E73</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2_2_1_27"><i><font color="Green">E74</font></i></a>, <a class="txt" href="goboard9.html#E3:28_1_1_1_2_2_1_27"><i><font color="Green">E76</font></i></a>, <a class="ref" href="goboard5.html#T28">GOBOARD5:28</a></i>;<br/><a NAME="E5:28_1_1_1_2_2_1_27"/><i><font color="Green">E78</font></i>: 
 <a href="goboard5.html#K5">left_cell</a> <font color="Maroon">c<sub>1</sub></font>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="hidden.html#R1">=</a>  <a href="goboard5.html#K3">cell</a> <span class="p1">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,0,<font color="Maroon">c<sub>6</sub></font>
 <b>by </b><i><a class="txt" href="goboard9.html#E1:28_1_1"><i><font color="Green">E31</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1"><i><font color="Green">E32</font></i></a>, <a class="txt" href="goboard9.html#E11:28_1_1_1_2"><i><font color="Green">E40</font></i></a>, <a class="txt" href="goboard9.html#E12:28_1_1_1_2"><i><font color="Green">E41</font></i></a>, <a class="txt" href="goboard9.html#E16:28_1_1_1_2"><i><font color="Green">E43</font></i></a>, <a class="txt" href="goboard9.html#E17:28_1_1_1_2"><i><font color="Green">E44</font></i></a>, <a class="txt" href="goboard9.html#E24:28_1_1_1_2"><i><font color="Green">E51</font></i></a>, <a class="txt" href="goboard9.html#E25:28_1_1_1_2"><i><font color="Green">E52</font></i></a>, <a class="txt" href="goboard9.html#E53:28_1_1_1_2"><i><font color="Green">E73</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2_2_1_27"><i><font color="Green">E74</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1_1_2_2_1_27"><i><font color="Green">E75</font></i></a>, <a class="txt" href="goboard9.html#E3:28_1_1_1_2_2_1_27"><i><font color="Green">E76</font></i></a>, <a class="ref" href="goboard5.html#T28">GOBOARD5:28</a></i>;<br/><a NAME="E6:28_1_1_1_2_2_1_27"/><i><font color="Green">E79</font></i>: 
 <a href="topreal1.html#K3">LSeg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> 1,<font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="euclid.html#K17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> 1,<font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K20">-</a> <span class="p2"><a href="euclid.html#K23">|[</a><span class="default">1,0</span><a href="euclid.html#K23">]|</a></span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> 1,<font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="euclid.html#K17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> 1,<font color="Maroon">c<sub>8</sub></font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K20">-</a> <span class="p2"><a href="euclid.html#K23">|[</a><span class="default">1,0</span><a href="euclid.html#K23">]|</a></span></span>)</span> is <a href="connsp_1.html#V2">connected</a>
 <b>by </b><i><a class="ref" href="goboard9.html#T8" target="_self">Th8</a></i>;<br/><a NAME="E7:28_1_1_1_2_2_1_27"/><i><font color="Green">E80</font></i>: 
 <a href="topreal1.html#K3">LSeg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> 1,<font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="euclid.html#K17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> 1,<font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K20">-</a> <span class="p2"><a href="euclid.html#K23">|[</a><span class="default">1,0</span><a href="euclid.html#K23">]|</a></span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> 1,<font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="euclid.html#K17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> 1,<font color="Maroon">c<sub>8</sub></font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K20">-</a> <span class="p2"><a href="euclid.html#K23">|[</a><span class="default">1,0</span><a href="euclid.html#K23">]|</a></span></span>)</span> <a href="xboole_0.html#NR5" target="_self">meets</a>  <a href="tops_1.html#K1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K3">cell</a> <span class="p2">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,0,<font color="Maroon">c<sub>4</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="goboard9.html#E21:28_1_1_1_2"><i><font color="Green">E48</font></i></a>, <a class="txt" href="goboard9.html#E22:28_1_1_1_2"><i><font color="Green">E49</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2_2_1_27"><i><font color="Green">E74</font></i></a>, <a class="ref" href="goboard6.html#T88">GOBOARD6:88</a></i>;<br/><a NAME="E8:28_1_1_1_2_2_1_27"/>
