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<b>let </b><font color="Maroon">c<sub>1</sub></font>, <font color="Maroon">c<sub>2</sub></font> be   <a href="nat_1.html#NM1">Nat</a>;<br/><b>let </b><font color="Maroon">c<sub>3</sub></font> be   <a href="goboard1.html#NM1">Go-board</a>;<br/>





<b>assume </b><b>that </b><br/><a NAME="E1:34"/><i><font color="Green">E33</font></i>: 
( 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>1</sub></font> &amp; <font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1 <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>3</sub></font> )
 <b>and </b><br/><a NAME="E2:34"/><i><font color="Green">E34</font></i>: 
( 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>2</sub></font> &amp; <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="matrix_1.html#K1">width</a> <font color="Maroon">c<sub>3</sub></font> )
 ;<br/>

<b>set </b><font color="Maroon">c<sub>4</sub></font> = <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> ;<br/>
<b>set </b><font color="Maroon">c<sub>5</sub></font> = <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> ;<br/>
<b>set </b><font color="Maroon">c<sub>6</sub></font> = <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="matrix_1.html#K3">*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<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="euclid.html#K21">`1</a> ;<br/>
<b>set </b><font color="Maroon">c<sub>7</sub></font> = <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="matrix_1.html#K3">*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<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="euclid.html#K22">`2</a> ;<br/>
<a NAME="E3:34"/><i><font color="Green">E35</font></i>: 
<font color="Maroon">c<sub>3</sub></font> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="euclid.html#K23">|[</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span></span><a href="euclid.html#K23">]|</a></span>
 
<b>by </b><i><a class="ref" href="euclid.html#T57">EUCLID:57</a></i>;<br/>
<a NAME="E4:34"/>
<font color="Maroon">c<sub>3</sub></font> <a href="matrix_1.html#K3">*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="euclid.html#K23">|[</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="matrix_1.html#K3">*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p4">(<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="euclid.html#K21">`1</a> </span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="matrix_1.html#K3">*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p4">(<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="euclid.html#K22">`2</a> </span>)</span></span><a href="euclid.html#K23">]|</a></span>
 
<b>by </b><i><a class="ref" href="euclid.html#T57">EUCLID:57</a></i>;<br/>
<a NAME="E5:34"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="euclid.html#K17">+</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="matrix_1.html#K3">*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<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="hidden.html#R1">=</a> <span class="p1"><a href="euclid.html#K23">|[</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="real_1.html#K3">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="matrix_1.html#K3">*</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p5">(<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="euclid.html#K21">`1</a> </span>)</span></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K3">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="matrix_1.html#K3">*</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p5">(<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="euclid.html#K22">`2</a> </span>)</span></span>)</span></span><a href="euclid.html#K23">]|</a></span>
 
<b>by </b><i><a class="txt" href="goboard6.html#E3:34"><i><font color="Green">E35</font></i></a>, <a class="ref" href="euclid.html#T60">EUCLID:60</a></i>;<br/>
<a NAME="E6:34"/><b>then </b><i><font color="Green">E36</font></i>: 
<span class="p1">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="euclid.html#K17">+</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="matrix_1.html#K3">*</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p3">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="euclid.html#K23">|[</a><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="real_1.html#K4">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="real_1.html#K3">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="matrix_1.html#K3">*</a> <span class="p0">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p0">(<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="euclid.html#K21">`1</a> </span>)</span></span>)</span></span>)</span>,<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="real_1.html#K4">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K3">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="matrix_1.html#K3">*</a> <span class="p0">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p0">(<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="euclid.html#K22">`2</a> </span>)</span></span>)</span></span>)</span></span><a href="euclid.html#K23">]|</a></span>
 
<b>by </b><i><a class="ref" href="euclid.html#T62">EUCLID:62</a></i>;<br/>
<a NAME="E7:34"/>
( <font color="Maroon">c<sub>1</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1 &amp; <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="E8:34"/><b>then </b><i><font color="Green">E37</font></i>: 
( <font color="Maroon">c<sub>1</sub></font> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>3</sub></font> &amp; <font color="Maroon">c<sub>2</sub></font> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="matrix_1.html#K1">width</a> <font color="Maroon">c<sub>3</sub></font> )
 
