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<b>let </b><font color="Maroon" title="c1">X</font> be   <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> ;<br/>

<b>given </b><font color="Maroon" title="c2">s</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> <b> such that </b><a NAME="E1:23"/><i><font color="Green" title="E15">A1</font></i>: 
for <font color="Olive" title="b1">t</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>   st <font color="Olive" title="b1">t</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">X</font> holds <br/><font color="Olive" title="b1">t</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c2">s</font>
 ; <i><font color="Red">:: according to </font></i><a class="ref" href="seq_4.html#D1" title="SEQ_4:def.1">SEQ_4:def 1</a><br/>

<b>take </b>
 <a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> <font color="Maroon" title="c2">s</font>
; <i><font color="Red">:: according to </font></i><a class="ref" href="seq_4.html#D2" title="SEQ_4:def.2">SEQ_4:def 2</a><br/>

<b>let </b><font color="Maroon" title="c3">t</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="E2:23"/>
<font color="Maroon" title="c3">t</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="pscomp_1.html#K4" title="PSCOMP_1:func.4">-</a> <font color="Maroon" title="c1">X</font>
 ;<br/>

<a NAME="E3:23"/><b>then </b>
<font color="Maroon" title="c3">t</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Olive" title="b1">r3</font></span>)</span> where <font color="Olive" title="b1">r3</font> is   <a href="real_1.html#NM1" title="REAL_1:NM.1">Real</a> : <font color="Olive" title="b1">r3</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">X</font> </span>}</span> 
 
;<br/>
<b>then consider </b><font color="Maroon" title="c4">r3</font> being   <a href="real_1.html#NM1" title="REAL_1:NM.1">Real</a><b> such that </b><br/><a NAME="E5:23"/><i><font color="Green" title="E16">A2</font></i>: 
( <font color="Maroon" title="c3">t</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c4">r3</font> &amp; <font color="Maroon" title="c4">r3</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">X</font> )
 ;<br/>
<a NAME="E6:23"/>
<font color="Maroon" title="c4">r3</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c2">s</font>
 
<b>by </b><i><a class="txt" href="pscomp_1.html#E1:23"><i><font color="Green" title="E15">A1</font></i></a>, <a class="txt" href="pscomp_1.html#E5:23"><i><font color="Green" title="E16">A2</font></i></a></i>;<br/>
<b>hence </b><a NAME="E7:23"/>
<font color="Maroon" title="c3">t</font> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a>  <a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> <font color="Maroon" title="c2">s</font>
 <b>by </b><i><a class="txt" href="pscomp_1.html#E5:23"><i><font color="Green" title="E16">A2</font></i></a>, <a class="ref" href="xreal_1.html#T26" title="XREAL_1:th.26">XREAL_1:26</a></i>;<br/>


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