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<div class="add">

<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="23_1_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:23_1_1_1"/>
(  not <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K2">rng</a> <font color="Maroon">c<sub>3</sub></font> or <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K2">rng</a> <font color="Maroon">c<sub>3</sub></font> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="23_1_1_1_1"><b>suppose </b></a><a NAME="E1:23_1_1_1_1"/>
not <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K2">rng</a> <font color="Maroon">c<sub>3</sub></font>
 ;<br/><div class="add"><b>hence </b><a NAME="E2:23_1_1_1_1"/>
not  <a href="finseq_6.html#K1">Rotate</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></font> is <a href="funct_1.html#V3">constant</a>
 <b>by </b><i><a class="ref" href="finseq_6.html#D2">FINSEQ_6:def 2</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="23_1_1_1_2"><b>suppose </b></a><a NAME="E1:23_1_1_1_2"/><i><font color="Green">E17</font></i>: 
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K2">rng</a> <font color="Maroon">c<sub>3</sub></font>
 ;<br/><div class="add"><b>consider </b><font color="Maroon">c<sub>4</sub></font>, <font color="Maroon">c<sub>5</sub></font> being   <a href="nat_1.html#NM1">Nat</a><b> such that </b><br/><a NAME="E3:23_1_1_1_2"/><i><font color="Green">E18</font></i>: 
<font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <font color="Maroon">c<sub>3</sub></font>
 <b>and </b><br/><a NAME="E4:23_1_1_1_2"/><i><font color="Green">E19</font></i>: 
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <font color="Maroon">c<sub>3</sub></font>
 <b>and </b><br/><a NAME="E5:23_1_1_1_2"/><i><font color="Green">E20</font></i>: 
<font color="Maroon">c<sub>3</sub></font> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>3</sub></font> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">c<sub>5</sub></font>
 <b>by </b><i><a class="ref" href="revrot_1.html#D1" target="_self">Def1</a></i>;<br/><a NAME="E6:23_1_1_1_2"/><i><font color="Green">E21</font></i>: 
 <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="finseq_6.html#K1">Rotate</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K4">dom</a> <font color="Maroon">c<sub>3</sub></font>
 <b>by </b><i><a class="ref" href="revrot_1.html#T15" target="_self">Th15</a></i>;<br/><a NAME="E7:23_1_1_1_2"/><i><font color="Green">E22</font></i>: 
( 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>4</sub></font> &amp; <font color="Maroon">c<sub>4</sub></font> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>3</sub></font> )
 <b>by </b><i><a class="txt" href="revrot_1.html#E3:23_1_1_1_2"><i><font color="Green">E18</font></i></a>, <a class="ref" href="finseq_3.html#T27">FINSEQ_3:27</a></i>;<br/><a NAME="E8:23_1_1_1_2"/><i><font color="Green">E23</font></i>: 
( 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>5</sub></font> &amp; <font color="Maroon">c<sub>5</sub></font> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>3</sub></font> )
 <b>by </b><i><a class="txt" href="revrot_1.html#E4:23_1_1_1_2"><i><font color="Green">E19</font></i></a>, <a class="ref" href="finseq_3.html#T27">FINSEQ_3:27</a></i>;<br/><b>thus </b><a NAME="E9:23_1_1_1_2"/>
not  <a href="finseq_6.html#K1">Rotate</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></font> is <a href="funct_1.html#V3">constant</a>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="23_1_1_1_2_1"><b>proof </b></a><div class="add">

<a NAME="E1:23_1_1_1_2_1"/><i><font color="Green">E24</font></i>: 
<font color="Maroon">c<sub>2</sub></font> <a href="finseq_4.html#K5">..</a> <font color="Maroon">c<sub>3</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="revrot_1.html#E1:23_1_1_1_2"><i><font color="Green">E17</font></i></a>, <a class="ref" href="finseq_4.html#T31">FINSEQ_4:31</a></i>;<br/>
<a NAME="E2:23_1_1_1_2_1"/><i><font color="Green">E25</font></i>: 
1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>2</sub></font> <a href="finseq_4.html#K5">..</a> <font color="Maroon">c<sub>3</sub></font>
 
<b>by </b><i><a class="txt" href="revrot_1.html#E1:23_1_1_1_2"><i><font color="Green">E17</font></i></a>, <a class="ref" href="finseq_4.html#T31">FINSEQ_4:31</a></i>;<br/>
<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="23_1_1_1_2_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:23_1_1_1_2_1_1"/>
