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<b>let </b><font color="Maroon">c<sub>1</sub></font> be   <a href="waybel_9.html#NM1">TopLattice</a>;<br/>

<b>assume </b><a NAME="E1:5_1_1"/>
<font color="Maroon">c<sub>1</sub></font> is <a href="realset2.html#V3">trivial</a>
 ;<br/>

<b>then reconsider </b><font color="Maroon">c<sub>2</sub></font> = <font color="Maroon">c<sub>1</sub></font> as  <a href="realset2.html#V3">trivial</a> <a href="waybel_9.html#NM1">TopLattice</a> ;<br/>
<b>consider </b><font color="Maroon">c<sub>3</sub></font> being   <a href="pre_topc.html#NM2">Point</a> of <font color="Maroon">c<sub>2</sub></font>;<br/>
<a NAME="E4:5_1_1"/>
the <a href="struct_0.html#U1">carrier</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> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>2</sub></font>
 
<b>by </b><i><a class="ref" href="yellow_6.html#D27">YELLOW_6:def 27</a></i>;<br/>
<b>then reconsider </b><font color="Maroon">c<sub>4</sub></font> =  <a href="yellow_6.html#K14">ConvergenceSpace</a> <span class="p1">(<span class="default"><a href="waybel28.html#K3">lim_inf-Convergence</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> as  non <a href="struct_0.html#V3">empty</a> <a href="realset2.html#V3">trivial</a> <a href="pre_topc.html#NM1">TopSpace</a> <b>by </b><i><a class="ref" href="realset2.html#D5">REALSET2:def 5</a></i>;<br/>
<b>reconsider </b><font color="Maroon">c<sub>5</sub></font> = <font color="Maroon">c<sub>3</sub></font> as   <a href="pre_topc.html#NM2">Point</a> of <font color="Maroon">c<sub>4</sub></font> <b>by </b><i><a class="ref" href="yellow_6.html#D27">YELLOW_6:def 27</a></i>;<br/>
<b>thus </b>the <a href="pre_topc.html#U1">topology</a> of <font color="Maroon">c<sub>1</sub></font> = 
<span class="p1"><a href="tarski.html#K2">{</a><span class="default"><a href="xboole_0.html#K1">{}</a> ,<span class="p2"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>5</sub></font></span><a href="domain_1.html#K6">}</a></span></span><a href="tarski.html#K2">}</a></span>
<b>by </b><i><a class="ref" href="yellow_9.html#T9">YELLOW_9:9</a></i>
<br/>.= 
the <a href="pre_topc.html#U1">topology</a> of <font color="Maroon">c<sub>4</sub></font>
<b>by </b><i><a class="ref" href="yellow_9.html#T9">YELLOW_9:9</a></i>
<br/>.= 
 <a href="waybel28.html#K4">xi</a> <font color="Maroon">c<sub>1</sub></font>
<b>by </b><i><a class="ref" href="waybel28.html#D4">WAYBEL28:def 4</a></i>
; <i><font color="Red">:: according to </font></i><a class="ref" href="waybel33.html#D2" target="_self">WAYBEL33:def 2</a><br/>


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