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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">p1</font> be   <a href="pre_topc.html#NM2">Point</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> <font color="Maroon">n</font></span>)</span>, <font color="Maroon">p2</font> be   <a href="pre_topc.html#NM2">Point</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> <font color="Maroon">n</font></span>)</span>;<br/>



<b>consider </b><font color="Maroon">f1</font> being    <a href="finseq_1.html#M2">FinSequence</a> of  <a href="numbers.html#K1">REAL</a> , <font color="Maroon">f2</font> being    <a href="finseq_1.html#M2">FinSequence</a> of  <a href="numbers.html#K1">REAL</a> <b> such that </b><br/><a NAME="E2:37"/><i><font color="Green">E35</font></i>: 
( <font color="Maroon">f1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">p1</font> &amp; <font color="Maroon">f2</font> <a href="hidden.html#R1">=</a> <font color="Maroon">p2</font> &amp; <span class="p1"><a href="euclid_2.html#K2" target="_self">|(</a><span class="default"><font color="Maroon">p1</font>,<font color="Maroon">p2</font></span><a href="euclid_2.html#K2" target="_self">)|</a></span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="euclid_2.html#K1" target="_self">|(</a><span class="default"><font color="Maroon">f1</font>,<font color="Maroon">f2</font></span><a href="euclid_2.html#K1" target="_self">)|</a></span> )
 <b>by </b><i/>;<br/>
<b>reconsider </b><font color="Maroon">q1</font> = <font color="Maroon">p1</font>, <font color="Maroon">q2</font> = <font color="Maroon">p2</font> as    <a href="finseq_2.html#M2">Element</a> of  <a href="euclid.html#K1">REAL</a> <font color="Maroon">n</font> <b>by </b><i><a class="ref" href="euclid.html#T25">EUCLID:25</a></i>;<br/>
<a NAME="E4:37"/>
<font color="Maroon">p1</font> <a href="euclid.html#K17">+</a> <font color="Maroon">p2</font> <a href="hidden.html#R1">=</a> <font color="Maroon">q1</font> <a href="euclid.html#K7">+</a> <font color="Maroon">q2</font>
 
<b>by </b><i><a class="ref" href="euclid.html#D10">EUCLID:def 10</a></i>;<br/>
<a NAME="E5:37"/><b>then </b><i><font color="Green">E36</font></i>: 
<span class="p1"><a href="toprns_1.html#K5">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">p1</font> <a href="euclid.html#K17">+</a> <font color="Maroon">p2</font></span>)</span></span><a href="toprns_1.html#K5">.|</a></span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="euclid.html#K12">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">q1</font> <a href="euclid.html#K7">+</a> <font color="Maroon">q2</font></span>)</span></span><a href="euclid.html#K12">.|</a></span>
 
<b>by </b><i><a class="ref" href="jgraph_1.html#D5">JGRAPH_1:def 5</a></i>;<br/>
<a NAME="E6:37"/>
<font color="Maroon">p1</font> <a href="euclid.html#K20">-</a> <font color="Maroon">p2</font> <a href="hidden.html#R1">=</a> <font color="Maroon">q1</font> <a href="euclid.html#K8">-</a> <font color="Maroon">q2</font>
 
<b>by </b><i><a class="ref" href="euclid.html#D13">EUCLID:def 13</a></i>;<br/>
<a NAME="E7:37"/><b>then </b>
<span class="p1"><a href="toprns_1.html#K5">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">p1</font> <a href="euclid.html#K20">-</a> <font color="Maroon">p2</font></span>)</span></span><a href="toprns_1.html#K5">.|</a></span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="euclid.html#K12">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">q1</font> <a href="euclid.html#K8">-</a> <font color="Maroon">q2</font></span>)</span></span><a href="euclid.html#K12">.|</a></span>
 
<b>by </b><i><a class="ref" href="jgraph_1.html#D5">JGRAPH_1:def 5</a></i>;<br/>
<b>hence </b><a NAME="E8:37"/>
<span class="p1"><a href="euclid_2.html#K2" target="_self">|(</a><span class="default"><font color="Maroon">p1</font>,<font color="Maroon">p2</font></span><a href="euclid_2.html#K2" target="_self">)|</a></span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default">1 <a href="xcmplx_0.html#K7">/</a> 4</span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3"><a href="toprns_1.html#K5">|.</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon">p1</font> <a href="euclid.html#K17">+</a> <font color="Maroon">p2</font></span>)</span></span><a href="toprns_1.html#K5">.|</a></span> <a href="square_1.html#K5">^2</a> </span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p2">(<span class="default"><span class="p3"><a href="toprns_1.html#K5">|.</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon">p1</font> <a href="euclid.html#K20">-</a> <font color="Maroon">p2</font></span>)</span></span><a href="toprns_1.html#K5">.|</a></span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span>
 <b>by </b><i>, , </i>;<br/>


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