( ( <font color="Maroon">c<sub>4</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>2</sub></font> <a href="finseq_4.html#K5">..</a> <font color="Maroon">c<sub>3</sub></font> &amp; <font color="Maroon">c<sub>5</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>2</sub></font> <a href="finseq_4.html#K5">..</a> <font color="Maroon">c<sub>3</sub></font> ) or ( <font color="Maroon">c<sub>4</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>2</sub></font> <a href="finseq_4.html#K5">..</a> <font color="Maroon">c<sub>3</sub></font> &amp; <font color="Maroon">c<sub>5</sub></font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <font color="Maroon">c<sub>2</sub></font> <a href="finseq_4.html#K5">..</a> <font color="Maroon">c<sub>3</sub></font> ) or ( <font color="Maroon">c<sub>5</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>2</sub></font> <a href="finseq_4.html#K5">..</a> <font color="Maroon">c<sub>3</sub></font> &amp; <font color="Maroon">c<sub>4</sub></font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <font color="Maroon">c<sub>2</sub></font> <a href="finseq_4.html#K5">..</a> <font color="Maroon">c<sub>3</sub></font> ) or ( <font color="Maroon">c<sub>5</sub></font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <font color="Maroon">c<sub>2</sub></font> <a href="finseq_4.html#K5">..</a> <font color="Maroon">c<sub>3</sub></font> &amp; <font color="Maroon">c<sub>4</sub></font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <font color="Maroon">c<sub>2</sub></font> <a href="finseq_4.html#K5">..</a> <font color="Maroon">c<sub>3</sub></font> ) )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="23_1_1_1_2_1_1_1"><b>suppose </b></a><b>that </b><a NAME="E1:23_1_1_1_2_1_1_1"/><i><font color="Green">E26</font></i>: 
<font color="Maroon">c<sub>4</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>2</sub></font> <a href="finseq_4.html#K5">..</a> <font color="Maroon">c<sub>3</sub></font>
 <b>and </b><br/><a NAME="E2:23_1_1_1_2_1_1_1"/><i><font color="Green">E27</font></i>: 
<font color="Maroon">c<sub>5</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>2</sub></font> <a href="finseq_4.html#K5">..</a> <font color="Maroon">c<sub>3</sub></font>
 ;<br/><div class="add"><a NAME="E3:23_1_1_1_2_1_1_1"/><i><font color="Green">E28</font></i>: 
<font color="Maroon">c<sub>3</sub></font> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="finseq_6.html#K1">Rotate</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="finseq_4.html#K4">/.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span> <a href="binarith.html#K5">-'</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="finseq_4.html#K5">..</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="revrot_1.html#E1:23_1_1_1_2"><i><font color="Green">E17</font></i></a>, <a class="txt" href="revrot_1.html#E7:23_1_1_1_2"><i><font color="Green">E22</font></i></a>, <a class="txt" href="revrot_1.html#E1:23_1_1_1_2_1_1_1"><i><font color="Green">E26</font></i></a>, <a class="ref" href="revrot_1.html#T18" target="_self">Th18</a></i>;<br/><a NAME="E4:23_1_1_1_2_1_1_1"/><i><font color="Green">E29</font></i>: 
<font color="Maroon">c<sub>3</sub></font> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="finseq_6.html#K1">Rotate</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="finseq_4.html#K4">/.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span> <a href="binarith.html#K5">-'</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="finseq_4.html#K5">..</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="revrot_1.html#E1:23_1_1_1_2"><i><font color="Green">E17</font></i></a>, <a class="txt" href="revrot_1.html#E8:23_1_1_1_2"><i><font color="Green">E23</font></i></a>, <a class="txt" href="revrot_1.html#E2:23_1_1_1_2_1_1_1"><i><font color="Green">E27</font></i></a>, <a class="ref" href="revrot_1.html#T18" target="_self">Th18</a></i>;<br/><a NAME="E5:23_1_1_1_2_1_1_1"/>
<font color="Maroon">c<sub>4</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="binarith.html#K5">-'</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="finseq_4.html#K5">..</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="nat_1.html#T29">NAT_1:29</a></i>;<br/><a NAME="E6:23_1_1_1_2_1_1_1"/><b>then </b>
1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="binarith.html#K5">-'</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="finseq_4.html#K5">..</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="revrot_1.html#E7:23_1_1_1_2"><i><font color="Green">E22</font></i></a>, <a class="ref" href="xxreal_0.html#T2">XXREAL_0:2</a></i>;<br/><a NAME="E7:23_1_1_1_2_1_1_1"/><b>then </b><i><font color="Green">E30</font></i>: 
