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<b>let </b><font color="Maroon">i</font> be    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/>

<div><b>hereby </b>
<div class="add"><b>assume </b><a NAME="E1:107_1"/>
 <a href="ami_1.html#K2">IC</a> <a href="scmpds_2.html#K1" target="_self">SCMPDS</a>  <a href="hidden.html#R1">=</a>  <a href="ami_3.html#K15">dl.</a> <font color="Maroon">i</font>
 ;<br/><a NAME="E2:107_1"/><b>then </b>
0 <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default">2 <a href="nat_1.html#K2">*</a> <font color="Maroon">i</font></span>)</span> <a href="nat_1.html#K1">+</a> 1
 <b>by </b><i><a class="ref" href="ami_3.html#D19">AMI_3:def 19</a></i>;<br/><b>hence </b><a NAME="E3:107_1"/>
contradiction
 ;<br/></div>
<b>end;</b></div>

<b>assume </b><a NAME="E2:107"/>
 <a href="ami_1.html#K2">IC</a> <a href="scmpds_2.html#K1" target="_self">SCMPDS</a>  <a href="hidden.html#R1">=</a>  <a href="ami_3.html#K16">il.</a> <font color="Maroon">i</font>
 ;<br/>

<b>then </b>0 = 
<span class="p1">(<span class="default">2 <a href="nat_1.html#K2">*</a> <font color="Maroon">i</font></span>)</span> <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span>
<b>by </b><i><a class="ref" href="ami_3.html#D20">AMI_3:def 20</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default">2 <a href="nat_1.html#K2">*</a> <font color="Maroon">i</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> 1

;<br/>
<b>hence </b><a NAME="E4:107"/>
contradiction
 ;<br/>


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