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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">x</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="euclid.html#K1">REAL</a> <font color="Maroon">n</font>;<br/>



<b>thus </b><a NAME="E1:28"/>
( <span class="p1"><a href="euclid_4.html#K5" target="_self">|(</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">x</font></span><a href="euclid_4.html#K5" target="_self">)|</a></span> <a href="hidden.html#R1">=</a> 0 implies <span class="p1"><a href="euclid_4.html#K4" target="_self">|.</a><span class="default"><font color="Maroon">x</font></span><a href="euclid_4.html#K4" target="_self">.|</a></span> <a href="hidden.html#R1">=</a> 0 )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="28_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:28_1"/>
<span class="p1"><a href="euclid_4.html#K5" target="_self">|(</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">x</font></span><a href="euclid_4.html#K5" target="_self">)|</a></span> <a href="hidden.html#R1">=</a> 0
 ;<br/>

<a NAME="E2:28_1"/><b>then </b>
<span class="p1"><a href="euclid_4.html#K4" target="_self">|.</a><span class="default"><font color="Maroon">x</font></span><a href="euclid_4.html#K4" target="_self">.|</a></span> <a href="square_1.html#K5">^2</a>  <a href="hidden.html#R1">=</a> 0
 
<b>by </b><i/>;<br/>
<b>hence </b><a NAME="E3:28_1"/>
<span class="p1"><a href="euclid_4.html#K4" target="_self">|.</a><span class="default"><font color="Maroon">x</font></span><a href="euclid_4.html#K4" target="_self">.|</a></span> <a href="hidden.html#R1">=</a> 0
 <b>by </b><i><a class="ref" href="xcmplx_1.html#T6">XCMPLX_1:6</a></i>;<br/>


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

<b>thus </b><a NAME="E2:28"/>
( <span class="p1"><a href="euclid_4.html#K4" target="_self">|.</a><span class="default"><font color="Maroon">x</font></span><a href="euclid_4.html#K4" target="_self">.|</a></span> <a href="hidden.html#R1">=</a> 0 implies <span class="p1"><a href="euclid_4.html#K5" target="_self">|(</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">x</font></span><a href="euclid_4.html#K5" target="_self">)|</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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