 <a href="topreal1.html#K3">LSeg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> 1,<font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="euclid.html#K17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> 1,<font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K20">-</a> <span class="p2"><a href="euclid.html#K23">|[</a><span class="default">1,0</span><a href="euclid.html#K23">]|</a></span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> 1,<font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="euclid.html#K17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> 1,<font color="Maroon">c<sub>8</sub></font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K20">-</a> <span class="p2"><a href="euclid.html#K23">|[</a><span class="default">1,0</span><a href="euclid.html#K23">]|</a></span></span>)</span> <a href="xboole_0.html#R1">misses</a>  <a href="topreal1.html#K5">L~</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="goboard9.html#E21:28_1_1_1_2"><i><font color="Green">E48</font></i></a>, <a class="txt" href="goboard9.html#E23:28_1_1_1_2"><i><font color="Green">E50</font></i></a>, <a class="txt" href="goboard9.html#E49:28_1_1_1_2"><i><font color="Green">E69</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2_2_1_27"><i><font color="Green">E74</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1_1_2_2_1_27"><i><font color="Green">E75</font></i></a>, <a class="ref" href="goboard8.html#T31">GOBOARD8:31</a></i>;<br/><a NAME="E9:28_1_1_1_2_2_1_27"/><b>then </b>
 <a href="topreal1.html#K3">LSeg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> 1,<font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="euclid.html#K17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> 1,<font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K20">-</a> <span class="p2"><a href="euclid.html#K23">|[</a><span class="default">1,0</span><a href="euclid.html#K23">]|</a></span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> 1,<font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="euclid.html#K17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> 1,<font color="Maroon">c<sub>8</sub></font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K20">-</a> <span class="p2"><a href="euclid.html#K23">|[</a><span class="default">1,0</span><a href="euclid.html#K23">]|</a></span></span>)</span> <a href="tarski.html#R1">c=</a> <span class="p1">(<span class="default"><a href="topreal1.html#K5">L~</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="subset_1.html#K3">`</a> 
 <b>by </b><i><a class="ref" href="subset_1.html#T43">SUBSET_1:43</a></i>;<br/><a NAME="E10:28_1_1_1_2_2_1_27"/><b>then </b><i><font color="Green">E81</font></i>: 
 <a href="topreal1.html#K3">LSeg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> 1,<font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="euclid.html#K17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> 1,<font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K20">-</a> <span class="p2"><a href="euclid.html#K23">|[</a><span class="default">1,0</span><a href="euclid.html#K23">]|</a></span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> 1,<font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="euclid.html#K17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> 1,<font color="Maroon">c<sub>8</sub></font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K20">-</a> <span class="p2"><a href="euclid.html#K23">|[</a><span class="default">1,0</span><a href="euclid.html#K23">]|</a></span></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="goboard9.html#K2" target="_self">LeftComp</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="goboard9.html#E1:28_1"><i><font color="Green">E30</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1"><i><font color="Green">E32</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2"><i><font color="Green">E33</font></i></a>, <a class="txt" href="goboard9.html#E51:28_1_1_1_2"><i><font color="Green">E71</font></i></a>, <a class="txt" href="goboard9.html#E4:28_1_1_1_2_2_1_27"><i><font color="Green">E77</font></i></a>, <a class="txt" href="goboard9.html#E6:28_1_1_1_2_2_1_27"><i><font color="Green">E79</font></i></a>, <a class="txt" href="goboard9.html#E7:28_1_1_1_2_2_1_27"><i><font color="Green">E80</font></i></a>, <a class="ref" href="goboard9.html#T6" target="_self">Th6</a>, <a class="ref" href="nat_1.html#T38">NAT_1:38</a></i>;<br/><a NAME="E11:28_1_1_1_2_2_1_27"/><i><font color="Green">E82</font></i>: 
