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<b>let </b><font color="Maroon">sn</font> be   <a href="real_1.html#NM1">Real</a>;<br/><b>let </b><font color="Maroon">K003</font> be   <a href="struct_0.html#NM2">Subset</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 2</span>)</span>;<br/>



<b>defpred </b><font color="Maroon">S<sub>1</sub></font>[  <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>] <b>means </b><font color="Maroon">a<sub>1</sub></font> <a href="euclid.html#K22">`2</a>  <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <font color="Maroon">sn</font> <a href="real_1.html#K4">*</a> <span class="p1"><a href="toprns_1.html#K5">|.</a><span class="default"><font color="Maroon">a<sub>1</sub></font></span><a href="toprns_1.html#K5">.|</a></span>;<br/>
<b>assume </b><a NAME="E1:37"/><i><font color="Green">E34</font></i>: 
<font color="Maroon">K003</font> <a href="hidden.html#R1">=</a> <span class="p1">{<span class="default"> <font color="Olive">p</font> where <font color="Olive">p</font> 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> : ( <font color="Olive">p</font> <a href="euclid.html#K22">`2</a>  <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <font color="Maroon">sn</font> <a href="real_1.html#K4">*</a> <span class="p1"><a href="toprns_1.html#K5">|.</a><span class="default"><font color="Olive">p</font></span><a href="toprns_1.html#K5">.|</a></span> &amp; <font color="Olive">p</font> <a href="euclid.html#K21">`1</a>  <a href="xxreal_0.html#R1">&lt;=</a> 0 ) </span>}</span> 
 ;<br/>

<b>reconsider </b><font color="Maroon">K1</font> = <span class="p1">{<span class="default"> <font color="Olive">p7</font> where <font color="Olive">p7</font> 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> : <font color="Maroon">S<sub>1</sub></font>[<font color="Olive">p7</font>] </span>}</span>  as   <a href="struct_0.html#NM2">Subset</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 2</span>)</span> <b>from </b><i><a class="ref" href="jgraph_2.html#S1">JGRAPH_2:sch 1</a>();<br/></i>
<a NAME="E3:37"/><i><font color="Green">E36</font></i>: 
<font color="Maroon">K1</font> is <a href="pre_topc.html#V4">closed</a>
 
<b>by </b><i><a class="txt" href="jgraph_4.html#E5:37"><i><font color="Green">E38</font></i></a></i>;<br/>
<b>defpred </b><font color="Maroon">S<sub>2</sub></font>[  <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>] <b>means </b><font color="Maroon">a<sub>1</sub></font> <a href="euclid.html#K21">`1</a>  <a href="xxreal_0.html#R1">&lt;=</a> 0;<br/>
<b>reconsider </b><font color="Maroon">KX</font> = <span class="p1">{<span class="default"> <font color="Olive">p</font> where <font color="Olive">p</font> 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> : <font color="Maroon">S<sub>2</sub></font>[<font color="Olive">p</font>] </span>}</span>  as   <a href="struct_0.html#NM2">Subset</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 2</span>)</span> <b>from </b><i><a class="ref" href="jgraph_2.html#S1">JGRAPH_2:sch 1</a>();<br/></i>
<a NAME="E5:37"/><i><font color="Green">E38</font></i>: 
<font color="Maroon">KX</font> is <a href="pre_topc.html#V4">closed</a>
 
<b>by </b><i><a class="ref" href="jordan6.html#T6">JORDAN6:6</a></i>;<br/>
<a NAME="E6:37"/>
<span class="p1">{<span class="default"> <font color="Olive">p</font> where <font color="Olive">p</font> 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> : ( <font color="Maroon">S<sub>1</sub></font>[<font color="Olive">p</font>] &amp; <font color="Maroon">S<sub>2</sub></font>[<font color="Olive">p</font>] ) </span>}</span>  <a href="hidden.html#R1">=</a> <span class="p1">{<span class="default"> <font color="Olive">p7</font> where <font color="Olive">p7</font> 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> : <font color="Maroon">S<sub>1</sub></font>[<font color="Olive">p7</font>] </span>}</span>  <a href="xboole_0.html#K3">/\</a> <span class="p1">{<span class="default"> <font color="Olive">p1</font> where <font color="Olive">p1</font> 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> : <font color="Maroon">S<sub>2</sub></font>[<font color="Olive">p1</font>] </span>}</span> 
 
<b>from </b><i><a class="ref" href="domain_1.html#S10">DOMAIN_1:sch 10</a>();<br/></i>
<b>hence </b><a NAME="E7:37"/>
<font color="Maroon">K003</font> is <a href="pre_topc.html#V4">closed</a>
 <b>by </b><i>, , , <a class="ref" href="tops_1.html#T35">TOPS_1:35</a></i>;<br/>


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