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

<b>let </b><font color="Maroon">c<sub>1</sub></font> be   <a href="pre_topc.html#NM2">Point</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 2</span>)</span>;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font> be  non <a href="funct_1.html#V3">constant</a> <a href="goboard5.html#V2">standard</a> <a href="sprect_2.html#V1">clockwise_oriented</a> <a href="goboard5.html#NM1">special_circular_sequence</a>;<br/>



<b>set </b><font color="Maroon">c<sub>3</sub></font> =  <a href="finseq_6.html#K1">Rotate</a> <font color="Maroon">c<sub>2</sub></font>,<span class="p1">(<span class="default"><a href="pscomp_1.html#K29">N-min</a> <span class="p2">(<span class="default"><a href="topreal1.html#K5">L~</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span>;<br/>
<a NAME="E1:26"/><i><font color="Green">E19</font></i>: 
 <a href="topreal1.html#K5">L~</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a>  <a href="topreal1.html#K5">L~</a> <span class="p1">(<span class="default"><a href="finseq_6.html#K1">Rotate</a> <font color="Maroon">c<sub>2</sub></font>,<span class="p2">(<span class="default"><a href="pscomp_1.html#K29">N-min</a> <span class="p3">(<span class="default"><a href="topreal1.html#K5">L~</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="revrot_1.html#T33">REVROT_1:33</a></i>;<br/>
<a NAME="E2:26"/>
 <a href="pscomp_1.html#K29">N-min</a> <span class="p1">(<span class="default"><a href="topreal1.html#K5">L~</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="hidden.html#R2">in</a>  <a href="relset_1.html#K5">rng</a> <font color="Maroon">c<sub>2</sub></font>
 
<b>by </b><i><a class="ref" href="sprect_2.html#T43">SPRECT_2:43</a></i>;<br/>
<a NAME="E3:26"/><b>then </b><i><font color="Green">E20</font></i>: 
<span class="p1">(<span class="default"><a href="finseq_6.html#K1">Rotate</a> <font color="Maroon">c<sub>2</sub></font>,<span class="p2">(<span class="default"><a href="pscomp_1.html#K29">N-min</a> <span class="p3">(<span class="default"><a href="topreal1.html#K5">L~</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span> <a href="finseq_4.html#K4">/.</a> 1 <a href="hidden.html#R1">=</a>  <a href="pscomp_1.html#K29">N-min</a> <span class="p1">(<span class="default"><a href="topreal1.html#K5">L~</a> <span class="p2">(<span class="default"><a href="finseq_6.html#K1">Rotate</a> <font color="Maroon">c<sub>2</sub></font>,<span class="p3">(<span class="default"><a href="pscomp_1.html#K29">N-min</a> <span class="p4">(<span class="default"><a href="topreal1.html#K5">L~</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span></span>)</span>
 
<b>by </b><i><a class="txt" href="gobrd14.html#E1:26"><i><font color="Green">E19</font></i></a>, <a class="ref" href="finseq_6.html#T98">FINSEQ_6:98</a></i>;<br/>
<b>reconsider </b><font color="Maroon">c<sub>4</sub></font> = <font color="Maroon">c<sub>1</sub></font> as   <a href="pre_topc.html#NM2">Point</a> of <span class="p1">(<span class="default"><a href="euclid.html#K14">Euclid</a> 2</span>)</span> <b>by </b><i><a class="ref" href="topreal3.html#T13">TOPREAL3:13</a></i>;<br/>
<b>assume </b><a NAME="E5:26"/>
<font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R2">in</a>  <a href="goboard9.html#K3">RightComp</a> <font color="Maroon">c<sub>2</sub></font>
 ;<br/>

