<?xml version="1.0"?>
<div class="add">

<span class="kw">set </span><font color="Maroon" title="c1">n</font> = 1;<br/>
<span class="kw">let </span><font color="Maroon" title="c2">f</font> be  non  <a href="funct_1.html#V3" title="FUNCT_1:attr.3">constant</a>   <a href="goboard5.html#V2" title="GOBOARD5:attr.2">standard</a>  <a href="goboard5.html#NM1" title="GOBOARD5:NM.1">special_circular_sequence</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">p</font> being  <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> 2</span>)</span>  st <font color="Olive" title="b1">p</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K2" title="RELSET_1:func.2">rng</a> <font color="Maroon" title="c2">f</font> holds <br/> <a href="goboard5.html#K5" title="GOBOARD5:func.5">left_cell</a> <font color="Maroon" title="c2">f</font>,<span class="p1">(<span class="default"><font color="Olive" title="b1">p</font> <a href="finseq_4.html#K4" title="FINSEQ_4:func.4">..</a> <font color="Maroon" title="c2">f</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="goboard5.html#K5" title="GOBOARD5:func.5">left_cell</a> <span class="p1">(<span class="default"><a href="finseq_6.html#K1" title="FINSEQ_6:func.1">Rotate</a> <font color="Maroon" title="c2">f</font>,<font color="Olive" title="b1">p</font></span>)</span>,1</span><br/><span class="kw">let </span><font color="Maroon" title="c3">p</font> be   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> 2</span>)</span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c3">p</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K2" title="RELSET_1:func.2">rng</a> <font color="Maroon" title="c2">f</font> implies  <a href="goboard5.html#K5" title="GOBOARD5:func.5">left_cell</a> <font color="Maroon" title="c2">f</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c3">p</font> <a href="finseq_4.html#K4" title="FINSEQ_4:func.4">..</a> <font color="Maroon" title="c2">f</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="goboard5.html#K5" title="GOBOARD5:func.5">left_cell</a> <span class="p1">(<span class="default"><a href="finseq_6.html#K1" title="FINSEQ_6:func.1">Rotate</a> <font color="Maroon" title="c2">f</font>,<font color="Maroon" title="c3">p</font></span>)</span>,1 )</span><br/>



<span class="kw">assume </span><a NAME="E1:6"/><span class="lab"><font color="Green" title="E4">A1</font></span>: 
<font color="Maroon" title="c3">p</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K2" title="RELSET_1:func.2">rng</a> <font color="Maroon" title="c2">f</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide">  <a href="goboard5.html#K5" title="GOBOARD5:func.5">left_cell</a> <font color="Maroon" title="c2">f</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c3">p</font> <a href="finseq_4.html#K4" title="FINSEQ_4:func.4">..</a> <font color="Maroon" title="c2">f</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="goboard5.html#K5" title="GOBOARD5:func.5">left_cell</a> <span class="p1">(<span class="default"><a href="finseq_6.html#K1" title="FINSEQ_6:func.1">Rotate</a> <font color="Maroon" title="c2">f</font>,<font color="Maroon" title="c3">p</font></span>)</span>,1</span><br/>

<span class="kw">set </span><font color="Maroon" title="c4">k</font> = <font color="Maroon" title="c3">p</font> <a href="finseq_4.html#K4" title="FINSEQ_4:func.4">..</a> <font color="Maroon" title="c2">f</font>;<br/>
<a NAME="E2:6"/>
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c2">f</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> 1
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="goboard7.html#T36" title="GOBOARD7:th.36">GOBOARD7:36</a>, <a class="ref" href="xxreal_0.html#T2" title="XXREAL_0:th.2">XXREAL_0:2</a></span>;<br/>
<a NAME="E3:6"/><span class="kw">then </span>
<font color="Maroon" title="c3">p</font> <a href="finseq_4.html#K4" title="FINSEQ_4:func.4">..</a> <font color="Maroon" title="c2">f</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c2">f</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:6"><span class="lab"><font color="Green" title="E4">A1</font></span></a>, <a class="ref" href="sprect_5.html#T7" title="SPRECT_5:th.7">SPRECT_5:7</a></span>;<br/>
<a NAME="E4:6"/><span class="kw">then </span><span class="lab"><font color="Green" title="E5">A2</font></span>: 
<span class="p1">(<span class="default"><font color="Maroon" title="c3">p</font> <a href="finseq_4.html#K4" title="FINSEQ_4:func.4">..</a> <font color="Maroon" title="c2">f</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c2">f</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="nat_1.html#T13" title="NAT_1:th.13">NAT_1:13</a></span>;<br/>
<a NAME="E5:6"/><span class="lab"><font color="Green" title="E6">A3</font></span>: 
1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c3">p</font> <a href="finseq_4.html#K4" title="FINSEQ_4:func.4">..</a> <font color="Maroon" title="c2">f</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:6"><span class="lab"><font color="Green" title="E4">A1</font></span></a>, <a class="ref" href="finseq_4.html#T31" title="FINSEQ_4:th.31">FINSEQ_4:31</a></span>;<br/>
<a NAME="E6:6"/><span class="lab"><font color="Green" title="E7">A4</font></span>: 
for <font color="Olive" title="b1">i1</font>, <font color="Olive" title="b2">j1</font>, <font color="Olive" title="b3">i2</font>, <font color="Olive" title="b4">j2</font> being   <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>   st <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Olive" title="b1">i1</font>,<font color="Olive" title="b2">j1</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="matrix_1.html#K2" title="MATRIX_1:func.2">Indices</a> <span class="p1">(<span class="default"><a href="goboard2.html#K2" title="GOBOARD2:func.2">GoB</a> <span class="p2">(<span class="default"><a href="finseq_6.html#K1" title="FINSEQ_6:func.1">Rotate</a> <font color="Maroon" title="c2">f</font>,<font color="Maroon" title="c3">p</font></span>)</span></span>)</span> &amp; <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Olive" title="b3">i2</font>,<font color="Olive" title="b4">j2</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="matrix_1.html#K2" title="MATRIX_1:func.2">Indices</a> <span class="p1">(<span class="default"><a href="goboard2.html#K2" title="GOBOARD2:func.2">GoB</a> <span class="p2">(<span class="default"><a