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<b>let </b><font color="Maroon">c<sub>1</sub></font> be   <a href="nat_1.html#NM1">Nat</a>;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font>, <font color="Maroon">c<sub>3</sub></font> be    <a href="subset_1.html#M1">Element</a> of  <a href="euclid.html#K1">REAL</a> <font color="Maroon">c<sub>1</sub></font>;<br/>



<b>thus </b><span class="p1"><a href="euclid_4.html#K4" target="_self">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="euclid.html#K7">+</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span><a href="euclid_4.html#K4" target="_self">.|</a></span> <a href="square_1.html#K5">^2</a>  = 
<span class="p1"><a href="euclid_4.html#K5" target="_self">|(</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="euclid.html#K7">+</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="euclid.html#K7">+</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span><a href="euclid_4.html#K5" target="_self">)|</a></span>
<b>by </b><i><a class="ref" href="euclid_4.html#T18" target="_self">Th18</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2"><a href="euclid_4.html#K5" target="_self">|(</a><span class="default"><font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>2</sub></font></span><a href="euclid_4.html#K5" target="_self">)|</a></span> <a href="real_1.html#K3">+</a> <span class="p2">(<span class="default">2 <a href="real_1.html#K4">*</a> <span class="p3"><a href="euclid_4.html#K5" target="_self">|(</a><span class="default"><font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font></span><a href="euclid_4.html#K5" target="_self">)|</a></span></span>)</span></span>)</span> <a href="real_1.html#K3">+</a> <span class="p1"><a href="euclid_4.html#K5" target="_self">|(</a><span class="default"><font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>3</sub></font></span><a href="euclid_4.html#K5" target="_self">)|</a></span>
<b>by </b><i><a class="ref" href="euclid_4.html#T37" target="_self">Th37</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3"><a href="euclid_4.html#K4" target="_self">|.</a><span class="default"><font color="Maroon">c<sub>2</sub></font></span><a href="euclid_4.html#K4" target="_self">.|</a></span> <a href="square_1.html#K5">^2</a> </span>)</span> <a href="real_1.html#K3">+</a> <span class="p2">(<span class="default">2 <a href="real_1.html#K4">*</a> <span class="p3"><a href="euclid_4.html#K5" target="_self">|(</a><span class="default"><font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font></span><a href="euclid_4.html#K5" target="_self">)|</a></span></span>)</span></span>)</span> <a href="real_1.html#K3">+</a> <span class="p1"><a href="euclid_4.html#K5" target="_self">|(</a><span class="default"><font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>3</sub></font></span><a href="euclid_4.html#K5" target="_self">)|</a></span>
<b>by </b><i><a class="ref" href="euclid_4.html#T18" target="_self">Th18</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3"><a href="euclid_4.html#K4" target="_self">|.</a><span class="default"><font color="Maroon">c<sub>2</sub></font></span><a href="euclid_4.html#K4" target="_self">.|</a></span> <a href="square_1.html#K5">^2</a> </span>)</span> <a href="real_1.html#K3">+</a> <span class="p2">(<span class="default">2 <a href="real_1.html#K4">*</a> <span class="p3"><a href="euclid_4.html#K5" target="_self">|(</a><span class="default"><font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font></span><a href="euclid_4.html#K5" target="_self">)|</a></span></span>)</span></span>)</span> <a href="real_1.html#K3">+</a> <span class="p1">(<span class="default"><span class="p2"><a href="euclid_4.html#K4" target="_self">|.</a><span class="default"><font color="Maroon">c<sub>3</sub></font></span><a href="euclid_4.html#K4" target="_self">.|</a></span> <a href="square_1.html#K5">^2</a> </span>)</span>
<b>by </b><i><a class="ref" href="euclid_4.html#T18" target="_self">Th18</a></i>
;<br/>


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