<a NAME="E6:26"/><b>then </b>
<font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R2">in</a>  <a href="goboard9.html#K3">RightComp</a> <span class="p1">(<span class="default"><a href="finseq_6.html#K1">Rotate</a> <font color="Maroon">c<sub>2</sub></font>,<span class="p2">(<span class="default"><a href="pscomp_1.html#K29">N-min</a> <span class="p3">(<span class="default"><a href="topreal1.html#K5">L~</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="revrot_1.html#T37">REVROT_1:37</a></i>;<br/>
<a NAME="E7:26"/><b>then </b>
<font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R2">in</a>  <a href="tops_1.html#K1">Int</a> <span class="p1">(<span class="default"><a href="goboard9.html#K3">RightComp</a> <span class="p2">(<span class="default"><a href="finseq_6.html#K1">Rotate</a> <font color="Maroon">c<sub>2</sub></font>,<span class="p3">(<span class="default"><a href="pscomp_1.html#K29">N-min</a> <span class="p4">(<span class="default"><a href="topreal1.html#K5">L~</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="tops_1.html#T55">TOPS_1:55</a></i>;<br/>
<b>then consider </b><font color="Maroon">c<sub>5</sub></font> being  <a href="xreal_0.html#V1">real</a>  <a href="ordinal1.html#NM1" target="_self">number</a> <b> such that </b><br/><a NAME="E9:26"/><i><font color="Green">E21</font></i>: 
<font color="Maroon">c<sub>5</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0
 <b>and </b><br/><a NAME="E10:26"/><i><font color="Green">E22</font></i>: 
 <a href="metric_1.html#K9">Ball</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font> <a href="tarski.html#R1">c=</a>  <a href="goboard9.html#K3">RightComp</a> <span class="p1">(<span class="default"><a href="finseq_6.html#K1">Rotate</a> <font color="Maroon">c<sub>2</sub></font>,<span class="p2">(<span class="default"><a href="pscomp_1.html#K29">N-min</a> <span class="p3">(<span class="default"><a href="topreal1.html#K5">L~</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="goboard6.html#T8">GOBOARD6:8</a></i>;<br/>
<b>reconsider </b><font color="Maroon">c<sub>6</sub></font> = <font color="Maroon">c<sub>5</sub></font> as   <a href="real_1.html#NM1">Real</a> <b>by </b><i><a class="ref" href="xreal_0.html#D1">XREAL_0:def 1</a></i>;<br/>
<a NAME="E12:26"/><i><font color="Green">E23</font></i>: 
 <a href="pscomp_1.html#K18">S-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K5">L~</a> <span class="p2">(<span class="default"><a href="sprect_1.html#K1">SpStSeq</a> <span class="p3">(<span class="default"><a href="topreal1.html#K5">L~</a> <span class="p4">(<span class="default"><a href="finseq_6.html#K1">Rotate</a> <font color="Maroon">c<sub>2</sub></font>,<span class="p5">(<span class="default"><a href="pscomp_1.html#K29">N-min</a> <span class="p0">(<span class="default"><a href="topreal1.html#K5">L~</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="pscomp_1.html#K18">S-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K5">L~</a> <span class="p2">(<span class="default"><a href="finseq_6.html#K1">Rotate</a> <font color="Maroon">c<sub>2</sub></font>,<span class="p3">(<span class="default"><a href="pscomp_1.html#K29">N-min</a> <span class="p4">(<span class="default"><a href="topreal1.html#K5">L~</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="sprect_1.html#T67">SPRECT_1:67</a></i>;<br/>
<a NAME="E13:26"/><i><font color="Green">E24</font></i>: 
 <a href="pscomp_1.html#K18">S-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K5">L~</a> <span class="p2">(<span class="default"><a href="sprect_1.html#K1">SpStSeq</a> <span class="p3">(<span class="default"><a href="topreal1.html#K5">L~</a> <span class="p4">(<span class="default"><a href="finseq_6.html#K1">Rotate</a> <font color="Maroon">c<sub>2</sub></font>,<span class="p5">(<span class="default"><a href="pscomp_1.html#K29">N-min</a> <span class="p0">(<span class="default"><a href="topreal1.html#K5">L~</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="pscomp_1.html#K3">inf</a> <span class="p1">(<span class="default"><a href="pscomp_1.html#K14">proj2</a>  <a href="relset_1.html#K10">.:</a> <span class="p2">(<span class="default"><a href="topreal1.html#K5">L~</a> <span class="p3">(<span class="default"><a href="sprect_1.html#K1">SpStSeq</a> <span class="p4">(<span class="default"><a href="topreal1.html#K5">L~</a> <span class="p5">(<span class="default"><a href="finseq_6.html#K1">Rotate</a> <font color="Maroon">c<sub>2</sub></font>,<span class="p0">(<span class="default"><a href="pscomp_1.html#K29">N-min</a> <span class="p1">(<span class="default"><a href="topreal1.html#K5">L~</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="sprect_1.html#T49">SPRECT_1:49</a></i>;<br/>
<a NAME="E14:26"/><i><font color="Green">E25</font></i>: 
<a href="pscomp_1.html#K14">proj2</a>  <a href="relset_1.html#K10">.:</a> <span class="p1">(<span class="default"><a href="topreal1.html#K5">L~</a> <span class="p2">(<span class="default"><a href="sprect_1.html#K1">SpStSeq</a> <span class="p3">(<span class="default"><a href="topreal1.html#K5">L~</a> <span class="p4">(<span class="default"><a href="finseq_6.html#K1">Rotate</a> <font color="Maroon">c<sub>2</sub></font>,<span class="p5">(<span class="default"><a href="pscomp_1.html#K29">N-min</a> <span class="p0">(<span class="default"><a href="topreal1.html#K5">L~</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> is <a href="seq_4.html#V2">bounded_below</a>
 