1 <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K1">+</a> <span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span> <a href="binarith.html#K5">-'</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="finseq_4.html#K5">..</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="revrot_1.html#E1:23_1_1_1_2_1"><i><font color="Green">E24</font></i></a>, <a class="ref" href="binarith.html#T56">BINARITH:56</a></i>;<br/><a NAME="E8:23_1_1_1_2_1_1_1"/>
<font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="finseq_4.html#K5">..</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="revrot_1.html#E1:23_1_1_1_2_1_1_1"><i><font color="Green">E26</font></i></a>, <a class="ref" href="xreal_1.html#T8">XREAL_1:8</a></i>;<br/><a NAME="E9:23_1_1_1_2_1_1_1"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K1">+</a> <span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span> <a href="binarith.html#K5">-'</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="finseq_4.html#K5">..</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <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="ref" href="sprect_3.html#T6">SPRECT_3:6</a></i>;<br/><a NAME="E10:23_1_1_1_2_1_1_1"/><b>then </b><i><font color="Green">E31</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K1">+</a> <span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span> <a href="binarith.html#K5">-'</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="finseq_4.html#K5">..</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <font color="Maroon">c<sub>3</sub></font>
 <b>by </b><i><a class="txt" href="revrot_1.html#E7:23_1_1_1_2_1_1_1"><i><font color="Green">E30</font></i></a>, <a class="ref" href="finseq_3.html#T27">FINSEQ_3:27</a></i>;<br/><a NAME="E11:23_1_1_1_2_1_1_1"/>
<font color="Maroon">c<sub>5</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>5</sub></font> <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="binarith.html#K5">-'</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="finseq_4.html#K5">..</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="nat_1.html#T29">NAT_1:29</a></i>;<br/><a NAME="E12:23_1_1_1_2_1_1_1"/><b>then </b>
1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>5</sub></font> <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="binarith.html#K5">-'</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="finseq_4.html#K5">..</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="revrot_1.html#E8:23_1_1_1_2"><i><font color="Green">E23</font></i></a>, <a class="ref" href="xxreal_0.html#T2">XXREAL_0:2</a></i>;<br/><a NAME="E13:23_1_1_1_2_1_1_1"/><b>then </b><i><font color="Green">E32</font></i>: 
1 <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="nat_1.html#K1">+</a> <span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span> <a href="binarith.html#K5">-'</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="finseq_4.html#K5">..</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="revrot_1.html#E1:23_1_1_1_2_1"><i><font color="Green">E24</font></i></a>, <a class="ref" href="binarith.html#T56">BINARITH:56</a></i>;<br/><a NAME="E14:23_1_1_1_2_1_1_1"/>
<font color="Maroon">c<sub>5</sub></font> <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="finseq_4.html#K5">..</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="revrot_1.html#E2:23_1_1_1_2_1_1_1"><i><font color="Green">E27</font></i></a>, <a class="ref" href="xreal_1.html#T8">XREAL_1:8</a></i>;<br/><a NAME="E15:23_1_1_1_2_1_1_1"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="nat_1.html#K1">+</a> <span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span> <a href="binarith.html#K5">-'</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="finseq_4.html#K5">..</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <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="ref" href="sprect_3.html#T6">SPRECT_3:6</a></i>;<br/><a NAME="E16:23_1_1_1_2_1_1_1"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="nat_1.html#K1">+</a> <span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span> <a href="binarith.html#K5">-'</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="finseq_4.html#K5">..</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <font color="Maroon">c<sub>3</sub></font>
 <b>by </b><i><a class="txt" href="revrot_1.html#E13:23_1_1_1_2_1_1_1"><i><font color="Green">E32</font></i></a>, <a class="ref" href="finseq_3.html#T27">FINSEQ_3:27</a></i>;<br/><b>hence </b><a NAME="E17:23_1_1_1_2_1_1_1"/>
not  <a href="finseq_6.html#K1">Rotate</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></font> is <a href="funct_1.html#V3">constant</a>
