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<b>let </b><font color="Maroon" title="c1">r2</font>, <font color="Maroon" title="c2">r</font>, <font color="Maroon" title="c3">r1</font> be  <a href="xreal_0.html#V1" title="XREAL_0:attr.1">real</a>  <a href="ordinal1.html#NM1" title="ORDINAL1:NM.1">number</a> ;<br/>





<b>assume </b><a NAME="E1:17"/><i><font color="Green" title="E8">A1</font></i>: 
<font color="Maroon" title="c1">r2</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c2">r</font>
 ;<br/>

<a NAME="E2:17"/>
<font color="Maroon" title="c3">r1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a> 
 
<b>by </b><i><a class="ref" href="xreal_0.html#D1" title="XREAL_0:def.1">XREAL_0:def 1</a></i>;<br/>
<a NAME="E3:17"/><b>then </b><i><font color="Green" title="E9">A2</font></i>: 
 <a href="xxreal_0.html#K2" title="XXREAL_0:func.2">-infty</a>  <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c3">r1</font>
 
<b>by </b><i><a class="ref" href="xxreal_0.html#T12" title="XXREAL_0:th.12">XXREAL_0:12</a></i>;<br/>
<b>hence </b><a NAME="E4:17"/>
<span class="p1"><a href="xxreal_1.html#K4" title="XXREAL_1:func.4">].</a><span class="default"><font color="Maroon" title="c3">r1</font>,<font color="Maroon" title="c1">r2</font></span><a href="xxreal_1.html#K4" title="XXREAL_1:func.4">.[</a></span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="limfunc1.html#NK2" title="LIMFUNC1:NK.2">left_open_halfline</a> <font color="Maroon" title="c2">r</font>
 <b>by </b><i><a class="txt" href="limfunc1.html#E1:17"><i><font color="Green" title="E8">A1</font></i></a>, <a class="ref" href="xxreal_1.html#T46" title="XXREAL_1:th.46">XXREAL_1:46</a></i>;<br/>

<b>thus </b><a NAME="E5:17"/>
<span class="p1"><a href="xxreal_1.html#K1" title="XXREAL_1:func.1">[.</a><span class="default"><font color="Maroon" title="c3">r1</font>,<font color="Maroon" title="c1">r2</font></span><a href="xxreal_1.html#K1" title="XXREAL_1:func.1">.]</a></span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="limfunc1.html#K2" title="LIMFUNC1:func.2">left_closed_halfline</a> <font color="Maroon" title="c2">r</font>
 <b>by </b><i><a class="txt" href="limfunc1.html#E1:17"><i><font color="Green" title="E8">A1</font></i></a>, <a class="txt" href="limfunc1.html#E3:17"><i><font color="Green" title="E9">A2</font></i></a>, <a class="ref" href="xxreal_1.html#T39" title="XXREAL_1:th.39">XXREAL_1:39</a></i>;<br/>


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