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<b>let </b><font color="Maroon">c<sub>1</sub></font>, <font color="Maroon">c<sub>2</sub></font> be  <a href="waybel_0.html#V24">up-complete</a> <a href="waybel_0.html#V25">/\-complete</a> <a href="waybel_0.html#NM6">Semilattice</a>;<br/>

<a NAME="E1:17"/><i><font color="Green">E12</font></i>: 
(  <a href="waybel28.html#K4">xi</a> <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</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">lim_inf-Convergence</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> &amp;  <a href="waybel28.html#K4">xi</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</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">lim_inf-Convergence</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> )
 
<b>by </b><i><a class="ref" href="waybel28.html#D4">WAYBEL28:def 4</a></i>;<br/>
<b>assume </b><a NAME="E2:17"/>
 <a href="orders_2.html#G1">RelStr</a>(# the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>1</sub></font>,the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">c<sub>1</sub></font> #) <a href="hidden.html#R1">=</a>  <a href="orders_2.html#G1">RelStr</a>(# the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>2</sub></font>,the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">c<sub>2</sub></font> #)
 ;<br/>

<b>hence </b><a NAME="E3:17"/>
(  <a href="waybel28.html#K4">xi</a> <font color="Maroon">c<sub>1</sub></font> <a href="tarski.html#R1">c=</a>  <a href="waybel28.html#K4">xi</a> <font color="Maroon">c<sub>2</sub></font> &amp;  <a href="waybel28.html#K4">xi</a> <font color="Maroon">c<sub>2</sub></font> <a href="tarski.html#R1">c=</a>  <a href="waybel28.html#K4">xi</a> <font color="Maroon">c<sub>1</sub></font> )
 <b>by </b><i><a class="txt" href="waybel33.html#E1:17"><i><font color="Green">E12</font></i></a>, <a class="txt" href="waybel33.html#E12"><i><font color="Green">Lemma10</font></i></a></i>; <i><font color="Red">:: according to </font></i><a class="ref" href="xboole_0.html#D10">XBOOLE_0:def 10</a><br/>


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