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<b>let </b><font color="Maroon" title="c1">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>;<br/><b>let </b><font color="Maroon" title="c2">p</font>, <font color="Maroon" title="c3">q</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>;<br/>





<b>assume </b><a NAME="E1:10"/><i><font color="Green" title="E10">A1</font></i>: 
( <font color="Maroon" title="c2">p</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <font color="Maroon" title="c1">f</font> &amp; <font color="Maroon" title="c3">q</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <font color="Maroon" title="c1">f</font> )
 ;<br/>

<a NAME="E2:10"/><b>then </b><i><font color="Green" title="E11">A2</font></i>: 
 <a href="finseq_6.html#K1" title="FINSEQ_6:func.1">Rotate</a> <font color="Maroon" title="c1">f</font>,<font color="Maroon" title="c3">q</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">f</font> <a href="finseq_5.html#K2" title="FINSEQ_5:func.2">:-</a> <font color="Maroon" title="c3">q</font></span>)</span> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">f</font> <a href="finseq_5.html#K1" title="FINSEQ_5:func.1">-:</a> <font color="Maroon" title="c3">q</font></span>)</span> <a href="rfinseq.html#K2" title="RFINSEQ:func.2">/^</a> 1</span>)</span>
 
<b>by </b><i><a class="ref" href="finseq_6.html#D2" title="FINSEQ_6:def.2">FINSEQ_6:def 2</a></i>;<br/>
<b>assume </b><a NAME="E3:10"/><i><font color="Green" title="E12">A3</font></i>: 
<font color="Maroon" title="c2">p</font> <a href="finseq_4.html#K5" title="FINSEQ_4:func.5">..</a> <font color="Maroon" title="c1">f</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c3">q</font> <a href="finseq_4.html#K5" title="FINSEQ_4:func.5">..</a> <font color="Maroon" title="c1">f</font>
 ;<br/>

<a NAME="E4:10"/><b>then </b><i><font color="Green" title="E13">A4</font></i>: 
<font color="Maroon" title="c2">p</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">f</font> <a href="finseq_5.html#K1" title="FINSEQ_5:func.1">-:</a> <font color="Maroon" title="c3">q</font></span>)</span>
 
<b>by </b><i><a class="txt" href="sprect_5.html#E1:10"><i><font color="Green" title="E10">A1</font></i></a>, <a class="ref" href="finseq_5.html#T49" title="FINSEQ_5:th.49">FINSEQ_5:49</a></i>;<br/>
<a NAME="E5:10"/><b>then </b><i><font color="Green" title="E14">A5</font></i>: 
<font color="Maroon" title="c2">p</font> <a href="finseq_4.html#K5" title="FINSEQ_4:func.5">..</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">f</font> <a href="finseq_5.html#K1" title="FINSEQ_5:func.1">-:</a> <font color="Maroon" title="c3">q</font></span>)</span> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> 1
 
<b>by </b><i><a class="ref" href="finseq_4.html#T31" title="FINSEQ_4:th.31">FINSEQ_4:31</a></i>;<br/>
<a NAME="E6:10"/><i><font color="Green" title="E15">A6</font></i>: 
<font color="Maroon" title="c2">p</font> <a href="finseq_4.html#K5" title="FINSEQ_4:func.5">..</a> <font color="Maroon" title="c1">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">p</font> <a href="finseq_4.html#K5" title="FINSEQ_4:func.5">..</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">f</font> <a href="finseq_5.html#K1" title="FINSEQ_5:func.1">-:</a> <font color="Maroon" title="c3">q</font></span>)</span>
 
<b>by </b><i><a class="txt" href="sprect_5.html#E1:10"><i><font color="Green" title="E10">A1</font></i></a>, <a class="txt" href="sprect_5.html#E3:10"><i><font color="Green" title="E12">A3</font></i></a>, <a class="ref" href="sprect_5.html#T3" target="_self" title="SPRECT_5:th.3">Th3</a></i>;<br/>
<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="10_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:10_1"/>