href="finseq_6.html#K1" title="FINSEQ_6:func.1">Rotate</a> <font color="Maroon" title="c2">f</font>,<font color="Maroon" title="c3">p</font></span>)</span></span>)</span> &amp; <span class="p1">(<span class="default"><a href="finseq_6.html#K1" title="FINSEQ_6:func.1">Rotate</a> <font color="Maroon" title="c2">f</font>,<font color="Maroon" title="c3">p</font></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="goboard2.html#K2" title="GOBOARD2:func.2">GoB</a> <span class="p2">(<span class="default"><a href="finseq_6.html#K1" title="FINSEQ_6:func.1">Rotate</a> <font color="Maroon" title="c2">f</font>,<font color="Maroon" title="c3">p</font></span>)</span></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Olive" title="b1">i1</font>,<font color="Olive" title="b2">j1</font> &amp; <span class="p1">(<span class="default"><a href="finseq_6.html#K1" title="FINSEQ_6:func.1">Rotate</a> <font color="Maroon" title="c2">f</font>,<font color="Maroon" title="c3">p</font></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p1">(<span class="default">1 <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="goboard2.html#K2" title="GOBOARD2:func.2">GoB</a> <span class="p2">(<span class="default"><a href="finseq_6.html#K1" title="FINSEQ_6:func.1">Rotate</a> <font color="Maroon" title="c2">f</font>,<font color="Maroon" title="c3">p</font></span>)</span></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Olive" title="b3">i2</font>,<font color="Olive" title="b4">j2</font> &amp; not <!--HUMANRECFAILED-->( <font color="Olive" title="b1">i1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b3">i2</font> &amp; <font color="Olive" title="b2">j1</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b4">j2</font> &amp;  <a href="goboard5.html#K5" title="GOBOARD5:func.5">left_cell</a> <font color="Maroon" title="c2">f</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c3">p</font> <a href="finseq_4.html#K4" title="FINSEQ_4:func.4">..</a> <font color="Maroon" title="c2">f</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="goboard5.html#K3" title="GOBOARD5:func.3">cell</a> <span class="p1">(<span class="default"><a href="goboard2.html#K2" title="GOBOARD2:func.2">GoB</a> <span class="p2">(<span class="default"><a href="finseq_6.html#K1" title="FINSEQ_6:func.1">Rotate</a> <font color="Maroon" title="c2">f</font>,<font color="Maroon" title="c3">p</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><font color="Olive" title="b1">i1</font> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> 1</span>)</span>,<font color="Olive" title="b2">j1</font> ) &amp; not <!--HUMANRECFAILED-->( <font color="Olive" title="b1">i1</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b3">i2</font> &amp; <font color="Olive" title="b2">j1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b4">j2</font> &amp;  <a href="goboard5.html#K5" title="GOBOARD5:func.5">left_cell</a> <font color="Maroon" title="c2">f</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c3">p</font> <a href="finseq_4.html#K4" title="FINSEQ_4:func.4">..</a> <font color="Maroon" title="c2">f</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="goboard5.html#K3" title="GOBOARD5:func.3">cell</a> <span class="p1">(<span class="default"><a href="goboard2.html#K2" title="GOBOARD2:func.2">GoB</a> <span class="p2">(<span class="default"><a href="finseq_6.html#K1" title="FINSEQ_6:func.1">Rotate</a> <font color="Maroon" title="c2">f</font>,<font color="Maroon" title="c3">p</font></span>)</span></span>)</span>,<font color="Olive" title="b1">i1</font>,<font color="Olive" title="b2">j1</font> ) &amp; not <!--HUMANRECFAILED-->( <font color="Olive" title="b1">i1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b3">i2</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 &amp; <font color="Olive" title="b2">j1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b4">j2</font> &amp;  <a href="goboard5.html#K5" title="GOBOARD5:func.5">left_cell</a> <font color="Maroon" title="c2">f</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c3">p</font> <a href="finseq_4.html#K4" title="FINSEQ_4:func.4">..</a> <font color="Maroon" title="c2">f</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="goboard5.html#K3" title="GOBOARD5:func.3">cell</a> <span class="p1">(<span class="default"><a href="goboard2.html#K2" title="GOBOARD2:func.2">GoB</a> <span class="p2">(<span class="default"><a href="finseq_6.html#K1" title="FINSEQ_6:func.1">Rotate</a> <font color="Maroon" title="c2">f</font>,<font color="Maroon" title="c3">p</font></span>)</span></span>)</span>,<font color="Olive" title="b3">i2</font>,<span class="p1">(<span class="default"><font color="Olive" title="b4">j2</font> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> 1</span>)</span> ) holds <br/>( <font color="Olive" title="b1">i1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b3">i2</font> &amp; <font color="Olive" title="b2">j1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b4">j2</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 &amp;  <a href="goboard5.html#K5" title="GOBOARD5:func.5">left_cell</a> <font color="Maroon" title="c2">f</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c3">p</font> <a href="finseq_4.html#K4" title="FINSEQ_4:func.4">..</a> <font color="Maroon" title="c2">f</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="goboard5.html#K3" title="GOBOARD5:func.3">cell</a> <span class="p1">(<span class="default"><a href="goboard2.html#K2" title="GOBOARD2:func.2">GoB</a> <span class="p2">(<span class="default"><a href="finseq_6.html#K1" title="FINSEQ_6:func.1">Rotate</a> <font color="Maroon" title="c2">f</font>,<font color="Maroon" title="c3">p</font></span>)</span></span>)</span>,<font color="Olive" title="b1">i1</font>,<font color="Olive" title="b4">j2</font> )
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="6_1"><span class="kw">proof </span></a><div class="add">

<a NAME="E1:6_1"/>
