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<b>let </b><font color="Maroon">c<sub>1</sub></font> be  <a href="compts_1.html#V2">compact</a> <a href="compts_1.html#V3">Hausdorff</a> <a href="waybel_9.html#NM1">TopLattice</a>;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font> be   <a href="pre_topc.html#NM2">Point</a> of <font color="Maroon">c<sub>1</sub></font>;<br/><b>let </b><font color="Maroon">c<sub>3</sub></font> be   <a href="waybel_0.html#NM2">net</a> of <font color="Maroon">c<sub>1</sub></font>;<br/>





<b>assume </b><b>that </b><br/><a NAME="E1:91"/><i><font color="Green">E44</font></i>: 
for <font color="Olive">b<sub>1</sub></font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>1</sub></font> holds <font color="Olive">b<sub>1</sub></font> <a href="waybel_1.html#K4">"/\"</a>  is <a href="pre_topc.html#V5">continuous</a>
 <b>and </b><br/><a NAME="E2:91"/><i><font color="Green">E45</font></i>: 
<font color="Maroon">c<sub>3</sub></font> is <a href="waybel_0.html#V10">eventually-directed</a>
 <b>and </b><br/><a NAME="E3:91"/><i><font color="Green">E46</font></i>: 
<font color="Maroon">c<sub>2</sub></font> <a href="waybel_9.html#R3" target="_self">is_a_cluster_point_of</a> <font color="Maroon">c<sub>3</sub></font>
 ;<br/>

<b>reconsider </b><font color="Maroon">c<sub>4</sub></font> = <font color="Maroon">c<sub>2</sub></font> as   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>1</sub></font> ;<br/>
<a NAME="E5:91"/><i><font color="Green">E47</font></i>: 
<font color="Maroon">c<sub>4</sub></font> <a href="lattice3.html#NR4" target="_self">is_&gt;=_than</a>  <a href="relset_1.html#K5">rng</a> the <a href="waybel_0.html#U1">mapping</a> of <font color="Maroon">c<sub>3</sub></font>
 
<b>by </b><i><a class="txt" href="waybel_9.html#E1:91"><i><font color="Green">E44</font></i></a>, <a class="txt" href="waybel_9.html#E2:91"><i><font color="Green">E45</font></i></a>, <a class="txt" href="waybel_9.html#E3:91"><i><font color="Green">E46</font></i></a>, <a class="txt" href="waybel_9.html#E48"><i><font color="Green">Lemma41</font></i></a></i>;<br/>
<a NAME="E6:91"/>
for <font color="Olive">b<sub>1</sub></font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>1</sub></font> st  <a href="relset_1.html#K5">rng</a> the <a href="waybel_0.html#U1">mapping</a> of <font color="Maroon">c<sub>3</sub></font> <a href="lattice3.html#R2">is_&lt;=_than</a> <font color="Olive">b<sub>1</sub></font> holds <br/><font color="Maroon">c<sub>4</sub></font> <a href="orders_2.html#R3">&lt;=</a> <font color="Olive">b<sub>1</sub></font>
 
<b>by </b><i><a class="txt" href="waybel_9.html#E1:91"><i><font color="Green">E44</font></i></a>, <a class="txt" href="waybel_9.html#E3:91"><i><font color="Green">E46</font></i></a>, <a class="txt" href="waybel_9.html#E49"><i><font color="Green">Lemma42</font></i></a></i>;<br/>
<b>hence </b><font color="Maroon">c<sub>2</sub></font> = 
 <a href="yellow_0.html#NK3" target="_self">sup</a> <span class="p1">(<span class="default"><a href="relset_1.html#K5">rng</a> the <a href="waybel_0.html#U1">mapping</a> of <font color="Maroon">c<sub>3</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="waybel_9.html#E5:91"><i><font color="Green">E47</font></i></a>, <a class="ref" href="yellow_0.html#T30">YELLOW_0:30</a></i>
<br/>.= 
 <a href="yellow_2.html#NK6" target="_self">Sup</a> 
<b>by </b><i><a class="ref" href="yellow_2.html#D5">YELLOW_2:def 5</a></i>
<br/>.= 
 <a href="waybel_2.html#K1">sup</a> <font color="Maroon">c<sub>3</sub></font>

;<br/><br/>


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