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<b>consider </b><font color="Maroon" title="c1">T</font> being  non <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a> <a href="pre_topc.html#NM1" title="PRE_TOPC:NM.1">TopSpace</a>;<br/>
<b>reconsider </b><font color="Maroon" title="c2">E</font> =  <a href="lopclset.html#K6" title="LOPCLSET:func.6">OpenClosedSetLatt</a> <font color="Maroon" title="c1">T</font> as   <a href="lattices.html#NM8" title="LATTICES:NM.8">B_Lattice</a> <b>by </b><i><a class="ref" href="lopclset.html#T14" target="_self" title="LOPCLSET:th.14">Th14</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c3">a</font> =  <a href="struct_0.html#K2" title="STRUCT_0:func.2">[#]</a> <font color="Maroon" title="c1">T</font>, <font color="Maroon" title="c4">b</font> =  <a href="struct_0.html#K1" title="STRUCT_0:func.1">{}</a> <font color="Maroon" title="c1">T</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c2">E</font> <b>by </b><i><a class="ref" href="lopclset.html#T7" target="_self" title="LOPCLSET:th.7">Th7</a>, <a class="ref" href="lopclset.html#T8" target="_self" title="LOPCLSET:th.8">Th8</a></i>;<br/>
<b>take </b>
<font color="Maroon" title="c2">E</font>
; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> not <font color="Maroon" title="c2">E</font> is <a href="struct_0.html#V7" title="STRUCT_0:attr.7">trivial</a></span><br/>

<b>take </b>
<font color="Maroon" title="c3">a</font>
; <i><font color="Red">:: according to </font></i><a class="ref" href="struct_0.html#D10" title="STRUCT_0:def.10">STRUCT_0:def 10</a> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> not for <font color="Olive">b<sub>1</sub></font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">E</font> holds  <font color="Maroon" title="c3">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive">b<sub>1</sub></font></span><br/>

<b>take </b>
<font color="Maroon" title="c4">b</font>
; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> not <font color="Maroon" title="c3">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">b</font></span><br/>

<b>thus </b><a NAME="E4:11_1_1"/>
<font color="Maroon" title="c3">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c4">b</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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