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<span class="kw">let </span><font color="Maroon" title="c1">L</font> be   <a href="waybel_9.html#NM1" title="WAYBEL_9:NM.1">TopLattice</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c1">L</font> is  <a href="struct_0.html#V7" title="STRUCT_0:attr.7">trivial</a>  implies <font color="Maroon" title="c1">L</font> is  <a href="waybel33.html#V1" title="WAYBEL33:attr.1">lim-inf</a>  )</span><br/>

<a NAME="E1:5_1_1"/><span class="lab"><font color="Green" title="E2">XX</font></span>: 
 not <font color="Maroon" title="c1">L</font> is  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a> 
 
;<br/>
<span class="kw">assume </span><a NAME="E2:5_1_1"/>
<font color="Maroon" title="c1">L</font> is  <a href="struct_0.html#V7" title="STRUCT_0:attr.7">trivial</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c1">L</font> is  <a href="waybel33.html#V1" title="WAYBEL33:attr.1">lim-inf</a> </span><br/>

<a NAME="E3:5_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E3">YY</font></span>: 
 the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">L</font> is 1 <a href="card_1.html#V3" title="CARD_1:attr.3">-element</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:5_1_1"><span class="lab"><font color="Green" title="E2">XX</font></span></a></span>;<br/>
<span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c2">L9</font> = <font color="Maroon" title="c1">L</font> as  1 <a href="struct_0.html#V13" title="STRUCT_0:attr.13">-element</a>  <a href="waybel_9.html#NM1" title="WAYBEL_9:NM.1">TopLattice</a> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:5_1_1"><span class="lab"><font color="Green" title="E2">XX</font></span></a>, <a class="ref" href="struct_0.html#D19" title="STRUCT_0:def.19">STRUCT_0:def 19</a></span>;<br/>
<a NAME="E5:5_1_1"/>
 the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="yellow_6.html#K13" title="YELLOW_6:func.13">ConvergenceSpace</a> <span class="p2">(<span class="default"><a href="waybel28.html#K3" title="WAYBEL28:func.3">lim_inf-Convergence</a> <font color="Maroon" title="c1">L</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">L9</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="yellow_6.html#D24" title="YELLOW_6:def.24">YELLOW_6:def 24</a></span>;<br/>
<span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c3">S</font> =  <a href="yellow_6.html#K13" title="YELLOW_6:func.13">ConvergenceSpace</a> <span class="p1">(<span class="default"><a href="waybel28.html#K3" title="WAYBEL28:func.3">lim_inf-Convergence</a> <font color="Maroon" title="c1">L</font></span>)</span> as  1 <a href="struct_0.html#V13" title="STRUCT_0:attr.13">-element</a>  <a href="pre_topc.html#NM1" title="PRE_TOPC:NM.1">TopSpace</a> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:5_1_1"><span class="lab"><font color="Green" title="E2">XX</font></span></a>, <a class="txt" href="#E3:5_1_1"><span class="lab"><font color="Green" title="E3">YY</font></span></a>, <a class="ref" href="struct_0.html#D19" title="STRUCT_0:def.19">STRUCT_0:def 19</a></span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c4">x</font> =  the   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <font color="Maroon" title="c2">L9</font>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c5">y</font> =  the   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <font color="Maroon" title="c2">L9</font> as   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <font color="Maroon" title="c3">S</font> <span class="kw">by</span> <span class="lab"><a class="ref" href="yellow_6.html#D24" title="YELLOW_6:def.24">YELLOW_6:def 24</a></span>;<br/>
<span class="kw">thus </span> the <a href="pre_topc.html#U1" title="PRE_TOPC:sel.1">topology</a> of <font color="Maroon" title="c1">L</font> = 
<span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>,<span class="p2"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c5">y</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:5_1_1"><span class="lab"><font color="Green" title="E2">XX</font></span></a>, <a class="ref" href="yellow_9.html#T9" title="YELLOW_9:th.9">YELLOW_9:9</a></span>
<br/>.= 
 the <a href="pre_topc.html#U1" title="PRE_TOPC:sel.1">topology</a> of <font color="Maroon" title="c3">S</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="yellow_9.html#T9" title="YELLOW_9:th.9">YELLOW_9:9</a></span>
<br/>.= 
 <a href="waybel28.html#K4" title="WAYBEL28:func.4">xi</a> <font color="Maroon" title="c1">L</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="waybel28.html#D4" title="WAYBEL28:def.4">WAYBEL28:def 4</a></span>
; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="waybel33.html#D2" target="_self" title="WAYBEL33:def.2">WAYBEL33:def 2</a> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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