 <a href="topreal1.html#K3">LSeg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> 1,<font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="euclid.html#K17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> 1,<font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K20">-</a> <span class="p2"><a href="euclid.html#K23">|[</a><span class="default">1,0</span><a href="euclid.html#K23">]|</a></span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> 1,<font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="euclid.html#K17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> 1,<font color="Maroon">c<sub>8</sub></font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K20">-</a> <span class="p2"><a href="euclid.html#K23">|[</a><span class="default">1,0</span><a href="euclid.html#K23">]|</a></span></span>)</span> <a href="xboole_0.html#NR5" target="_self">meets</a>  <a href="tops_1.html#K1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K3">cell</a> <span class="p2">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,0,<font color="Maroon">c<sub>6</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="goboard9.html#E22:28_1_1_1_2"><i><font color="Green">E49</font></i></a>, <a class="txt" href="goboard9.html#E23:28_1_1_1_2"><i><font color="Green">E50</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1_1_2_2_1_27"><i><font color="Green">E75</font></i></a>, <a class="ref" href="goboard6.html#T88">GOBOARD6:88</a></i>;<br/><a NAME="E12:28_1_1_1_2_2_1_27"/>
 <a href="tops_1.html#K1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K5">left_cell</a> <font color="Maroon">c<sub>1</sub></font>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="xboole_0.html#R1">misses</a>  <a href="topreal1.html#K5">L~</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="goboard9.html#E1:28_1_1"><i><font color="Green">E31</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1"><i><font color="Green">E32</font></i></a>, <a class="ref" href="goboard8.html#T37">GOBOARD8:37</a></i>;<br/><a NAME="E13:28_1_1_1_2_2_1_27"/><b>then </b>
 <a href="tops_1.html#K1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K5">left_cell</a> <font color="Maroon">c<sub>1</sub></font>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="tarski.html#R1">c=</a> <span class="p1">(<span class="default"><a href="topreal1.html#K5">L~</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="subset_1.html#K3">`</a> 
 <b>by </b><i><a class="ref" href="subset_1.html#T43">SUBSET_1:43</a></i>;<br/><b>hence </b><a NAME="E14:28_1_1_1_2_2_1_27"/>
 <a href="tops_1.html#K1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K5">left_cell</a> <font color="Maroon">c<sub>1</sub></font>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="goboard9.html#K2" target="_self">LeftComp</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="goboard9.html#E51:28_1_1_1_2"><i><font color="Green">E71</font></i></a>, <a class="txt" href="goboard9.html#E52:28_1_1_1_2"><i><font color="Green">E72</font></i></a>, <a class="txt" href="goboard9.html#E5:28_1_1_1_2_2_1_27"><i><font color="Green">E78</font></i></a>, <a class="txt" href="goboard9.html#E10:28_1_1_1_2_2_1_27"><i><font color="Green">E81</font></i></a>, <a class="txt" href="goboard9.html#E11:28_1_1_1_2_2_1_27"><i><font color="Green">E82</font></i></a>, <a class="ref" href="goboard9.html#T6" target="_self">Th6</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="28_1_1_1_2_2_1_28"><b>suppose </b></a><b>that </b><a NAME="E1:28_1_1_1_2_2_1_28"/><i><font color="Green">E74</font></i>: 
<font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K1">+</a> 1 <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>6</sub></font>
 <b>and </b><br/><a NAME="E2:28_1_1_1_2_2_1_28"/><i><font color="Green">E75</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>
 <b>and </b><br/><a NAME="E3:28_1_1_1_2_2_1_28"/><i><font color="Green">E76</font></i>: 
<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 1
 ;<br/><div class="add"><a NAME="E4:28_1_1_1_2_2_1_28"/><i><font color="Green">E77</font></i>: 
 <a href="goboard5.html#K5">left_cell</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a>  <a href="goboard5.html#K3">cell</a> <span class="p1">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span>,<font color="Maroon">c<sub>4</sub></font>