( <font color="Maroon" title="c2">p</font> <a href="finseq_4.html#K5" title="FINSEQ_4:func.5">..</a> <font color="Maroon" title="c1">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 or <font color="Maroon" title="c2">p</font> <a href="finseq_4.html#K5" title="FINSEQ_4:func.5">..</a> <font color="Maroon" title="c1">f</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> 1 )
 </span><b>by </b><i><a class="txt" href="sprect_5.html#E5:10"><i><font color="Green" title="E14">A5</font></i></a>, <a class="txt" href="sprect_5.html#E6:10"><i><font color="Green" title="E15">A6</font></i></a>, <a class="ref" href="xxreal_0.html#T1" title="XXREAL_0:th.1">XXREAL_0:1</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="10_1_1"><b>suppose </b></a><a NAME="E1:10_1_1"/><i><font color="Green" title="E16">A7</font></i>: 
<font color="Maroon" title="c2">p</font> <a href="finseq_4.html#K5" title="FINSEQ_4:func.5">..</a> <font color="Maroon" title="c1">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1
 ;<br/><div class="add"><a NAME="E2:10_1_1"/><b>then </b>
<font color="Maroon" title="c2">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">f</font> <a href="finseq_4.html#K4" title="FINSEQ_4:func.4">/.</a> 1
 <b>by </b><i><a class="txt" href="sprect_5.html#E1:10"><i><font color="Green" title="E10">A1</font></i></a>, <a class="ref" href="finseq_5.html#T41" title="FINSEQ_5:th.41">FINSEQ_5:41</a></i>;<br/><b>hence </b><a NAME="E3:10_1_1"/>
<font color="Maroon" title="c2">p</font> <a href="finseq_4.html#K5" title="FINSEQ_4:func.5">..</a> <span class="p1">(<span class="default"><a href="finseq_6.html#K1" title="FINSEQ_6:func.1">Rotate</a> <font color="Maroon" title="c1">f</font>,<font color="Maroon" title="c3">q</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="finseq_4.html#K5" title="FINSEQ_4:func.5">..</a> <font color="Maroon" title="c1">f</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">q</font> <a href="finseq_4.html#K5" title="FINSEQ_4:func.5">..</a> <font color="Maroon" title="c1">f</font></span>)</span>
 <b>by </b><i><a class="txt" href="sprect_5.html#E1:10"><i><font color="Green" title="E10">A1</font></i></a>, <a class="txt" href="sprect_5.html#E3:10"><i><font color="Green" title="E12">A3</font></i></a>, <a class="txt" href="sprect_5.html#E1:10_1_1"><i><font color="Green" title="E16">A7</font></i></a>, <a class="ref" href="sprect_5.html#T9" target="_self" title="SPRECT_5:th.9">Th9</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="10_1_2"><b>suppose </b></a><a NAME="E1:10_1_2"/><i><font color="Green" title="E16">A8</font></i>: 
<font color="Maroon" title="c2">p</font> <a href="finseq_4.html#K5" title="FINSEQ_4:func.5">..</a> <font color="Maroon" title="c1">f</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> 1
 ;<br/><div class="add"><a NAME="E2:10_1_2"/><b>then </b><i><font color="Green" title="E17">A9</font></i>: 
<font color="Maroon" title="c2">p</font> <a href="finseq_4.html#K5" title="FINSEQ_4:func.5">..</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">f</font> <a href="finseq_5.html#K1" title="FINSEQ_5:func.1">-:</a> <font color="Maroon" title="c3">q</font></span>)</span> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> 1
 <b>by </b><i><a class="txt" href="sprect_5.html#E1:10"><i><font color="Green" title="E10">A1</font></i></a>, <a class="txt" href="sprect_5.html#E3:10"><i><font color="Green" title="E12">A3</font></i></a>, <a class="ref" href="sprect_5.html#T3" target="_self" title="SPRECT_5:th.3">Th3</a></i>;<br/><a NAME="E3:10_1_2"/><i><font color="Green" title="E18">A10</font></i>: 
