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<a NAME="E1:60_3_1"/>
 <a href="topreal1.html#K6" title="TOPREAL1:func.6">south_halfline</a> <font color="Maroon" title="c1">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">{<span class="default"> <span class="p2"><a href="euclid.html#K19" title="EUCLID:func.19">|[</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c1">p</font> <a href="euclid.html#K17" title="EUCLID:func.17">`1</a> </span>)</span>,<font color="Olive" title="b1">r</font></span><a href="euclid.html#K19" title="EUCLID:func.19">]|</a></span> where <font color="Olive" title="b1">r</font> is    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a>  : <font color="Olive" title="b1">r</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c1">p</font> <a href="euclid.html#K18" title="EUCLID:func.18">`2</a>  </span>}</span> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="topreal1.html#T42" title="TOPREAL1:th.42">TOPREAL1:42</a></span>;<br/>
<span class="kw">hence </span><a NAME="E2:60_3_1"/>
 <a href="topreal1.html#K6" title="TOPREAL1:func.6">south_halfline</a> <font color="Maroon" title="c1">p</font> is  <a href="convex1.html#V1" title="CONVEX1:attr.1">convex</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="jordan1.html#E67"><span class="lab"><font color="Green" title="E48">Lm13</font></span></a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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