<b>by </b><i><a class="ref" href="sprect_1.html#T46">SPRECT_1:46</a></i>;<br/>
<b>set </b><font color="Maroon">c<sub>7</sub></font> = <span class="p1"><a href="euclid.html#K23">|[</a><span class="default"><span class="p2">(<span class="default"><a href="pscomp_1.html#K17">E-bound</a> <span class="p3">(<span class="default"><a href="topreal1.html#K5">L~</a> <span class="p4">(<span class="default"><a href="sprect_1.html#K1">SpStSeq</a> <span class="p5">(<span class="default"><a href="topreal1.html#K5">L~</a> <span class="p0">(<span class="default"><a href="finseq_6.html#K1">Rotate</a> <font color="Maroon">c<sub>2</sub></font>,<span class="p1">(<span class="default"><a href="pscomp_1.html#K29">N-min</a> <span class="p2">(<span class="default"><a href="topreal1.html#K5">L~</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K5">-</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="real_1.html#K6">/</a> 2</span>)</span></span>)</span></span><a href="euclid.html#K23">]|</a></span>;<br/>
<b>reconsider </b><font color="Maroon">c<sub>8</sub></font> = <span class="p1"><a href="euclid.html#K23">|[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K5">-</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="real_1.html#K6">/</a> 2</span>)</span></span>)</span></span><a href="euclid.html#K23">]|</a></span> as   <a href="pre_topc.html#NM2">Point</a> of <span class="p1">(<span class="default"><a href="euclid.html#K14">Euclid</a> 2</span>)</span> <b>by </b><i><a class="ref" href="topreal3.html#T13">TOPREAL3:13</a></i>;<br/>
<a NAME="E16:26"/><i><font color="Green">E26</font></i>: 
<font color="Maroon">c<sub>6</sub></font> <a href="real_1.html#K6">/</a> 2 <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0
 
<b>by </b><i><a class="txt" href="gobrd14.html#E9:26"><i><font color="Green">E21</font></i></a>, <a class="ref" href="real_2.html#T127">REAL_2:127</a></i>;<br/>
 <a href="metric_1.html#K4">dist</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>8</sub></font> = 
<span class="p1">(<span class="default"><a href="euclid.html#K13">Pitag_dist</a> 2</span>)</span> <a href="binop_1.html#K1">.</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>8</sub></font>
<b>by </b><i><a class="ref" href="metric_1.html#D1">METRIC_1:def 1</a></i>
<br/>.= 
 <a href="square_1.html#K7">sqrt</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">c<sub>1</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="real_1.html#K5">-</a> <span class="p4">(<span class="default"><span class="p5"><a href="euclid.html#K23">|[</a><span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span>,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K5">-</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="real_1.html#K6">/</a> 2</span>)</span></span>)</span></span><a href="euclid.html#K23">]|</a></span> <a href="euclid.html#K21">`1</a> </span>)</span></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span> <a href="real_1.html#K3">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K5">-</a> <span class="p4">(<span class="default"><span class="p5"><a href="euclid.html#K23">|[</a><span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span>,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K5">-</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="real_1.html#K6">/</a> 2</span>)</span></span>)</span></span><a href="euclid.html#K23">]|</a></span> <a href="euclid.html#K22">`2</a> </span>)</span></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="topreal3.html#T12">TOPREAL3:12</a></i>
<br/>.= 
 <a href="square_1.html#K7">sqrt</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">c<sub>1</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="real_1.html#K5">-</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span> <a href="real_1.html#K3">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K5">-</a> <span class="p4">(<span class="default"><span class="p5"><a href="euclid.html#K23">|[</a><span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span>,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K5">-</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="real_1.html#K6">/</a> 2</span>)</span></span>)</span></span><a href="euclid.html#K23">]|</a></span> <a href="euclid.html#K22">`2</a> </span>)</span></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="euclid.html#T56">EUCLID:56</a></i>
<br/>.= 
 <a href="square_1.html#K7">sqrt</a> <span class="p1">(<span class="default">0 <a href="real_1.html#K3">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K5">-</a> <span class="p4">(<span class="default"><span class="p5"><a href="euclid.html#K23">|[</a><span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span>,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K5">-</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="real_1.html#K6">/</a> 2</span>)</span></span>)</span></span><a href="euclid.html#K23">]|</a></span> <a href="euclid.html#K22">`2</a> </span>)</span></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span>

<br/>.= 
 <a href="square_1.html#K7">sqrt</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K5">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K5">-</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="real_1.html#K6">/</a> 2</span>)</span></span>)</span></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span>
<b>by </b><i><a class="ref" href="euclid.html#T56">EUCLID:56</a></i>
<br/>.= 
<font color="Maroon">c<sub>6</sub></font> <a href="real_1.html#K6">/</a> 2
<b>by </b><i><a class="txt" href="gobrd14.html#E16:26"><i><font color="Green">E26</font></i></a>, <a class="ref" href="square_1.html#T89">SQUARE_1:89</a></i>
;<br/>
<a NAME="E18:26"/><b>then </b>
 <a href="metric_1.html#K4">dist</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>8</sub></font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">c<sub>6</sub></font> <a href="real_1.html#K6">/</a> 1
 
