<?xml version="1.0"?>
<div class="add">

<b>let </b><font color="Maroon">p</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> 2</span>)</span>;<br/><b>let </b><font color="Maroon">e</font> be   <a href="pre_topc.html#NM2">Point</a> of <span class="p1">(<span class="default"><a href="euclid.html#K14">Euclid</a> 2</span>)</span>;<br/><b>let </b><font color="Maroon">r</font> be  <a href="xreal_0.html#V1">real</a>  <a href="ordinal1.html#NM1" target="_self">number</a> ;<br/>





<b>set </b><font color="Maroon">A</font> = <span class="p1"><a href="rcomp_1.html#K2">].</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p</font> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">r</font></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p</font> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">r</font></span>)</span></span><a href="rcomp_1.html#K2">.[</a></span>;<br/>
<b>set </b><font color="Maroon">B</font> = <span class="p1"><a href="rcomp_1.html#K2">].</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p</font> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">r</font></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p</font> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">r</font></span>)</span></span><a href="rcomp_1.html#K2">.[</a></span>;<br/>
<b>set </b><font color="Maroon">f</font> = 1,2 <a href="funct_4.html#K5">--&gt;</a> <span class="p1"><a href="rcomp_1.html#K2">].</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p</font> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">r</font></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p</font> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">r</font></span>)</span></span><a href="rcomp_1.html#K2">.[</a></span>,<span class="p1"><a href="rcomp_1.html#K2">].</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p</font> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">r</font></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p</font> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">r</font></span>)</span></span><a href="rcomp_1.html#K2">.[</a></span>;<br/>
<b>assume </b><a NAME="E1:50"/><i><font color="Green">E56</font></i>: 
<font color="Maroon">p</font> <a href="hidden.html#R1">=</a> <font color="Maroon">e</font>
 ;<br/>

<b>let </b><font color="Maroon">a</font> be    <a href="hidden.html#M1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3">TARSKI:def 3</a><br/>

<b>assume </b><a NAME="E2:50"/><i><font color="Green">E57</font></i>: 
<font color="Maroon">a</font> <a href="hidden.html#R2">in</a>  <a href="metric_1.html#K9">Ball</a> <font color="Maroon">e</font>,<font color="Maroon">r</font>
 ;<br/>

<b>then reconsider </b><font color="Maroon">b</font> = <font color="Maroon">a</font> as   <a href="pre_topc.html#NM2">Point</a> of <span class="p1">(<span class="default"><a href="euclid.html#K14">Euclid</a> 2</span>)</span> ;<br/>
<b>reconsider </b><font color="Maroon">q</font> = <font color="Maroon">b</font> as   <a href="pre_topc.html#NM2">Point</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 2</span>)</span> <b>by </b><i><a class="ref" href="topreal3.html#T13">TOPREAL3:13</a></i>;<br/>
<b>reconsider </b><font color="Maroon">g</font> = <font color="Maroon">q</font> as   <a href="finseq_1.html#NM1">FinSequence</a> <b>by </b><i><a class="ref" href="euclid.html#T27">EUCLID:27</a></i>;<br/>
<a NAME="E6:50"/><i><font color="Green">E58</font></i>: 
 <a href="relset_1.html#K4">dom</a> <span class="p1">(<span class="default">1,2 <a href="funct_4.html#K5">--&gt;</a> <span class="p2"><a href="rcomp_1.html#K2">].</a><span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p</font> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">r</font></span>)</span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p</font> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">r</font></span>)</span></span><a href="rcomp_1.html#K2">.[</a></span>,<span class="p2"><a href="rcomp_1.html#K2">].</a><span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p</font> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">r</font></span>)</span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p</font> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">r</font></span>)</span></span><a href="rcomp_1.html#K2">.[</a></span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K2">{</a><span class="default">1,2</span><a href="tarski.html#K2">}</a></span>
 
<b>by </b><i><a class="ref" href="funct_4.html#T65">FUNCT_4:65</a></i>;<br/>
<a NAME="E7:50"/>
<font color="Maroon">q</font> is   <a href="funct_2.html#NM1">Function</a> of  <a href="finseq_1.html#K2">Seg</a> 2, <a href="numbers.html#K1">REAL</a> 
 
<b>by </b><i><a class="ref" href="euclid.html#T26">EUCLID:26</a></i>;<br/>
<a NAME="E8:50"/><b>then </b><i><font color="Green">E59</font></i>: 
 <a href="finseq_1.html#K4">dom</a> <font color="Maroon">g</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K2">{</a><span class="default">1,2</span><a href="tarski.html#K2">}</a></span>
 
