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<b>let </b><font color="Maroon">P</font> be   <a href="topreal2.html#NM1">Simple_closed_curve</a>;<br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="18_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:18_1"/><i><font color="Green">E38</font></i>: 
 <a href="pscomp_1.html#K27">W-min</a> <font color="Maroon">P</font> <a href="hidden.html#R1">=</a>  <a href="pscomp_1.html#K32">E-min</a> <font color="Maroon">P</font>
 ;<br/><a NAME="E2:18_1"/>
 <a href="pscomp_1.html#K15">W-bound</a> <font color="Maroon">P</font> <a href="hidden.html#R1">=</a>  <a href="pscomp_1.html#K17">E-bound</a> <font color="Maroon">P</font>
 <b>by </b><i>, <a class="ref" href="sppol_2.html#T1">SPPOL_2:1</a></i>;<br/><b>hence </b><a NAME="E3:18_1"/>
contradiction
 <b>by </b><i><a class="ref" href="topreal5.html#T23">TOPREAL5:23</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E2:18"/>
 <a href="pscomp_1.html#K27">W-min</a> <font color="Maroon">P</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="pscomp_1.html#K32">E-min</a> <font color="Maroon">P</font>
 ;<br/>


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