<b>by </b><i><a class="txt" href="gobrd14.html#E9:26"><i><font color="Green">E21</font></i></a>, <a class="ref" href="real_2.html#T200">REAL_2:200</a></i>;<br/>
<a NAME="E19:26"/><b>then </b><i><font color="Green">E27</font></i>: 
<font color="Maroon">c<sub>8</sub></font> <a href="hidden.html#R2">in</a>  <a href="metric_1.html#K9">Ball</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>6</sub></font>
 
<b>by </b><i><a class="ref" href="metric_1.html#T12">METRIC_1:12</a></i>;<br/>
<a NAME="E20:26"/>
 <a href="goboard9.html#K3">RightComp</a> <span class="p1">(<span class="default"><a href="finseq_6.html#K1">Rotate</a> <font color="Maroon">c<sub>2</sub></font>,<span class="p2">(<span class="default"><a href="pscomp_1.html#K29">N-min</a> <span class="p3">(<span class="default"><a href="topreal1.html#K5">L~</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span> <a href="subset_1.html#R1">misses</a>  <a href="goboard9.html#K2">LeftComp</a> <span class="p1">(<span class="default"><a href="finseq_6.html#K1">Rotate</a> <font color="Maroon">c<sub>2</sub></font>,<span class="p2">(<span class="default"><a href="pscomp_1.html#K29">N-min</a> <span class="p3">(<span class="default"><a href="topreal1.html#K5">L~</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="gobrd14.html#T24" target="_self">Th24</a></i>;<br/>
<a NAME="E21:26"/><b>then </b><i><font color="Green">E28</font></i>: 
not <span class="p1"><a href="euclid.html#K23">|[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K5">-</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="real_1.html#K6">/</a> 2</span>)</span></span>)</span></span><a href="euclid.html#K23">]|</a></span> <a href="hidden.html#R2">in</a>  <a href="goboard9.html#K2">LeftComp</a> <span class="p1">(<span class="default"><a href="finseq_6.html#K1">Rotate</a> <font color="Maroon">c<sub>2</sub></font>,<span class="p2">(<span class="default"><a href="pscomp_1.html#K29">N-min</a> <span class="p3">(<span class="default"><a href="topreal1.html#K5">L~</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span>
 
<b>by </b><i><a class="txt" href="gobrd14.html#E10:26"><i><font color="Green">E22</font></i></a>, <a class="txt" href="gobrd14.html#E19:26"><i><font color="Green">E27</font></i></a>, <a class="ref" href="xboole_0.html#T3">XBOOLE_0:3</a></i>;<br/>
<a NAME="E22:26"/><b>then </b>
<span class="p1"><a href="euclid.html#K23">|[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K5">-</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="real_1.html#K6">/</a> 2</span>)</span></span>)</span></span><a href="euclid.html#K23">]|</a></span> <a href="euclid.html#K22">`2</a>  <a href="xxreal_0.html#R1">&lt;=</a>  <a href="pscomp_1.html#K16">N-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K5">L~</a> <span class="p2">(<span class="default"><a href="finseq_6.html#K1">Rotate</a> <font color="Maroon">c<sub>2</sub></font>,<span class="p3">(<span class="default"><a href="pscomp_1.html#K29">N-min</a> <span class="p4">(<span class="default"><a href="topreal1.html#K5">L~</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span></span>)</span>
 
<b>by </b><i><a class="txt" href="gobrd14.html#E3:26"><i><font color="Green">E20</font></i></a>, <a class="ref" href="jordan2c.html#T121">JORDAN2C:121</a></i>;<br/>
<a NAME="E23:26"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K5">-</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="pscomp_1.html#K16">N-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K5">L~</a> <span class="p2">(<span class="default"><a href="finseq_6.html#K1">Rotate</a> <font color="Maroon">c<sub>2</sub></font>,<span class="p3">(<span class="default"><a href="pscomp_1.html#K29">N-min</a> <span class="p4">(<span class="default"><a href="topreal1.html#K5">L~</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="euclid.html#T56">EUCLID:56</a></i>;<br/>
<a NAME="E24:26"/><b>then </b><i><font color="Green">E29</font></i>: 
<span class="p1"><a href="euclid.html#K23">|[</a><span class="default"><span class="p2">(<span class="default"><a href="pscomp_1.html#K17">E-bound</a> <span class="p3">(<span class="default"><a href="topreal1.html#K5">L~</a> <span class="p4">(<span class="default"><a href="sprect_1.html#K1">SpStSeq</a> <span class="p5">(<span class="default"><a href="topreal1.html#K5">L~</a> <span class="p0">(<span class="default"><a href="finseq_6.html#K1">Rotate</a> <font color="Maroon">c<sub>2</sub></font>,<span class="p1">(<span class="default"><a href="pscomp_1.html#K29">N-min</a> <span class="p2">(<span class="default"><a href="topreal1.html#K5">L~</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K5">-</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="real_1.html#K6">/</a> 2</span>)</span></span>)</span></span><a href="euclid.html#K23">]|</a></span> <a href="euclid.html#K22">`2</a>  <a href="xxreal_0.html#R1">&lt;=</a>  <a href="pscomp_1.html#K16">N-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K5">L~</a> <span class="p2">(<span class="default"><a href="finseq_6.html#K1">Rotate</a> <font color="Maroon">c<sub>2</sub></font>,<span class="p3">(<span class="default"><a href="pscomp_1.html#K29">N-min</a> <span class="p4">(<span class="default"><a href="topreal1.html#K5">L~</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="euclid.html#T56">EUCLID:56</a></i>;<br/>
<a NAME="E25:26"/>
<span class="p1"><a href="euclid.html#K23">|[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K5">-</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="real_1.html#K6">/</a> 2</span>)</span></span>)</span></span><a href="euclid.html#K23">]|</a></span> <a href="euclid.html#K22">`2</a>  <a href="xxreal_0.html#NR2" target="_self">&gt;=</a>  <a href="pscomp_1.html#K18">S-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K5">L~</a> <span class="p2">(<span class="default"><a href="finseq_6.html#K1">Rotate</a> <font color="Maroon">c<sub>2</sub></font>,<span class="p3">(<span class="default"><a href="pscomp_1.html#K29">N-min</a> <span class="p4">(<span class="default"><a href="topreal1.html#K5">L~</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span></span>)</span>
 