<span class="p1">(<span class="default"><a href="finseq_6.html#K1" title="FINSEQ_6:func.1">Rotate</a> <font color="Maroon" title="c2">f</font>,<font color="Maroon" title="c3">p</font></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p3">(<span class="default"><font color="Maroon" title="c3">p</font> <a href="finseq_4.html#K4" title="FINSEQ_4:func.4">..</a> <font color="Maroon" title="c2">f</font></span>)</span></span>)</span> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">p</font> <a href="finseq_4.html#K4" title="FINSEQ_4:func.4">..</a> <font color="Maroon" title="c2">f</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="finseq_6.html#K1" title="FINSEQ_6:func.1">Rotate</a> <font color="Maroon" title="c2">f</font>,<font color="Maroon" title="c3">p</font></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p1">(<span class="default">1 <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="nat_d.html#T34" title="NAT_D:th.34">NAT_D:34</a></span>;<br/>
<a NAME="E2:6_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E8">A5</font></span>: 
<span class="p1">(<span class="default"><a href="finseq_6.html#K1" title="FINSEQ_6:func.1">Rotate</a> <font color="Maroon" title="c2">f</font>,<font color="Maroon" title="c3">p</font></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c3">p</font> <a href="finseq_4.html#K4" title="FINSEQ_4:func.4">..</a> <font color="Maroon" title="c2">f</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">p</font> <a href="finseq_4.html#K4" title="FINSEQ_4:func.4">..</a> <font color="Maroon" title="c2">f</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="finseq_6.html#K1" title="FINSEQ_6:func.1">Rotate</a> <font color="Maroon" title="c2">f</font>,<font color="Maroon" title="c3">p</font></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p1">(<span class="default">1 <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>
 
;<br/>
<a NAME="E3:6_1"/><span class="lab"><font color="Green" title="E9">A6</font></span>: 
 <a href="goboard5.html#K5" title="GOBOARD5:func.5">left_cell</a> <font color="Maroon" title="c2">f</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c3">p</font> <a href="finseq_4.html#K4" title="FINSEQ_4:func.4">..</a> <font color="Maroon" title="c2">f</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="goboard5.html#K5" title="GOBOARD5:func.5">left_cell</a> <font color="Maroon" title="c2">f</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c3">p</font> <a href="finseq_4.html#K4" title="FINSEQ_4:func.4">..</a> <font color="Maroon" title="c2">f</font></span>)</span>
 
;<br/>
<span class="kw">let </span><font color="Maroon" title="c5">i1</font>, <font color="Maroon" title="c6">j1</font>, <font color="Maroon" title="c7">i2</font>, <font color="Maroon" title="c8">j2</font> be    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c5">i1</font>,<font color="Maroon" title="c6">j1</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="matrix_1.html#K2" title="MATRIX_1:func.2">Indices</a> <span class="p1">(<span class="default"><a href="goboard2.html#K2" title="GOBOARD2:func.2">GoB</a> <span class="p2">(<span class="default"><a href="finseq_6.html#K1" title="FINSEQ_6:func.1">Rotate</a> <font color="Maroon" title="c2">f</font>,<font color="Maroon" title="c3">p</font></span>)</span></span>)</span> &amp; <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c7">i2</font>,<font color="Maroon" title="c8">j2</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="matrix_1.html#K2" title="MATRIX_1:func.2">Indices</a> <span class="p1">(<span class="default"><a href="goboard2.html#K2" title="GOBOARD2:func.2">GoB</a> <span class="p2">(<span class="default"><a href="finseq_6.html#K1" title="FINSEQ_6:func.1">Rotate</a> <font color="Maroon" title="c2">f</font>,<font color="Maroon" title="c3">p</font></span>)</span></span>)</span> &amp; <span class="p1">(<span class="default"><a href="finseq_6.html#K1" title="FINSEQ_6:func.1">Rotate</a> <font color="Maroon" title="c2">f</font>,<font color="Maroon" title="c3">p</font></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="goboard2.html#K2" title="GOBOARD2:func.2">GoB</a> <span class="p2">(<span class="default"><a href="finseq_6.html#K1" title="FINSEQ_6:func.1">Rotate</a> <font color="Maroon" title="c2">f</font>,<font color="Maroon" title="c3">p</font></span>)</span></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c5">i1</font>,<font color="Maroon" title="c6">j1</font> &amp; <span class="p1">(<span class="default"><a href="finseq_6.html#K1" title="FINSEQ_6:func.1">Rotate</a> <font color="Maroon" title="c2">f</font>,<font color="Maroon" title="c3">p</font></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p1">(<span class="default">1 <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="goboard2.html#K2" title="GOBOARD2:func.2">GoB</a> <span class="p2">(<span class="default"><a href="finseq_6.html#K1" title="FINSEQ_6:func.1">Rotate</a> <font color="Maroon" title="c2">f</font>,<font color="Maroon" title="c3">p</font></span>)</span></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c7">i2</font>,<font color="Maroon" title="c8">j2</font> &amp; not <!--HUMANRECFAILED-->( <font color="Maroon" title="c5">i1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">i2</font> &amp; <font color="Maroon" title="c6">j1</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">j2</font> &amp;  <a href="goboard5.html#K5" title="GOBOARD5:func.5">left_cell</a> <font color="Maroon" title="c2">f</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c3">p</font> <a href="finseq_4.html#K4" title="FINSEQ_4:func.4">..</a> <font color="Maroon" title="c2">f</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="goboard5.html#K3" title="GOBOARD5:func.3">cell</a> <span class="p1">(<span class="default"><a href="goboard2.html#K2" title="GOBOARD2:func.2">GoB</a> <span class="p2">(<span class="default"><a href="finseq_6.html#K1" title="FINSEQ_6:func.1">Rotate</a> <font color="Maroon" title="c2">f</font>,<font color="Maroon" title="c3">p</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c5">i1</font> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> 1</span>)</span>,<font color="Maroon" title="c6">j1</font> ) &amp; not <!--HUMANRECFAILED-->( <font color="Maroon" title="c5">i1</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">i2</font> &amp; <font color="Maroon" title="c6">j1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">j2</font> &amp;  <a href="goboard5.html#K5" title="GOBOARD5:func.5">left_cell</a> <font color="Maroon" title="c2">f</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c3">p</font> <a href="finseq_4.html#K4" title="FINSEQ_4:func.4">..