<b>by </b><i><a class="txt" href="goboard6.html#E1:34"><i><font color="Green">E33</font></i></a>, <a class="txt" href="goboard6.html#E2:34"><i><font color="Green">E34</font></i></a>, <a class="ref" href="xxreal_0.html#T2">XXREAL_0:2</a></i>;<br/>
<a NAME="E9:34"/><i><font color="Green">E38</font></i>: 
( 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1 &amp; 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>by </b><i><a class="ref" href="nat_1.html#T29">NAT_1:29</a></i>;<br/>
<a NAME="E10:34"/><i><font color="Green">E39</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>1</sub></font>,1</span>)</span> <a href="euclid.html#K21">`1</a>  <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> 
 
<b>by </b><i><a class="txt" href="goboard6.html#E1:34"><i><font color="Green">E33</font></i></a>, <a class="txt" href="goboard6.html#E2:34"><i><font color="Green">E34</font></i></a>, <a class="txt" href="goboard6.html#E8:34"><i><font color="Green">E37</font></i></a>, <a class="ref" href="goboard5.html#T3">GOBOARD5:3</a></i>;<br/>
<a NAME="E11:34"/><i><font color="Green">E40</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="matrix_1.html#K3">*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,1</span>)</span> <a href="euclid.html#K21">`1</a>  <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="matrix_1.html#K3">*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<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="euclid.html#K21">`1</a> 
 
<b>by </b><i><a class="txt" href="goboard6.html#E1:34"><i><font color="Green">E33</font></i></a>, <a class="txt" href="goboard6.html#E2:34"><i><font color="Green">E34</font></i></a>, <a class="txt" href="goboard6.html#E9:34"><i><font color="Green">E38</font></i></a>, <a class="ref" href="goboard5.html#T3">GOBOARD5:3</a></i>;<br/>
<a NAME="E12:34"/><i><font color="Green">E41</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="matrix_1.html#K3">*</a> 1,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="euclid.html#K22">`2</a>  <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> 
 
<b>by </b><i><a class="txt" href="goboard6.html#E1:34"><i><font color="Green">E33</font></i></a>, <a class="txt" href="goboard6.html#E2:34"><i><font color="Green">E34</font></i></a>, <a class="txt" href="goboard6.html#E8:34"><i><font color="Green">E37</font></i></a>, <a class="ref" href="goboard5.html#T2">GOBOARD5:2</a></i>;<br/>
<a NAME="E13:34"/><i><font color="Green">E42</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="matrix_1.html#K3">*</a> 1,<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="euclid.html#K22">`2</a>  <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="matrix_1.html#K3">*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<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="euclid.html#K22">`2</a> 
 
<b>by </b><i><a class="txt" href="goboard6.html#E1:34"><i><font color="Green">E33</font></i></a>, <a class="txt" href="goboard6.html#E2:34"><i><font color="Green">E34</font></i></a>, <a class="txt" href="goboard6.html#E9:34"><i><font color="Green">E38</font></i></a>, <a class="ref" href="goboard5.html#T2">GOBOARD5:2</a></i>;<br/>
<a NAME="E14:34"/>
( 1 <a href="xxreal_0.html#R1">&lt;=</a>  <a href="matrix_1.html#K1">width</a> <font color="Maroon">c<sub>3</sub></font> &amp; <font color="Maroon">c<sub>1</sub></font> <a href="xxreal_0.html#R1">&lt;</a> <font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1 )
 