<b>by </b><i><a class="txt" href="gobrd14.html#E3:26"><i><font color="Green">E20</font></i></a>, <a class="txt" href="gobrd14.html#E21:26"><i><font color="Green">E28</font></i></a>, <a class="ref" href="jordan2c.html#T120">JORDAN2C:120</a></i>;<br/>
<a NAME="E26:26"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K5">-</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a>  <a href="pscomp_1.html#K18">S-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K5">L~</a> <span class="p2">(<span class="default"><a href="finseq_6.html#K1">Rotate</a> <font color="Maroon">c<sub>2</sub></font>,<span class="p3">(<span class="default"><a href="pscomp_1.html#K29">N-min</a> <span class="p4">(<span class="default"><a href="topreal1.html#K5">L~</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="euclid.html#T56">EUCLID:56</a></i>;<br/>
<a NAME="E27:26"/><b>then </b><i><font color="Green">E30</font></i>: 
<span class="p1"><a href="euclid.html#K23">|[</a><span class="default"><span class="p2">(<span class="default"><a href="pscomp_1.html#K17">E-bound</a> <span class="p3">(<span class="default"><a href="topreal1.html#K5">L~</a> <span class="p4">(<span class="default"><a href="sprect_1.html#K1">SpStSeq</a> <span class="p5">(<span class="default"><a href="topreal1.html#K5">L~</a> <span class="p0">(<span class="default"><a href="finseq_6.html#K1">Rotate</a> <font color="Maroon">c<sub>2</sub></font>,<span class="p1">(<span class="default"><a href="pscomp_1.html#K29">N-min</a> <span class="p2">(<span class="default"><a href="topreal1.html#K5">L~</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K5">-</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="real_1.html#K6">/</a> 2</span>)</span></span>)</span></span><a href="euclid.html#K23">]|</a></span> <a href="euclid.html#K22">`2</a>  <a href="xxreal_0.html#NR2" target="_self">&gt;=</a>  <a href="pscomp_1.html#K18">S-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K5">L~</a> <span class="p2">(<span class="default"><a href="finseq_6.html#K1">Rotate</a> <font color="Maroon">c<sub>2</sub></font>,<span class="p3">(<span class="default"><a href="pscomp_1.html#K29">N-min</a> <span class="p4">(<span class="default"><a href="topreal1.html#K5">L~</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="euclid.html#T56">EUCLID:56</a></i>;<br/>
<a NAME="E28:26"/>
<span class="p1"><a href="euclid.html#K23">|[</a><span class="default"><span class="p2">(<span class="default"><a href="pscomp_1.html#K17">E-bound</a> <span class="p3">(<span class="default"><a href="topreal1.html#K5">L~</a> <span class="p4">(<span class="default"><a href="sprect_1.html#K1">SpStSeq</a> <span class="p5">(<span class="default"><a href="topreal1.html#K5">L~</a> <span class="p0">(<span class="default"><a href="finseq_6.html#K1">Rotate</a> <font color="Maroon">c<sub>2</sub></font>,<span class="p1">(<span class="default"><a href="pscomp_1.html#K29">N-min</a> <span class="p2">(<span class="default"><a href="topreal1.html#K5">L~</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K5">-</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="real_1.html#K6">/</a> 2</span>)</span></span>)</span></span><a href="euclid.html#K23">]|</a></span> <a href="euclid.html#K21">`1</a>  <a href="hidden.html#R1">=</a>  <a href="pscomp_1.html#K17">E-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K5">L~</a> <span class="p2">(<span class="default"><a href="sprect_1.html#K1">SpStSeq</a> <span class="p3">(<span class="default"><a href="topreal1.html#K5">L~</a> <span class="p4">(<span class="default"><a href="finseq_6.html#K1">Rotate</a> <font color="Maroon">c<sub>2</sub></font>,<span class="p5">(<span class="default"><a href="pscomp_1.html#K29">N-min</a> <span class="p0">(<span class="default"><a href="topreal1.html#K5">L~</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="euclid.html#T56">EUCLID:56</a></i>;<br/>
<a NAME="E29:26"/><b>then </b><i><font color="Green">E31</font></i>: 
<span class="p1"><a href="euclid.html#K23">|[</a><span class="default"><span class="p2">(<span class="default"><a href="pscomp_1.html#K17">E-bound</a> <span class="p3">(<span class="default"><a href="topreal1.html#K5">L~</a> <span class="p4">(<span class="default"><a href="sprect_1.html#K1">SpStSeq</a> <span class="p5">(<span class="default"><a href="topreal1.html#K5">L~</a> <span class="p0">(<span class="default"><a href="finseq_6.html#K1">Rotate</a> <font color="Maroon">c<sub>2</sub></font>,<span class="p1">(<span class="default"><a href="pscomp_1.html#K29">N-min</a> <span class="p2">(<span class="default"><a href="topreal1.html#K5">L~</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K5">-</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="real_1.html#K6">/</a> 2</span>)</span></span>)</span></span><a href="euclid.html#K23">]|</a></span> <a href="euclid.html#K21">`1</a>  <a href="hidden.html#R1">=</a>  <a href="pscomp_1.html#K17">E-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K5">L~</a> <span class="p2">(<span class="default"><a href="finseq_6.html#K1">Rotate</a> <font color="Maroon">c<sub>2</sub></font>,<span class="p3">(<span class="default"><a href="pscomp_1.html#K29">N-min</a> <span class="p4">(<span class="default"><a href="topreal1.html#K5">L~</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="sprect_1.html#T69">SPRECT_1:69</a></i>;<br/>
<a NAME="E30:26"/>
 <a href="topreal1.html#K3">LSeg</a> <span class="p1">(<span class="default"><a href="pscomp_1.html#K22">SE-corner</a> <span class="p2">(<span class="default"><a href="topreal1.html#K5">L~</a> <span class="p3">(<span class="default"><a href="finseq_6.html#K1">Rotate</a> <font color="Maroon">c<sub>2</sub></font>,<span class="p4">(<span class="default"><a href="pscomp_1.html#K29">N-min</a> <span class="p5">(<span class="default"><a href="topreal1.html#K5">L~</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="pscomp_1.html#K21">NE-corner</a> <span class="p2">(<span class="default"><a href="topreal1.html#K5">L~</a> <span class="p3">(<span class="default"><a href="finseq_6.html#K1">Rotate</a> <font color="Maroon">c<sub>2</sub></font>,<span class="p4">(<span class="default"><a href="pscomp_1.html#K29">N-min</a> <span class="p5">(<span class="default"><a href="topreal1.html#K5">L~</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">{<span class="default"> <font color="Olive">b<sub>1</sub></font> where B is   <a href="pre_topc.html#NM2">Point</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 2</span>)</span> : ( <font color="Olive">b<sub>1</sub></font> <a href="euclid.html#K21">`1</a>  <a href="hidden.html#R1">=</a>  <a href="pscomp_1.html#K17">E-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K5">L~</a> <span class="p2">(<span class="default"><a href="finseq_6.html#K1">Rotate</a> <font color="Maroon">c<sub>2</sub></font>,<span class="p3">(<span class="default"><a href="pscomp_1.html#K29">N-min</a> <span class="p4">(<span class="default"><a href="topreal1.html#K5">L~</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span></span>)</span> &amp; <font color="Olive">b<sub>1</sub></font> <a href="euclid.html#K22">`2</a>  <a href="xxreal_0.html#R1">&lt;=</a>  <a href="pscomp_1.html#K16">N-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K5">L~</a> <span class="p2">(<span class="default"><a href="finseq_6.html#K1">Rotate</a> <font color="Maroon">c<sub>2</sub></font>,<span class="p3">(<span class="default"><a href="pscomp_1.html#K29">N-min</a> <span class="p4">(<span class="default"><a href="topreal1.html#K5">L~</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span></span>)</span> &amp; <font color="Olive">b<sub>1</sub></font> <a href="euclid.html#K22">`2</a>  <a href="xxreal_0.html#NR2" target="_self">&gt;=</a>  <a href="pscomp_1.html#K18">S-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K5">L~</a> <span class="p2">(<span class="default"><a href="finseq_6.html#K1">Rotate</a> <font color="Maroon">c<sub>2</sub></font>,<span class="p3">(<span class="default"><a href="pscomp_1.html#K29">N-min</a> <span class="p4">(<span class="default"><a href="topreal1.html#K5">L~</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span></span>)</span> ) </span>}</span> 
 
