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<b>let </b><font color="Maroon" title="c2">r</font> be  non <a href="xxreal_0.html#V3" title="XXREAL_0:attr.3">negative</a> <a href="xreal_0.html#V1" title="XREAL_0:attr.1">real</a>  <a href="ordinal1.html#NM1" title="ORDINAL1:NM.1">number</a> ;<br/><b>let </b><font color="Maroon" title="c3">n</font> be  non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> ;<br/><b>let </b><font color="Maroon" title="c4">s</font>, <font color="Maroon" title="c5">o</font>, <font color="Maroon" title="c6">t</font> be   <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> <font color="Maroon" title="c3">n</font></span>)</span>;<br/>









<b>assume </b><a NAME="E1:12"/><i><font color="Green" title="E7">A1</font></i>: 
( <font color="Maroon" title="c4">s</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="c5">o</font>,<font color="Maroon" title="c2">r</font></span>)</span> &amp; <font color="Maroon" title="c6">t</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="c5">o</font>,<font color="Maroon" title="c2">r</font></span>)</span> &amp; <font color="Maroon" title="c4">s</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c6">t</font> )
 ;<br/>

<a NAME="E2:12"/><i><font color="Green" title="E8">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="toprealb.html#K7" title="TOPREALB:func.7">Tcircle</a> <font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c2">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="c5">o</font>,<font color="Maroon" title="c2">r</font>
 
<b>by </b><i><a class="ref" href="toprealb.html#T9" title="TOPREALB:th.9">TOPREALB:9</a></i>;<br/>
<a NAME="E3:12"/>
 <a href="brouwer.html#K3" title="BROUWER:func.3">HC</a> <font color="Maroon" title="c4">s</font>,<font color="Maroon" title="c6">t</font>,<font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c2">r</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><a href="topreal9.html#K4" title="TOPREAL9:func.4">halfline</a> <font color="Maroon" title="c4">s</font>,<font color="Maroon" title="c6">t</font></span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p1">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c2">r</font></span>)</span>
 
<b>by </b><i><a class="txt" href="brouwer.html#E1:12"><i><font color="Green" title="E7">A1</font></i></a>, <a class="ref" href="brouwer.html#D3" target="_self" title="BROUWER:def.3">Def3</a></i>;<br/>
<b>hence </b><a NAME="E4:12"/>
 <a href="brouwer.html#K3" title="BROUWER:func.3">HC</a> <font color="Maroon" title="c4">s</font>,<font color="Maroon" title="c6">t</font>,<font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c2">r</font> is   <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="c5">o</font>,<font color="Maroon" title="c2">r</font></span>)</span>
 <b>by </b><i><a class="txt" href="brouwer.html#E2:12"><i><font color="Green" title="E8">A2</font></i></a>, <a class="ref" href="xboole_0.html#D3" title="XBOOLE_0:def.3">XBOOLE_0:def 3</a></i>;<br/>


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