 <b>by </b><i><a class="txt" href="revrot_1.html#E5:23_1_1_1_2"><i><font color="Green">E20</font></i></a>, <a class="txt" href="revrot_1.html#E6:23_1_1_1_2"><i><font color="Green">E21</font></i></a>, <a class="txt" href="revrot_1.html#E3:23_1_1_1_2_1_1_1"><i><font color="Green">E28</font></i></a>, <a class="txt" href="revrot_1.html#E4:23_1_1_1_2_1_1_1"><i><font color="Green">E29</font></i></a>, <a class="txt" href="revrot_1.html#E10:23_1_1_1_2_1_1_1"><i><font color="Green">E31</font></i></a>, <a class="ref" href="revrot_1.html#D1" target="_self">Def1</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="23_1_1_1_2_1_1_2"><b>suppose </b></a><b>that </b><a NAME="E1:23_1_1_1_2_1_1_2"/><i><font color="Green">E26</font></i>: 
<font color="Maroon">c<sub>4</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>2</sub></font> <a href="finseq_4.html#K5">..</a> <font color="Maroon">c<sub>3</sub></font>
 <b>and </b><br/><a NAME="E2:23_1_1_1_2_1_1_2"/><i><font color="Green">E27</font></i>: 
<font color="Maroon">c<sub>5</sub></font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <font color="Maroon">c<sub>2</sub></font> <a href="finseq_4.html#K5">..</a> <font color="Maroon">c<sub>3</sub></font>
 ;<br/><div class="add"><a NAME="E3:23_1_1_1_2_1_1_2"/><i><font color="Green">E28</font></i>: 
<font color="Maroon">c<sub>3</sub></font> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="finseq_6.html#K1">Rotate</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="finseq_4.html#K4">/.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span> <a href="binarith.html#K5">-'</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="finseq_4.html#K5">..</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="revrot_1.html#E1:23_1_1_1_2"><i><font color="Green">E17</font></i></a>, <a class="txt" href="revrot_1.html#E7:23_1_1_1_2"><i><font color="Green">E22</font></i></a>, <a class="txt" href="revrot_1.html#E1:23_1_1_1_2_1_1_2"><i><font color="Green">E26</font></i></a>, <a class="ref" href="revrot_1.html#T18" target="_self">Th18</a></i>;<br/><a NAME="E4:23_1_1_1_2_1_1_2"/><i><font color="Green">E29</font></i>: 
<font color="Maroon">c<sub>3</sub></font> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="finseq_6.html#K1">Rotate</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="finseq_4.html#K4">/.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="binarith.html#K5">-'</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="finseq_4.html#K5">..</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="revrot_1.html#E1:23_1_1_1_2"><i><font color="Green">E17</font></i></a>, <a class="txt" href="revrot_1.html#E8:23_1_1_1_2"><i><font color="Green">E23</font></i></a>, <a class="txt" href="revrot_1.html#E2:23_1_1_1_2_1_1_2"><i><font color="Green">E27</font></i></a>, <a class="ref" href="revrot_1.html#T10" target="_self">Th10</a></i>;<br/><a NAME="E5:23_1_1_1_2_1_1_2"/>
<font color="Maroon">c<sub>4</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="binarith.html#K5">-'</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="finseq_4.html#K5">..</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="nat_1.html#T29">NAT_1:29</a></i>;<br/><a NAME="E6:23_1_1_1_2_1_1_2"/><b>then </b>
1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="binarith.html#K5">-'</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="finseq_4.html#K5">..</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="revrot_1.html#E7:23_1_1_1_2"><i><font color="Green">E22</font></i></a>, <a class="ref" href="xxreal_0.html#T2">XXREAL_0:2</a></i>;<br/><a NAME="E7:23_1_1_1_2_1_1_2"/><b>then </b><i><font color="Green">E30</font></i>: 
1 <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K1">+</a> <span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span> <a href="binarith.html#K5">-'</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="finseq_4.html#K5">..</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="revrot_1.html#E1:23_1_1_1_2_1"><i><font color="Green">E24</font></i></a>, <a class="ref" href="binarith.html#T56">BINARITH:56</a></i>;<br/><a NAME="E8:23_1_1_1_2_1_1_2"/>
<font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="finseq_4.html#K5">..</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="revrot_1.html#E1:23_1_1_1_2_1_1_2"><i><font color="Green">E26</font></i></a>, <a class="ref" href="xreal_1.html#T8">XREAL_1:8</a></i>;<br/><a NAME="E9:23_1_1_1_2_1_1_2"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K1">+</a> <span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span> <a href="binarith.html#K5">-'</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="finseq_4.html#K5">..</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <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="ref" href="sprect_3.html#T6">SPRECT_3:6</a></i>;<br/><a NAME="E10:23_1_1_1_2_1_1_2"/><b>then </b><i><font color="Green">E31</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K1">+</a> <span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span> <a href="binarith.html#K5">-'</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="finseq_4.html#K5">..</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <font color="Maroon">c<sub>3</sub></font>