<b>by </b><i><a class="ref" href="sprect_1.html#T25">SPRECT_1:25</a></i>;<br/>
<a NAME="E31:26"/><b>then </b><i><font color="Green">E32</font></i>: 
<span class="p1"><a href="euclid.html#K23">|[</a><span class="default"><span class="p2">(<span class="default"><a href="pscomp_1.html#K17">E-bound</a> <span class="p3">(<span class="default"><a href="topreal1.html#K5">L~</a> <span class="p4">(<span class="default"><a href="sprect_1.html#K1">SpStSeq</a> <span class="p5">(<span class="default"><a href="topreal1.html#K5">L~</a> <span class="p0">(<span class="default"><a href="finseq_6.html#K1">Rotate</a> <font color="Maroon">c<sub>2</sub></font>,<span class="p1">(<span class="default"><a href="pscomp_1.html#K29">N-min</a> <span class="p2">(<span class="default"><a href="topreal1.html#K5">L~</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K5">-</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="real_1.html#K6">/</a> 2</span>)</span></span>)</span></span><a href="euclid.html#K23">]|</a></span> <a href="hidden.html#R2">in</a>  <a href="topreal1.html#K3">LSeg</a> <span class="p1">(<span class="default"><a href="pscomp_1.html#K22">SE-corner</a> <span class="p2">(<span class="default"><a href="topreal1.html#K5">L~</a> <span class="p3">(<span class="default"><a href="finseq_6.html#K1">Rotate</a> <font color="Maroon">c<sub>2</sub></font>,<span class="p4">(<span class="default"><a href="pscomp_1.html#K29">N-min</a> <span class="p5">(<span class="default"><a href="topreal1.html#K5">L~</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="pscomp_1.html#K21">NE-corner</a> <span class="p2">(<span class="default"><a href="topreal1.html#K5">L~</a> <span class="p3">(<span class="default"><a href="finseq_6.html#K1">Rotate</a> <font color="Maroon">c<sub>2</sub></font>,<span class="p4">(<span class="default"><a href="pscomp_1.html#K29">N-min</a> <span class="p5">(<span class="default"><a href="topreal1.html#K5">L~</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>
 
