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<b>let </b><font color="Maroon">x</font> be    <a href="finseq_1.html#M2">FinSequence</a> of  <a href="numbers.html#K1">REAL</a> ;<br/>

<a NAME="E1:17"/>
( <span class="p1"><a href="euclid_2.html#K1" target="_self">|(</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">x</font></span><a href="euclid_2.html#K1" target="_self">)|</a></span> <a href="hidden.html#R1">=</a> 0 implies <span class="p1"><a href="euclid.html#K12">|.</a><span class="default"><font color="Maroon">x</font></span><a href="euclid.html#K12">.|</a></span> <a href="hidden.html#R1">=</a> 0 )
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="17_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:17_1"/>
<span class="p1"><a href="euclid_2.html#K1" target="_self">|(</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">x</font></span><a href="euclid_2.html#K1" target="_self">)|</a></span> <a href="hidden.html#R1">=</a> 0
 ;<br/>

<a NAME="E2:17_1"/><b>then </b>
<font color="Maroon">x</font> <a href="hidden.html#R1">=</a>  <a href="euclid.html#K5">0*</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">x</font></span>)</span>
 
<b>by </b><i/>;<br/>
<b>hence </b><a NAME="E3:17_1"/>
<span class="p1"><a href="euclid.html#K12">|.</a><span class="default"><font color="Maroon">x</font></span><a href="euclid.html#K12">.|</a></span> <a href="hidden.html#R1">=</a> 0
 <b>by </b><i><a class="ref" href="euclid.html#T10">EUCLID:10</a></i>;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E2:17"/>
( <span class="p1"><a href="euclid_2.html#K1" target="_self">|(</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">x</font></span><a href="euclid_2.html#K1" target="_self">)|</a></span> <a href="hidden.html#R1">=</a> 0 iff <span class="p1"><a href="euclid.html#K12">|.</a><span class="default"><font color="Maroon">x</font></span><a href="euclid.html#K12">.|</a></span> <a href="hidden.html#R1">=</a> 0 )
 <b>by </b><i>, <a class="ref" href="square_1.html#T60">SQUARE_1:60</a></i>;<br/>


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