 <b>by </b><i><a class="txt" href="revrot_1.html#E7:23_1_1_1_2_1_1_2"><i><font color="Green">E30</font></i></a>, <a class="ref" href="finseq_3.html#T27">FINSEQ_3:27</a></i>;<br/><a NAME="E11:23_1_1_1_2_1_1_2"/>
1 <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="finseq_4.html#K5">..</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>5</sub></font> <a href="nat_1.html#K1">+</a> 1
 <b>by </b><i><a class="txt" href="revrot_1.html#E2:23_1_1_1_2_1_1_2"><i><font color="Green">E27</font></i></a>, <a class="ref" href="xreal_1.html#T8">XREAL_1:8</a></i>;<br/><a NAME="E12:23_1_1_1_2_1_1_2"/><b>then </b><i><font color="Green">E32</font></i>: 
1 <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="binarith.html#K5">-'</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="finseq_4.html#K5">..</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>
 <b>by </b><i><a class="ref" href="sprect_3.html#T8">SPRECT_3:8</a></i>;<br/><a NAME="E13:23_1_1_1_2_1_1_2"/>
<font color="Maroon">c<sub>5</sub></font> <a href="nat_1.html#K1">+</a> 1 <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="finseq_4.html#K5">..</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="revrot_1.html#E8:23_1_1_1_2"><i><font color="Green">E23</font></i></a>, <a class="txt" href="revrot_1.html#E2:23_1_1_1_2_1"><i><font color="Green">E25</font></i></a>, <a class="ref" href="xreal_1.html#T9">XREAL_1:9</a></i>;<br/><a NAME="E14:23_1_1_1_2_1_1_2"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="binarith.html#K5">-'</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="finseq_4.html#K5">..</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <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="ref" href="sprect_3.html#T6">SPRECT_3:6</a></i>;<br/><a NAME="E15:23_1_1_1_2_1_1_2"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="binarith.html#K5">-'</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="finseq_4.html#K5">..</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <font color="Maroon">c<sub>3</sub></font>
 <b>by </b><i><a class="txt" href="revrot_1.html#E12:23_1_1_1_2_1_1_2"><i><font color="Green">E32</font></i></a>, <a class="ref" href="finseq_3.html#T27">FINSEQ_3:27</a></i>;<br/><b>hence </b><a NAME="E16:23_1_1_1_2_1_1_2"/>
not  <a href="finseq_6.html#K1">Rotate</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></font> is <a href="funct_1.html#V3">constant</a>
 <b>by </b><i><a class="txt" href="revrot_1.html#E5:23_1_1_1_2"><i><font color="Green">E20</font></i></a>, <a class="txt" href="revrot_1.html#E6:23_1_1_1_2"><i><font color="Green">E21</font></i></a>, <a class="txt" href="revrot_1.html#E3:23_1_1_1_2_1_1_2"><i><font color="Green">E28</font></i></a>, <a class="txt" href="revrot_1.html#E4:23_1_1_1_2_1_1_2"><i><font color="Green">E29</font></i></a>, <a class="txt" href="revrot_1.html#E10:23_1_1_1_2_1_1_2"><i><font color="Green">E31</font></i></a>, <a class="ref" href="revrot_1.html#D1" target="_self">Def1</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="23_1_1_1_2_1_1_3"><b>suppose </b></a><b>that </b><a NAME="E1:23_1_1_1_2_1_1_3"/><i><font color="Green">E26</font></i>: 
<font color="Maroon">c<sub>5</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>2</sub></font> <a href="finseq_4.html#K5">..</a> <font color="Maroon">c<sub>3</sub></font>
 <b>and </b><br/><a NAME="E2:23_1_1_1_2_1_1_3"/><i><font color="Green">E27</font></i>: 
<font color="Maroon">c<sub>4</sub></font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <font color="Maroon">c<sub>2</sub></font> <a href="finseq_4.html#K5">..</a> <font color="Maroon">c<sub>3</sub></font>
 ;<br/><div class="add"><a NAME="E3:23_1_1_1_2_1_1_3"/><i><font color="Green">E28</font></i>: 
<font color="Maroon">c<sub>3</sub></font> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="finseq_6.html#K1">Rotate</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="finseq_4.html#K4">/.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span> <a href="binarith.html#K5">-'</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="finseq_4.html#K5">..</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="revrot_1.html#E1:23_1_1_1_2"><i><font color="Green">E17</font></i></a>, <a class="txt" href="revrot_1.html#E8:23_1_1_1_2"><i><font color="Green">E23</font></i></a>, <a class="txt" href="revrot_1.html#E1:23_1_1_1_2_1_1_3"><i><font color="Green">E26</font></i></a>, <a class="ref" href="revrot_1.html#T18" target="_self">Th18</a></i>;<br/><a NAME="E4:23_1_1_1_2_1_1_3"/><i><font color="Green">E29</font></i>: 
