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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">set </span><font color="Maroon" title="c2">OL</font> =  <a href="openlatt.html#K6" title="OPENLATT:func.6">Open_setLatt</a> <font color="Maroon" title="c1">T</font>;<br/>
<a NAME="E2:47_1_1"/>
the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">T</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="lattices.html#K6" title="LATTICES:func.6">Top</a> <span class="p1">(<span class="default"><a href="openlatt.html#K6" title="OPENLATT:func.6">Open_setLatt</a> <font color="Maroon" title="c1">T</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="openlatt.html#T11" target="_self" title="OPENLATT:th.11">Th11</a></span>;<br/>
<span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c3">a</font> = the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">T</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="openlatt.html#K6" title="OPENLATT:func.6">Open_setLatt</a> <font color="Maroon" title="c1">T</font></span>)</span> ;<br/>
<a NAME="E4:47_1_1"/>
 <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="lattices.html#K5" title="LATTICES:func.5">Bottom</a> <span class="p1">(<span class="default"><a href="openlatt.html#K6" title="OPENLATT:func.6">Open_setLatt</a> <font color="Maroon" title="c1">T</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="openlatt.html#T10" target="_self" title="OPENLATT:th.10">Th10</a></span>;<br/>
<span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c4">b</font> =  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="openlatt.html#K6" title="OPENLATT:func.6">Open_setLatt</a> <font color="Maroon" title="c1">T</font></span>)</span> ;<br/>
<span class="kw">take </span>
 <a href="openlatt.html#K6" title="OPENLATT:func.6">Open_setLatt</a> <font color="Maroon" title="c1">T</font>
; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> not  <a href="openlatt.html#K6" title="OPENLATT:func.6">Open_setLatt</a> <font color="Maroon" title="c1">T</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 <span class="p1">(<span class="default"><a href="openlatt.html#K6" title="OPENLATT:func.6">Open_setLatt</a> <font color="Maroon" title="c1">T</font></span>)</span> 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="E6:47_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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