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<b>let </b><font color="Maroon" title="c1">x</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>let </b><font color="Maroon" title="c2">x1</font>, <font color="Maroon" title="c3">x2</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a> ;<br/>



<b>assume </b><a NAME="E1:4"/><i><font color="Green" title="E3">A1</font></i>: 
<font color="Maroon" title="c1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="arytm_0.html#K5" title="ARYTM_0:func.5">[*</a><span class="default"><font color="Maroon" title="c2">x1</font>,<font color="Maroon" title="c3">x2</font></span><a href="arytm_0.html#K5" title="ARYTM_0:func.5">*]</a></span>
 ;<br/>

<a NAME="E2:4"/><i><font color="Green" title="E4">A2</font></i>: 
<font color="Maroon" title="c1">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="ref" href="xreal_0.html#D1" title="XREAL_0:def.1">XREAL_0:def 1</a></i>;<br/>
<div><b>hereby </b>
<div class="add"><b>assume </b><a NAME="E1:4_1"/>
<font color="Maroon" title="c3">x2</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> 0
 ;<br/><a NAME="E2:4_1"/><b>then </b>
<font color="Maroon" title="c1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 0,1 <a href="funct_4.html#K5" title="FUNCT_4:func.5">--&gt;</a> <font color="Maroon" title="c2">x1</font>,<font color="Maroon" title="c3">x2</font>
 <b>by </b><i><a class="txt" href="axioms.html#E1:4"><i><font color="Green" title="E3">A1</font></i></a>, <a class="ref" href="arytm_0.html#D7" title="ARYTM_0:def.7">ARYTM_0:def 7</a></i>;<br/><b>hence </b><a NAME="E3:4_1"/>
contradiction
 <b>by </b><i><a class="txt" href="axioms.html#E2:4"><i><font color="Green" title="E4">A2</font></i></a>, <a class="ref" href="arytm_0.html#T10" title="ARYTM_0:th.10">ARYTM_0:10</a></i>;<br/></div>
<b>end;</b></div>

<b>hence </b><a NAME="E4:4"/>
<font color="Maroon" title="c1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">x1</font>
 <b>by </b><i><a class="txt" href="axioms.html#E1:4"><i><font color="Green" title="E3">A1</font></i></a>, <a class="ref" href="arytm_0.html#D7" title="ARYTM_0:def.7">ARYTM_0:def 7</a></i>;<br/>


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