<font color="Maroon">c<sub>3</sub></font> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="finseq_6.html#K1">Rotate</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="finseq_4.html#K4">/.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="binarith.html#K5">-'</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="finseq_4.html#K5">..</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="revrot_1.html#E1:23_1_1_1_2"><i><font color="Green">E17</font></i></a>, <a class="txt" href="revrot_1.html#E7:23_1_1_1_2"><i><font color="Green">E22</font></i></a>, <a class="txt" href="revrot_1.html#E2:23_1_1_1_2_1_1_3"><i><font color="Green">E27</font></i></a>, <a class="ref" href="revrot_1.html#T10" target="_self">Th10</a></i>;<br/><a NAME="E5:23_1_1_1_2_1_1_3"/>
<font color="Maroon">c<sub>5</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>5</sub></font> <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="binarith.html#K5">-'</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="finseq_4.html#K5">..</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="nat_1.html#T29">NAT_1:29</a></i>;<br/><a NAME="E6:23_1_1_1_2_1_1_3"/><b>then </b>
1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>5</sub></font> <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="binarith.html#K5">-'</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="finseq_4.html#K5">..</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="revrot_1.html#E8:23_1_1_1_2"><i><font color="Green">E23</font></i></a>, <a class="ref" href="xxreal_0.html#T2">XXREAL_0:2</a></i>;<br/><a NAME="E7:23_1_1_1_2_1_1_3"/><b>then </b><i><font color="Green">E30</font></i>: 
1 <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="nat_1.html#K1">+</a> <span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span> <a href="binarith.html#K5">-'</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="finseq_4.html#K5">..</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="revrot_1.html#E1:23_1_1_1_2_1"><i><font color="Green">E24</font></i></a>, <a class="ref" href="binarith.html#T56">BINARITH:56</a></i>;<br/><a NAME="E8:23_1_1_1_2_1_1_3"/>
<font color="Maroon">c<sub>5</sub></font> <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="finseq_4.html#K5">..</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="revrot_1.html#E1:23_1_1_1_2_1_1_3"><i><font color="Green">E26</font></i></a>, <a class="ref" href="xreal_1.html#T8">XREAL_1:8</a></i>;<br/><a NAME="E9:23_1_1_1_2_1_1_3"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="nat_1.html#K1">+</a> <span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span> <a href="binarith.html#K5">-'</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="finseq_4.html#K5">..</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <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="ref" href="sprect_3.html#T6">SPRECT_3:6</a></i>;<br/><a NAME="E10:23_1_1_1_2_1_1_3"/><b>then </b><i><font color="Green">E31</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="nat_1.html#K1">+</a> <span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span> <a href="binarith.html#K5">-'</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="finseq_4.html#K5">..</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <font color="Maroon">c<sub>3</sub></font>
 <b>by </b><i><a class="txt" href="revrot_1.html#E7:23_1_1_1_2_1_1_3"><i><font color="Green">E30</font></i></a>, <a class="ref" href="finseq_3.html#T27">FINSEQ_3:27</a></i>;<br/><a NAME="E11:23_1_1_1_2_1_1_3"/>
1 <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="finseq_4.html#K5">..</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K1">+</a> 1
 <b>by </b><i><a class="txt" href="revrot_1.html#E2:23_1_1_1_2_1_1_3"><i><font color="Green">E27</font></i></a>, <a class="ref" href="xreal_1.html#T8">XREAL_1:8</a></i>;<br/><a NAME="E12:23_1_1_1_2_1_1_3"/><b>then </b><i><font color="Green">E32</font></i>: 
1 <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="binarith.html#K5">-'</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="finseq_4.html#K5">..</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>
 <b>by </b><i><a class="ref" href="sprect_3.html#T8">SPRECT_3:8</a></i>;<br/><a NAME="E13:23_1_1_1_2_1_1_3"/>
