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<span class="kw">reconsider </span><font color="Maroon" title="c12">e</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> <font color="Maroon" title="c9">n</font></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="E2:38_1_1"/><span class="lab"><font color="Green" title="E21">A1</font></span>: 
<font color="Maroon" title="c9">n</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="ordinal1.html#D13" title="ORDINAL1:def.13">ORDINAL1:def 13</a></span>;<br/>
<span class="kw">then </span>the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="toprealb.html#K7" title="TOPREALB:func.7">Tcircle</a> <font color="Maroon" title="c10">x</font>,<font color="Maroon" title="c11">r</font></span>)</span> = 
 <a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c10">x</font>,<font color="Maroon" title="c11">r</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="toprealb.html#T9" target="_self" title="TOPREALB:th.9">Th9</a></span>
<br/>.= 
 <a href="metric_1.html#K11" title="METRIC_1:func.11">Sphere</a> <font color="Maroon" title="c12">e</font>,<font color="Maroon" title="c11">r</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:38_1_1"><span class="lab"><font color="Green" title="E21">A1</font></span></a>, <a class="ref" href="topreal9.html#T15" title="TOPREAL9:th.15">TOPREAL9:15</a></span>
<br/>.= 
<span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c12">e</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="topreal6.html#T62" title="TOPREAL6:th.62">TOPREAL6:62</a></span>
;<br/>
<span class="kw">hence </span><a NAME="E4:38_1_1"/>
 <a href="toprealb.html#K7" title="TOPREALB:func.7">Tcircle</a> <font color="Maroon" title="c10">x</font>,<font color="Maroon" title="c11">r</font> is  <a href="struct_0.html#V7" title="STRUCT_0:attr.7">trivial</a> 
 ; <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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