<font color="Maroon" title="c2">p</font> <a href="finseq_4.html#K5" title="FINSEQ_4:func.5">..</a> <font color="Maroon" title="c1">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="finseq_4.html#K5" title="FINSEQ_4:func.5">..</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c1">f</font> <a href="finseq_5.html#K1" title="FINSEQ_5:func.1">-:</a> <font color="Maroon" title="c3">q</font></span>)</span> <a href="rfinseq.html#K2" title="RFINSEQ:func.2">/^</a> 1</span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="sprect_5.html#E4:10"><i><font color="Green" title="E13">A4</font></i></a>, <a class="txt" href="sprect_5.html#E6:10"><i><font color="Green" title="E15">A6</font></i></a>, <a class="txt" href="sprect_5.html#E1:10_1_2"><i><font color="Green" title="E16">A8</font></i></a>, <a class="ref" href="finseq_6.html#T61" title="FINSEQ_6:th.61">FINSEQ_6:61</a></i>;<br/><a NAME="E4:10_1_2"/><i><font color="Green" title="E19">A11</font></i>: 
<font color="Maroon" title="c1">f</font> <a href="rfinseq.html#K2" title="RFINSEQ:func.2">/^</a> 1 is <a href="funct_1.html#V2" title="FUNCT_1:attr.2">one-to-one</a>
 <b>by </b><i><a class="ref" href="sprect_5.html#T8" target="_self" title="SPRECT_5:th.8">Th8</a></i>;<br/><a NAME="E5:10_1_2"/><i><font color="Green" title="E20">A12</font></i>: 
<font color="Maroon" title="c2">p</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">f</font> <a href="finseq_5.html#K1" title="FINSEQ_5:func.1">-:</a> <font color="Maroon" title="c3">q</font></span>)</span> <a href="rfinseq.html#K2" title="RFINSEQ:func.2">/^</a> 1</span>)</span>
 <b>by </b><i><a class="txt" href="sprect_5.html#E4:10"><i><font color="Green" title="E13">A4</font></i></a>, <a class="txt" href="sprect_5.html#E2:10_1_2"><i><font color="Green" title="E17">A9</font></i></a>, <a class="ref" href="finseq_6.html#T62" title="FINSEQ_6:th.62">FINSEQ_6:62</a></i>;<br/><a NAME="E6:10_1_2"/><b>then </b><i><font color="Green" title="E21">A13</font></i>: 
<font color="Maroon" title="c2">p</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">f</font> <a href="rfinseq.html#K2" title="RFINSEQ:func.2">/^</a> 1</span>)</span> <a href="finseq_5.html#K1" title="FINSEQ_5:func.1">-:</a> <font color="Maroon" title="c3">q</font></span>)</span>
 <b>by </b><i><a class="txt" href="sprect_5.html#E1:10"><i><font color="Green" title="E10">A1</font></i></a>, <a class="txt" href="sprect_5.html#E3:10"><i><font color="Green" title="E12">A3</font></i></a>, <a class="txt" href="sprect_5.html#E1:10_1_2"><i><font color="Green" title="E16">A8</font></i></a>, <a class="ref" href="finseq_6.html#T65" title="FINSEQ_6:th.65">FINSEQ_6:65</a></i>;<br/><a NAME="E7:10_1_2"/><i><font color="Green" title="E22">A14</font></i>: 
<font color="Maroon" title="c3">q</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">f</font> <a href="rfinseq.html#K2" title="RFINSEQ:func.2">/^</a> 1</span>)</span>
 <b>by </b><i><a class="txt" href="sprect_5.html#E1:10"><i><font color="Green" title="E10">A1</font></i></a>, <a class="txt" href="sprect_5.html#E3:10"><i><font color="Green" title="E12">A3</font></i></a>, <a class="txt" href="sprect_5.html#E1:10_1_2"><i><font color="Green" title="E16">A8</font></i></a>, <a class="ref" href="finseq_6.html#T83" title="FINSEQ_6:th.83">FINSEQ_6:83</a></i>;<br/><a NAME="E8:10_1_2"/><b>then </b><i><font color="Green" title="E23">A15</font></i>: 
 <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">f</font> <a href="rfinseq.html#K2" title="RFINSEQ:func.2">/^</a> 1</span>)</span> <a href="finseq_4.html#K6" title="FINSEQ_4:func.6">-|</a> <font color="Maroon" title="c3">q</font></span>)</span> <a href="xboole_0.html#R1" title="XBOOLE_0:pred.1">misses</a>  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">f</font> <a href="rfinseq.html#K2" title="RFINSEQ:func.2">/^</a> 1</span>)</span> <a href="finseq_4.html#K7" title="FINSEQ_4:func.7">|--</a> <font color="Maroon" title="c3">q</font></span>)</span>
