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<b>let </b><font color="Maroon">c<sub>1</sub></font>, <font color="Maroon">c<sub>2</sub></font>, <font color="Maroon">c<sub>3</sub></font>, <font color="Maroon">c<sub>4</sub></font> be   <a href="real_1.html#NM1">Real</a>;<br/><b>let </b><font color="Maroon">c<sub>5</sub></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>assume </b><a NAME="E1:34"/><i><font color="Green">E36</font></i>: 
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">{<span class="default"> <span class="p2"><a href="euclid.html#K23">|[</a><span class="default"><font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>2</sub></font></span><a href="euclid.html#K23">]|</a></span> where B is   <a href="real_1.html#NM1">Real</a>, B is   <a href="real_1.html#NM1">Real</a> : ( <font color="Maroon">c<sub>1</sub></font> <a href="xxreal_0.html#R1">&lt;</a> <font color="Olive">b<sub>1</sub></font> &amp; <font color="Olive">b<sub>1</sub></font> <a href="xxreal_0.html#R1">&lt;</a> <font color="Maroon">c<sub>3</sub></font> &amp; <font color="Maroon">c<sub>2</sub></font> <a href="xxreal_0.html#R1">&lt;</a> <font color="Olive">b<sub>2</sub></font> &amp; <font color="Olive">b<sub>2</sub></font> <a href="xxreal_0.html#R1">&lt;</a> <font color="Maroon">c<sub>4</sub></font> ) </span>}</span> 
 ;<br/>

<b>reconsider </b><font color="Maroon">c<sub>6</sub></font> = <span class="p1">{<span class="default"> <span class="p2"><a href="euclid.html#K23">|[</a><span class="default"><font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>2</sub></font></span><a href="euclid.html#K23">]|</a></span> where B is   <a href="real_1.html#NM1">Real</a>, B is   <a href="real_1.html#NM1">Real</a> : <font color="Maroon">c<sub>1</sub></font> <a href="xxreal_0.html#R1">&lt;</a> <font color="Olive">b<sub>1</sub></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>by </b><i><a class="txt" href="jordan1.html#E12"><i><font color="Green">Lemma10</font></i></a>, <a class="txt" href="jordan1.html#E15"><i><font color="Green">Lemma13</font></i></a></i>;<br/>
<b>reconsider </b><font color="Maroon">c<sub>7</sub></font> = <span class="p1">{<span class="default"> <span class="p2"><a href="euclid.html#K23">|[</a><span class="default"><font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>2</sub></font></span><a href="euclid.html#K23">]|</a></span> where B is   <a href="real_1.html#NM1">Real</a>, B is   <a href="real_1.html#NM1">Real</a> : <font color="Olive">b<sub>1</sub></font> <a href="xxreal_0.html#R1">&lt;</a> <font color="Maroon">c<sub>3</sub></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>by </b><i><a class="txt" href="jordan1.html#E12"><i><font color="Green">Lemma10</font></i></a>, <a class="txt" href="jordan1.html#E13"><i><font color="Green">Lemma11</font></i></a></i>;<br/>
<b>reconsider </b><font color="Maroon">c<sub>8</sub></font> = <span class="p1">{<span class="default"> <span class="p2"><a href="euclid.html#K23">|[</a><span class="default"><font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>2</sub></font></span><a href="euclid.html#K23">]|</a></span> where B is   <a href="real_1.html#NM1">Real</a>, B is   <a href="real_1.html#NM1">Real</a> : <font color="Maroon">c<sub>2</sub></font> <a href="xxreal_0.html#R1">&lt;</a> <font color="Olive">b<sub>2</sub></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>by </b><i><a class="txt" href="jordan1.html#E12"><i><font color="Green">Lemma10</font></i></a>, <a class="txt" href="jordan1.html#E16"><i><font color="Green">Lemma14</font></i></a></i>;<br/>
<b>reconsider </b><font color="Maroon">c<sub>9</sub></font> = <span class="p1">{<span class="default"> <span class="p2"><a href="euclid.html#K23">|[</a><span class="default"><font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>2</sub></font></span><a href="euclid.html#K23">]|</a></span> where B is   <a href="real_1.html#NM1">Real</a>, B is   <a href="real_1.html#NM1">Real</a> : <font color="Olive">b<sub>2</sub></font> <a href="xxreal_0.html#R1">&lt;</a> <font color="Maroon">c<sub>4</sub></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>by </b><i><a class="txt" href="jordan1.html#E12"><i><font color="Green">Lemma10</font></i></a>, <a class="txt" href="jordan1.html#E14"><i><font color="Green">Lemma12</font></i></a></i>;<br/>
<a NAME="E6:34"/><i><font color="Green">E37</font></i>: 
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="subset_1.html#K9">/\</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="subset_1.html#K9">/\</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="subset_1.html#K9">/\</a> <font color="Maroon">c<sub>9</sub></font>
 
<b>by </b><i><a class="txt" href="jordan1.html#E1:34"><i><font color="Green">E36</font></i></a>, <a class="ref" href="jordan1.html#T12" target="_self">Th12</a></i>;<br/>
<a NAME="E7:34"/>
( <font color="Maroon">c<sub>6</sub></font> is <a href="pre_topc.html#V3">open</a> &amp; <font color="Maroon">c<sub>7</sub></font> is <a href="pre_topc.html#V3">open</a> )
 
<b>by </b><i><a class="ref" href="jordan1.html#T25" target="_self">Th25</a>, <a class="ref" href="jordan1.html#T26" target="_self">Th26</a></i>;<br/>
<a NAME="E8:34"/><b>then </b><i><font color="Green">E38</font></i>: 
<font color="Maroon">c<sub>6</sub></font> <a href="subset_1.html#K9">/\</a> <font color="Maroon">c<sub>7</sub></font> is <a href="pre_topc.html#V3">open</a>
 
<b>by </b><i><a class="ref" href="tops_1.html#T38">TOPS_1:38</a></i>;<br/>
<a NAME="E9:34"/><i><font color="Green">E39</font></i>: 
( <font color="Maroon">c<sub>8</sub></font> is <a href="pre_topc.html#V3">open</a> &amp; <font color="Maroon">c<sub>9</sub></font> is <a href="pre_topc.html#V3">open</a> )
 
<b>by </b><i><a class="ref" href="jordan1.html#T27" target="_self">Th27</a>, <a class="ref" href="jordan1.html#T28" target="_self">Th28</a></i>;<br/>
<a NAME="E10:34"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="subset_1.html#K9">/\</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="subset_1.html#K9">/\</a> <font color="Maroon">c<sub>8</sub></font> is <a href="pre_topc.html#V3">open</a>
 
<b>by </b><i><a class="txt" href="jordan1.html#E8:34"><i><font color="Green">E38</font></i></a>, <a class="ref" href="tops_1.html#T38">TOPS_1:38</a></i>;<br/>
<b>hence </b><a NAME="E11:34"/>
<font color="Maroon">c<sub>5</sub></font> is <a href="pre_topc.html#V3">open</a>
 <b>by </b><i><a class="txt" href="jordan1.html#E6:34"><i><font color="Green">E37</font></i></a>, <a class="txt" href="jordan1.html#E9:34"><i><font color="Green">E39</font></i></a>, <a class="ref" href="tops_1.html#T38">TOPS_1:38</a></i>;<br/>


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