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<b>let </b><font color="Maroon" title="c1">p</font>, <font color="Maroon" title="c2">q</font> be   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> 2</span>)</span>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c1">p</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c2">q</font> &amp;  <a href="topreal1.html#K3" title="TOPREAL1:func.3">LSeg</a> <font color="Maroon" title="c1">p</font>,<font color="Maroon" title="c2">q</font> is <a href="sppol_1.html#V1" title="SPPOL_1:attr.1">horizontal</a> implies <span class="p1"><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">&lt;*</a><span class="default"><font color="Maroon" title="c1">p</font>,<font color="Maroon" title="c2">q</font></span><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">*&gt;</a></span> <a href="topreal1.html#NR2" title="TOPREAL1:NR.2">is_S-Seq</a>  )</span><br/>

<b>assume </b><b>that </b><br/><a NAME="E1:8"/><i><font color="Green" title="E2">A1</font></i>: 
<font color="Maroon" title="c1">p</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c2">q</font>
 <b>and </b><br/><a NAME="E2:8"/><i><font color="Green" title="E3">A2</font></i>: 
 <a href="topreal1.html#K3" title="TOPREAL1:func.3">LSeg</a> <font color="Maroon" title="c1">p</font>,<font color="Maroon" title="c2">q</font> is <a href="sppol_1.html#V1" title="SPPOL_1:attr.1">horizontal</a>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <span class="p1"><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">&lt;*</a><span class="default"><font color="Maroon" title="c1">p</font>,<font color="Maroon" title="c2">q</font></span><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">*&gt;</a></span> <a href="topreal1.html#NR2" title="TOPREAL1:NR.2">is_S-Seq</a> </span><br/>

<a NAME="E3:8"/>
<font color="Maroon" title="c1">p</font> <a href="euclid.html#K22" title="EUCLID:func.22">`2</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">q</font> <a href="euclid.html#K22" title="EUCLID:func.22">`2</a> 
 
<b>by </b><i><a class="txt" href="jordan1b.html#E2:8"><i><font color="Green" title="E3">A2</font></i></a>, <a class="ref" href="sppol_1.html#T36" title="SPPOL_1:th.36">SPPOL_1:36</a></i>;<br/>
<b>hence </b><a NAME="E4:8"/>
<span class="p1"><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">&lt;*</a><span class="default"><font color="Maroon" title="c1">p</font>,<font color="Maroon" title="c2">q</font></span><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">*&gt;</a></span> <a href="topreal1.html#NR2" title="TOPREAL1:NR.2">is_S-Seq</a> 
 <b>by </b><i><a class="txt" href="jordan1b.html#E1:8"><i><font color="Green" title="E2">A1</font></i></a>, <a class="ref" href="sppol_2.html#T46" title="SPPOL_2:th.46">SPPOL_2:46</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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