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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="orders_2.html#L1">RelStr</a> ;<br/>

<a NAME="E1:32"/>
for <font color="Olive">b<sub>1</sub></font> being  <a href="subset_1.html#NM2">Subset</a> of <span class="p1">(<span class="default"><a href="pre_topc.html#K2">[#]</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> st  <a href="yellow_0.html#R2">ex_inf_of</a> <font color="Olive">b<sub>1</sub></font>,<font color="Maroon">c<sub>1</sub></font> holds <br/> <a href="yellow_0.html#K2">"/\"</a> <font color="Olive">b<sub>1</sub></font>,<font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R2">in</a>  <a href="pre_topc.html#K2">[#]</a> <font color="Maroon">c<sub>1</sub></font>
 
;<br/>
<b>hence </b><a NAME="E2:32"/>
 <a href="pre_topc.html#K2">[#]</a> <font color="Maroon">c<sub>1</sub></font> is <a href="waybel23.html#V3">infs-closed</a>
 <b>by </b><i><a class="ref" href="waybel23.html#T19">WAYBEL23:19</a></i>;<br/>

<a NAME="E3:32"/>
for <font color="Olive">b<sub>1</sub></font> being  <a href="subset_1.html#NM2">Subset</a> of <span class="p1">(<span class="default"><a href="pre_topc.html#K2">[#]</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> st  <a href="yellow_0.html#R1">ex_sup_of</a> <font color="Olive">b<sub>1</sub></font>,<font color="Maroon">c<sub>1</sub></font> holds <br/> <a href="yellow_0.html#K1">"\/"</a> <font color="Olive">b<sub>1</sub></font>,<font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R2">in</a>  <a href="pre_topc.html#K2">[#]</a> <font color="Maroon">c<sub>1</sub></font>
 
;<br/>
<b>hence </b><a NAME="E4:32"/>
 <a href="pre_topc.html#K2">[#]</a> <font color="Maroon">c<sub>1</sub></font> is <a href="waybel23.html#V4">sups-closed</a>
 <b>by </b><i><a class="ref" href="waybel23.html#T20">WAYBEL23:20</a></i>;<br/>


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