</a> <font color="Maroon" title="c2">f</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="goboard5.html#K3" title="GOBOARD5:func.3">cell</a> <span class="p1">(<span class="default"><a href="goboard2.html#K2" title="GOBOARD2:func.2">GoB</a> <span class="p2">(<span class="default"><a href="finseq_6.html#K1" title="FINSEQ_6:func.1">Rotate</a> <font color="Maroon" title="c2">f</font>,<font color="Maroon" title="c3">p</font></span>)</span></span>)</span>,<font color="Maroon" title="c5">i1</font>,<font color="Maroon" title="c6">j1</font> ) &amp; not <!--HUMANRECFAILED-->( <font color="Maroon" title="c5">i1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">i2</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 &amp; <font color="Maroon" title="c6">j1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">j2</font> &amp;  <a href="goboard5.html#K5" title="GOBOARD5:func.5">left_cell</a> <font color="Maroon" title="c2">f</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c3">p</font> <a href="finseq_4.html#K4" title="FINSEQ_4:func.4">..</a> <font color="Maroon" title="c2">f</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="goboard5.html#K3" title="GOBOARD5:func.3">cell</a> <span class="p1">(<span class="default"><a href="goboard2.html#K2" title="GOBOARD2:func.2">GoB</a> <span class="p2">(<span class="default"><a href="finseq_6.html#K1" title="FINSEQ_6:func.1">Rotate</a> <font color="Maroon" title="c2">f</font>,<font color="Maroon" title="c3">p</font></span>)</span></span>)</span>,<font color="Maroon" title="c7">i2</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c8">j2</font> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> 1</span>)</span> ) implies ( <font color="Maroon" title="c5">i1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">i2</font> &amp; <font color="Maroon" title="c6">j1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">j2</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 &amp;  <a href="goboard5.html#K5" title="GOBOARD5:func.5">left_cell</a> <font color="Maroon" title="c2">f</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c3">p</font> <a href="finseq_4.html#K4" title="FINSEQ_4:func.4">..</a> <font color="Maroon" title="c2">f</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="goboard5.html#K3" title="GOBOARD5:func.3">cell</a> <span class="p1">(<span class="default"><a href="goboard2.html#K2" title="GOBOARD2:func.2">GoB</a> <span class="p2">(<span class="default"><a href="finseq_6.html#K1" title="FINSEQ_6:func.1">Rotate</a> <font color="Maroon" title="c2">f</font>,<font color="Maroon" title="c3">p</font></span>)</span></span>)</span>,<font color="Maroon" title="c5">i1</font>,<font color="Maroon" title="c8">j2</font> ) )</span><br/>

<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E4:6_1"/><span class="lab"><font color="Green" title="E10">A7</font></span>: 
( <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c5">i1</font>,<font color="Maroon" title="c6">j1</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="matrix_1.html#K2" title="MATRIX_1:func.2">Indices</a> <span class="p1">(<span class="default"><a href="goboard2.html#K2" title="GOBOARD2:func.2">GoB</a> <span class="p2">(<span class="default"><a href="finseq_6.html#K1" title="FINSEQ_6:func.1">Rotate</a> <font color="Maroon" title="c2">f</font>,<font color="Maroon" title="c3">p</font></span>)</span></span>)</span> &amp; <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c7">i2</font>,<font color="Maroon" title="c8">j2</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="matrix_1.html#K2" title="MATRIX_1:func.2">Indices</a> <span class="p1">(<span class="default"><a href="goboard2.html#K2" title="GOBOARD2:func.2">GoB</a> <span class="p2">(<span class="default"><a href="finseq_6.html#K1" title="FINSEQ_6:func.1">Rotate</a> <font color="Maroon" title="c2">f</font>,<font color="Maroon" title="c3">p</font></span>)</span></span>)</span> )
 <span class="kw">and </span><br/><a NAME="E5:6_1"/><span class="lab"><font color="Green" title="E11">A8</font></span>: 
<span class="p1">(<span class="default"><a href="finseq_6.html#K1" title="FINSEQ_6:func.1">Rotate</a> <font color="Maroon" title="c2">f</font>,<font color="Maroon" title="c3">p</font></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="goboard2.html#K2" title="GOBOARD2:func.2">GoB</a> <span class="p2">(<span class="default"><a href="finseq_6.html#K1" title="FINSEQ_6:func.1">Rotate</a> <font color="Maroon" title="c2">f</font>,<font color="Maroon" title="c3">p</font></span>)</span></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c5">i1</font>,<font color="Maroon" title="c6">j1</font>
 <span class="kw">and </span><br/><a NAME="E6:6_1"/><span class="lab"><font color="Green" title="E12">A9</font></span>: 
<span class="p1">(<span class="default"><a href="finseq_6.html#K1" title="FINSEQ_6:func.1">Rotate</a> <font color="Maroon" title="c2">f</font>,<font color="Maroon" title="c3">p</font></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p1">(<span class="default">1 <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="goboard2.html#K2" title="GOBOARD2:func.2">GoB</a> <span class="p2">(<span class="default"><a href="finseq_6.html#K1" title="FINSEQ_6:func.1">Rotate</a> <font color="Maroon" title="c2">f</font>,<font color="Maroon" title="c3">p</font></span>)</span></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c7">i2</font>,<font color="Maroon" title="c8">j2</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( ( <font color="Maroon" title="c5">i1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">i2</font> &amp; <font color="Maroon" title="c6">j1</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">j2</font> &amp;  <a href="goboard5.html#K5" title="GOBOARD5:func.5">left_cell</a> <font color="Maroon" title="c2">f</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c3">p</font> <a href="finseq_4.html#K4" title="FINSEQ_4:func.4">..</a> <font color="Maroon" title="c2">f</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="goboard5.html#K3" title="GOBOARD5:func.3">cell</a> <span class="p1">(<span class="default"><a href="goboard2.html#K2" title="GOBOARD2:func.2">GoB</a> <span class="p2">(<span class="default"><a href="finseq_6.html#K1" title="FINSEQ_6:func.1">Rotate</a> <font color="Maroon" title="c2">f</font>,<font color="Maroon" title="c3">p</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c5">i1</font> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> 1</span>)</span>,<font color="Maroon" title="c6">j1</font> ) or ( <font color="Maroon" title="c5">i1</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">i2</font> &amp; <font color="Maroon" title="c6">j1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">j2</font> &amp;  <a href="goboard5.html#K5" title="GOBOARD5:func.5">left_cell</a> <font color="Maroon" title="c2">f</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c3">p</font> <a href="finseq_4.html#K4" title="FINSEQ_4:func.4">..