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<b>let </b><font color="Maroon">D</font> be  non <a href="xboole_0.html#V1">empty</a> <a href="compts_1.html#V6">compact</a> non <a href="sppol_1.html#V1">horizontal</a> non <a href="sppol_1.html#V2">vertical</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="E1:110"/><i><font color="Green">E47</font></i>: 
 <a href="jordan2c.html#K1" target="_self">BDD</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> <font color="Maroon">D</font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="goboard9.html#K3">RightComp</a> <span class="p1">(<span class="default"><a href="sprect_1.html#K1">SpStSeq</a> <font color="Maroon">D</font></span>)</span>
 
<b>by </b><i/>;<br/>
<a NAME="E2:110"/><i><font color="Green">E56</font></i>: 
 <a href="jordan2c.html#K2" target="_self">UBD</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> <font color="Maroon">D</font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="goboard9.html#K2">LeftComp</a> <span class="p1">(<span class="default"><a href="sprect_1.html#K1">SpStSeq</a> <font color="Maroon">D</font></span>)</span>
 
<b>by </b><i/>;<br/>
<b>hence </b><a NAME="E3:110"/>
 <a href="jordan2c.html#K2" target="_self">UBD</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> <font color="Maroon">D</font></span>)</span></span>)</span> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a> 
 ;<br/>

<b>set </b><font color="Maroon">f</font> =  <a href="sprect_1.html#K1">SpStSeq</a> <font color="Maroon">D</font>;<br/>
<a NAME="E4:110"/><i><font color="Green">E57</font></i>: 
 <a href="goboard9.html#K2">LeftComp</a> <span class="p1">(<span class="default"><a href="sprect_1.html#K1">SpStSeq</a> <font color="Maroon">D</font></span>)</span> <a href="connsp_1.html#R4">is_a_component_of</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> <font color="Maroon">D</font></span>)</span></span>)</span> <a href="subset_1.html#K3">`</a> 
 
<b>by </b><i><a class="ref" href="goboard9.html#D1">GOBOARD9:def 1</a></i>;<br/>
<a NAME="E5:110"/>
not  <a href="goboard9.html#K2">LeftComp</a> <span class="p1">(<span class="default"><a href="sprect_1.html#K1">SpStSeq</a> <font color="Maroon">D</font></span>)</span> is <a href="jordan2c.html#V1" target="_self">Bounded</a>
 
<b>by </b><i><a class="ref" href="jordan2c.html#D3" target="_self">Def3</a></i>;<br/>
<b>hence </b><a NAME="E6:110"/>
 <a href="jordan2c.html#K2" target="_self">UBD</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> <font color="Maroon">D</font></span>)</span></span>)</span> <a href="jordan2c.html#R2" target="_self">is_outside_component_of</a>  <a href="topreal1.html#K5">L~</a> <span class="p1">(<span class="default"><a href="sprect_1.html#K1">SpStSeq</a> <font color="Maroon">D</font></span>)</span>
 <b>by </b><i>, , </i>;<br/>

<b>thus </b><a NAME="E7:110"/>
 <a href="jordan2c.html#K1" target="_self">BDD</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> <font color="Maroon">D</font></span>)</span></span>)</span> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a> 
 <b>by </b><i><a class="ref" href="jordan2c.html#T21" target="_self">Th21</a></i>;<br/>

<a NAME="E8:110"/><i><font color="Green">E58</font></i>: 
 <a href="goboard9.html#K3">RightComp</a> <span class="p1">(<span class="default"><a href="sprect_1.html#K1">SpStSeq</a> <font color="Maroon">D</font></span>)</span> <a href="connsp_1.html#R4">is_a_component_of</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> <font color="Maroon">D</font></span>)</span></span>)</span> <a href="subset_1.html#K3">`</a> 
 
<b>by </b><i><a class="ref" href="goboard9.html#D2">GOBOARD9:def 2</a></i>;<br/>
<a NAME="E9:110"/>
 <a href="goboard9.html#K3">RightComp</a> <span class="p1">(<span class="default"><a href="sprect_1.html#K1">SpStSeq</a> <font color="Maroon">D</font></span>)</span> is <a href="jordan2c.html#V1" target="_self">Bounded</a>
 
<b>by </b><i><a class="ref" href="jordan2c.html#T18" target="_self">Th18</a></i>;<br/>
<b>hence </b><a NAME="E10:110"/>
 <a href="jordan2c.html#K1" target="_self">BDD</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> <font color="Maroon">D</font></span>)</span></span>)</span> <a href="jordan2c.html#R1" target="_self">is_inside_component_of</a>  <a href="topreal1.html#K5">L~</a> <span class="p1">(<span class="default"><a href="sprect_1.html#K1">SpStSeq</a> <font color="Maroon">D</font></span>)</span>
 <b>by </b><i><a class="ref" href="jordan2c.html#T21" target="_self">Th21</a>, <a class="ref" href="jordan2c.html#T22" target="_self">Th22</a>, </i>;<br/>


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