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<b>let </b><font color="Maroon">f</font> be  non <a href="funct_1.html#V3">constant</a> <a href="goboard5.html#V2">standard</a> <a href="goboard5.html#NM1">special_circular_sequence</a>;<br/>

<a NAME="E1:5"/>
 <a href="goboard9.html#K2">LeftComp</a> <font color="Maroon">f</font> <a href="connsp_1.html#R4">is_a_component_of</a> <span class="p1">(<span class="default"><a href="topreal1.html#K5">L~</a> <font color="Maroon">f</font></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/>
<b>then consider </b><font color="Maroon">B1</font> being   <a href="struct_0.html#NM2">Subset</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 2</span>)</span> <a href="pre_topc.html#K3">|</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="topreal1.html#K5">L~</a> <font color="Maroon">f</font></span>)</span> <a href="subset_1.html#K3">`</a> </span>)</span></span>)</span><b> such that </b><br/><a NAME="E3:5"/><i><font color="Green">E37</font></i>: 
( <font color="Maroon">B1</font> <a href="hidden.html#R1">=</a>  <a href="goboard9.html#K2">LeftComp</a> <font color="Maroon">f</font> &amp; <font color="Maroon">B1</font> <a href="connsp_1.html#R3">is_a_component_of</a> <span class="p1">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 2</span>)</span> <a href="pre_topc.html#K3">|</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="topreal1.html#K5">L~</a> <font color="Maroon">f</font></span>)</span> <a href="subset_1.html#K3">`</a> </span>)</span> )
 <b>by </b><i><a class="ref" href="connsp_1.html#D6">CONNSP_1:def 6</a></i>;<br/>
<a NAME="E4:5"/><i><font color="Green">E41</font></i>: 
the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 2</span>)</span> <a href="pre_topc.html#K3">|</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="topreal1.html#K5">L~</a> <font color="Maroon">f</font></span>)</span> <a href="subset_1.html#K3">`</a> </span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="topreal1.html#K5">L~</a> <font color="Maroon">f</font></span>)</span> <a href="subset_1.html#K3">`</a> 
 
<b>by </b><i><a class="ref" href="pre_topc.html#T29">PRE_TOPC:29</a></i>;<br/>
<a NAME="E5:5"/><b>then </b>
 <a href="connsp_3.html#K4">Down</a> <span class="p1">(<span class="default"><a href="goboard9.html#K2">LeftComp</a> <font color="Maroon">f</font></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="topreal1.html#K5">L~</a> <font color="Maroon">f</font></span>)</span> <a href="subset_1.html#K3">`</a> </span>)</span> <a href="hidden.html#R1">=</a>  <a href="goboard9.html#K2">LeftComp</a> <font color="Maroon">f</font>
 
<b>by </b><i>, <a class="ref" href="xboole_1.html#T28">XBOOLE_1:28</a></i>;<br/>
<a NAME="E6:5"/><b>then </b>
 <a href="connsp_3.html#K4">Down</a> <span class="p1">(<span class="default"><a href="goboard9.html#K2">LeftComp</a> <font color="Maroon">f</font></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="topreal1.html#K5">L~</a> <font color="Maroon">f</font></span>)</span> <a href="subset_1.html#K3">`</a> </span>)</span> is <a href="connsp_1.html#V2">connected</a>
 
<b>by </b><i>, <a class="ref" href="connsp_1.html#D5">CONNSP_1:def 5</a></i>;<br/>
<b>hence </b><a NAME="E7:5"/>
 <a href="pre_topc.html#K4">Cl</a> <span class="p1">(<span class="default"><a href="connsp_3.html#K4">Down</a> <span class="p2">(<span class="default"><a href="goboard9.html#K2">LeftComp</a> <font color="Maroon">f</font></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="topreal1.html#K5">L~</a> <font color="Maroon">f</font></span>)</span> <a href="subset_1.html#K3">`</a> </span>)</span></span>)</span> is <a href="connsp_1.html#V2">connected</a>
 <b>by </b><i><a class="ref" href="connsp_1.html#T20">CONNSP_1:20</a></i>;<br/>

<b>thus </b><a NAME="E8:5"/>
(  <a href="connsp_3.html#K4">Down</a> <span class="p1">(<span class="default"><a href="goboard9.html#K2">LeftComp</a> <font color="Maroon">f</font></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="topreal1.html#K5">L~</a> <font color="Maroon">f</font></span>)</span> <a href="subset_1.html#K3">`</a> </span>)</span> <a href="hidden.html#R1">=</a>  <a href="goboard9.html#K2">LeftComp</a> <font color="Maroon">f</font> &amp;  <a href="connsp_3.html#K4">Down</a> <span class="p1">(<span class="default"><a href="goboard9.html#K2">LeftComp</a> <font color="Maroon">f</font></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="topreal1.html#K5">L~</a> <font color="Maroon">f</font></span>)</span> <a href="subset_1.html#K3">`</a> </span>)</span> <a href="connsp_1.html#R3">is_a_component_of</a> <span class="p1">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 2</span>)</span> <a href="pre_topc.html#K3">|</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="topreal1.html#K5">L~</a> <font color="Maroon">f</font></span>)</span> <a href="subset_1.html#K3">`</a> </span>)</span> )
 <b>by </b><i>, , <a class="ref" href="xboole_1.html#T28">XBOOLE_1:28</a></i>;<br/>


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