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<b>assume </b><a NAME="E1:14_1_1"/><i><font color="Green" title="E10">A1</font></i>: 
 <a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> <font color="Maroon" title="c2">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 ; <i><font color="Red">:: according to </font></i><a class="ref" href="xcmplx_0.html#D3" target="_self" title="XCMPLX_0:def.3">XCMPLX_0:def 3</a><br/>

<a NAME="E2:14_1_1"/>
<font color="Maroon" title="c2">x</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> <font color="Maroon" title="c2">x</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 
<b>by </b><i><a class="ref" href="xcmplx_0.html#D6" target="_self" title="XCMPLX_0:def.6">Def6</a></i>;<br/>
<b>then consider </b><font color="Maroon" title="c3">x1</font>, <font color="Maroon" title="c4">x2</font>, <font color="Maroon" title="c5">y1</font>, <font color="Maroon" title="c6">y2</font> being    <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> <b> such that </b><br/><a NAME="E4:14_1_1"/><i><font color="Green" title="E11">A2</font></i>: 
<font color="Maroon" title="c2">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="c3">x1</font>,<font color="Maroon" title="c4">x2</font></span><a href="arytm_0.html#K5" title="ARYTM_0:func.5">*]</a></span>
 <b>and </b><br/><a NAME="E5:14_1_1"/><i><font color="Green" title="E12">A3</font></i>: 
 <a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> <font color="Maroon" title="c2">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="c5">y1</font>,<font color="Maroon" title="c6">y2</font></span><a href="arytm_0.html#K5" title="ARYTM_0:func.5">*]</a></span>
 <b>and </b><br/><a NAME="E6:14_1_1"/><i><font color="Green" title="E13">A4</font></i>: 
 <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <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"><span class="p2">(<span class="default"><a href="arytm_0.html#K1" title="ARYTM_0:func.1">+</a> <font color="Maroon" title="c3">x1</font>,<font color="Maroon" title="c5">y1</font></span>)</span>,<span class="p2">(<span class="default"><a href="arytm_0.html#K1" title="ARYTM_0:func.1">+</a> <font color="Maroon" title="c4">x2</font>,<font color="Maroon" title="c6">y2</font></span>)</span></span><a href="arytm_0.html#K5" title="ARYTM_0:func.5">*]</a></span>
 <b>by </b><i><a class="ref" href="xcmplx_0.html#D4" target="_self" title="XCMPLX_0:def.4">Def4</a></i>;<br/>
<a NAME="E7:14_1_1"/><i><font color="Green" title="E14">A5</font></i>: 
 <a href="arytm_0.html#K1" title="ARYTM_0:func.1">+</a> <font color="Maroon" title="c4">x2</font>,<font color="Maroon" title="c6">y2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 
<b>by </b><i><a class="txt" href="xcmplx_0.html#E6:14_1_1"><i><font color="Green" title="E13">A4</font></i></a>, <a class="ref" href="arytm_0.html#T26" title="ARYTM_0:th.26">ARYTM_0:26</a></i>;<br/>
<a NAME="E8:14_1_1"/><b>then </b><i><font color="Green" title="E15">A6</font></i>: 
 <a href="arytm_0.html#K1" title="ARYTM_0:func.1">+</a> <font color="Maroon" title="c3">x1</font>,<font color="Maroon" title="c5">y1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 
<b>by </b><i><a class="txt" href="xcmplx_0.html#E6:14_1_1"><i><font color="Green" title="E13">A4</font></i></a>, <a class="ref" href="arytm_0.html#D7" title="ARYTM_0:def.7">ARYTM_0:def 7</a></i>;<br/>
<a NAME="E9:14_1_1"/>
<font color="Maroon" title="c6">y2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 
<b>by </b><i><a class="txt" href="xcmplx_0.html#E1:14_1_1"><i><font color="Green" title="E10">A1</font></i></a>, <a class="txt" href="xcmplx_0.html#E5:14_1_1"><i><font color="Green" title="E12">A3</font></i></a>, <a class="ref" href="arytm_0.html#T26" title="ARYTM_0:th.26">ARYTM_0:26</a></i>;<br/>
<a NAME="E10:14_1_1"/><b>then </b><i><font color="Green" title="E16">A7</font></i>: 
<font color="Maroon" title="c5">y1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 
<b>by </b><i><a class="txt" href="xcmplx_0.html#E1:14_1_1"><i><font color="Green" title="E10">A1</font></i></a>, <a class="txt" href="xcmplx_0.html#E5:14_1_1"><i><font color="Green" title="E12">A3</font></i></a>, <a class="ref" href="arytm_0.html#D7" title="ARYTM_0:def.7">ARYTM_0:def 7</a></i>;<br/>
<a NAME="E11:14_1_1"/>
<font color="Maroon" title="c4">x2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 
<b>by </b><i><a class="txt" href="xcmplx_0.html#E1:14_1_1"><i><font color="Green" title="E10">A1</font></i></a>, <a class="txt" href="xcmplx_0.html#E5:14_1_1"><i><font color="Green" title="E12">A3</font></i></a>, <a class="txt" href="xcmplx_0.html#E7:14_1_1"><i><font color="Green" title="E14">A5</font></i></a>, <a class="ref" href="arytm_0.html#T13" title="ARYTM_0:th.13">ARYTM_0:13</a>, <a class="ref" href="arytm_0.html#T26" title="ARYTM_0:th.26">ARYTM_0:26</a></i>;<br/>
<b>then </b><font color="Maroon" title="c2">x</font> = 
<font color="Maroon" title="c3">x1</font>
<b>by </b><i><a class="txt" href="xcmplx_0.html#E4:14_1_1"><i><font color="Green" title="E11">A2</font></i></a>, <a class="ref" href="arytm_0.html#D7" title="ARYTM_0:def.7">ARYTM_0:def 7</a></i>
<br/>.= 
 <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
<b>by </b><i><a class="txt" href="xcmplx_0.html#E8:14_1_1"><i><font color="Green" title="E15">A6</font></i></a>, <a class="txt" href="xcmplx_0.html#E10:14_1_1"><i><font color="Green" title="E16">A7</font></i></a>, <a class="ref" href="arytm_0.html#T13" title="ARYTM_0:th.13">ARYTM_0:13</a></i>
;<br/>
<b>hence </b><a NAME="E13:14_1_1"/>
contradiction
 ;<br/>


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