 <b>by </b><i><a class="txt" href="goboard9.html#E1:28_1_1_1_2"><i><font color="Green">E33</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1_1_2"><i><font color="Green">E34</font></i></a>, <a class="txt" href="goboard9.html#E7:28_1_1_1_2"><i><font color="Green">E37</font></i></a>, <a class="txt" href="goboard9.html#E8:28_1_1_1_2"><i><font color="Green">E38</font></i></a>, <a class="txt" href="goboard9.html#E11:28_1_1_1_2"><i><font color="Green">E40</font></i></a>, <a class="txt" href="goboard9.html#E12:28_1_1_1_2"><i><font color="Green">E41</font></i></a>, <a class="txt" href="goboard9.html#E24:28_1_1_1_2"><i><font color="Green">E51</font></i></a>, <a class="txt" href="goboard9.html#E37:28_1_1_1_2"><i><font color="Green">E61</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2_2_1_28"><i><font color="Green">E74</font></i></a>, <a class="ref" href="goboard5.html#T28">GOBOARD5:28</a></i>;<br/><a NAME="E5:28_1_1_1_2_2_1_28"/>
1 <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">c<sub>3</sub></font>
 <b>by </b><i><a class="txt" href="goboard9.html#E18:28_1_1_1_2"><i><font color="Green">E45</font></i></a>, <a class="txt" href="goboard9.html#E3:28_1_1_1_2_2_1_28"><i><font color="Green">E76</font></i></a>, <a class="ref" href="xxreal_0.html#T1">XXREAL_0:1</a></i>;<br/><a NAME="E6:28_1_1_1_2_2_1_28"/><b>then </b><i><font color="Green">E78</font></i>: 
1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>3</sub></font> <a href="binarith.html#K5">-'</a> 1
 <b>by </b><i><a class="txt" href="goboard9.html#E24:28_1_1_1_2"><i><font color="Green">E51</font></i></a>, <a class="txt" href="goboard9.html#E37:28_1_1_1_2"><i><font color="Green">E61</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2_2_1_28"><i><font color="Green">E74</font></i></a>, <a class="ref" href="nat_1.html#T38">NAT_1:38</a></i>;<br/><a NAME="E7:28_1_1_1_2_2_1_28"/><i><font color="Green">E79</font></i>: 
 <a href="goboard5.html#K5">left_cell</a> <font color="Maroon">c<sub>1</sub></font>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="hidden.html#R1">=</a>  <a href="goboard5.html#K3">cell</a> <span class="p1">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span>,<font color="Maroon">c<sub>6</sub></font>
 <b>by </b><i><a class="txt" href="goboard9.html#E1:28_1_1"><i><font color="Green">E31</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1"><i><font color="Green">E32</font></i></a>, <a class="txt" href="goboard9.html#E11:28_1_1_1_2"><i><font color="Green">E40</font></i></a>, <a class="txt" href="goboard9.html#E12:28_1_1_1_2"><i><font color="Green">E41</font></i></a>, <a class="txt" href="goboard9.html#E16:28_1_1_1_2"><i><font color="Green">E43</font></i></a>, <a class="txt" href="goboard9.html#E17:28_1_1_1_2"><i><font color="Green">E44</font></i></a>, <a class="txt" href="goboard9.html#E25:28_1_1_1_2"><i><font color="Green">E52</font></i></a>, <a class="txt" href="goboard9.html#E37:28_1_1_1_2"><i><font color="Green">E61</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1_1_2_2_1_28"><i><font color="Green">E75</font></i></a>, <a class="ref" href="goboard5.html#T28">GOBOARD5:28</a></i>;<br/><a NAME="E8:28_1_1_1_2_2_1_28"/><i><font color="Green">E80</font></i>: 
 <a href="topreal1.html#K3">LSeg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span>,<font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="euclid.html#K17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span>,<font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="euclid.html#K17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>8</sub></font></span>)</span></span>)</span></span>)</span> is <a href="connsp_1.html#V2">connected</a>
 <b>by </b><i><a class="ref" href="goboard9.html#T8" target="_self">Th8</a></i>;<br/><a NAME="E9:28_1_1_1_2_2_1_28"/><i><font color="Green">E81</font></i>: 
 <a href="topreal1.html#K3">LSeg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span>,<font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="euclid.html#K17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span>,<font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="euclid.html#K17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>8</sub></font></span>)</span></span>)</span></span>)</span> <a href="xboole_0.html#NR5" target="_self">meets</a>  <a href="tops_1.html#K1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K3">cell</a> <span class="p2">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span>,<font color="Maroon">c<sub>4</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="goboard9.html#E19:28_1_1_1_2"><i><font color="Green">E46</font></i></a>, <a class="txt" href="goboard9.html#E21:28_1_1_1_2"><i><font color="Green">E48</font></i></a>, <a class="txt" href="goboard9.html#E22:28_1_1_1_2"><i><font color="Green">E49</font></i></a>, <a class="txt" href="goboard9.html#E24:28_1_1_1_2"><i><font color="Green">E51</font></i></a>, <a class="txt" href="goboard9.html#E37:28_1_1_1_2"><i><font color="Green">E61</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2_2_1_28"><i><font color="Green">E74</font></i></a>, <a class="txt" href="goboard9.html#E6:28_1_1_1_2_2_1_28"><i><font color="Green">E78</font></i></a>, <a class="ref" href="goboard6.html#T85">GOBOARD6:85</a></i>;<br/><a NAME="E10:28_1_1_1_2_2_1_28"/>
