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<span class="kw">set </span><font color="Maroon" title="c4">Cb</font> =  <a href="jgraph_6.html#K5" title="JGRAPH_6:func.5">circle</a> (<font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">b</font>,<font color="Maroon" title="c3">r</font>);<br/>
<a NAME="E1:34_1_1"/><span class="lab"><font color="Green" title="E38">A1</font></span>: 
<span class="p1"><a href="euclid.html#K19" title="EUCLID:func.19">|[</a><span class="default"><font color="Maroon" title="c3">r</font>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span><a href="euclid.html#K19" title="EUCLID:func.19">]|</a></span> <a href="euclid.html#K17" title="EUCLID:func.17">`1</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">r</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="euclid.html#T52" title="EUCLID:th.52">EUCLID:52</a></span>;<br/>
<a NAME="E2:34_1_1"/><span class="lab"><font color="Green" title="E39">A2</font></span>: 
<span class="p1"><a href="euclid.html#K19" title="EUCLID:func.19">|[</a><span class="default"><font color="Maroon" title="c3">r</font>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span><a href="euclid.html#K19" title="EUCLID:func.19">]|</a></span> <a href="euclid.html#K18" title="EUCLID:func.18">`2</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="euclid.html#T52" title="EUCLID:th.52">EUCLID:52</a></span>;<br/>
<span class="p1"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p2">(<span class="default"><span class="p3"><a href="euclid.html#K19" title="EUCLID:func.19">|[</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c3">r</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c1">a</font></span>)</span>,<font color="Maroon" title="c2">b</font></span><a href="euclid.html#K19" title="EUCLID:func.19">]|</a></span> <a href="algstr_0.html#K5" title="ALGSTR_0:func.5">-</a> <span class="p3"><a href="euclid.html#K19" title="EUCLID:func.19">|[</a><span class="default"><font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">b</font></span><a href="euclid.html#K19" title="EUCLID:func.19">]|</a></span></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span> = 
<span class="p1"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p2">(<span class="default"><span class="p3"><a href="euclid.html#K19" title="EUCLID:func.19">|[</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c3">r</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c1">a</font></span>)</span>,<span class="p4">(<span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <font color="Maroon" title="c2">b</font></span>)</span></span><a href="euclid.html#K19" title="EUCLID:func.19">]|</a></span> <a href="algstr_0.html#K5" title="ALGSTR_0:func.5">-</a> <span class="p3"><a href="euclid.html#K19" title="EUCLID:func.19">|[</a><span class="default"><font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">b</font></span><a href="euclid.html#K19" title="EUCLID:func.19">]|</a></span></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span>

<br/>.= 
<span class="p1"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4"><a href="euclid.html#K19" title="EUCLID:func.19">|[</a><span class="default"><font color="Maroon" title="c3">r</font>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span><a href="euclid.html#K19" title="EUCLID:func.19">]|</a></span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p4"><a href="euclid.html#K19" title="EUCLID:func.19">|[</a><span class="default"><font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">b</font></span><a href="euclid.html#K19" title="EUCLID:func.19">]|</a></span></span>)</span> <a href="algstr_0.html#K5" title="ALGSTR_0:func.5">-</a> <span class="p3"><a href="euclid.html#K19" title="EUCLID:func.19">|[</a><span class="default"><font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">b</font></span><a href="euclid.html#K19" title="EUCLID:func.19">]|</a></span></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="euclid.html#T56" title="EUCLID:th.56">EUCLID:56</a></span>
<br/>.= 
<span class="p1"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p2">(<span class="default"><span class="p3"><a href="euclid.html#K19" title="EUCLID:func.19">|[</a><span class="default"><font color="Maroon" title="c3">r</font>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span><a href="euclid.html#K19" title="EUCLID:func.19">]|</a></span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p3">(<span class="default"><span class="p4"><a href="euclid.html#K19" title="EUCLID:func.19">|[</a><span class="default"><font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">b</font></span><a href="euclid.html#K19" title="EUCLID:func.19">]|</a></span> <a href="algstr_0.html#K5" title="ALGSTR_0:func.5">-</a> <span class="p4"><a href="euclid.html#K19" title="EUCLID:func.19">|[</a><span class="default"><font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">b</font></span><a href="euclid.html#K19" title="EUCLID:func.19">]|</a></span></span>)</span></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="euclid.html#T45" title="EUCLID:th.45">EUCLID:45</a></span>
<br/>.= 
<span class="p1"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p2">(<span class="default"><span class="p3"><a href="euclid.html#K19" title="EUCLID:func.19">|[</a><span class="default"><font color="Maroon" title="c3">r</font>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span><a href="euclid.html#K19" title="EUCLID:func.19">]|</a></span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p3">(<span class="default"><a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <span class="p4">(<span class="default"><a href="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> 2</span>)</span></span>)</span></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="euclid.html#T42" title="EUCLID:th.42">EUCLID:42</a></span>
<br/>.= 
<span class="p1"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p2"><a href="euclid.html#K19" title="EUCLID:func.19">|[</a><span class="default"><font color="Maroon" title="c3">r</font>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span><a href="euclid.html#K19" title="EUCLID:func.19">]|</a></span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="euclid.html#T27" title="EUCLID:th.27">EUCLID:27</a></span>
<br/>.= 
 <a href="square_1.html#K7" title="SQUARE_1:func.7">sqrt</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">r</font> <a href="square_1.html#K3" title="SQUARE_1:func.3">^2</a></span>)</span> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <span class="p2">(<span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> <a href="square_1.html#K5" title="SQUARE_1:func.5">^2</a></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:34_1_1"><span class="lab"><font color="Green" title="E38">A1</font></span></a>, <a class="txt" href="#E2:34_1_1"><span class="lab"><font color="Green" title="E39">A2</font></span></a>, <a class="ref" href="jgraph_3.html#T1" title="JGRAPH_3:th.1">JGRAPH_3:1</a></span>
<br/>.= 
<font color="Maroon" title="c3">r</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="square_1.html#T22" title="SQUARE_1:th.22">SQUARE_1:22</a></span>
;<br/>
<a NAME="E4:34_1_1"/><span class="kw">then </span>
<span class="p1"><a href="euclid.html#K19" title="EUCLID:func.19">|[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">r</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c1">a</font></span>)</span>,<font color="Maroon" title="c2">b</font></span><a href="euclid.html#K19" title="EUCLID:func.19">]|</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="jgraph_6.html#K5" title="JGRAPH_6:func.5">circle</a> (<font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">b</font>,<font color="Maroon" title="c3">r</font>)
 
;<br/>
<span class="kw">hence </span><a NAME="E5:34_1_1"/>
 not  <a href="jgraph_6.html#K5" title="JGRAPH_6:func.5">circle</a> (<font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">b</font>,<font color="Maroon" title="c3">r</font>) is  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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