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<b>let </b><font color="Maroon" title="c1">g</font>, <font color="Maroon" title="c2">r</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>let </b><font color="Maroon" title="c3">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3" title="TARSKI:def.3">TARSKI:def 3</a><br/>





<b>assume </b><a NAME="E1:16"/>
<font color="Maroon" title="c3">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="rcomp_1.html#K1" title="RCOMP_1:func.1">[.</a><span class="default"><font color="Maroon" title="c1">g</font>,<font color="Maroon" title="c2">r</font></span><a href="rcomp_1.html#K1" title="RCOMP_1:func.1">.]</a></span>
 ;<br/>

<a NAME="E2:16"/><b>then </b>
<font color="Maroon" title="c3">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">{<span class="default"> <font color="Olive" title="b1">r1</font> where <font color="Olive" title="b1">r1</font> is   <a href="real_1.html#NM1" title="REAL_1:NM.1">Real</a> : ( <font color="Maroon" title="c1">g</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Olive" title="b1">r1</font> &amp; <font color="Olive" title="b1">r1</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c2">r</font> ) </span>}</span> 
 
<b>by </b><i><a class="ref" href="rcomp_1.html#D1" title="RCOMP_1:def.1">RCOMP_1:def 1</a></i>;<br/>
<a NAME="E3:16"/><b>then </b>
 ex <font color="Olive" title="b1">g1</font> being  <a href="real_1.html#NM1" title="REAL_1:NM.1">Real</a> st <br/>( <font color="Olive" title="b1">g1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">x</font> &amp; <font color="Maroon" title="c1">g</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Olive" title="b1">g1</font> &amp; <font color="Olive" title="b1">g1</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c2">r</font> )
 
;<br/>
<a NAME="E4:16"/><b>then </b>
<font color="Maroon" title="c3">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">{<span class="default"> <font color="Olive" title="b1">g2</font> where <font color="Olive" title="b1">g2</font> is   <a href="real_1.html#NM1" title="REAL_1:NM.1">Real</a> : <font color="Olive" title="b1">g2</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c2">r</font> </span>}</span> 
 
;<br/>
<b>hence </b><a NAME="E5:16"/>
<font color="Maroon" title="c3">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="limfunc1.html#K2" title="LIMFUNC1:func.2">left_closed_halfline</a> <font color="Maroon" title="c2">r</font>
 ;<br/>


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