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<b>reconsider </b><font color="Maroon">c<sub>11</sub></font> = <font color="Maroon">c<sub>10</sub></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> <b>by </b><i><a class="ref" href="topreal3.html#T13">TOPREAL3:13</a></i>;<br/>
<a NAME="E2:34_1_1"/><i><font color="Green">E21</font></i>: 
<font color="Maroon">c<sub>10</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="euclid.html#K23">|[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="euclid.html#K22">`2</a> </span>)</span></span><a href="euclid.html#K23">]|</a></span>
 
<b>by </b><i><a class="ref" href="euclid.html#T57">EUCLID:57</a></i>;<br/>
 <a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>9</sub></font> = 
 <a href="metric_1.html#K11">Sphere</a> <font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>9</sub></font>
<b>by </b><i><a class="ref" href="topreal9.html#T15">TOPREAL9:15</a></i>
<br/>.= 
 <a href="jgraph_6.html#K5">circle</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="euclid.html#K22">`2</a> </span>)</span>,<font color="Maroon">c<sub>9</sub></font>
<b>by </b><i><a class="txt" href="toprealb.html#E2:34_1_1"><i><font color="Green">E21</font></i></a>, <a class="ref" href="topreal9.html#T49">TOPREAL9:49</a></i>
<br/>.= 
<span class="p1">{<span class="default"> <font color="Olive">b<sub>1</sub></font> where B is   <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> : <span class="p1"><a href="toprns_1.html#K5">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Olive">b<sub>1</sub></font> <a href="euclid.html#K20">-</a> <span class="p3"><a href="euclid.html#K23">|[</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span>,<span class="p4">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="euclid.html#K22">`2</a> </span>)</span></span><a href="euclid.html#K23">]|</a></span></span>)</span></span><a href="toprns_1.html#K5">.|</a></span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>9</sub></font> </span>}</span> 
<b>by </b><i><a class="ref" href="jgraph_6.html#D5">JGRAPH_6:def 5</a></i>
;<br/>
<b>hence </b><a NAME="E4:34_1_1"/>
 <a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>9</sub></font> is <a href="topreal2.html#V1">being_simple_closed_curve</a>
 <b>by </b><i><a class="ref" href="jgraph_6.html#T32">JGRAPH_6:32</a></i>;<br/>


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