<b>by </b><i><a class="txt" href="goboard6.html#E2:34"><i><font color="Green">E34</font></i></a>, <a class="txt" href="goboard6.html#E8:34"><i><font color="Green">E37</font></i></a>, <a class="ref" href="xxreal_0.html#T2">XXREAL_0:2</a>, <a class="ref" href="xreal_1.html#T31">XREAL_1:31</a></i>;<br/>
<a NAME="E15:34"/><b>then </b><i><font color="Green">E43</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="euclid.html#K21">`1</a>  <a href="xxreal_0.html#R1">&lt;</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="matrix_1.html#K3">*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<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="euclid.html#K21">`1</a> 
 
<b>by </b><i><a class="txt" href="goboard6.html#E1:34"><i><font color="Green">E33</font></i></a>, <a class="txt" href="goboard6.html#E10:34"><i><font color="Green">E39</font></i></a>, <a class="txt" href="goboard6.html#E11:34"><i><font color="Green">E40</font></i></a>, <a class="ref" href="goboard5.html#T4">GOBOARD5:4</a></i>;<br/>
<a NAME="E16:34"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="real_1.html#K3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="xxreal_0.html#R1">&lt;</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="real_1.html#K3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="matrix_1.html#K3">*</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p3">(<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="euclid.html#K21">`1</a> </span>)</span>
 
<b>by </b><i><a class="ref" href="xreal_1.html#T8">XREAL_1:8</a></i>;<br/>
<a NAME="E17:34"/><b>then </b><i><font color="Green">E44</font></i>: 
<span class="p1">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="real_1.html#K4">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="real_1.html#K3">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span></span>)</span> <a href="xxreal_0.html#R1">&lt;</a> <span class="p1">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="real_1.html#K4">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="real_1.html#K3">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="matrix_1.html#K3">*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p4">(<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="euclid.html#K21">`1</a> </span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="xreal_1.html#T70">XREAL_1:70</a></i>;<br/>
<a NAME="E18:34"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="real_1.html#K3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="matrix_1.html#K3">*</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p3">(<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="euclid.html#K21">`1</a> </span>)</span> <a href="xxreal_0.html#R1">&lt;</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="matrix_1.html#K3">*</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p3">(<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="euclid.html#K21">`1</a> </span>)</span> <a href="real_1.html#K3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="matrix_1.html#K3">*</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p3">(<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="euclid.html#K21">`1</a> </span>)</span>
 
<b>by </b><i><a class="txt" href="goboard6.html#E15:34"><i><font color="Green">E43</font></i></a>, <a class="ref" href="xreal_1.html#T8">XREAL_1:8</a></i>;<br/>
<a NAME="E19:34"/><b>then </b>
<span class="p1">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="real_1.html#K4">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="real_1.html#K3">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="matrix_1.html#K3">*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p4">(<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="euclid.html#K21">`1</a> </span>)</span></span>)</span> <a href="xxreal_0.html#R1">&lt;</a> <span class="p1">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="real_1.html#K4">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="matrix_1.html#K3">*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p4">(<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="euclid.html#K21">`1</a> </span>)</span> <a href="real_1.html#K3">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="matrix_1.html#K3">*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p4">(<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="euclid.html#K21">`1</a> </span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="xreal_1.html#T70">XREAL_1:70</a></i>;<br/>
<a NAME="E20:34"/><b>then </b><i><font color="Green">E45</font></i>: 
<span class="p1">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="real_1.html#K4">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="real_1.html#K3">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="matrix_1.html#K3">*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p4">(<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="euclid.html#K21">`1</a> </span>)</span></span>)</span> <a href="xxreal_0.html#R1">&lt;</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="matrix_1.html#K3">*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,1</span>)</span> <a href="euclid.html#K21">`1</a> 
 