</a> <font color="Maroon" title="c2">f</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="goboard5.html#K3" title="GOBOARD5:func.3">cell</a> <span class="p1">(<span class="default"><a href="goboard2.html#K2" title="GOBOARD2:func.2">GoB</a> <span class="p2">(<span class="default"><a href="finseq_6.html#K1" title="FINSEQ_6:func.1">Rotate</a> <font color="Maroon" title="c2">f</font>,<font color="Maroon" title="c3">p</font></span>)</span></span>)</span>,<font color="Maroon" title="c5">i1</font>,<font color="Maroon" title="c6">j1</font> ) or ( <font color="Maroon" title="c5">i1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">i2</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 &amp; <font color="Maroon" title="c6">j1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">j2</font> &amp;  <a href="goboard5.html#K5" title="GOBOARD5:func.5">left_cell</a> <font color="Maroon" title="c2">f</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c3">p</font> <a href="finseq_4.html#K4" title="FINSEQ_4:func.4">..</a> <font color="Maroon" title="c2">f</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="goboard5.html#K3" title="GOBOARD5:func.3">cell</a> <span class="p1">(<span class="default"><a href="goboard2.html#K2" title="GOBOARD2:func.2">GoB</a> <span class="p2">(<span class="default"><a href="finseq_6.html#K1" title="FINSEQ_6:func.1">Rotate</a> <font color="Maroon" title="c2">f</font>,<font color="Maroon" title="c3">p</font></span>)</span></span>)</span>,<font color="Maroon" title="c7">i2</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c8">j2</font> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> 1</span>)</span> ) or ( <font color="Maroon" title="c5">i1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">i2</font> &amp; <font color="Maroon" title="c6">j1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">j2</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 &amp;  <a href="goboard5.html#K5" title="GOBOARD5:func.5">left_cell</a> <font color="Maroon" title="c2">f</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c3">p</font> <a href="finseq_4.html#K4" title="FINSEQ_4:func.4">..</a> <font color="Maroon" title="c2">f</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="goboard5.html#K3" title="GOBOARD5:func.3">cell</a> <span class="p1">(<span class="default"><a href="goboard2.html#K2" title="GOBOARD2:func.2">GoB</a> <span class="p2">(<span class="default"><a href="finseq_6.html#K1" title="FINSEQ_6:func.1">Rotate</a> <font color="Maroon" title="c2">f</font>,<font color="Maroon" title="c3">p</font></span>)</span></span>)</span>,<font color="Maroon" title="c5">i1</font>,<font color="Maroon" title="c8">j2</font> ) )</span><br/>

<a NAME="E7:6_1"/><span class="lab"><font color="Green" title="E13">A10</font></span>: 
 <a href="goboard2.html#K2" title="GOBOARD2:func.2">GoB</a> <span class="p1">(<span class="default"><a href="finseq_6.html#K1" title="FINSEQ_6:func.1">Rotate</a> <font color="Maroon" title="c2">f</font>,<font color="Maroon" title="c3">p</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="goboard2.html#K2" title="GOBOARD2:func.2">GoB</a> <font color="Maroon" title="c2">f</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="revrot_1.html#T28" title="REVROT_1:th.28">REVROT_1:28</a></span>;<br/>
<a NAME="E8:6_1"/>
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="finseq_6.html#K1" title="FINSEQ_6:func.1">Rotate</a> <font color="Maroon" title="c2">f</font>,<font color="Maroon" title="c3">p</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c2">f</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="revrot_1.html#T14" title="REVROT_1:th.14">REVROT_1:14</a></span>;<br/>
<a NAME="E9:6_1"/><span class="kw">then </span>
<span class="p1">(<span class="default"><a href="finseq_6.html#K1" title="FINSEQ_6:func.1">Rotate</a> <font color="Maroon" title="c2">f</font>,<font color="Maroon" title="c3">p</font></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c2">f</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="finseq_6.html#K1" title="FINSEQ_6:func.1">Rotate</a> <font color="Maroon" title="c2">f</font>,<font color="Maroon" title="c3">p</font></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 1
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_6.html#D1" title="FINSEQ_6:def.1">FINSEQ_6:def 1</a></span>;<br/>
<a NAME="E10:6_1"/><span class="kw">then </span>
<span class="p1">(<span class="default"><a href="finseq_6.html#K1" title="FINSEQ_6:func.1">Rotate</a> <font color="Maroon" title="c2">f</font>,<font color="Maroon" title="c3">p</font></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c3">p</font> <a href="finseq_4.html#K4" title="FINSEQ_4:func.4">..</a> <font color="Maroon" title="c2">f</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p3">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c2">f</font></span>)</span></span>)</span> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">p</font> <a href="finseq_4.html#K4" title="FINSEQ_4:func.4">..</a> <font color="Maroon" title="c2">f</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="finseq_6.html#K1" title="FINSEQ_6:func.1">Rotate</a> <font color="Maroon" title="c2">f</font>,<font color="Maroon" title="c3">p</font></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 1
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="nat_d.html#T34" title="NAT_D:th.34">NAT_D:34</a></span>;<br/>
<a NAME="E11:6_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E14">A11</font></span>: 