<font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K1">+</a> 1 <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="finseq_4.html#K5">..</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="revrot_1.html#E7:23_1_1_1_2"><i><font color="Green">E22</font></i></a>, <a class="txt" href="revrot_1.html#E2:23_1_1_1_2_1"><i><font color="Green">E25</font></i></a>, <a class="ref" href="xreal_1.html#T9">XREAL_1:9</a></i>;<br/><a NAME="E14:23_1_1_1_2_1_1_3"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="binarith.html#K5">-'</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="finseq_4.html#K5">..</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <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="ref" href="sprect_3.html#T6">SPRECT_3:6</a></i>;<br/><a NAME="E15:23_1_1_1_2_1_1_3"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="binarith.html#K5">-'</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="finseq_4.html#K5">..</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <font color="Maroon">c<sub>3</sub></font>
 <b>by </b><i><a class="txt" href="revrot_1.html#E12:23_1_1_1_2_1_1_3"><i><font color="Green">E32</font></i></a>, <a class="ref" href="finseq_3.html#T27">FINSEQ_3:27</a></i>;<br/><b>hence </b><a NAME="E16:23_1_1_1_2_1_1_3"/>
not  <a href="finseq_6.html#K1">Rotate</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></font> is <a href="funct_1.html#V3">constant</a>
 <b>by </b><i><a class="txt" href="revrot_1.html#E5:23_1_1_1_2"><i><font color="Green">E20</font></i></a>, <a class="txt" href="revrot_1.html#E6:23_1_1_1_2"><i><font color="Green">E21</font></i></a>, <a class="txt" href="revrot_1.html#E3:23_1_1_1_2_1_1_3"><i><font color="Green">E28</font></i></a>, <a class="txt" href="revrot_1.html#E4:23_1_1_1_2_1_1_3"><i><font color="Green">E29</font></i></a>, <a class="txt" href="revrot_1.html#E10:23_1_1_1_2_1_1_3"><i><font color="Green">E31</font></i></a>, <a class="ref" href="revrot_1.html#D1" target="_self">Def1</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="23_1_1_1_2_1_1_4"><b>suppose </b></a><b>that </b><a NAME="E1:23_1_1_1_2_1_1_4"/><i><font color="Green">E26</font></i>: 
<font color="Maroon">c<sub>5</sub></font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <font color="Maroon">c<sub>2</sub></font> <a href="finseq_4.html#K5">..</a> <font color="Maroon">c<sub>3</sub></font>
 <b>and </b><br/><a NAME="E2:23_1_1_1_2_1_1_4"/><i><font color="Green">E27</font></i>: 
<font color="Maroon">c<sub>4</sub></font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <font color="Maroon">c<sub>2</sub></font> <a href="finseq_4.html#K5">..</a> <font color="Maroon">c<sub>3</sub></font>
 ;<br/><div class="add"><a NAME="E3:23_1_1_1_2_1_1_4"/><i><font color="Green">E28</font></i>: 
<font color="Maroon">c<sub>3</sub></font> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="finseq_6.html#K1">Rotate</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="finseq_4.html#K4">/.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="binarith.html#K5">-'</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="finseq_4.html#K5">..</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="revrot_1.html#E1:23_1_1_1_2"><i><font color="Green">E17</font></i></a>, <a class="txt" href="revrot_1.html#E8:23_1_1_1_2"><i><font color="Green">E23</font></i></a>, <a class="txt" href="revrot_1.html#E1:23_1_1_1_2_1_1_4"><i><font color="Green">E26</font></i></a>, <a class="ref" href="revrot_1.html#T10" target="_self">Th10</a></i>;<br/><a NAME="E4:23_1_1_1_2_1_1_4"/><i><font color="Green">E29</font></i>: 
<font color="Maroon">c<sub>3</sub></font> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="finseq_6.html#K1">Rotate</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="finseq_4.html#K4">/.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="binarith.html#K5">-'</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="finseq_4.html#K5">..</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="revrot_1.html#E1:23_1_1_1_2"><i><font color="Green">E17</font></i></a>, <a class="txt" href="revrot_1.html#E7:23_1_1_1_2"><i><font color="Green">E22</font></i></a>, <a class="txt" href="revrot_1.html#E2:23_1_1_1_2_1_1_4"><i><font color="Green">E27</font></i></a>, <a class="ref" href="revrot_1.html#T10" target="_self">Th10</a></i>;<br/><a NAME="E5:23_1_1_1_2_1_1_4"/>
1 <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="finseq_4.html#K5">..</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>5</sub></font> <a href="nat_1.html#K1">+</a> 1
