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<span class="kw">consider </span><font color="Maroon" title="c1">m</font> being   <a href="xreal_0.html#V1" title="XREAL_0:attr.1">real</a>   <a href="ordinal1.html#NM1" title="ORDINAL1:NM.1">number</a> <span class="kw"> such that </span><br/><a NAME="E2:18_1_1"/><span class="lab"><font color="Green" title="E9">J0</font></span>: 
<font color="Maroon" title="c1">m</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a>  <a href="xxreal_0.html#K2" title="XXREAL_0:func.2">-infty</a> 
 ;<br/>
<span class="kw">set </span><font color="Maroon" title="c2">L</font> =  <a href="prob_1.html#K10" title="PROB_1:func.10">halfline</a> <font color="Maroon" title="c1">m</font>;<br/>
<span class="kw">set </span><font color="Maroon" title="c3">LL</font> =  <a href="prob_1.html#K11" title="PROB_1:func.11">Family_of_halflines</a> ;<br/>
<a NAME="E3:18_1_1"/><span class="lab"><font color="Green" title="E10">Q30</font></span>: 
 not  <a href="prob_1.html#K10" title="PROB_1:func.10">halfline</a> <font color="Maroon" title="c1">m</font> is  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:18_1_1"><span class="lab"><font color="Green" title="E9">J0</font></span></a>, <a class="ref" href="xxreal_1.html#T33" title="XXREAL_1:th.33">XXREAL_1:33</a></span>;<br/>
<a NAME="E4:18_1_1"/>
<font color="Maroon" title="c1">m</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="xreal_0.html#D1" title="XREAL_0:def.1">XREAL_0:def 1</a></span>;<br/>
<a NAME="E5:18_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E11">Q0</font></span>: 
 <a href="prob_1.html#K10" title="PROB_1:func.10">halfline</a> <font color="Maroon" title="c1">m</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="prob_1.html#K11" title="PROB_1:func.11">Family_of_halflines</a> 
 
;<br/>
<a NAME="E6:18_1_1"/>
 <a href="prob_1.html#K11" title="PROB_1:func.11">Family_of_halflines</a>  is   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <a href="prob_1.html#K12" title="PROB_1:func.12">Borel_Sets</a>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="prob_1.html#D9" title="PROB_1:def.9">PROB_1:def 9</a></span>;<br/>
<span class="kw">hence </span><a NAME="E7:18_1_1"/>
 not  for <font color="Olive">b<sub>1</sub></font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="prob_1.html#K12" title="PROB_1:func.12">Borel_Sets</a>  holds  <font color="Olive">b<sub>1</sub></font> is  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:18_1_1"><span class="lab"><font color="Green" title="E11">Q0</font></span></a>, <a class="txt" href="#E3:18_1_1"><span class="lab"><font color="Green" title="E10">Q30</font></span></a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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