<font color="Maroon" title="c2">f</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">p</font> <a href="finseq_4.html#K4" title="FINSEQ_4:func.4">..</a> <font color="Maroon" title="c2">f</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="goboard2.html#K2" title="GOBOARD2:func.2">GoB</a> <font color="Maroon" title="c2">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c5">i1</font>,<font color="Maroon" title="c6">j1</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:6"><span class="lab"><font color="Green" title="E4">A1</font></span></a>, <a class="txt" href="#E5:6"><span class="lab"><font color="Green" title="E6">A3</font></span></a>, <a class="txt" href="#E5:6_1"><span class="lab"><font color="Green" title="E11">A8</font></span></a>, <a class="txt" href="#E7:6_1"><span class="lab"><font color="Green" title="E13">A10</font></span></a>, <a class="ref" href="revrot_1.html#T18" title="REVROT_1:th.18">REVROT_1:18</a></span>;<br/>
<a NAME="E12:6_1"/>
<font color="Maroon" title="c3">p</font> <a href="finseq_4.html#K4" title="FINSEQ_4:func.4">..</a> <font color="Maroon" title="c2">f</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">p</font> <a href="finseq_4.html#K4" title="FINSEQ_4:func.4">..</a> <font color="Maroon" title="c2">f</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="nat_1.html#T13" title="NAT_1:th.13">NAT_1:13</a></span>;<br/>
<a NAME="E13:6_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E15">A12</font></span>: 
<font color="Maroon" title="c2">f</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">p</font> <a href="finseq_4.html#K4" title="FINSEQ_4:func.4">..</a> <font color="Maroon" title="c2">f</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="goboard2.html#K2" title="GOBOARD2:func.2">GoB</a> <font color="Maroon" title="c2">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c7">i2</font>,<font color="Maroon" title="c8">j2</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:6"><span class="lab"><font color="Green" title="E4">A1</font></span></a>, <a class="txt" href="#E4:6"><span class="lab"><font color="Green" title="E5">A2</font></span></a>, <a class="txt" href="#E6:6_1"><span class="lab"><font color="Green" title="E12">A9</font></span></a>, <a class="txt" href="#E7:6_1"><span class="lab"><font color="Green" title="E13">A10</font></span></a>, <a class="txt" href="#E2:6_1"><span class="lab"><font color="Green" title="E8">A5</font></span></a>, <a class="ref" href="revrot_1.html#T10" title="REVROT_1:th.10">REVROT_1:10</a></span>;<br/>
<a NAME="E14:6_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E16">A13</font></span>: 
( ( <font color="Maroon" title="c5">i1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">i2</font> &amp; <font color="Maroon" title="c6">j1</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">j2</font> &amp;  <a href="goboard5.html#K5" title="GOBOARD5:func.5">left_cell</a> <font color="Maroon" title="c2">f</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c3">p</font> <a href="finseq_4.html#K4" title="FINSEQ_4:func.4">..</a> <font color="Maroon" title="c2">f</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="goboard5.html#K3" title="GOBOARD5:func.3">cell</a> <span class="p1">(<span class="default"><a href="goboard2.html#K2" title="GOBOARD2:func.2">GoB</a> <font color="Maroon" title="c2">f</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c5">i1</font> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> 1</span>)</span>,<font color="Maroon" title="c6">j1</font> ) or ( <font color="Maroon" title="c5">i1</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">i2</font> &amp; <font color="Maroon" title="c6">j1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">j2</font> &amp;  <a href="goboard5.html#K5" title="GOBOARD5:func.5">left_cell</a> <font color="Maroon" title="c2">f</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c3">p</font> <a href="finseq_4.html#K4" title="FINSEQ_4:func.4">..</a> <font color="Maroon" title="c2">f</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="goboard5.html#K3" title="GOBOARD5:func.3">cell</a> <span class="p1">(<span class="default"><a href="goboard2.html#K2" title="GOBOARD2:func.2">GoB</a> <font color="Maroon" title="c2">f</font></span>)</span>,<font color="Maroon" title="c5">i1</font>,<font color="Maroon" title="c6">j1</font> ) or ( <font color="Maroon" title="c5">i1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">i2</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 &amp; <font color="Maroon" title="c6">j1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">j2</font> &amp;  <a href="goboard5.html#K5" title="GOBOARD5:func.5">left_cell</a> <font color="Maroon" title="c2">f</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c3">p</font> <a href="finseq_4.html#K4" title="FINSEQ_4:func.4">..</a> <font color="Maroon" title="c2">f</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="goboard5.html#K3" title="GOBOARD5:func.3">cell</a> <span class="p1">(<span class="default"><a href="goboard2.html#K2" title="GOBOARD2:func.2">GoB</a> <font color="Maroon" title="c2">f</font></span>)</span>,<font color="Maroon" title="c7">i2</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c8">j2</font> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> 1</span>)</span> ) or ( <font color="Maroon" title="c5">i1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">i2</font> &amp; <font color="Maroon" title="c6">j1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">j2</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 &amp;  <a href="goboard5.html#K5" title="GOBOARD5:func.5">left_cell</a> <font color="Maroon" title="c2">f</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c3">p</font> <a href="finseq_4.html#K4" title="FINSEQ_4:func.4">..</a> <font color="Maroon" title="c2">f</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="goboard5.html#K3" title="GOBOARD5:func.3">cell</a> <span class="p1">(<span class="default"><a href="goboard2.html#K2" title="GOBOARD2:func.2">GoB</a> <font color="Maroon" title="c2">f</font></span>)</span>,<font color="Maroon" title="c5">i1</font>,<font color="Maroon" title="c8">j2</font> ) )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:6"><span class="lab"><font color="Green" title="E6">A3</font></span></a>, <a class="txt" href="#E4:6"><span class="lab"><font color="Green" title="E5">A2</font></span></a>, <a class="txt" href="#E4:6_1"><span class="lab"><font color="Green" title="E10">A7</font></span></a>, <a class="txt" href="#E7:6_1"><span class="lab"><font color="Green" title="E13">A10</font></span></a>, <a class="txt" href="#E11:6_1"><span class="lab"><font color="Green" title="E14">A11</font></span></a>, <a class="txt" href="#E3:6_1"><span class="lab"><font color="Green" title="E9">A6</font></span></a>, <a class="ref" href="goboard5.html#D7" title="GOBOARD5:def.7">GOBOARD5:def 7</a></span>;<br/>
