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<b>let </b><font color="Maroon" title="c1">s1</font> be   <a href="real_1.html#NM1" title="REAL_1:NM.1">Real</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="E1:22"/><i><font color="Green" title="E21">A1</font></i>: 
<font color="Maroon" title="c2">P</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">{<span class="default"> <span class="p2"><a href="euclid.html#K23" title="EUCLID:func.23">|[</a><span class="default"><font color="Olive" title="b1">s</font>,<font color="Olive" title="b2">t</font></span><a href="euclid.html#K23" title="EUCLID:func.23">]|</a></span> where <font color="Olive" title="b1">s</font>, <font color="Olive" title="b2">t</font> is   <a href="real_1.html#NM1" title="REAL_1:NM.1">Real</a> : <font color="Maroon" title="c1">s1</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;</a> <font color="Olive" title="b1">s</font> </span>}</span> 
 ;<br/>

<b>set </b><font color="Maroon" title="c3">s3</font> = <font color="Maroon" title="c1">s1</font> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> 1;<br/>
<a NAME="E2:22"/>
<font color="Maroon" title="c1">s1</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;</a> <font color="Maroon" title="c1">s1</font> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> 1
 
<b>by </b><i><a class="ref" href="real_2.html#T174" title="REAL_2:th.174">REAL_2:174</a></i>;<br/>
<a NAME="E3:22"/><b>then </b>
<span class="p1"><a href="euclid.html#K23" title="EUCLID:func.23">|[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">s1</font> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> 1</span>)</span>,0</span><a href="euclid.html#K23" title="EUCLID:func.23">]|</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">{<span class="default"> <span class="p2"><a href="euclid.html#K23" title="EUCLID:func.23">|[</a><span class="default"><font color="Olive" title="b1">s</font>,<font color="Olive" title="b2">t</font></span><a href="euclid.html#K23" title="EUCLID:func.23">]|</a></span> where <font color="Olive" title="b1">s</font>, <font color="Olive" title="b2">t</font> is   <a href="real_1.html#NM1" title="REAL_1:NM.1">Real</a> : <font color="Maroon" title="c1">s1</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;</a> <font color="Olive" title="b1">s</font> </span>}</span> 
 
;<br/>
<a NAME="E4:22"/><b>then </b>
( <font color="Maroon" title="c2">P</font> is <a href="jordan1.html#V1" title="JORDAN1:attr.1">convex</a> &amp; not <font color="Maroon" title="c2">P</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> )
 
<b>by </b><i><a class="txt" href="jordan1.html#E1:22"><i><font color="Green" title="E21">A1</font></i></a>, <a class="ref" href="jordan1.html#T16" target="_self" title="JORDAN1:th.16">Th16</a></i>;<br/>
<b>hence </b><a NAME="E5:22"/>
<font color="Maroon" title="c2">P</font> is <a href="connsp_1.html#V2" title="CONNSP_1:attr.2">connected</a>
 <b>by </b><i><a class="ref" href="jordan1.html#T9" target="_self" title="JORDAN1:th.9">Th9</a></i>;<br/>


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