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<b>let </b><font color="Maroon" title="c1">g</font> be  non <a href="funct_1.html#V3" title="FUNCT_1:attr.3">constant</a> <a href="goboard5.html#V2" title="GOBOARD5:attr.2">standard</a> <a href="sprect_2.html#V1" title="SPRECT_2:attr.1">clockwise_oriented</a> <a href="goboard5.html#NM1" title="GOBOARD5:NM.1">special_circular_sequence</a>;<br/><b>let </b><font color="Maroon" title="c2">P</font> be   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> 2</span>)</span>;<br/>



<b>assume </b><a NAME="E1:40"/><i><font color="Green" title="E27">A1</font></i>: 
<font color="Maroon" title="c2">P</font> <a href="jordan2c.html#R1" title="JORDAN2C:pred.1">is_inside_component_of</a>  <a href="topreal1.html#K5" title="TOPREAL1:func.5">L~</a> <font color="Maroon" title="c1">g</font>
 ;<br/>

<a NAME="E2:40"/><b>then </b><i><font color="Green" title="E28">A2</font></i>: 
<font color="Maroon" title="c2">P</font> <a href="connsp_1.html#R4" title="CONNSP_1:pred.4">is_a_component_of</a> <span class="p1">(<span class="default"><a href="topreal1.html#K5" title="TOPREAL1:func.5">L~</a> <font color="Maroon" title="c1">g</font></span>)</span> <a href="subset_1.html#K3" title="SUBSET_1:func.3">`</a> 
 
<b>by </b><i><a class="ref" href="jordan2c.html#D3" title="JORDAN2C:def.3">JORDAN2C:def 3</a></i>;<br/>
<a NAME="E3:40"/><i><font color="Green" title="E29">A3</font></i>: 
<font color="Maroon" title="c2">P</font> <a href="xboole_0.html#NR5" title="XBOOLE_0:NR.5">meets</a>  <a href="goboard9.html#K3" title="GOBOARD9:func.3">RightComp</a> <font color="Maroon" title="c1">g</font>
 
<b>by </b><i><a class="txt" href="gobrd14.html#E1:40"><i><font color="Green" title="E27">A1</font></i></a>, <a class="ref" href="gobrd14.html#T49" target="_self" title="GOBRD14:th.49">Th49</a></i>;<br/>
<a NAME="E4:40"/><i><font color="Green" title="E30">A4</font></i>: 
 <a href="goboard9.html#K3" title="GOBOARD9:func.3">RightComp</a> <font color="Maroon" title="c1">g</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="jordan2c.html#K1" title="JORDAN2C:func.1">BDD</a> <span class="p1">(<span class="default"><a href="topreal1.html#K5" title="TOPREAL1:func.5">L~</a> <font color="Maroon" title="c1">g</font></span>)</span>
 
<b>by </b><i><a class="ref" href="gobrd14.html#T47" target="_self" title="GOBRD14:th.47">Th47</a></i>;<br/>
<a NAME="E5:40"/>
 <a href="jordan2c.html#K1" title="JORDAN2C:func.1">BDD</a> <span class="p1">(<span class="default"><a href="topreal1.html#K5" title="TOPREAL1:func.5">L~</a> <font color="Maroon" title="c1">g</font></span>)</span> <a href="jordan2c.html#R1" title="JORDAN2C:pred.1">is_inside_component_of</a>  <a href="topreal1.html#K5" title="TOPREAL1:func.5">L~</a> <font color="Maroon" title="c1">g</font>
 
<b>by </b><i><a class="ref" href="jordan2c.html#T116" title="JORDAN2C:th.116">JORDAN2C:116</a></i>;<br/>
<a NAME="E6:40"/><b>then </b>
 <a href="jordan2c.html#K1" title="JORDAN2C:func.1">BDD</a> <span class="p1">(<span class="default"><a href="topreal1.html#K5" title="TOPREAL1:func.5">L~</a> <font color="Maroon" title="c1">g</font></span>)</span> <a href="connsp_1.html#R4" title="CONNSP_1:pred.4">is_a_component_of</a> <span class="p1">(<span class="default"><a href="topreal1.html#K5" title="TOPREAL1:func.5">L~</a> <font color="Maroon" title="c1">g</font></span>)</span> <a href="subset_1.html#K3" title="SUBSET_1:func.3">`</a> 
 
<b>by </b><i><a class="ref" href="jordan2c.html#D3" title="JORDAN2C:def.3">JORDAN2C:def 3</a></i>;<br/>
<b>hence </b><a NAME="E7:40"/>
<font color="Maroon" title="c2">P</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="jordan2c.html#K1" title="JORDAN2C:func.1">BDD</a> <span class="p1">(<span class="default"><a href="topreal1.html#K5" title="TOPREAL1:func.5">L~</a> <font color="Maroon" title="c1">g</font></span>)</span>
 <b>by </b><i><a class="txt" href="gobrd14.html#E2:40"><i><font color="Green" title="E28">A2</font></i></a>, <a class="txt" href="gobrd14.html#E3:40"><i><font color="Green" title="E29">A3</font></i></a>, <a class="txt" href="gobrd14.html#E4:40"><i><font color="Green" title="E30">A4</font></i></a>, <a class="ref" href="goboard9.html#T3" title="GOBOARD9:th.3">GOBOARD9:3</a></i>;<br/>


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