<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="6_1_1"><span class="kw">per </span></a><a class="txt" onclick="hs(this)" href="javascript:()"><span class="kw">cases </span></a><span class="hide"><a NAME="E1:6_1_1"/>
( ( <font color="Maroon" title="c5">i1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">i2</font> &amp; <font color="Maroon" title="c6">j1</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">j2</font> ) or ( <font color="Maroon" title="c5">i1</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">i2</font> &amp; <font color="Maroon" title="c6">j1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">j2</font> ) or ( <font color="Maroon" title="c5">i1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">i2</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 &amp; <font color="Maroon" title="c6">j1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">j2</font> ) or ( <font color="Maroon" title="c5">i1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">i2</font> &amp; <font color="Maroon" title="c6">j1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">j2</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 ) )
 </span><span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:6"><span class="lab"><font color="Green" title="E6">A3</font></span></a>, <a class="txt" href="#E4:6"><span class="lab"><font color="Green" title="E5">A2</font></span></a>, <a class="txt" href="#E4:6_1"><span class="lab"><font color="Green" title="E10">A7</font></span></a>, <a class="txt" href="#E7:6_1"><span class="lab"><font color="Green" title="E13">A10</font></span></a>, <a class="txt" href="#E11:6_1"><span class="lab"><font color="Green" title="E14">A11</font></span></a>, <a class="txt" href="#E13:6_1"><span class="lab"><font color="Green" title="E15">A12</font></span></a>, <a class="txt" href="#E3:6_1"><span class="lab"><font color="Green" title="E9">A6</font></span></a>, <a class="ref" href="goboard5.html#D7" title="GOBOARD5:def.7">GOBOARD5:def 7</a></span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="6_1_1_1"><span class="kw">case </span></a><a NAME="E1:6_1_1_1"/>
( <font color="Maroon" title="c5">i1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">i2</font> &amp; <font color="Maroon" title="c6">j1</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">j2</font> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide">  <a href="goboard5.html#K5" title="GOBOARD5:func.5">left_cell</a> <font color="Maroon" title="c2">f</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c3">p</font> <a href="finseq_4.html#K4" title="FINSEQ_4:func.4">..</a> <font color="Maroon" title="c2">f</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="goboard5.html#K3" title="GOBOARD5:func.3">cell</a> <span class="p1">(<span class="default"><a href="goboard2.html#K2" title="GOBOARD2:func.2">GoB</a> <span class="p2">(<span class="default"><a href="finseq_6.html#K1" title="FINSEQ_6:func.1">Rotate</a> <font color="Maroon" title="c2">f</font>,<font color="Maroon" title="c3">p</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c5">i1</font> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> 1</span>)</span>,<font color="Maroon" title="c6">j1</font></span><br/><div class="add"><span class="kw">hence </span><a NAME="E2:6_1_1_1"/>
 <a href="goboard5.html#K5" title="GOBOARD5:func.5">left_cell</a> <font color="Maroon" title="c2">f</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c3">p</font> <a href="finseq_4.html#K4" title="FINSEQ_4:func.4">..</a> <font color="Maroon" title="c2">f</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="goboard5.html#K3" title="GOBOARD5:func.3">cell</a> <span class="p1">(<span class="default"><a href="goboard2.html#K2" title="GOBOARD2:func.2">GoB</a> <span class="p2">(<span class="default"><a href="finseq_6.html#K1" title="FINSEQ_6:func.1">Rotate</a> <font color="Maroon" title="c2">f</font>,<font color="Maroon" title="c3">p</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c5">i1</font> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> 1</span>)</span>,<font color="Maroon" title="c6">j1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E14:6_1"><span class="lab"><font color="Green" title="E16">A13</font></span></a>, <a class="ref" href="revrot_1.html#T28" title="REVROT_1:th.28">REVROT_1:28</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="6_1_1_2"><span class="kw">case </span></a><a NAME="E1:6_1_1_2"/>
( <font color="Maroon" title="c5">i1</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">i2</font> &amp; <font color="Maroon" title="c6">j1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">j2</font> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide">  <a href="goboard5.html#K5" title="GOBOARD5:func.5">left_cell</a> <font color="Maroon" title="c2">f</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c3">p</font> <a href="finseq_4.html#K4" title="FINSEQ_4:func.4">..</a> <font color="Maroon" title="c2">f</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="goboard5.html#K3" title="GOBOARD5:func.3">cell</a> <span class="p1">(<span class="default"><a href="goboard2.html#K2" title="GOBOARD2:func.2">GoB</a> <span class="p2">(<span class="default"><a href="finseq_6.html#K1" title="FINSEQ_6:func.1">Rotate</a> <font color="Maroon" title="c2">f</font>,<font color="Maroon" title="c3">p</font></span>)</span></span>)</span>,<font color="Maroon" title="c5">i1</font>,<font color="Maroon" title="c6">j1</font></span><br/><div class="add"><span class="kw">hence </span><a NAME="E2:6_1_1_2"/>
 <a href="goboard5.html#K5" title="GOBOARD5:func.5">left_cell</a> <font color="Maroon" title="c2">f</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c3">p</font> <a href="finseq_4.html#K4" title="FINSEQ_4:func.4">..</a> <font color="Maroon" title="c2">f</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="goboard5.html#K3" title="GOBOARD5:func.3">cell</a> <span class="p1">(<span class="default"><a href="goboard2.html#K2" title="GOBOARD2:func.2">GoB</a> <span class="p2">(<span class="default"><a href="finseq_6.html#K1" title="FINSEQ_6:func.1">Rotate</a> <font color="Maroon" title="c2">f</font>,<font color="Maroon" title="c3">p</font></span>)</span></span>)</span>,<font color="Maroon" title="c5">i1</font>,<font color="Maroon" title="c6">j1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E14:6_1"><span class="lab"><font color="Green" title="E16">A13</font></span></a>, <a class="ref" href="revrot_1.html#T28" title="REVROT_1:th.28">REVROT_1:28</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="6_1_1_3"><span class="kw">case </span></a><a NAME="E1:6_1_1_3"/>
