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<b>let </b><font color="Maroon">c<sub>1</sub></font> be  non <a href="struct_0.html#V3">empty</a> <a href="pre_topc.html#NM1">TopSpace</a>;<br/>

<b>thus </b><a NAME="E1:43"/>
( <font color="Maroon">c<sub>1</sub></font> is <a href="compts_1.html#V2">compact</a> implies for <font color="Olive">b<sub>1</sub></font> being  <a href="waybel_0.html#NM2">net</a> of <font color="Maroon">c<sub>1</sub></font>ex <font color="Olive">b<sub>2</sub></font> being  <a href="pre_topc.html#NM2">Point</a> of <font color="Maroon">c<sub>1</sub></font> st <font color="Olive">b<sub>2</sub></font> <a href="waybel_9.html#R3">is_a_cluster_point_of</a> <font color="Olive">b<sub>1</sub></font> )
 <b>by </b><i><a class="txt" href="yellow19.html#E37"><i><font color="Green">Lemma24</font></i></a></i>;<br/>

<b>assume </b><a NAME="E2:43"/>
for <font color="Olive">b<sub>1</sub></font> being  <a href="waybel_0.html#NM2">net</a> of <font color="Maroon">c<sub>1</sub></font>ex <font color="Olive">b<sub>2</sub></font> being  <a href="pre_topc.html#NM2">Point</a> of <font color="Maroon">c<sub>1</sub></font> st <font color="Olive">b<sub>2</sub></font> <a href="waybel_9.html#R3">is_a_cluster_point_of</a> <font color="Olive">b<sub>1</sub></font>
 ;<br/>

<a NAME="E3:43"/><b>then </b>
for <font color="Olive">b<sub>1</sub></font> being  <a href="waybel_0.html#NM2">net</a> of <font color="Maroon">c<sub>1</sub></font> st <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a>  <a href="yellow_6.html#K7">NetUniv</a> <font color="Maroon">c<sub>1</sub></font> holds <br/>ex <font color="Olive">b<sub>2</sub></font> being  <a href="pre_topc.html#NM2">Point</a> of <font color="Maroon">c<sub>1</sub></font> st <font color="Olive">b<sub>2</sub></font> <a href="waybel_9.html#R3">is_a_cluster_point_of</a> <font color="Olive">b<sub>1</sub></font>
 
;<br/>
<b>hence </b><a NAME="E4:43"/>
<font color="Maroon">c<sub>1</sub></font> is <a href="compts_1.html#V2">compact</a>
 <b>by </b><i><a class="txt" href="yellow19.html#E38"><i><font color="Green">Lemma25</font></i></a></i>;<br/>


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