 <b>by </b><i><a class="txt" href="revrot_1.html#E1:23_1_1_1_2_1_1_4"><i><font color="Green">E26</font></i></a>, <a class="ref" href="xreal_1.html#T8">XREAL_1:8</a></i>;<br/><a NAME="E6:23_1_1_1_2_1_1_4"/><b>then </b><i><font color="Green">E30</font></i>: 
1 <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="binarith.html#K5">-'</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="finseq_4.html#K5">..</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>
 <b>by </b><i><a class="ref" href="sprect_3.html#T8">SPRECT_3:8</a></i>;<br/><a NAME="E7:23_1_1_1_2_1_1_4"/>
<font color="Maroon">c<sub>5</sub></font> <a href="nat_1.html#K1">+</a> 1 <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="finseq_4.html#K5">..</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="revrot_1.html#E8:23_1_1_1_2"><i><font color="Green">E23</font></i></a>, <a class="txt" href="revrot_1.html#E2:23_1_1_1_2_1"><i><font color="Green">E25</font></i></a>, <a class="ref" href="xreal_1.html#T9">XREAL_1:9</a></i>;<br/><a NAME="E8:23_1_1_1_2_1_1_4"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="binarith.html#K5">-'</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="finseq_4.html#K5">..</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <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="ref" href="sprect_3.html#T6">SPRECT_3:6</a></i>;<br/><a NAME="E9:23_1_1_1_2_1_1_4"/><b>then </b><i><font color="Green">E31</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="binarith.html#K5">-'</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="finseq_4.html#K5">..</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <font color="Maroon">c<sub>3</sub></font>
 <b>by </b><i><a class="txt" href="revrot_1.html#E6:23_1_1_1_2_1_1_4"><i><font color="Green">E30</font></i></a>, <a class="ref" href="finseq_3.html#T27">FINSEQ_3:27</a></i>;<br/><a NAME="E10:23_1_1_1_2_1_1_4"/>
1 <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="finseq_4.html#K5">..</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K1">+</a> 1
 <b>by </b><i><a class="txt" href="revrot_1.html#E2:23_1_1_1_2_1_1_4"><i><font color="Green">E27</font></i></a>, <a class="ref" href="xreal_1.html#T8">XREAL_1:8</a></i>;<br/><a NAME="E11:23_1_1_1_2_1_1_4"/><b>then </b><i><font color="Green">E32</font></i>: 
1 <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="binarith.html#K5">-'</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="finseq_4.html#K5">..</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>
 <b>by </b><i><a class="ref" href="sprect_3.html#T8">SPRECT_3:8</a></i>;<br/><a NAME="E12:23_1_1_1_2_1_1_4"/>
<font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K1">+</a> 1 <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="finseq_4.html#K5">..</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="revrot_1.html#E7:23_1_1_1_2"><i><font color="Green">E22</font></i></a>, <a class="txt" href="revrot_1.html#E2:23_1_1_1_2_1"><i><font color="Green">E25</font></i></a>, <a class="ref" href="xreal_1.html#T9">XREAL_1:9</a></i>;<br/><a NAME="E13:23_1_1_1_2_1_1_4"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="binarith.html#K5">-'</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="finseq_4.html#K5">..</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <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="ref" href="sprect_3.html#T6">SPRECT_3:6</a></i>;<br/><a NAME="E14:23_1_1_1_2_1_1_4"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="binarith.html#K5">-'</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="finseq_4.html#K5">..</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <font color="Maroon">c<sub>3</sub></font>
 <b>by </b><i><a class="txt" href="revrot_1.html#E11:23_1_1_1_2_1_1_4"><i><font color="Green">E32</font></i></a>, <a class="ref" href="finseq_3.html#T27">FINSEQ_3:27</a></i>;<br/><b>hence </b><a NAME="E15:23_1_1_1_2_1_1_4"/>
not  <a href="finseq_6.html#K1">Rotate</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></font> is <a href="funct_1.html#V3">constant</a>
 <b>by </b><i><a class="txt" href="revrot_1.html#E5:23_1_1_1_2"><i><font color="Green">E20</font></i></a>, <a class="txt" href="revrot_1.html#E6:23_1_1_1_2"><i><font color="Green">E21</font></i></a>, <a class="txt" href="revrot_1.html#E3:23_1_1_1_2_1_1_4"><i><font color="Green">E28</font></i></a>, <a class="txt" href="revrot_1.html#E4:23_1_1_1_2_1_1_4"><i><font color="Green">E29</font></i></a>, <a class="txt" href="revrot_1.html#E9:23_1_1_1_2_1_1_4"><i><font color="Green">E31</font></i></a>, <a class="ref" href="revrot_1.html#D1" target="_self">Def1</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div>

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

</div>