 <a href="topreal1.html#K3">LSeg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span>,<font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="euclid.html#K17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span>,<font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="euclid.html#K17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>8</sub></font></span>)</span></span>)</span></span>)</span> <a href="xboole_0.html#R1">misses</a>  <a href="topreal1.html#K5">L~</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="goboard9.html#E2:28_1_1"><i><font color="Green">E32</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2"><i><font color="Green">E33</font></i></a>, <a class="txt" href="goboard9.html#E8:28_1_1_1_2"><i><font color="Green">E38</font></i></a>, <a class="txt" href="goboard9.html#E12:28_1_1_1_2"><i><font color="Green">E41</font></i></a>, <a class="txt" href="goboard9.html#E17:28_1_1_1_2"><i><font color="Green">E44</font></i></a>, <a class="txt" href="goboard9.html#E18:28_1_1_1_2"><i><font color="Green">E45</font></i></a>, <a class="txt" href="goboard9.html#E21:28_1_1_1_2"><i><font color="Green">E48</font></i></a>, <a class="txt" href="goboard9.html#E23:28_1_1_1_2"><i><font color="Green">E50</font></i></a>, <a class="txt" href="goboard9.html#E24:28_1_1_1_2"><i><font color="Green">E51</font></i></a>, <a class="txt" href="goboard9.html#E25:28_1_1_1_2"><i><font color="Green">E52</font></i></a>, <a class="txt" href="goboard9.html#E37:28_1_1_1_2"><i><font color="Green">E61</font></i></a>, <a class="txt" href="goboard9.html#E46:28_1_1_1_2"><i><font color="Green">E66</font></i></a>, <a class="txt" href="goboard9.html#E49:28_1_1_1_2"><i><font color="Green">E69</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2_2_1_28"><i><font color="Green">E74</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1_1_2_2_1_28"><i><font color="Green">E75</font></i></a>, <a class="txt" href="goboard9.html#E6:28_1_1_1_2_2_1_28"><i><font color="Green">E78</font></i></a>, <a class="ref" href="goboard8.html#T1">GOBOARD8:1</a></i>;<br/><a NAME="E11:28_1_1_1_2_2_1_28"/><b>then </b>
 <a href="topreal1.html#K3">LSeg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span>,<font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="euclid.html#K17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span>,<font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="euclid.html#K17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>8</sub></font></span>)</span></span>)</span></span>)</span> <a href="tarski.html#R1">c=</a> <span class="p1">(<span class="default"><a href="topreal1.html#K5">L~</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="subset_1.html#K3">`</a> 
 <b>by </b><i><a class="ref" href="subset_1.html#T43">SUBSET_1:43</a></i>;<br/><a NAME="E12:28_1_1_1_2_2_1_28"/><b>then </b><i><font color="Green">E82</font></i>: 
 <a href="topreal1.html#K3">LSeg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span>,<font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="euclid.html#K17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span>,<font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="euclid.html#K17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>8</sub></font></span>)</span></span>)</span></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="goboard9.html#K2" target="_self">LeftComp</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="goboard9.html#E1:28_1"><i><font color="Green">E30</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1"><i><font color="Green">E32</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2"><i><font color="Green">E33</font></i></a>, <a class="txt" href="goboard9.html#E51:28_1_1_1_2"><i><font color="Green">E71</font></i></a>, <a class="txt" href="goboard9.html#E4:28_1_1_1_2_2_1_28"><i><font color="Green">E77</font></i></a>, <a class="txt" href="goboard9.html#E8:28_1_1_1_2_2_1_28"><i><font color="Green">E80</font></i></a>, <a class="txt" href="goboard9.html#E9:28_1_1_1_2_2_1_28"><i><font color="Green">E81</font></i></a>, <a class="ref" href="goboard9.html#T6" target="_self">Th6</a>, <a class="ref" href="nat_1.html#T38">NAT_1:38</a></i>;<br/><a NAME="E13:28_1_1_1_2_2_1_28"/><i><font color="Green">E83</font></i>: 