<b>by </b><i><a class="txt" href="gobrd14.html#E24:26"><i><font color="Green">E29</font></i></a>, <a class="txt" href="gobrd14.html#E27:26"><i><font color="Green">E30</font></i></a>, <a class="txt" href="gobrd14.html#E29:26"><i><font color="Green">E31</font></i></a></i>;<br/>
<a NAME="E32:26"/><i><font color="Green">E33</font></i>: 
 <a href="topreal1.html#K3">LSeg</a> <span class="p1">(<span class="default"><a href="pscomp_1.html#K22">SE-corner</a> <span class="p2">(<span class="default"><a href="topreal1.html#K5">L~</a> <span class="p3">(<span class="default"><a href="finseq_6.html#K1">Rotate</a> <font color="Maroon">c<sub>2</sub></font>,<span class="p4">(<span class="default"><a href="pscomp_1.html#K29">N-min</a> <span class="p5">(<span class="default"><a href="topreal1.html#K5">L~</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="pscomp_1.html#K21">NE-corner</a> <span class="p2">(<span class="default"><a href="topreal1.html#K5">L~</a> <span class="p3">(<span class="default"><a href="finseq_6.html#K1">Rotate</a> <font color="Maroon">c<sub>2</sub></font>,<span class="p4">(<span class="default"><a href="pscomp_1.html#K29">N-min</a> <span class="p5">(<span class="default"><a href="topreal1.html#K5">L~</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="topreal1.html#K5">L~</a> <span class="p1">(<span class="default"><a href="sprect_1.html#K1">SpStSeq</a> <span class="p2">(<span class="default"><a href="topreal1.html#K5">L~</a> <span class="p3">(<span class="default"><a href="finseq_6.html#K1">Rotate</a> <font color="Maroon">c<sub>2</sub></font>,<span class="p4">(<span class="default"><a href="pscomp_1.html#K29">N-min</a> <span class="p5">(<span class="default"><a href="topreal1.html#K5">L~</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="topreal6.html#T43">TOPREAL6:43</a></i>;<br/>
<a href="pscomp_1.html#K14">proj2</a>  <a href="funct_2.html#K3">.</a> <span class="p1"><a href="euclid.html#K23">|[</a><span class="default"><span class="p2">(<span class="default"><a href="pscomp_1.html#K17">E-bound</a> <span class="p3">(<span class="default"><a href="topreal1.html#K5">L~</a> <span class="p4">(<span class="default"><a href="sprect_1.html#K1">SpStSeq</a> <span class="p5">(<span class="default"><a href="topreal1.html#K5">L~</a> <span class="p0">(<span class="default"><a href="finseq_6.html#K1">Rotate</a> <font color="Maroon">c<sub>2</sub></font>,<span class="p1">(<span class="default"><a href="pscomp_1.html#K29">N-min</a> <span class="p2">(<span class="default"><a href="topreal1.html#K5">L~</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K5">-</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="real_1.html#K6">/</a> 2</span>)</span></span>)</span></span><a href="euclid.html#K23">]|</a></span> = 
<span class="p1"><a href="euclid.html#K23">|[</a><span class="default"><span class="p2">(<span class="default"><a href="pscomp_1.html#K17">E-bound</a> <span class="p3">(<span class="default"><a href="topreal1.html#K5">L~</a> <span class="p4">(<span class="default"><a href="sprect_1.html#K1">SpStSeq</a> <span class="p5">(<span class="default"><a href="topreal1.html#K5">L~</a> <span class="p0">(<span class="default"><a href="finseq_6.html#K1">Rotate</a> <font color="Maroon">c<sub>2</sub></font>,<span class="p1">(<span class="default"><a href="pscomp_1.html#K29">N-min</a> <span class="p2">(<span class="default"><a href="topreal1.html#K5">L~</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K5">-</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="real_1.html#K6">/</a> 2</span>)</span></span>)</span></span><a href="euclid.html#K23">]|</a></span> <a href="euclid.html#K22">`2</a> 
<b>by </b><i><a class="ref" href="pscomp_1.html#D29">PSCOMP_1:def 29</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K5">-</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="real_1.html#K6">/</a> 2</span>)</span>
<b>by </b><i><a class="ref" href="euclid.html#T56">EUCLID:56</a></i>
;<br/>
<a NAME="E34:26"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K5">-</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="hidden.html#R2">in</a> <a href="pscomp_1.html#K14">proj2</a>  <a href="relset_1.html#K10">.:</a> <span class="p1">(<span class="default"><a href="topreal1.html#K5">L~</a> <span class="p2">(<span class="default"><a href="sprect_1.html#K1">SpStSeq</a> <span class="p3">(<span class="default"><a href="topreal1.html#K5">L~</a> <span class="p4">(<span class="default"><a href="finseq_6.html#K1">Rotate</a> <font color="Maroon">c<sub>2</sub></font>,<span class="p5">(<span class="default"><a href="pscomp_1.html#K29">N-min</a> <span class="p0">(<span class="default"><a href="topreal1.html#K5">L~</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>
 
