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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> 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">c<sub>1</sub></font></span>)</span>;<br/>



<b>consider </b><font color="Maroon">c<sub>3</sub></font>, <font color="Maroon">c<sub>4</sub></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="E2:50"/><i><font color="Green">E41</font></i>: 
( <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>2</sub></font> &amp; <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>2</sub></font> &amp; <span class="p1"><a href="euclid_2.html#K2" 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_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">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font></span><a href="euclid_2.html#K1" target="_self">)|</a></span> )
 <b>by </b><i><a class="ref" href="euclid_2.html#D2" target="_self">Def2</a></i>;<br/>
<a NAME="E3:50"/><i><font color="Green">E42</font></i>: 
<span class="p1"><a href="euclid_2.html#K1" 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_2.html#K1" target="_self">)|</a></span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="euclid.html#K12">|.</a><span class="default"><font color="Maroon">c<sub>3</sub></font></span><a href="euclid.html#K12">.|</a></span> <a href="square_1.html#K5">^2</a> 
 
<b>by </b><i><a class="ref" href="euclid_2.html#T12" target="_self">Th12</a></i>;<br/>
<a NAME="E4:50"/>
<font color="Maroon">c<sub>2</sub></font> is    <a href="finseq_2.html#M2">Element</a> of  <a href="euclid.html#K1">REAL</a> <font color="Maroon">c<sub>1</sub></font>
 
<b>by </b><i><a class="ref" href="euclid.html#T25">EUCLID:25</a></i>;<br/>
<b>hence </b><a NAME="E5:50"/>
<span class="p1"><a href="euclid_2.html#K2" 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_2.html#K2" target="_self">)|</a></span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="toprns_1.html#K5">|.</a><span class="default"><font color="Maroon">c<sub>2</sub></font></span><a href="toprns_1.html#K5">.|</a></span> <a href="square_1.html#K5">^2</a> 
 <b>by </b><i><a class="txt" href="euclid_2.html#E2:50"><i><font color="Green">E41</font></i></a>, <a class="txt" href="euclid_2.html#E3:50"><i><font color="Green">E42</font></i></a>, <a class="ref" href="jgraph_1.html#D5">JGRAPH_1:def 5</a></i>;<br/>


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