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<b>let </b><font color="Maroon">g</font> be  <a href="xreal_0.html#V1">real</a>  <a href="ordinal1.html#NM1" target="_self">number</a> ;<br/><b>let </b><font color="Maroon">r</font> be  <a href="xreal_0.html#V1">real</a>  <a href="ordinal1.html#NM1" target="_self">number</a> ;<br/><b>let </b><font color="Maroon">x</font> be    <a href="hidden.html#M1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3">TARSKI:def 3</a><br/>





<b>assume </b><a NAME="E1:16"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="rcomp_1.html#K1">[.</a><span class="default"><font color="Maroon">g</font>,<font color="Maroon">r</font></span><a href="rcomp_1.html#K1">.]</a></span>
 ;<br/>

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


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