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

<b>let </b><font color="Maroon">g</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">A</font> = <span class="p1">(<span class="default"><a href="pre_topc.html#K4">Cl</a> <span class="p2">(<span class="default"><a href="goboard9.html#K3">RightComp</a> <font color="Maroon">g</font></span>)</span></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p1">(<span class="default"><a href="goboard9.html#K3">RightComp</a> <font color="Maroon">g</font></span>)</span>;<br/>
<a NAME="E1:42"/><i><font color="Green">E54</font></i>: 
 <a href="topreal1.html#K5">L~</a> <font color="Maroon">g</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="pre_topc.html#K4">Cl</a> <span class="p2">(<span class="default"><a href="goboard9.html#K3">RightComp</a> <font color="Maroon">g</font></span>)</span></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p1">(<span class="default"><a href="goboard9.html#K3">RightComp</a> <font color="Maroon">g</font></span>)</span>
 
<b>by </b><i/>;<br/>
<b>then reconsider </b><font color="Maroon">A</font> = <span class="p1">(<span class="default"><a href="pre_topc.html#K4">Cl</a> <span class="p2">(<span class="default"><a href="goboard9.html#K3">RightComp</a> <font color="Maroon">g</font></span>)</span></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p1">(<span class="default"><a href="goboard9.html#K3">RightComp</a> <font color="Maroon">g</font></span>)</span> as  non <a href="xboole_0.html#V1">empty</a> <a href="struct_0.html#NM2">Subset</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 2</span>)</span> ;<br/>
<a NAME="E3:42"/><i><font color="Green">E55</font></i>: 
<a href="pscomp_1.html#K13">proj1</a>  <a href="relset_1.html#K10">.:</a> <span class="p1">(<span class="default"><a href="pre_topc.html#K4">Cl</a> <span class="p2">(<span class="default"><a href="goboard9.html#K3">RightComp</a> <font color="Maroon">g</font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <a href="pscomp_1.html#K13">proj1</a>  <a href="relset_1.html#K10">.:</a> <span class="p1">(<span class="default"><a href="topreal1.html#K5">L~</a> <font color="Maroon">g</font></span>)</span>
 
<b>by </b><i/>;<br/>
<a NAME="E4:42"/>
 <a href="pre_topc.html#K4">Cl</a> <span class="p1">(<span class="default"><a href="goboard9.html#K3">RightComp</a> <font color="Maroon">g</font></span>)</span> is <a href="compts_1.html#V6">compact</a>
 
<b>by </b><i/>;<br/>
<a NAME="E5:42"/><b>then </b>
(  <a href="goboard9.html#K3">RightComp</a> <font color="Maroon">g</font> <a href="tarski.html#R1">c=</a>  <a href="pre_topc.html#K4">Cl</a> <span class="p1">(<span class="default"><a href="goboard9.html#K3">RightComp</a> <font color="Maroon">g</font></span>)</span> &amp;  <a href="pre_topc.html#K4">Cl</a> <span class="p1">(<span class="default"><a href="goboard9.html#K3">RightComp</a> <font color="Maroon">g</font></span>)</span> is <a href="jordan2c.html#V1">Bounded</a> )
 
<b>by </b><i><a class="ref" href="jordan2c.html#T73">JORDAN2C:73</a>, <a class="ref" href="pre_topc.html#T48">PRE_TOPC:48</a></i>;<br/>
<a NAME="E6:42"/><b>then </b><i><font color="Green">E58</font></i>: 
 <a href="goboard9.html#K3">RightComp</a> <font color="Maroon">g</font> is <a href="jordan2c.html#V1">Bounded</a>
 
<b>by </b><i><a class="ref" href="jordan2c.html#T16">JORDAN2C:16</a></i>;<br/>
<a NAME="E7:42"/>
(  <a href="pscomp_1.html#K17">E-bound</a> <font color="Maroon">A</font> <a href="hidden.html#R1">=</a>  <a href="pscomp_1.html#K2">sup</a> <span class="p1">(<span class="default"><a href="pscomp_1.html#K13">proj1</a>  <a href="relset_1.html#K10">.:</a> <font color="Maroon">A</font></span>)</span> &amp;  <a href="pscomp_1.html#K17">E-bound</a> <span class="p1">(<span class="default"><a href="pre_topc.html#K4">Cl</a> <span class="p2">(<span class="default"><a href="goboard9.html#K3">RightComp</a> <font color="Maroon">g</font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="pscomp_1.html#K2">sup</a> <span class="p1">(<span class="default"><a href="pscomp_1.html#K13">proj1</a>  <a href="relset_1.html#K10">.:</a> <span class="p2">(<span class="default"><a href="pre_topc.html#K4">Cl</a> <span class="p3">(<span class="default"><a href="goboard9.html#K3">RightComp</a> <font color="Maroon">g</font></span>)</span></span>)</span></span>)</span> )
 
<b>by </b><i><a class="ref" href="sprect_1.html#T51">SPRECT_1:51</a></i>;<br/>
<b>hence </b><a NAME="E8:42"/>
 <a href="pscomp_1.html#K17">E-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K5">L~</a> <font color="Maroon">g</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="pscomp_1.html#K17">E-bound</a> <span class="p1">(<span class="default"><a href="goboard9.html#K3">RightComp</a> <font color="Maroon">g</font></span>)</span>
 <b>by </b><i>, , , <a class="ref" href="topreal6.html#T95">TOPREAL6:95</a></i>;<br/>


</div>