( <font color="Maroon" title="c5">i1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">i2</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 &amp; <font color="Maroon" title="c6">j1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">j2</font> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide">  <a href="goboard5.html#K5" title="GOBOARD5:func.5">left_cell</a> <font color="Maroon" title="c2">f</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c3">p</font> <a href="finseq_4.html#K4" title="FINSEQ_4:func.4">..</a> <font color="Maroon" title="c2">f</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="goboard5.html#K3" title="GOBOARD5:func.3">cell</a> <span class="p1">(<span class="default"><a href="goboard2.html#K2" title="GOBOARD2:func.2">GoB</a> <span class="p2">(<span class="default"><a href="finseq_6.html#K1" title="FINSEQ_6:func.1">Rotate</a> <font color="Maroon" title="c2">f</font>,<font color="Maroon" title="c3">p</font></span>)</span></span>)</span>,<font color="Maroon" title="c7">i2</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c8">j2</font> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> 1</span>)</span></span><br/><div class="add"><span class="kw">hence </span><a NAME="E2:6_1_1_3"/>
 <a href="goboard5.html#K5" title="GOBOARD5:func.5">left_cell</a> <font color="Maroon" title="c2">f</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c3">p</font> <a href="finseq_4.html#K4" title="FINSEQ_4:func.4">..</a> <font color="Maroon" title="c2">f</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="goboard5.html#K3" title="GOBOARD5:func.3">cell</a> <span class="p1">(<span class="default"><a href="goboard2.html#K2" title="GOBOARD2:func.2">GoB</a> <span class="p2">(<span class="default"><a href="finseq_6.html#K1" title="FINSEQ_6:func.1">Rotate</a> <font color="Maroon" title="c2">f</font>,<font color="Maroon" title="c3">p</font></span>)</span></span>)</span>,<font color="Maroon" title="c7">i2</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c8">j2</font> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> 1</span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E14:6_1"><span class="lab"><font color="Green" title="E16">A13</font></span></a>, <a class="ref" href="revrot_1.html#T28" title="REVROT_1:th.28">REVROT_1:28</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="6_1_1_4"><span class="kw">case </span></a><a NAME="E1:6_1_1_4"/>
( <font color="Maroon" title="c5">i1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">i2</font> &amp; <font color="Maroon" title="c6">j1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">j2</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide">  <a href="goboard5.html#K5" title="GOBOARD5:func.5">left_cell</a> <font color="Maroon" title="c2">f</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c3">p</font> <a href="finseq_4.html#K4" title="FINSEQ_4:func.4">..</a> <font color="Maroon" title="c2">f</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="goboard5.html#K3" title="GOBOARD5:func.3">cell</a> <span class="p1">(<span class="default"><a href="goboard2.html#K2" title="GOBOARD2:func.2">GoB</a> <span class="p2">(<span class="default"><a href="finseq_6.html#K1" title="FINSEQ_6:func.1">Rotate</a> <font color="Maroon" title="c2">f</font>,<font color="Maroon" title="c3">p</font></span>)</span></span>)</span>,<font color="Maroon" title="c5">i1</font>,<font color="Maroon" title="c8">j2</font></span><br/><div class="add"><span class="kw">hence </span><a NAME="E2:6_1_1_4"/>
 <a href="goboard5.html#K5" title="GOBOARD5:func.5">left_cell</a> <font color="Maroon" title="c2">f</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c3">p</font> <a href="finseq_4.html#K4" title="FINSEQ_4:func.4">..</a> <font color="Maroon" title="c2">f</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="goboard5.html#K3" title="GOBOARD5:func.3">cell</a> <span class="p1">(<span class="default"><a href="goboard2.html#K2" title="GOBOARD2:func.2">GoB</a> <span class="p2">(<span class="default"><a href="finseq_6.html#K1" title="FINSEQ_6:func.1">Rotate</a> <font color="Maroon" title="c2">f</font>,<font color="Maroon" title="c3">p</font></span>)</span></span>)</span>,<font color="Maroon" title="c5">i1</font>,<font color="Maroon" title="c8">j2</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E14:6_1"><span class="lab"><font color="Green" title="E16">A13</font></span></a>, <a class="ref" href="revrot_1.html#T28" title="REVROT_1:th.28">REVROT_1:28</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div>

</div><span class="kw">end;</span></div>
<a NAME="E7:6"/>
1 <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="finseq_6.html#K1" title="FINSEQ_6:func.1">Rotate</a> <font color="Maroon" title="c2">f</font>,<font color="Maroon" title="c3">p</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="goboard7.html#T36" title="GOBOARD7:th.36">GOBOARD7:36</a>, <a class="ref" href="xxreal_0.html#T2" title="XXREAL_0:th.2">XXREAL_0:2</a></span>;<br/>
<span class="kw">hence </span><a NAME="E8:6"/>
 <a href="goboard5.html#K5" title="GOBOARD5:func.5">left_cell</a> <font color="Maroon" title="c2">f</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c3">p</font> <a href="finseq_4.html#K4" title="FINSEQ_4:func.4">..</a> <font color="Maroon" title="c2">f</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="goboard5.html#K5" title="GOBOARD5:func.5">left_cell</a> <span class="p1">(<span class="default"><a href="finseq_6.html#K1" title="FINSEQ_6:func.1">Rotate</a> <font color="Maroon" title="c2">f</font>,<font color="Maroon" title="c3">p</font></span>)</span>,1
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:6"><span class="lab"><font color="Green" title="E7">A4</font></span></a>, <a class="ref" href="goboard5.html#D7" title="GOBOARD5:def.7">GOBOARD5:def 7</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div>