<b>by </b><i><a class="txt" href="gobrd14.html#E31:26"><i><font color="Green">E32</font></i></a>, <a class="txt" href="gobrd14.html#E32:26"><i><font color="Green">E33</font></i></a>, <a class="ref" href="funct_2.html#T43">FUNCT_2:43</a></i>;<br/>
<a NAME="E35:26"/><b>then </b><i><font color="Green">E34</font></i>: 
 <a href="pscomp_1.html#K3">inf</a> <span class="p1">(<span class="default"><a href="pscomp_1.html#K14">proj2</a>  <a href="relset_1.html#K10">.:</a> <span class="p2">(<span class="default"><a href="topreal1.html#K5">L~</a> <span class="p3">(<span class="default"><a href="sprect_1.html#K1">SpStSeq</a> <span class="p4">(<span class="default"><a href="topreal1.html#K5">L~</a> <span class="p5">(<span class="default"><a href="finseq_6.html#K1">Rotate</a> <font color="Maroon">c<sub>2</sub></font>,<span class="p0">(<span class="default"><a href="pscomp_1.html#K29">N-min</a> <span class="p1">(<span class="default"><a href="topreal1.html#K5">L~</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K5">-</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="real_1.html#K6">/</a> 2</span>)</span>
 
<b>by </b><i><a class="txt" href="gobrd14.html#E14:26"><i><font color="Green">E25</font></i></a>, <a class="ref" href="seq_4.html#D5">SEQ_4:def 5</a></i>;<br/>
<a NAME="E36:26"/>
<span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K5">-</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K5">-</a> 0
 
<b>by </b><i><a class="txt" href="gobrd14.html#E16:26"><i><font color="Green">E26</font></i></a>, <a class="ref" href="real_1.html#T92">REAL_1:92</a></i>;<br/>
<b>hence </b><a NAME="E37:26"/>
 <a href="pscomp_1.html#K18">S-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K5">L~</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">c<sub>1</sub></font> <a href="euclid.html#K22">`2</a> 
 <b>by </b><i><a class="txt" href="gobrd14.html#E1:26"><i><font color="Green">E19</font></i></a>, <a class="txt" href="gobrd14.html#E12:26"><i><font color="Green">E23</font></i></a>, <a class="txt" href="gobrd14.html#E13:26"><i><font color="Green">E24</font></i></a>, <a class="txt" href="gobrd14.html#E35:26"><i><font color="Green">E34</font></i></a>, <a class="ref" href="xxreal_0.html#T2">XXREAL_0:2</a></i>;<br/>


</div>
