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<b>let </b><font color="Maroon">c<sub>1</sub></font> be   <a href="topreal2.html#NM1">Simple_closed_curve</a>;<br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="5_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:5_1"/><i><font color="Green">E2</font></i>: 
 <a href="pscomp_1.html#K28">W-max</a> <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a>  <a href="pscomp_1.html#K31">E-max</a> <font color="Maroon">c<sub>1</sub></font>
 ;<br/><a NAME="E2:5_1"/><i><font color="Green">E3</font></i>: 
<span class="p1"><a href="euclid.html#K23">|[</a><span class="default"><span class="p2">(<span class="default"><a href="pscomp_1.html#K15">W-bound</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<span class="p2">(<span class="default"><a href="pscomp_1.html#K11">sup</a> <span class="p3">(<span class="default"><a href="pscomp_1.html#K14">proj2</a>  <a href="pscomp_1.html#K12">||</a> <span class="p4">(<span class="default"><a href="pscomp_1.html#K23">W-most</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span></span>)</span></span><a href="euclid.html#K23">]|</a></span> <a href="hidden.html#R1">=</a>  <a href="pscomp_1.html#K28">W-max</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="ref" href="pscomp_1.html#D43">PSCOMP_1:def 43</a></i>;<br/><a NAME="E3:5_1"/>
<span class="p1"><a href="euclid.html#K23">|[</a><span class="default"><span class="p2">(<span class="default"><a href="pscomp_1.html#K17">E-bound</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<span class="p2">(<span class="default"><a href="pscomp_1.html#K11">sup</a> <span class="p3">(<span class="default"><a href="pscomp_1.html#K14">proj2</a>  <a href="pscomp_1.html#K12">||</a> <span class="p4">(<span class="default"><a href="pscomp_1.html#K25">E-most</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span></span>)</span></span><a href="euclid.html#K23">]|</a></span> <a href="hidden.html#R1">=</a>  <a href="pscomp_1.html#K31">E-max</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="ref" href="pscomp_1.html#D46">PSCOMP_1:def 46</a></i>;<br/><a NAME="E4:5_1"/><b>then </b>
 <a href="pscomp_1.html#K15">W-bound</a> <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a>  <a href="pscomp_1.html#K17">E-bound</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="jordan1b.html#E1:5_1"><i><font color="Green">E2</font></i></a>, <a class="txt" href="jordan1b.html#E2:5_1"><i><font color="Green">E3</font></i></a>, <a class="ref" href="sppol_2.html#T1">SPPOL_2:1</a></i>;<br/><b>hence </b><a NAME="E5:5_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="E2:5"/>
 <a href="pscomp_1.html#K28">W-max</a> <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="pscomp_1.html#K31">E-max</a> <font color="Maroon">c<sub>1</sub></font>
 ;<br/>


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