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<b>let </b><font color="Maroon">n</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/><b>let </b><font color="Maroon">x1</font> be    <a href="finseq_2.html#M2">Element</a> of  <a href="euclid.html#K1" target="_self">REAL</a> <font color="Maroon">n</font>;<br/><b>let </b><font color="Maroon">x2</font> be    <a href="finseq_2.html#M2">Element</a> of  <a href="euclid.html#K1" target="_self">REAL</a> <font color="Maroon">n</font>;<br/>





<b>assume </b><a NAME="E1:30"/>
<font color="Maroon">x1</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">x2</font>
 ;<br/>

<a NAME="E2:30"/><b>then </b>
( <span class="p1"><a href="euclid.html#K12" target="_self">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">x1</font> <a href="euclid.html#K8" target="_self">-</a> <font color="Maroon">x2</font></span>)</span></span><a href="euclid.html#K12" target="_self">.|</a></span> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 0 &amp; 0 <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <span class="p1"><a href="euclid.html#K12" target="_self">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">x1</font> <a href="euclid.html#K8" target="_self">-</a> <font color="Maroon">x2</font></span>)</span></span><a href="euclid.html#K12" target="_self">.|</a></span> )
 
<b>by </b><i>, </i>;<br/>
<b>hence </b><a NAME="E3:30"/>
<span class="p1"><a href="euclid.html#K12" target="_self">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">x1</font> <a href="euclid.html#K8" target="_self">-</a> <font color="Maroon">x2</font></span>)</span></span><a href="euclid.html#K12" target="_self">.|</a></span> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0
 ;<br/>


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