<b>by </b><i><a class="ref" href="finseq_1.html#T4">FINSEQ_1:4</a>, <a class="ref" href="funct_2.html#D1">FUNCT_2:def 1</a></i>;<br/>
<a NAME="E9:50"/>
for <font color="Olive">x</font> being   <a href="hidden.html#M1">set</a>   st <font color="Olive">x</font> <a href="hidden.html#R2">in</a>  <a href="relset_1.html#K4">dom</a> <span class="p1">(<span class="default">1,2 <a href="funct_4.html#K5">--&gt;</a> <span class="p2"><a href="rcomp_1.html#K2">].</a><span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p</font> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">r</font></span>)</span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p</font> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">r</font></span>)</span></span><a href="rcomp_1.html#K2">.[</a></span>,<span class="p2"><a href="rcomp_1.html#K2">].</a><span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p</font> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">r</font></span>)</span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p</font> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">r</font></span>)</span></span><a href="rcomp_1.html#K2">.[</a></span></span>)</span> holds <br/><font color="Maroon">g</font> <a href="funct_1.html#K1">.</a> <font color="Olive">x</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default">1,2 <a href="funct_4.html#K5">--&gt;</a> <span class="p2"><a href="rcomp_1.html#K2">].</a><span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p</font> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">r</font></span>)</span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p</font> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">r</font></span>)</span></span><a href="rcomp_1.html#K2">.[</a></span>,<span class="p2"><a href="rcomp_1.html#K2">].</a><span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p</font> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">r</font></span>)</span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p</font> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">r</font></span>)</span></span><a href="rcomp_1.html#K2">.[</a></span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Olive">x</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="50_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">x</font> be    <a href="hidden.html#M1">set</a> ;<br/>

<b>assume </b><a NAME="E1:50_1"/><i><font color="Green">E66</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="relset_1.html#K4">dom</a> <span class="p1">(<span class="default">1,2 <a href="funct_4.html#K5">--&gt;</a> <span class="p2"><a href="rcomp_1.html#K2">].</a><span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p</font> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">r</font></span>)</span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p</font> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">r</font></span>)</span></span><a href="rcomp_1.html#K2">.[</a></span>,<span class="p2"><a href="rcomp_1.html#K2">].</a><span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p</font> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">r</font></span>)</span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p</font> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">r</font></span>)</span></span><a href="rcomp_1.html#K2">.[</a></span></span>)</span>
 ;<br/>

