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<b>let </b><font color="Maroon" title="c1">r</font>, <font color="Maroon" title="c2">s</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="E1:11"/><i><font color="Green" title="E4">A1</font></i>: 
<font color="Maroon" title="c1">r</font> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> <font color="Maroon" title="c2">s</font>
 ;<br/>

<b>assume </b><a NAME="E2:11"/>
<span class="p1"><a href="int_1.html#K1" title="INT_1:func.1">[\</a><span class="default"><font color="Maroon" title="c1">r</font></span><a href="int_1.html#K1" title="INT_1:func.1">/]</a></span> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <span class="p1"><a href="int_1.html#K1" title="INT_1:func.1">[\</a><span class="default"><font color="Maroon" title="c2">s</font></span><a href="int_1.html#K1" title="INT_1:func.1">/]</a></span>
 ;<br/>

<a NAME="E3:11"/><b>then </b><i><font color="Green" title="E5">A2</font></i>: 
<span class="p1"><a href="int_1.html#K1" title="INT_1:func.1">[\</a><span class="default"><font color="Maroon" title="c1">r</font></span><a href="int_1.html#K1" title="INT_1:func.1">/]</a></span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <span class="p1"><a href="int_1.html#K1" title="INT_1:func.1">[\</a><span class="default"><font color="Maroon" title="c2">s</font></span><a href="int_1.html#K1" title="INT_1:func.1">/]</a></span>
 
<b>by </b><i><a class="ref" href="int_1.html#T20" title="INT_1:th.20">INT_1:20</a></i>;<br/>
<a NAME="E4:11"/>
<font color="Maroon" title="c1">r</font> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 1 <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <span class="p1"><a href="int_1.html#K1" title="INT_1:func.1">[\</a><span class="default"><font color="Maroon" title="c1">r</font></span><a href="int_1.html#K1" title="INT_1:func.1">/]</a></span>
 
<b>by </b><i><a class="ref" href="int_1.html#D4" title="INT_1:def.4">INT_1:def 4</a></i>;<br/>
<a NAME="E5:11"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon" title="c1">r</font> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 1</span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> 1 <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <span class="p1"><a href="int_1.html#K1" title="INT_1:func.1">[\</a><span class="default"><font color="Maroon" title="c1">r</font></span><a href="int_1.html#K1" title="INT_1:func.1">/]</a></span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> 1
 
<b>by </b><i><a class="ref" href="xreal_1.html#T8" title="XREAL_1:th.8">XREAL_1:8</a></i>;<br/>
<a NAME="E6:11"/><b>then </b>
( <font color="Maroon" title="c1">r</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <span class="p1"><a href="int_1.html#K1" title="INT_1:func.1">[\</a><span class="default"><font color="Maroon" title="c2">s</font></span><a href="int_1.html#K1" title="INT_1:func.1">/]</a></span> &amp; <span class="p1"><a href="int_1.html#K1" title="INT_1:func.1">[\</a><span class="default"><font color="Maroon" title="c2">s</font></span><a href="int_1.html#K1" title="INT_1:func.1">/]</a></span> <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="pre_ff.html#E3:11"><i><font color="Green" title="E5">A2</font></i></a>, <a class="ref" href="xxreal_0.html#T2" title="XXREAL_0:th.2">XXREAL_0:2</a>, <a class="ref" href="int_1.html#D4" title="INT_1:def.4">INT_1:def 4</a></i>;<br/>
<b>hence </b><a NAME="E7:11"/>
contradiction
 <b>by </b><i><a class="txt" href="pre_ff.html#E1:11"><i><font color="Green" title="E4">A1</font></i></a>, <a class="ref" href="xxreal_0.html#T2" title="XXREAL_0:th.2">XXREAL_0:2</a></i>;<br/>


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