 <a href="topreal1.html#K3">LSeg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span>,<font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="euclid.html#K17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span>,<font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="euclid.html#K17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>8</sub></font></span>)</span></span>)</span></span>)</span> <a href="xboole_0.html#NR5" target="_self">meets</a>  <a href="tops_1.html#K1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K3">cell</a> <span class="p2">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span>,<font color="Maroon">c<sub>6</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="goboard9.html#E18:28_1_1_1_2"><i><font color="Green">E45</font></i></a>, <a class="txt" href="goboard9.html#E22:28_1_1_1_2"><i><font color="Green">E49</font></i></a>, <a class="txt" href="goboard9.html#E23:28_1_1_1_2"><i><font color="Green">E50</font></i></a>, <a class="txt" href="goboard9.html#E24:28_1_1_1_2"><i><font color="Green">E51</font></i></a>, <a class="txt" href="goboard9.html#E37:28_1_1_1_2"><i><font color="Green">E61</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2_2_1_28"><i><font color="Green">E74</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1_1_2_2_1_28"><i><font color="Green">E75</font></i></a>, <a class="txt" href="goboard9.html#E6:28_1_1_1_2_2_1_28"><i><font color="Green">E78</font></i></a>, <a class="ref" href="goboard6.html#T85">GOBOARD6:85</a></i>;<br/><a NAME="E14:28_1_1_1_2_2_1_28"/>
 <a href="tops_1.html#K1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K5">left_cell</a> <font color="Maroon">c<sub>1</sub></font>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="xboole_0.html#R1">misses</a>  <a href="topreal1.html#K5">L~</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="goboard9.html#E1:28_1_1"><i><font color="Green">E31</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1"><i><font color="Green">E32</font></i></a>, <a class="ref" href="goboard8.html#T37">GOBOARD8:37</a></i>;<br/><a NAME="E15:28_1_1_1_2_2_1_28"/><b>then </b>
 <a href="tops_1.html#K1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K5">left_cell</a> <font color="Maroon">c<sub>1</sub></font>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="tarski.html#R1">c=</a> <span class="p1">(<span class="default"><a href="topreal1.html#K5">L~</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="subset_1.html#K3">`</a> 
 <b>by </b><i><a class="ref" href="subset_1.html#T43">SUBSET_1:43</a></i>;<br/><b>hence </b><a NAME="E16:28_1_1_1_2_2_1_28"/>
 <a href="tops_1.html#K1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K5">left_cell</a> <font color="Maroon">c<sub>1</sub></font>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="goboard9.html#K2" target="_self">LeftComp</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="goboard9.html#E24:28_1_1_1_2"><i><font color="Green">E51</font></i></a>, <a class="txt" href="goboard9.html#E51:28_1_1_1_2"><i><font color="Green">E71</font></i></a>, <a class="txt" href="goboard9.html#E52:28_1_1_1_2"><i><font color="Green">E72</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2_2_1_28"><i><font color="Green">E74</font></i></a>, <a class="txt" href="goboard9.html#E7:28_1_1_1_2_2_1_28"><i><font color="Green">E79</font></i></a>, <a class="txt" href="goboard9.html#E12:28_1_1_1_2_2_1_28"><i><font color="Green">E82</font></i></a>, <a class="txt" href="goboard9.html#E13:28_1_1_1_2_2_1_28"><i><font color="Green">E83</font></i></a>, <a class="ref" href="goboard9.html#T6" target="_self">Th6</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div><b>hence </b><a NAME="E55:28_1_1_1_2"/>
 <a href="tops_1.html#K1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K5">left_cell</a> <font color="Maroon">c<sub>1</sub></font>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="goboard9.html#K2" target="_self">LeftComp</a> <font color="Maroon">c<sub>1</sub></font>
 ;<br/></div><b>end;</b></div></div><b>end;</b></div>

</div><b>end;</b></div></div><b>end;</b></div>
<b>thus </b><a NAME="E3:28"/>
for <font color="Olive">b<sub>1</sub></font> being  <a href="nat_1.html#NM1">Nat</a> holds <font color="Maroon">S<sub>1</sub></font>[<font color="Olive">b<sub>1</sub></font>]
 <b>from </b><i><a class="ref" href="nat_1.html#S1">NAT_1:sch 1</a>(<a class="txt" href="goboard9.html#E1:28"><i><font color="Green">E28</font></i></a>, <a class="txt" href="goboard9.html#E2:28"><i><font color="Green">E29</font></i></a>);</i><br/>


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