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<span class="kw">reconsider </span><font color="Maroon" title="c11">a</font> = <font color="Maroon" title="c10">x</font> as   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <span class="p1">(<span class="default"><a href="euclid.html#K14" title="EUCLID:func.14">Euclid</a> 2</span>)</span> <span class="kw">by</span> <span class="lab"><a class="ref" href="topreal3.html#T13" title="TOPREAL3:th.13">TOPREAL3:13</a></span>;<br/>
<a NAME="E2:34_1_1"/><span class="lab"><font color="Green" title="E20">A1</font></span>: 
<font color="Maroon" title="c10">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <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="c10">x</font> <a href="euclid.html#K17" title="EUCLID:func.17">`1</a> </span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c10">x</font> <a href="euclid.html#K18" title="EUCLID:func.18">`2</a> </span>)</span></span><a href="euclid.html#K19" title="EUCLID:func.19">]|</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="euclid.html#T57" title="EUCLID:th.57">EUCLID:57</a></span>;<br/>
 <a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c10">x</font>,<font color="Maroon" title="c9">r</font> = 
 <a href="metric_1.html#K11" title="METRIC_1:func.11">Sphere</a> <font color="Maroon" title="c11">a</font>,<font color="Maroon" title="c9">r</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="topreal9.html#T15" title="TOPREAL9:th.15">TOPREAL9:15</a></span>
<br/>.= 
 <a href="jgraph_6.html#K5" title="JGRAPH_6:func.5">circle</a> <span class="p1">(<span class="default"><font color="Maroon" title="c10">x</font> <a href="euclid.html#K17" title="EUCLID:func.17">`1</a> </span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c10">x</font> <a href="euclid.html#K18" title="EUCLID:func.18">`2</a> </span>)</span>,<font color="Maroon" title="c9">r</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:34_1_1"><span class="lab"><font color="Green" title="E20">A1</font></span></a>, <a class="ref" href="topreal9.html#T49" title="TOPREAL9:th.49">TOPREAL9:49</a></span>
<br/>.= 
<span class="p1">{<span class="default"> <font color="Olive" title="b1">w</font> where <font color="Olive" title="b1">w</font> is   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> 2</span>)</span> : <span class="p1"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Olive" title="b1">w</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <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="c10">x</font> <a href="euclid.html#K17" title="EUCLID:func.17">`1</a> </span>)</span>,<span class="p4">(<span class="default"><font color="Maroon" title="c10">x</font> <a href="euclid.html#K18" title="EUCLID:func.18">`2</a> </span>)</span></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> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">r</font> </span>}</span> 
<span class="kw">by</span> <span class="lab"><a class="ref" href="jgraph_6.html#D5" title="JGRAPH_6:def.5">JGRAPH_6:def 5</a></span>
;<br/>
<span class="kw">hence </span><a NAME="E4:34_1_1"/>
 <a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c10">x</font>,<font color="Maroon" title="c9">r</font> is  <a href="topreal2.html#V1" title="TOPREAL2:attr.1">being_simple_closed_curve</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="jgraph_6.html#T32" title="JGRAPH_6:th.32">JGRAPH_6:32</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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