 <b>by </b><i><a class="txt" href="sprect_5.html#E4:10_1_2"><i><font color="Green" title="E19">A11</font></i></a>, <a class="ref" href="finseq_4.html#T72" title="FINSEQ_4:th.72">FINSEQ_4:72</a></i>;<br/><span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">f</font> <a href="rfinseq.html#K2" title="RFINSEQ:func.2">/^</a> 1</span>)</span> <a href="finseq_4.html#K6" title="FINSEQ_4:func.6">-|</a> <font color="Maroon" title="c3">q</font></span>)</span> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <span class="p1"><a href="binarith.html#K11" title="BINARITH:func.11">&lt;*</a><span class="default"><font color="Maroon" title="c3">q</font></span><a href="binarith.html#K11" title="BINARITH:func.11">*&gt;</a></span> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c1">f</font> <a href="rfinseq.html#K2" title="RFINSEQ:func.2">/^</a> 1</span>)</span> <a href="finseq_1.html#K17" title="FINSEQ_1:func.17">|</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">q</font> <a href="finseq_4.html#K5" title="FINSEQ_4:func.5">..</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">f</font> <a href="rfinseq.html#K2" title="RFINSEQ:func.2">/^</a> 1</span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="sprect_5.html#E7:10_1_2"><i><font color="Green" title="E22">A14</font></i></a>, <a class="ref" href="finseq_5.html#T27" title="FINSEQ_5:th.27">FINSEQ_5:27</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c1">f</font> <a href="rfinseq.html#K2" title="RFINSEQ:func.2">/^</a> 1</span>)</span> <a href="finseq_5.html#K1" title="FINSEQ_5:func.1">-:</a> <font color="Maroon" title="c3">q</font>
<b>by </b><i><a class="ref" href="finseq_5.html#D1" title="FINSEQ_5:def.1">FINSEQ_5:def 1</a></i>
;<br/><a NAME="E10:10_1_2"/><b>then </b><i><font color="Green" title="E24">A16</font></i>: 
 <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">f</font> <a href="rfinseq.html#K2" title="RFINSEQ:func.2">/^</a> 1</span>)</span> <a href="finseq_5.html#K1" title="FINSEQ_5:func.1">-:</a> <font color="Maroon" title="c3">q</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c1">f</font> <a href="rfinseq.html#K2" title="RFINSEQ:func.2">/^</a> 1</span>)</span> <a href="finseq_4.html#K6" title="FINSEQ_4:func.6">-|</a> <font color="Maroon" title="c3">q</font></span>)</span></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1">(<span class="default"><a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p2"><a href="binarith.html#K11" title="BINARITH:func.11">&lt;*</a><span class="default"><font color="Maroon" title="c3">q</font></span><a href="binarith.html#K11" title="BINARITH:func.11">*&gt;</a></span></span>)</span>
 <b>by </b><i><a class="ref" href="finseq_1.html#T44" title="FINSEQ_1:th.44">FINSEQ_1:44</a></i>;<br/><a NAME="E11:10_1_2"/>
not <font color="Maroon" title="c2">p</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c3">q</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 <b>by </b><i><a class="txt" href="sprect_5.html#E3:10"><i><font color="Green" title="E12">A3</font></i></a>, <a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></i>;<br/><a NAME="E12:10_1_2"/><b>then </b><i><font color="Green" title="E25">A17</font></i>: 
not <font color="Maroon" title="c2">p</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p1"><a href="binarith.html#K11" title="BINARITH:func.11">&lt;*</a><span class="default"><font color="Maroon" title="c3">q</font></span><a href="binarith.html#K11" title="BINARITH:func.11">*&gt;</a></span>
 <b>by </b><i><a class="ref" href="finseq_1.html#T55" title="FINSEQ_1:th.55">FINSEQ_1:55</a></i>;<br/><a NAME="E13:10_1_2"/><b>then </b>