<b>by </b><i><a class="txt" href="goboard6.html#E1:34"><i><font color="Green">E33</font></i></a>, <a class="txt" href="goboard6.html#E2:34"><i><font color="Green">E34</font></i></a>, <a class="txt" href="goboard6.html#E9:34"><i><font color="Green">E38</font></i></a>, <a class="ref" href="goboard5.html#T3">GOBOARD5:3</a></i>;<br/>
<a NAME="E21:34"/>
( 1 <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>3</sub></font> &amp; <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="txt" href="goboard6.html#E1:34"><i><font color="Green">E33</font></i></a>, <a class="txt" href="goboard6.html#E8:34"><i><font color="Green">E37</font></i></a>, <a class="ref" href="xxreal_0.html#T2">XXREAL_0:2</a>, <a class="ref" href="xreal_1.html#T31">XREAL_1:31</a></i>;<br/>
<a NAME="E22:34"/><b>then </b><i><font color="Green">E46</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="euclid.html#K22">`2</a>  <a href="xxreal_0.html#R1">&lt;</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="matrix_1.html#K3">*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<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="euclid.html#K22">`2</a> 
 
<b>by </b><i><a class="txt" href="goboard6.html#E2:34"><i><font color="Green">E34</font></i></a>, <a class="txt" href="goboard6.html#E12:34"><i><font color="Green">E41</font></i></a>, <a class="txt" href="goboard6.html#E13:34"><i><font color="Green">E42</font></i></a>, <a class="ref" href="goboard5.html#T5">GOBOARD5:5</a></i>;<br/>
<a NAME="E23:34"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="xxreal_0.html#R1">&lt;</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="matrix_1.html#K3">*</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p3">(<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="euclid.html#K22">`2</a> </span>)</span>
 
<b>by </b><i><a class="ref" href="xreal_1.html#T8">XREAL_1:8</a></i>;<br/>
<a NAME="E24:34"/><b>then </b>
<span class="p1">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="real_1.html#K4">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K3">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span></span>)</span> <a href="xxreal_0.html#R1">&lt;</a> <span class="p1">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="real_1.html#K4">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K3">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="matrix_1.html#K3">*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p4">(<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="euclid.html#K22">`2</a> </span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="xreal_1.html#T70">XREAL_1:70</a></i>;<br/>
<a NAME="E25:34"/><b>then </b><i><font color="Green">E47</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="matrix_1.html#K3">*</a> 1,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="euclid.html#K22">`2</a>  <a href="xxreal_0.html#R1">&lt;</a> <span class="p1">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="real_1.html#K4">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K3">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="matrix_1.html#K3">*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p4">(<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="euclid.html#K22">`2</a> </span>)</span></span>)</span>
 
<b>by </b><i><a class="txt" href="goboard6.html#E1:34"><i><font color="Green">E33</font></i></a>, <a class="txt" href="goboard6.html#E2:34"><i><font color="Green">E34</font></i></a>, <a class="txt" href="goboard6.html#E8:34"><i><font color="Green">E37</font></i></a>, <a class="ref" href="goboard5.html#T2">GOBOARD5:2</a></i>;<br/>
<a NAME="E26:34"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="matrix_1.html#K3">*</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p3">(<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="euclid.html#K22">`2</a> </span>)</span> <a href="xxreal_0.html#R1">&lt;</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="matrix_1.html#K3">*</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p3">(<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="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="matrix_1.html#K3">*</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p3">(<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="euclid.html#K22">`2</a> </span>)</span>
 
<b>by </b><i><a class="txt" href="goboard6.html#E22:34"><i><font color="Green">E46</font></i></a>, <a class="ref" href="xreal_1.html#T8">XREAL_1:8</a></i>;<br/>
<a NAME="E27:34"/><b>then </b>
<span class="p1">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="real_1.html#K4">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K3">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="matrix_1.html#K3">*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p4">(<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="euclid.html#K22">`2</a> </span>)</span></span>)</span> <a href="xxreal_0.html#R1">&lt;</a> <span class="p1">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="real_1.html#K4">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="matrix_1.html#K3">*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p4">(<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="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K3">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="matrix_1.html#K3">*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p4">(<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="euclid.html#K22">`2</a> </span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="xreal_1.html#T70">XREAL_1:70</a></i>;<br/>
<a NAME="E28:34"/><b>then </b><i><font color="Green">E48</font></i>: 
<span class="p1">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="real_1.html#K4">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K3">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="matrix_1.html#K3">*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p4">(<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="euclid.html#K22">`2</a> </span>)</span></span>)</span> <a href="xxreal_0.html#R1">&lt;</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="matrix_1.html#K3">*</a> 1,<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="euclid.html#K22">`2</a> 
 
