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<b>let </b><font color="Maroon">L</font> be  non <a href="struct_0.html#V3">empty</a> <a href="orders_2.html#V2">reflexive</a>  <a href="orders_2.html#L1">RelStr</a> ;<br/><b>let </b><font color="Maroon">A</font> be   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">L</font>;<br/>



<a NAME="E1:39"/>
 <a href="waybel28.html#K3" target="_self">lim_inf-Convergence</a> <font color="Maroon">L</font> <a href="tarski.html#R1">c=</a>  <a href="waybel11.html#K2">Scott-Convergence</a> <font color="Maroon">L</font>
 
<b>by </b><i/>;<br/>
<a NAME="E2:39"/><b>then </b><i><font color="Green">E25</font></i>: 
the <a href="pre_topc.html#U1">topology</a> of <span class="p1">(<span class="default"><a href="yellow_6.html#K14">ConvergenceSpace</a> <span class="p2">(<span class="default"><a href="waybel11.html#K2">Scott-Convergence</a> <font color="Maroon">L</font></span>)</span></span>)</span> <a href="tarski.html#R1">c=</a> the <a href="pre_topc.html#U1">topology</a> of <span class="p1">(<span class="default"><a href="yellow_6.html#K14">ConvergenceSpace</a> <span class="p2">(<span class="default"><a href="waybel28.html#K3" target="_self">lim_inf-Convergence</a> <font color="Maroon">L</font></span>)</span></span>)</span>
 
<b>by </b><i/>;<br/>
<b>assume </b><a NAME="E3:39"/>
<font color="Maroon">A</font> <a href="hidden.html#R2">in</a>  <a href="waybel11.html#K5">sigma</a> <font color="Maroon">L</font>
 ;<br/>

<a NAME="E4:39"/><b>then </b>
<font color="Maroon">A</font> <a href="hidden.html#R2">in</a> the <a href="pre_topc.html#U1">topology</a> of <span class="p1">(<span class="default"><a href="yellow_6.html#K14">ConvergenceSpace</a> <span class="p2">(<span class="default"><a href="waybel11.html#K2">Scott-Convergence</a> <font color="Maroon">L</font></span>)</span></span>)</span>
 
;<br/>
<a NAME="E5:39"/><b>then </b>
<font color="Maroon">A</font> <a href="hidden.html#R2">in</a> the <a href="pre_topc.html#U1">topology</a> of <span class="p1">(<span class="default"><a href="yellow_6.html#K14">ConvergenceSpace</a> <span class="p2">(<span class="default"><a href="waybel28.html#K3" target="_self">lim_inf-Convergence</a> <font color="Maroon">L</font></span>)</span></span>)</span>
 
<b>by </b><i/>;<br/>
<b>hence </b><a NAME="E6:39"/>
<font color="Maroon">A</font> <a href="hidden.html#R2">in</a>  <a href="waybel28.html#K4" target="_self">xi</a> <font color="Maroon">L</font>
 ;<br/>


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