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<b>let </b><font color="Maroon" title="c1">N</font> be  <a href="lattice3.html#V3" title="LATTICE3:attr.3">complete</a> <a href="waybel19.html#V2" title="WAYBEL19:attr.2">Lawson</a> <a href="waybel_9.html#NM1" title="WAYBEL_9:NM.1">TopLattice</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c1">N</font> is <a href="waybel_3.html#V3" title="WAYBEL_3:attr.3">continuous</a> implies <font color="Maroon" title="c1">N</font> is <a href="waybel30.html#V3" title="WAYBEL30:attr.3">with_open_semilattices</a> )</span><br/>

<b>assume </b><a NAME="E1:58_1_1"/>
<font color="Maroon" title="c1">N</font> is <a href="waybel_3.html#V3" title="WAYBEL_3:attr.3">continuous</a>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c1">N</font> is <a href="waybel30.html#V3" title="WAYBEL30:attr.3">with_open_semilattices</a></span><br/>

<b>then reconsider </b><font color="Maroon" title="c2">M</font> = <font color="Maroon" title="c1">N</font> as  <a href="lattice3.html#V3" title="LATTICE3:attr.3">complete</a> <a href="waybel19.html#V2" title="WAYBEL19:attr.2">Lawson</a> <a href="waybel_3.html#V3" title="WAYBEL_3:attr.3">continuous</a> <a href="waybel_9.html#NM1" title="WAYBEL_9:NM.1">TopLattice</a> ;<br/>
<a NAME="E3:58_1_1"/>
<font color="Maroon" title="c2">M</font> is <a href="waybel30.html#V3" title="WAYBEL30:attr.3">with_open_semilattices</a>
 
<b>by </b><i><a class="ref" href="waybel30.html#T35" target="_self" title="WAYBEL30:th.35">Th35</a></i>;<br/>
<b>hence </b><a NAME="E4:58_1_1"/>
<font color="Maroon" title="c1">N</font> is <a href="waybel30.html#V3" title="WAYBEL30:attr.3">with_open_semilattices</a>
 ; <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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