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<div class="add">

<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/>

<b>thus </b><a NAME="E1:14"/>
( <a href="ami_2.html#K5" target="_self">SCM-OK</a>  <a href="funct_2.html#K3">.</a> <font color="Maroon">i</font> <a href="hidden.html#R1">=</a>  <a href="ami_2.html#K3" target="_self">SCM-Instr-Loc</a>  implies <font color="Maroon">i</font> <a href="hidden.html#R1">=</a> 0 )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="14_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:14_1"/><i><font color="Green">E33</font></i>: 
<a href="ami_2.html#K5" target="_self">SCM-OK</a>  <a href="funct_2.html#K3">.</a> <font color="Maroon">i</font> <a href="hidden.html#R1">=</a>  <a href="ami_2.html#K3" target="_self">SCM-Instr-Loc</a> 
 ;<br/>

<b>assume </b><a NAME="E2:14_1"/>
<font color="Maroon">i</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 0
 ;<br/>

<a NAME="E3:14_1"/><b>then </b>
(  ex <font color="Olive">j</font> being   <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a>  st <font color="Maroon">i</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default">2 <a href="nat_1.html#K2">*</a> <font color="Olive">j</font></span>)</span> <a href="nat_1.html#K1">+</a> 1 or  ex <font color="Olive">j</font> being   <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a>  st <font color="Maroon">i</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default">2 <a href="nat_1.html#K2">*</a> <font color="Olive">j</font></span>)</span> <a href="nat_1.html#K1">+</a> 2 )
 
<b>by </b><i/>;<br/>
<b>hence </b><a NAME="E4:14_1"/>
contradiction
 <b>by </b><i>, , </i>;<br/>


</div><b>end;</b></div>

<b>thus </b><a NAME="E2:14"/>
( <font color="Maroon">i</font> <a href="hidden.html#R1">=</a> 0 implies <a href="ami_2.html#K5" target="_self">SCM-OK</a>  <a href="funct_2.html#K3">.</a> <font color="Maroon">i</font> <a href="hidden.html#R1">=</a>  <a href="ami_2.html#K3" target="_self">SCM-Instr-Loc</a>  )
 <b>by </b><i/>;<br/>


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