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<span class="kw">consider </span><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/>
<span class="kw">reconsider </span><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> <span class="kw">by</span> <span class="lab"><a class="ref" href="lopclset.html#T14" target="_self" title="LOPCLSET:th.14">Th14</a></span>;<br/>
<span class="kw">reconsider </span><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> <span class="kw">by</span> <span class="lab"><a class="ref" href="lopclset.html#T4" target="_self" title="LOPCLSET:th.4">Th4</a>, <a class="ref" href="tops_1.html#T52" title="TOPS_1:th.52">TOPS_1:52</a>, <a class="ref" href="tops_1.html#T53" title="TOPS_1:th.53">TOPS_1:53</a></span>;<br/>
<span class="kw">take </span>
<font color="Maroon" title="c2">E</font>
; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></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/>

<span class="kw">take </span>
<font color="Maroon" title="c3">a</font>
; <span class="comment"><font color="Red">:: according to </font></span><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:()"><span class="comment"><font color="Red">::  thesis: </font></span></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/>

<span class="kw">take </span>
<font color="Maroon" title="c4">b</font>
; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></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/>

<span class="kw">thus </span><a NAME="E4:12_1_1"/>
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>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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