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<b>let </b><font color="Maroon" title="c2">b</font>, <font color="Maroon" title="c3">c</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="E1:77"/><i><font color="Green" title="E46">A1</font></i>: 
for <font color="Olive" title="b1">a</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">a</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> 0 holds <br/><font color="Maroon" title="c2">b</font> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <font color="Olive" title="b1">a</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c3">c</font>
 ;<br/>

<b>assume </b><a NAME="E2:77"/>
<font color="Maroon" title="c2">b</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> <font color="Maroon" title="c3">c</font>
 ;<br/>

<a NAME="E3:77"/><b>then </b><i><font color="Green" title="E47">A2</font></i>: 
0 <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c2">b</font> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <font color="Maroon" title="c3">c</font>
 
<b>by </b><i><a class="txt" href="xreal_1.html#E51"><i><font color="Green" title="E28">Lm24</font></i></a></i>;<br/>
<b>set </b><font color="Maroon" title="c4">d</font> = <font color="Maroon" title="c2">b</font> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <font color="Maroon" title="c3">c</font>;<br/>
<a NAME="E4:77"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c2">b</font> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <font color="Maroon" title="c3">c</font></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2 <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c2">b</font> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <font color="Maroon" title="c3">c</font>
 
<b>by </b><i><a class="txt" href="xreal_1.html#E3:77"><i><font color="Green" title="E47">A2</font></i></a>, <a class="txt" href="xreal_1.html#E76"><i><font color="Green" title="E44">Lm33</font></i></a></i>;<br/>
<a NAME="E5:77"/><b>then </b>
<font color="Maroon" title="c3">c</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">b</font> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <font color="Maroon" title="c3">c</font></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c3">c</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">b</font> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <font color="Maroon" title="c3">c</font></span>)</span>
 
<b>by </b><i><a class="txt" href="xreal_1.html#E18"><i><font color="Green" title="E13">Lm13</font></i></a></i>;<br/>
<a NAME="E6:77"/><b>then </b><i><font color="Green" title="E48">A3</font></i>: 
<font color="Maroon" title="c3">c</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c2">b</font> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">b</font> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <font color="Maroon" title="c3">c</font></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span>
 
<b>by </b><i><a class="txt" href="xreal_1.html#E35"><i><font color="Green" title="E24">Lm22</font></i></a></i>;<br/>
<a NAME="E7:77"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c2">b</font> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <font color="Maroon" title="c3">c</font></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2 <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> 0
 
<b>by </b><i><a class="txt" href="xreal_1.html#E3:77"><i><font color="Green" title="E47">A2</font></i></a>, <a class="txt" href="xreal_1.html#E75"><i><font color="Green" title="E43">Lm32</font></i></a></i>;<br/>
<b>hence </b><a NAME="E8:77"/>
contradiction
 <b>by </b><i><a class="txt" href="xreal_1.html#E1:77"><i><font color="Green" title="E46">A1</font></i></a>, <a class="txt" href="xreal_1.html#E6:77"><i><font color="Green" title="E48">A3</font></i></a></i>;<br/>


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