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

<b>assume </b><a NAME="E1:30"/><i><font color="Green">E35</font></i>: 
 <a href="finseq_1.html#K3">len</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">y</font>
 ;<br/>

<span class="p1"><a href="euclid.html#K12">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">x</font> <a href="rvsum_1.html#K3">+</a> <font color="Maroon">y</font></span>)</span></span><a href="euclid.html#K12">.|</a></span> <a href="square_1.html#K5">^2</a>  = 
<span class="p1"><a href="euclid_2.html#K1" target="_self">|(</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">x</font> <a href="rvsum_1.html#K3">+</a> <font color="Maroon">y</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">x</font> <a href="rvsum_1.html#K3">+</a> <font color="Maroon">y</font></span>)</span></span><a href="euclid_2.html#K1" target="_self">)|</a></span>
<b>by </b><i/>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2"><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="xcmplx_0.html#K2">+</a> <span class="p2">(<span class="default">2 <a href="xcmplx_0.html#K3">*</a> <span class="p3"><a href="euclid_2.html#K1" target="_self">|(</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</font></span><a href="euclid_2.html#K1" target="_self">)|</a></span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1"><a href="euclid_2.html#K1" target="_self">|(</a><span class="default"><font color="Maroon">y</font>,<font color="Maroon">y</font></span><a href="euclid_2.html#K1" target="_self">)|</a></span>
<b>by </b><i>, </i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3"><a href="euclid.html#K12">|.</a><span class="default"><font color="Maroon">x</font></span><a href="euclid.html#K12">.|</a></span> <a href="square_1.html#K5">^2</a> </span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p2">(<span class="default">2 <a href="xcmplx_0.html#K3">*</a> <span class="p3"><a href="euclid_2.html#K1" target="_self">|(</a><span class="default"><font color="Maroon">y</font>,<font color="Maroon">x</font></span><a href="euclid_2.html#K1" target="_self">)|</a></span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1"><a href="euclid_2.html#K1" target="_self">|(</a><span class="default"><font color="Maroon">y</font>,<font color="Maroon">y</font></span><a href="euclid_2.html#K1" target="_self">)|</a></span>
<b>by </b><i/>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3"><a href="euclid.html#K12">|.</a><span class="default"><font color="Maroon">x</font></span><a href="euclid.html#K12">.|</a></span> <a href="square_1.html#K5">^2</a> </span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p2">(<span class="default">2 <a href="xcmplx_0.html#K3">*</a> <span class="p3"><a href="euclid_2.html#K1" target="_self">|(</a><span class="default"><font color="Maroon">y</font>,<font color="Maroon">x</font></span><a href="euclid_2.html#K1" target="_self">)|</a></span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><span class="p2"><a href="euclid.html#K12">|.</a><span class="default"><font color="Maroon">y</font></span><a href="euclid.html#K12">.|</a></span> <a href="square_1.html#K5">^2</a> </span>)</span>
<b>by </b><i/>
;<br/>
<b>hence </b><a NAME="E3:30"/>
<span class="p1"><a href="euclid.html#K12">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">x</font> <a href="rvsum_1.html#K3">+</a> <font color="Maroon">y</font></span>)</span></span><a href="euclid.html#K12">.|</a></span> <a href="square_1.html#K5">^2</a>  <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3"><a href="euclid.html#K12">|.</a><span class="default"><font color="Maroon">x</font></span><a href="euclid.html#K12">.|</a></span> <a href="square_1.html#K5">^2</a> </span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p2">(<span class="default">2 <a href="xcmplx_0.html#K3">*</a> <span class="p3"><a href="euclid_2.html#K1" target="_self">|(</a><span class="default"><font color="Maroon">y</font>,<font color="Maroon">x</font></span><a href="euclid_2.html#K1" target="_self">)|</a></span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><span class="p2"><a href="euclid.html#K12">|.</a><span class="default"><font color="Maroon">y</font></span><a href="euclid.html#K12">.|</a></span> <a href="square_1.html#K5">^2</a> </span>)</span>
 ;<br/>


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