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<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="6_1_1_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c2">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/><b>assume </b><a NAME="E1:6_1_1_1"/><i><font color="Green" title="E4">A1</font></i>: 
<font color="Maroon" title="c2">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="xxreal_1.html#K3" title="XXREAL_1:func.3">].</a><span class="default"><a href="xxreal_0.html#K2" title="XXREAL_0:func.2">-infty</a> ,<font color="Maroon" title="c1">r</font></span><a href="xxreal_1.html#K3" title="XXREAL_1:func.3">.]</a></span>
 ;<br/><b>then reconsider </b><font color="Maroon" title="c3">s</font> = <font color="Maroon" title="c2">x</font> as  <a href="xxreal_0.html#V1" title="XXREAL_0:attr.1">ext-real</a>  <a href="ordinal1.html#NM1" title="ORDINAL1:NM.1">number</a>  <b>by </b><i><a class="ref" href="membered.html#D2" title="MEMBERED:def.2">MEMBERED:def 2</a></i>;<br/><a NAME="E3:6_1_1_1"/><i><font color="Green" title="E5">A2</font></i>: 
<font color="Maroon" title="c1">r</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="E4:6_1_1_1"/><i><font color="Green" title="E6">A3</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">s</font>
 <b>by </b><i><a class="txt" href="limfunc1.html#E1:6_1_1_1"><i><font color="Green" title="E4">A1</font></i></a>, <a class="ref" href="xxreal_1.html#T2" title="XXREAL_1:th.2">XXREAL_1:2</a></i>;<br/><a NAME="E5:6_1_1_1"/>
<font color="Maroon" title="c3">s</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c1">r</font>
 <b>by </b><i><a class="txt" href="limfunc1.html#E1:6_1_1_1"><i><font color="Green" title="E4">A1</font></i></a>, <a class="ref" href="xxreal_1.html#T2" title="XXREAL_1:th.2">XXREAL_1:2</a></i>;<br/><b>hence </b><a NAME="E6:6_1_1_1"/>
<font color="Maroon" title="c2">x</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="txt" href="limfunc1.html#E4:6_1_1_1"><i><font color="Green" title="E6">A3</font></i></a>, <a class="ref" href="xxreal_0.html#T13" title="XXREAL_0:th.13">XXREAL_0:13</a>, <a class="txt" href="limfunc1.html#E3:6_1_1_1"><i><font color="Green" title="E5">A2</font></i></a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E2:6_1_1"/>
<span class="p1"><a href="xxreal_1.html#K3" title="XXREAL_1:func.3">].</a><span class="default"><a href="xxreal_0.html#K2" title="XXREAL_0:func.2">-infty</a> ,<font color="Maroon" title="c1">r</font></span><a href="xxreal_1.html#K3" title="XXREAL_1:func.3">.]</a></span> is   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a> 
 <b>by </b><i><a class="ref" href="tarski.html#D3" title="TARSKI:def.3">TARSKI:def 3</a></i>;<br/>


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