<font color="Maroon" title="c2">p</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">f</font> <a href="rfinseq.html#K2" title="RFINSEQ:func.2">/^</a> 1</span>)</span> <a href="finseq_4.html#K6" title="FINSEQ_4:func.6">-|</a> <font color="Maroon" title="c3">q</font></span>)</span>
 <b>by </b><i><a class="txt" href="sprect_5.html#E6:10_1_2"><i><font color="Green" title="E21">A13</font></i></a>, <a class="txt" href="sprect_5.html#E10:10_1_2"><i><font color="Green" title="E24">A16</font></i></a>, <a class="ref" href="xboole_0.html#D2" title="XBOOLE_0:def.2">XBOOLE_0:def 2</a></i>;<br/><a NAME="E14:10_1_2"/><b>then </b><i><font color="Green" title="E26">A18</font></i>: 
not <font color="Maroon" title="c2">p</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">f</font> <a href="rfinseq.html#K2" title="RFINSEQ:func.2">/^</a> 1</span>)</span> <a href="finseq_4.html#K7" title="FINSEQ_4:func.7">|--</a> <font color="Maroon" title="c3">q</font></span>)</span>
 <b>by </b><i><a class="txt" href="sprect_5.html#E8:10_1_2"><i><font color="Green" title="E23">A15</font></i></a>, <a class="ref" href="xboole_0.html#T3" title="XBOOLE_0:th.3">XBOOLE_0:3</a></i>;<br/><a NAME="E15:10_1_2"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c1">f</font> <a href="rfinseq.html#K2" title="RFINSEQ:func.2">/^</a> 1</span>)</span> <a href="finseq_5.html#K2" title="FINSEQ_5:func.2">:-</a> <font color="Maroon" title="c3">q</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="binarith.html#K11" title="BINARITH:func.11">&lt;*</a><span class="default"><font color="Maroon" title="c3">q</font></span><a href="binarith.html#K11" title="BINARITH:func.11">*&gt;</a></span> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">f</font> <a href="rfinseq.html#K2" title="RFINSEQ:func.2">/^</a> 1</span>)</span> <a href="finseq_4.html#K7" title="FINSEQ_4:func.7">|--</a> <font color="Maroon" title="c3">q</font></span>)</span>
 <b>by </b><i><a class="txt" href="sprect_5.html#E7:10_1_2"><i><font color="Green" title="E22">A14</font></i></a>, <a class="ref" href="finseq_6.html#T45" title="FINSEQ_6:th.45">FINSEQ_6:45</a></i>;<br/><a NAME="E16:10_1_2"/><b>then </b>
 <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">f</font> <a href="rfinseq.html#K2" title="RFINSEQ:func.2">/^</a> 1</span>)</span> <a href="finseq_5.html#K2" title="FINSEQ_5:func.2">:-</a> <font color="Maroon" title="c3">q</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p2"><a href="binarith.html#K11" title="BINARITH:func.11">&lt;*</a><span class="default"><font color="Maroon" title="c3">q</font></span><a href="binarith.html#K11" title="BINARITH:func.11">*&gt;</a></span></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1">(<span class="default"><a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c1">f</font> <a href="rfinseq.html#K2" title="RFINSEQ:func.2">/^</a> 1</span>)</span> <a href="finseq_4.html#K7" title="FINSEQ_4:func.7">|--</a> <font color="Maroon" title="c3">q</font></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="finseq_1.html#T44" title="FINSEQ_1:th.44">FINSEQ_1:44</a></i>;<br/><a NAME="E17:10_1_2"/><b>then </b>
not <font color="Maroon" title="c2">p</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">f</font> <a href="rfinseq.html#K2" title="RFINSEQ:func.2">/^</a> 1</span>)</span> <a href="finseq_5.html#K2" title="FINSEQ_5:func.2">:-</a> <font color="Maroon" title="c3">q</font></span>)</span>
 <b>by </b><i><a class="txt" href="sprect_5.html#E12:10_1_2"><i><font color="Green" title="E25">A17</font></i></a>, <a class="txt" href="sprect_5.html#E14:10_1_2"><i><font color="Green" title="E26">A18</font></i></a>, <a class="ref" href="xboole_0.html#D2" title="XBOOLE_0:def.2">XBOOLE_0:def 2</a></i>;<br/><a NAME="E18:10_1_2"/><b>then </b>
