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

<b>consider </b><font color="Maroon">p1</font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E2:20_1_1"/><i><font color="Green">E49</font></i>: 
<font color="Maroon">p1</font> <a href="hidden.html#R2">in</a> <font color="Maroon">S</font>
 <b>by </b><i><a class="ref" href="xboole_0.html#D1">XBOOLE_0:def 1</a></i>;<br/>
<b>reconsider </b><font color="Maroon">p1</font> = <font color="Maroon">p1</font> as   <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> <b>by </b><i/>;<br/>
<a NAME="E4:20_1_1"/>
 ex <font color="Olive">p2</font> being  <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> st <br/>( <font color="Olive">p2</font> <a href="hidden.html#R2">in</a> <font color="Maroon">S</font> &amp; <font color="Olive">p2</font> <a href="euclid.html#K21">`1</a>  <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">p1</font> <a href="euclid.html#K21">`1</a>  )
 
<b>by </b><i/>;<br/>
<b>hence </b><a NAME="E5:20_1_1"/>
not <font color="Maroon">S</font> is <a href="sppol_1.html#V2">vertical</a>
 <b>by </b><i>, <a class="ref" href="sppol_1.html#D3">SPPOL_1:def 3</a></i>;<br/>

<a NAME="E6:20_1_1"/>
 ex <font color="Olive">p2</font> being  <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> st <br/>( <font color="Olive">p2</font> <a href="hidden.html#R2">in</a> <font color="Maroon">S</font> &amp; <font color="Olive">p2</font> <a href="euclid.html#K22">`2</a>  <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">p1</font> <a href="euclid.html#K22">`2</a>  )
 
<b>by </b><i/>;<br/>
<b>hence </b><a NAME="E7:20_1_1"/>
not <font color="Maroon">S</font> is <a href="sppol_1.html#V1">horizontal</a>
 <b>by </b><i>, <a class="ref" href="sppol_1.html#D2">SPPOL_1:def 2</a></i>;<br/>


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