<b>by </b><i><a class="txt" href="goboard6.html#E1:34"><i><font color="Green">E33</font></i></a>, <a class="txt" href="goboard6.html#E2:34"><i><font color="Green">E34</font></i></a>, <a class="txt" href="goboard6.html#E9:34"><i><font color="Green">E38</font></i></a>, <a class="ref" href="goboard5.html#T2">GOBOARD5:2</a></i>;<br/>
<a NAME="E29:34"/><i><font color="Green">E49</font></i>: 
( 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>1</sub></font> &amp; <font color="Maroon">c<sub>1</sub></font> <a href="xxreal_0.html#R1">&lt;</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>3</sub></font> )
 
<b>by </b><i><a class="txt" href="goboard6.html#E1:34"><i><font color="Green">E33</font></i></a>, <a class="ref" href="nat_1.html#T38">NAT_1:38</a></i>;<br/>
<a NAME="E30:34"/>
( 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>2</sub></font> &amp; <font color="Maroon">c<sub>2</sub></font> <a href="xxreal_0.html#R1">&lt;</a>  <a href="matrix_1.html#K1">width</a> <font color="Maroon">c<sub>3</sub></font> )
 
<b>by </b><i><a class="txt" href="goboard6.html#E2:34"><i><font color="Green">E34</font></i></a>, <a class="ref" href="nat_1.html#T38">NAT_1:38</a></i>;<br/>
<a NAME="E31:34"/><b>then </b>
 <a href="tops_1.html#K1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K3">cell</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">{<span class="default"> <span class="p2"><a href="euclid.html#K23">|[</a><span class="default"><font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>2</sub></font></span><a href="euclid.html#K23">]|</a></span> where B is   <a href="real_1.html#NM1">Real</a>, B is   <a href="real_1.html#NM1">Real</a> : ( <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>1</sub></font>,1</span>)</span> <a href="euclid.html#K21">`1</a>  <a href="xxreal_0.html#R1">&lt;</a> <font color="Olive">b<sub>1</sub></font> &amp; <font color="Olive">b<sub>1</sub></font> <a href="xxreal_0.html#R1">&lt;</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="matrix_1.html#K3">*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,1</span>)</span> <a href="euclid.html#K21">`1</a>  &amp; <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="matrix_1.html#K3">*</a> 1,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="euclid.html#K22">`2</a>  <a href="xxreal_0.html#R1">&lt;</a> <font color="Olive">b<sub>2</sub></font> &amp; <font color="Olive">b<sub>2</sub></font> <a href="xxreal_0.html#R1">&lt;</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="matrix_1.html#K3">*</a> 1,<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="euclid.html#K22">`2</a>  ) </span>}</span> 
 
<b>by </b><i><a class="txt" href="goboard6.html#E29:34"><i><font color="Green">E49</font></i></a>, <a class="ref" href="goboard6.html#T29" target="_self">Th29</a></i>;<br/>
<b>hence </b><a NAME="E32:34"/>
<span class="p1">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="euclid.html#K18">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="euclid.html#K17">+</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="matrix_1.html#K3">*</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p3">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="hidden.html#R2">in</a>  <a href="tops_1.html#K1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K3">cell</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="goboard6.html#E6:34"><i><font color="Green">E36</font></i></a>, <a class="txt" href="goboard6.html#E10:34"><i><font color="Green">E39</font></i></a>, <a class="txt" href="goboard6.html#E17:34"><i><font color="Green">E44</font></i></a>, <a class="txt" href="goboard6.html#E20:34"><i><font color="Green">E45</font></i></a>, <a class="txt" href="goboard6.html#E25:34"><i><font color="Green">E47</font></i></a>, <a class="txt" href="goboard6.html#E28:34"><i><font color="Green">E48</font></i></a></i>;<br/>


</div>