not <font color="Maroon" title="c2">p</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">f</font> <a href="finseq_5.html#K2" title="FINSEQ_5:func.2">:-</a> <font color="Maroon" title="c3">q</font></span>)</span>
 <b>by </b><i><a class="txt" href="sprect_5.html#E1:10"><i><font color="Green" title="E10">A1</font></i></a>, <a class="txt" href="sprect_5.html#E3:10"><i><font color="Green" title="E12">A3</font></i></a>, <a class="txt" href="sprect_5.html#E1:10_1_2"><i><font color="Green" title="E16">A8</font></i></a>, <a class="ref" href="finseq_6.html#T89" title="FINSEQ_6:th.89">FINSEQ_6:89</a></i>;<br/><a NAME="E19:10_1_2"/><b>then </b>
<font color="Maroon" title="c2">p</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c1">f</font> <a href="finseq_5.html#K1" title="FINSEQ_5:func.1">-:</a> <font color="Maroon" title="c3">q</font></span>)</span> <a href="rfinseq.html#K2" title="RFINSEQ:func.2">/^</a> 1</span>)</span></span>)</span> <a href="subset_1.html#K6" title="SUBSET_1:func.6">\</a> <span class="p1">(<span class="default"><a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">f</font> <a href="finseq_5.html#K2" title="FINSEQ_5:func.2">:-</a> <font color="Maroon" title="c3">q</font></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="sprect_5.html#E5:10_1_2"><i><font color="Green" title="E20">A12</font></i></a>, <a class="ref" href="xboole_0.html#D4" title="XBOOLE_0:def.4">XBOOLE_0:def 4</a></i>;<br/><b>hence </b><font color="Maroon" title="c2">p</font> <a href="finseq_4.html#K5" title="FINSEQ_4:func.5">..</a> <span class="p1">(<span class="default"><a href="finseq_6.html#K1" title="FINSEQ_6:func.1">Rotate</a> <font color="Maroon" title="c1">f</font>,<font color="Maroon" title="c3">q</font></span>)</span> = 
<span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">f</font> <a href="finseq_5.html#K2" title="FINSEQ_5:func.2">:-</a> <font color="Maroon" title="c3">q</font></span>)</span></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="finseq_4.html#K5" title="FINSEQ_4:func.5">..</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c1">f</font> <a href="finseq_5.html#K1" title="FINSEQ_5:func.1">-:</a> <font color="Maroon" title="c3">q</font></span>)</span> <a href="rfinseq.html#K2" title="RFINSEQ:func.2">/^</a> 1</span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="sprect_5.html#E2:10"><i><font color="Green" title="E11">A2</font></i></a>, <a class="ref" href="finseq_6.html#T9" title="FINSEQ_6:th.9">FINSEQ_6:9</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p3">(<span class="default"><font color="Maroon" title="c3">q</font> <a href="finseq_4.html#K5" title="FINSEQ_4:func.5">..</a> <font color="Maroon" title="c1">f</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> 1</span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="finseq_4.html#K5" title="FINSEQ_4:func.5">..</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 1</span>)</span>
<b>by </b><i><a class="txt" href="sprect_5.html#E1:10"><i><font color="Green" title="E10">A1</font></i></a>, <a class="txt" href="sprect_5.html#E3:10_1_2"><i><font color="Green" title="E18">A10</font></i></a>, <a class="ref" href="finseq_5.html#T53" title="FINSEQ_5:th.53">FINSEQ_5:53</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="finseq_4.html#K5" title="FINSEQ_4:func.5">..</a> <font color="Maroon" title="c1">f</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">q</font> <a href="finseq_4.html#K5" title="FINSEQ_4:func.5">..</a> <font color="Maroon" title="c1">f</font></span>)</span>

;<br/><br/></div><b>end;</b></div></div><b>end;</b></div>

</div>