<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="50_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:50_1_1"/>
( <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> 1 or <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> 2 )
 </span><b>by </b><i>, <a class="ref" href="tarski.html#D2">TARSKI:def 2</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="50_1_1_1"><b>suppose </b></a><a NAME="E1:50_1_1_1"/><i><font color="Green">E67</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R1">=</a> 1
 ;<br/><div class="add"><a NAME="E2:50_1_1_1"/><i><font color="Green">E69</font></i>: 
<span class="p1">(<span class="default">1,2 <a href="funct_4.html#K5">--&gt;</a> <span class="p2"><a href="rcomp_1.html#K2">].</a><span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p</font> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">r</font></span>)</span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p</font> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">r</font></span>)</span></span><a href="rcomp_1.html#K2">.[</a></span>,<span class="p2"><a href="rcomp_1.html#K2">].</a><span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p</font> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">r</font></span>)</span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p</font> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">r</font></span>)</span></span><a href="rcomp_1.html#K2">.[</a></span></span>)</span> <a href="funct_1.html#K1">.</a> 1 <a href="hidden.html#R1">=</a> <span class="p1"><a href="rcomp_1.html#K2">].</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p</font> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">r</font></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p</font> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">r</font></span>)</span></span><a href="rcomp_1.html#K2">.[</a></span>
 <b>by </b><i><a class="ref" href="funct_4.html#T66">FUNCT_4:66</a></i>;<br/><a NAME="E3:50_1_1_1"/><i><font color="Green">E70</font></i>: 
<font color="Maroon">g</font> <a href="funct_1.html#K1">.</a> 1 <a href="hidden.html#R1">=</a> <font color="Maroon">q</font> <a href="euclid.html#K21">`1</a> 
 <b>by </b><i><a class="ref" href="euclid.html#D14">EUCLID:def 14</a></i>;<br/><a NAME="E4:50_1_1_1"/>
( <span class="p1">(<span class="default"><font color="Maroon">p</font> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">r</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">q</font> <a href="euclid.html#K21">`1</a>  &amp; <font color="Maroon">q</font> <a href="euclid.html#K21">`1</a>  <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <span class="p1">(<span class="default"><font color="Maroon">p</font> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">r</font> )
 <b>by </b><i>, , </i>;<br/><b>hence </b><a NAME="E5:50_1_1_1"/>
<font color="Maroon">g</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default">1,2 <a href="funct_4.html#K5">--&gt;</a> <span class="p2"><a href="rcomp_1.html#K2">].</a><span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p</font> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">r</font></span>)</span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p</font> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">r</font></span>)</span></span><a href="rcomp_1.html#K2">.[</a></span>,<span class="p2"><a href="rcomp_1.html#K2">].</a><span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p</font> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">r</font></span>)</span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p</font> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">r</font></span>)</span></span><a href="rcomp_1.html#K2">.[</a></span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font>
 <b>by </b><i>, , , <a class="ref" href="rcomp_1.html#T47">RCOMP_1:47</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="50_1_1_2"><b>suppose </b></a><a NAME="E1:50_1_1_2"/><i><font color="Green">E71</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R1">=</a> 2
 ;<br/><div class="add"><a NAME="E2:50_1_1_2"/><i><font color="Green">E72</font></i>: 
<span class="p1">(<span class="default">1,2 <a href="funct_4.html#K5">--&gt;</a> <span class="p2"><a href="rcomp_1.html#K2">].</a><span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p</font> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">r</font></span>)</span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p</font> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">r</font></span>)</span></span><a href="rcomp_1.html#K2">.[</a></span>,<span class="p2"><a href="rcomp_1.html#K2">].</a><span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p</font> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">r</font></span>)</span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p</font> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">r</font></span>)</span></span><a href="rcomp_1.html#K2">.[</a></span></span>)</span> <a href="funct_1.html#K1">.</a> 2 <a href="hidden.html#R1">=</a> <span class="p1"><a href="rcomp_1.html#K2">].</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p</font> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">r</font></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p</font> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">r</font></span>)</span></span><a href="rcomp_1.html#K2">.[</a></span>
 <b>by </b><i><a class="ref" href="funct_4.html#T66">FUNCT_4:66</a></i>;<br/><a NAME="E3:50_1_1_2"/><i><font color="Green">E83</font></i>: 
<font color="Maroon">g</font> <a href="funct_1.html#K1">.</a> 2 <a href="hidden.html#R1">=</a> <font color="Maroon">q</font> <a href="euclid.html#K22">`2</a> 
 <b>by </b><i><a class="ref" href="euclid.html#D15">EUCLID:def 15</a></i>;<br/><a NAME="E4:50_1_1_2"/>
( <span class="p1">(<span class="default"><font color="Maroon">p</font> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">r</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">q</font> <a href="euclid.html#K22">`2</a>  &amp; <font color="Maroon">q</font> <a href="euclid.html#K22">`2</a>  <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <span class="p1">(<span class="default"><font color="Maroon">p</font> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">r</font> )
 <b>by </b><i>, , </i>;<br/><b>hence </b><a NAME="E5:50_1_1_2"/>
<font color="Maroon">g</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default">1,2 <a href="funct_4.html#K5">--&gt;</a> <span class="p2"><a href="rcomp_1.html#K2">].</a><span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p</font> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">r</font></span>)</span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p</font> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">r</font></span>)</span></span><a href="rcomp_1.html#K2">.[</a></span>,<span class="p2"><a href="rcomp_1.html#K2">].</a><span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p</font> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">r</font></span>)</span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p</font> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">r</font></span>)</span></span><a href="rcomp_1.html#K2">.[</a></span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font>
 <b>by </b><i>, , , <a class="ref" href="rcomp_1.html#T47">RCOMP_1:47</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div>

</div><b>end;</b></div>
<b>hence </b><a NAME="E10:50"/>
<font color="Maroon">a</font> <a href="hidden.html#R2">in</a>  <a href="card_3.html#K4">product</a> <span class="p1">(<span class="default">1,2 <a href="funct_4.html#K5">--&gt;</a> <span class="p2"><a href="rcomp_1.html#K2">].</a><span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p</font> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">r</font></span>)</span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p</font> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">r</font></span>)</span></span><a href="rcomp_1.html#K2">.[</a></span>,<span class="p2"><a href="rcomp_1.html#K2">].</a><span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p</font> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">r</font></span>)</span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p</font> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">r</font></span>)</span></span><a href="rcomp_1.html#K2">.[</a></span></span>)</span>
 <b>by </b><i>, , <a class="ref" href="card_3.html#T18">CARD_3:18</a></i>;<br/>


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