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<b>let </b><font color="Maroon">c<sub>1</sub></font>, <font color="Maroon">c<sub>2</sub></font> be   <a href="nat_1.html#NM1">Nat</a>;<br/>

<b>assume </b><a NAME="E1:20"/><i><font color="Green">E13</font></i>: 
<font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>2</sub></font>
 ;<br/>

<b>assume </b><a NAME="E2:20"/><i><font color="Green">E14</font></i>: 
 <a href="scmpds_2.html#K3">DataLoc</a> <font color="Maroon">c<sub>1</sub></font>,0 <a href="hidden.html#R1">=</a>  <a href="scmpds_2.html#K3">DataLoc</a> <font color="Maroon">c<sub>2</sub></font>,0
 ;<br/>

<a NAME="E3:20"/>
(  <a href="scmpds_2.html#K3">DataLoc</a> <font color="Maroon">c<sub>1</sub></font>,0 <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default">2 <a href="nat_1.html#K2">*</a> <span class="p2">(<span class="default"><a href="int_2.html#K1">abs</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 0</span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1 &amp;  <a href="scmpds_2.html#K3">DataLoc</a> <font color="Maroon">c<sub>2</sub></font>,0 <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default">2 <a href="nat_1.html#K2">*</a> <span class="p2">(<span class="default"><a href="int_2.html#K1">abs</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="nat_1.html#K1">+</a> 0</span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1 )
 
<b>by </b><i><a class="ref" href="scmpds_2.html#D4">SCMPDS_2:def 4</a></i>;<br/>
<a NAME="E4:20"/><b>then </b>
2 <a href="nat_1.html#K2">*</a> <span class="p1">(<span class="default"><a href="int_2.html#K1">abs</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="hidden.html#R1">=</a> 2 <a href="nat_1.html#K2">*</a> <span class="p1">(<span class="default"><a href="int_2.html#K1">abs</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>
 
<b>by </b><i><a class="txt" href="scmpds_4.html#E2:20"><i><font color="Green">E14</font></i></a></i>;<br/>
<a NAME="E5:20"/><b>then </b>
 <a href="int_2.html#K1">abs</a> <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a>  <a href="int_2.html#K1">abs</a> <font color="Maroon">c<sub>2</sub></font>
 
;<br/>
<a NAME="E6:20"/><b>then </b>
<font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a>  <a href="int_2.html#K1">abs</a> <font color="Maroon">c<sub>2</sub></font>
 
<b>by </b><i><a class="ref" href="absvalue.html#D1">ABSVALUE:def 1</a></i>;<br/>
<b>hence </b><a NAME="E7:20"/>
contradiction
 <b>by </b><i><a class="txt" href="scmpds_4.html#E1:20"><i><font color="Green">E13</font></i></a>, <a class="ref" href="absvalue.html#D1">ABSVALUE:def 1</a></i>;<br/>


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