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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="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/>





<i><font color="Green">E48</font></i>: <span class="p1"><a href="euclid_2.html#K2" target="_self">|(</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="euclid.html#K20">-</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#K20">-</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span><a href="euclid_2.html#K2" target="_self">)|</a></span> = 
<span class="p1">(<span class="default"><span class="p2"><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="xcmplx_0.html#K6">-</a> <span class="p2">(<span class="default">2 <a href="xcmplx_0.html#K3">*</a> <span class="p3"><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>3</sub></font></span><a href="euclid_2.html#K2" target="_self">)|</a></span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1"><a href="euclid_2.html#K2" 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#K2" target="_self">)|</a></span>
<b>by </b><i><a class="ref" href="euclid_2.html#T53" target="_self">Th53</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2"><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="xcmplx_0.html#K2">+</a> <span class="p2"><a href="euclid_2.html#K2" 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#K2" target="_self">)|</a></span></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p1">(<span class="default">2 <a href="xcmplx_0.html#K3">*</a> <span class="p2"><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>3</sub></font></span><a href="euclid_2.html#K2" target="_self">)|</a></span></span>)</span>

;<br/>
<a NAME="E2:63"/>
( 0 <a href="xxreal_0.html#R1">&lt;=</a> <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> &amp; 0 <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1"><a href="euclid_2.html#K2" 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#K2" target="_self">)|</a></span> )
 
<b>by </b><i><a class="ref" href="euclid_2.html#T57" target="_self">Th57</a></i>;<br/>
<a NAME="E3:63"/><b>then </b>
0 <a href="xcmplx_0.html#K2">+</a> 0 <a href="xxreal_0.html#R1">&lt;=</a> <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="xcmplx_0.html#K2">+</a> <span class="p1"><a href="euclid_2.html#K2" 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#K2" target="_self">)|</a></span>
 
<b>by </b><i><a class="ref" href="xreal_1.html#T9">XREAL_1:9</a></i>;<br/>
<a NAME="E4:63"/><b>then </b><i><font color="Green">E49</font></i>: 
0 <a href="xcmplx_0.html#K7">/</a> 2 <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><span class="p2"><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="xcmplx_0.html#K2">+</a> <span class="p2"><a href="euclid_2.html#K2" 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#K2" target="_self">)|</a></span></span>)</span> <a href="xcmplx_0.html#K7">/</a> 2
 
<b>by </b><i><a class="ref" href="real_1.html#T73">REAL_1:73</a></i>;<br/>
<a NAME="E5:63"/>
0 <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1"><a href="euclid_2.html#K2" target="_self">|(</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="euclid.html#K20">-</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#K20">-</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span><a href="euclid_2.html#K2" target="_self">)|</a></span>
 
<b>by </b><i><a class="ref" href="euclid_2.html#T57" target="_self">Th57</a></i>;<br/>
<a NAME="E6:63"/><b>then </b>
2 <a href="xcmplx_0.html#K3">*</a> <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>3</sub></font></span><a href="euclid_2.html#K2" target="_self">)|</a></span> <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><span class="p2"><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="xcmplx_0.html#K2">+</a> <span class="p2"><a href="euclid_2.html#K2" 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#K2" target="_self">)|</a></span></span>)</span> <a href="xcmplx_0.html#K6">-</a> 0
 
<b>by </b><i><a class="txt" href="euclid_2.html#E1:63"><i><font color="Green">E48</font></i></a>, <a class="ref" href="real_2.html#T165">REAL_2:165</a></i>;<br/>
<a NAME="E7:63"/><b>then </b>
<span class="p1">(<span class="default">2 <a href="xcmplx_0.html#K3">*</a> <span class="p2"><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>3</sub></font></span><a href="euclid_2.html#K2" target="_self">)|</a></span></span>)</span> <a href="xcmplx_0.html#K7">/</a> 2 <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><span class="p2"><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="xcmplx_0.html#K2">+</a> <span class="p2"><a href="euclid_2.html#K2" 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#K2" target="_self">)|</a></span></span>)</span> <a href="xcmplx_0.html#K7">/</a> 2
 
<b>by </b><i><a class="ref" href="real_1.html#T73">REAL_1:73</a></i>;<br/>
<a NAME="E8:63"/><b>then </b>
0 <a href="xcmplx_0.html#K2">+</a> <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>3</sub></font></span><a href="euclid_2.html#K2" target="_self">)|</a></span> <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3"><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="xcmplx_0.html#K2">+</a> <span class="p3"><a href="euclid_2.html#K2" 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#K2" target="_self">)|</a></span></span>)</span> <a href="xcmplx_0.html#K7">/</a> 2</span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3"><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="xcmplx_0.html#K2">+</a> <span class="p3"><a href="euclid_2.html#K2" 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#K2" target="_self">)|</a></span></span>)</span> <a href="xcmplx_0.html#K7">/</a> 2</span>)</span>
 
<b>by </b><i><a class="txt" href="euclid_2.html#E4:63"><i><font color="Green">E49</font></i></a>, <a class="ref" href="xreal_1.html#T9">XREAL_1:9</a></i>;<br/>
<b>hence </b><a NAME="E9:63"/>
<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>3</sub></font></span><a href="euclid_2.html#K2" target="_self">)|</a></span> <a href="xxreal_0.html#R1">&lt;=</a> <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="xcmplx_0.html#K2">+</a> <span class="p1"><a href="euclid_2.html#K2" 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#K2" target="_self">)|</a></span>
 ;<br/>


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