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<b>let </b><font color="Maroon">P</font> be   <a href="topreal2.html#NM1">Simple_closed_curve</a>;<br/><b>let </b><font color="Maroon">a</font> be   <a href="pre_topc.html#NM2">Point</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 2</span>)</span>;<br/><b>let </b><font color="Maroon">b</font> be   <a href="pre_topc.html#NM2">Point</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 2</span>)</span>;<br/><b>let </b><font color="Maroon">c</font> be   <a href="pre_topc.html#NM2">Point</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 2</span>)</span>;<br/><b>let </b><font color="Maroon">d</font> be   <a href="pre_topc.html#NM2">Point</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 2</span>)</span>;<br/>









<b>assume </b><a NAME="E1:12"/>
( (  <a href="jordan6.html#R1">LE</a> <font color="Maroon">a</font>,<font color="Maroon">b</font>,<font color="Maroon">P</font> &amp;  <a href="jordan6.html#R1">LE</a> <font color="Maroon">b</font>,<font color="Maroon">c</font>,<font color="Maroon">P</font> &amp;  <a href="jordan6.html#R1">LE</a> <font color="Maroon">c</font>,<font color="Maroon">d</font>,<font color="Maroon">P</font> ) or (  <a href="jordan6.html#R1">LE</a> <font color="Maroon">b</font>,<font color="Maroon">c</font>,<font color="Maroon">P</font> &amp;  <a href="jordan6.html#R1">LE</a> <font color="Maroon">c</font>,<font color="Maroon">d</font>,<font color="Maroon">P</font> &amp;  <a href="jordan6.html#R1">LE</a> <font color="Maroon">d</font>,<font color="Maroon">a</font>,<font color="Maroon">P</font> ) or (  <a href="jordan6.html#R1">LE</a> <font color="Maroon">c</font>,<font color="Maroon">d</font>,<font color="Maroon">P</font> &amp;  <a href="jordan6.html#R1">LE</a> <font color="Maroon">d</font>,<font color="Maroon">a</font>,<font color="Maroon">P</font> &amp;  <a href="jordan6.html#R1">LE</a> <font color="Maroon">a</font>,<font color="Maroon">b</font>,<font color="Maroon">P</font> ) or (  <a href="jordan6.html#R1">LE</a> <font color="Maroon">d</font>,<font color="Maroon">a</font>,<font color="Maroon">P</font> &amp;  <a href="jordan6.html#R1">LE</a> <font color="Maroon">a</font>,<font color="Maroon">b</font>,<font color="Maroon">P</font> &amp;  <a href="jordan6.html#R1">LE</a> <font color="Maroon">b</font>,<font color="Maroon">c</font>,<font color="Maroon">P</font> ) )
 ; <i><font color="Red">:: according to </font></i><a class="ref" href="jordan17.html#D1" target="_self">JORDAN17:def 1</a><br/>

<b>hence </b><a NAME="E2:12"/>
( (  <a href="jordan6.html#R1">LE</a> <font color="Maroon">c</font>,<font color="Maroon">d</font>,<font color="Maroon">P</font> &amp;  <a href="jordan6.html#R1">LE</a> <font color="Maroon">d</font>,<font color="Maroon">a</font>,<font color="Maroon">P</font> &amp;  <a href="jordan6.html#R1">LE</a> <font color="Maroon">a</font>,<font color="Maroon">b</font>,<font color="Maroon">P</font> ) or (  <a href="jordan6.html#R1">LE</a> <font color="Maroon">d</font>,<font color="Maroon">a</font>,<font color="Maroon">P</font> &amp;  <a href="jordan6.html#R1">LE</a> <font color="Maroon">a</font>,<font color="Maroon">b</font>,<font color="Maroon">P</font> &amp;  <a href="jordan6.html#R1">LE</a> <font color="Maroon">b</font>,<font color="Maroon">c</font>,<font color="Maroon">P</font> ) or (  <a href="jordan6.html#R1">LE</a> <font color="Maroon">a</font>,<font color="Maroon">b</font>,<font color="Maroon">P</font> &amp;  <a href="jordan6.html#R1">LE</a> <font color="Maroon">b</font>,<font color="Maroon">c</font>,<font color="Maroon">P</font> &amp;  <a href="jordan6.html#R1">LE</a> <font color="Maroon">c</font>,<font color="Maroon">d</font>,<font color="Maroon">P</font> ) or (  <a href="jordan6.html#R1">LE</a> <font color="Maroon">b</font>,<font color="Maroon">c</font>,<font color="Maroon">P</font> &amp;  <a href="jordan6.html#R1">LE</a> <font color="Maroon">c</font>,<font color="Maroon">d</font>,<font color="Maroon">P</font> &amp;  <a href="jordan6.html#R1">LE</a> <font color="Maroon">d</font>,<font color="Maroon">a</font>,<font color="Maroon">P</font> ) )
 ; <i><font color="Red">:: according to </font></i><a class="ref" href="jordan17.html#D1" target="_self">JORDAN17:def 1</a><br/>


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