<?xml version="1.0"?>
<div class="add">

<a NAME="E1:31_1_1"/><i><font color="Green" title="E21">A1</font></i>: 
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="c9">p</font>,<font color="Maroon" title="c7">r</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c9">p</font>,<font color="Maroon" title="c7">r</font>
 
<b>by </b><i><a class="ref" href="toprealb.html#T9" title="TOPREALB:th.9">TOPREALB:9</a></i>;<br/>
<a NAME="E2:31_1_1"/><i><font color="Green" title="E22">A2</font></i>: 
the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="brouwer.html#K2" title="BROUWER:func.2">Tdisk</a> <font color="Maroon" title="c9">p</font>,<font color="Maroon" title="c7">r</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="topreal9.html#K2" title="TOPREAL9:func.2">cl_Ball</a> <font color="Maroon" title="c9">p</font>,<font color="Maroon" title="c7">r</font>
 
<b>by </b><i><a class="ref" href="brouwer.html#T3" title="BROUWER:th.3">BROUWER:3</a></i>;<br/>
<a NAME="E3:31_1_1"/><i><font color="Green" title="E23">A3</font></i>: 
 <a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c9">p</font>,<font color="Maroon" title="c7">r</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="topreal9.html#K2" title="TOPREAL9:func.2">cl_Ball</a> <font color="Maroon" title="c9">p</font>,<font color="Maroon" title="c7">r</font>
 
<b>by </b><i><a class="ref" href="topreal9.html#T17" title="TOPREAL9:th.17">TOPREAL9:17</a></i>;<br/>
<b>consider </b><font color="Maroon" title="c11">a</font> being   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <span class="p1">(<span class="default"><a href="toprealb.html#K7" title="TOPREALB:func.7">Tcircle</a> <font color="Maroon" title="c9">p</font>,<font color="Maroon" title="c7">r</font></span>)</span>;<br/>
<a NAME="E5:31_1_1"/><i><font color="Green" title="E24">A4</font></i>: 
<font color="Maroon" title="c11">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c9">p</font>,<font color="Maroon" title="c7">r</font>
 
<b>by </b><i><a class="txt" href="jordan.html#E1:31_1_1"><i><font color="Green" title="E21">A1</font></i></a></i>;<br/>
<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="31_1_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:31_1_1_1"/>
( <font color="Maroon" title="c11">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c10">q</font> or <font color="Maroon" title="c11">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c10">q</font> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="31_1_1_1_1"><b>suppose </b></a><a NAME="E1:31_1_1_1_1"/><i><font color="Green" title="E25">A5</font></i>: 
<font color="Maroon" title="c11">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c10">q</font>
 ;<br/><div class="add"><a NAME="E2:31_1_1_1_1"/><i><font color="Green" title="E26">A6</font></i>: 
<font color="Maroon" title="c9">p</font> is   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <span class="p1">(<span class="default"><a href="brouwer.html#K2" title="BROUWER:func.2">Tdisk</a> <font color="Maroon" title="c9">p</font>,<font color="Maroon" title="c7">r</font></span>)</span>
 <b>by </b><i><a class="ref" href="jordan.html#T17" target="_self" title="JORDAN:th.17">Th17</a></i>;<br/><a NAME="E3:31_1_1_1_1"/>
<span class="p1"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c9">p</font> <a href="euclid.html#K20" title="EUCLID:func.20">-</a> <font color="Maroon" title="c9">p</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c7">r</font>
 <b>by </b><i><a class="ref" href="toprns_1.html#T29" title="TOPRNS_1:th.29">TOPRNS_1:29</a></i>;<br/><a NAME="E4:31_1_1_1_1"/><b>then </b>
<font color="Maroon" title="c9">p</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c10">q</font>
 <b>by </b><i><a class="txt" href="jordan.html#E1:31_1_1_1_1"><i><font color="Green" title="E25">A5</font></i></a>, <a class="txt" href="jordan.html#E1:31_1_1"><i><font color="Green" title="E21">A1</font></i></a>, <a class="ref" href="topreal9.html#T9" title="TOPREAL9:th.9">TOPREAL9:9</a></i>;<br/><b>hence </b><a NAME="E5:31_1_1_1_1"/>
not <span class="p1">(<span class="default"><a href="topreal9.html#K2" title="TOPREAL9:func.2">cl_Ball</a> <font color="Maroon" title="c9">p</font>,<font color="Maroon" title="c7">r</font></span>)</span> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c10">q</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>
 <b>by </b><i><a class="txt" href="jordan.html#E2:31_1_1_1_1"><i><font color="Green" title="E26">A6</font></i></a>, <a class="txt" href="jordan.html#E2:31_1_1"><i><font color="Green" title="E22">A2</font></i></a>, <a class="ref" href="zfmisc_1.html#T64" title="ZFMISC_1:th.64">ZFMISC_1:64</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="31_1_1_1_2"><b>suppose </b></a><a NAME="E1:31_1_1_1_2"/>
<font color="Maroon" title="c11">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c10">q</font>
 ;<br/><div class="add"><b>hence </b><a NAME="E2:31_1_1_1_2"/>
not <span class="p1">(<span class="default"><a href="topreal9.html#K2" title="TOPREAL9:func.2">cl_Ball</a> <font color="Maroon" title="c9">p</font>,<font color="Maroon" title="c7">r</font></span>)</span> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c10">q</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>
 <b>by </b><i><a class="txt" href="jordan.html#E5:31_1_1"><i><font color="Green" title="E24">A4</font></i></a>, <a class="txt" href="jordan.html#E3:31_1_1"><i><font color="Green" title="E23">A3</font></i></a>, <a class="ref" href="zfmisc_1.html#T64" title="ZFMISC_1:th.64">ZFMISC_1:64</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div>

</div>
