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<b>let </b><font color="Maroon" title="c1">L</font> be   <a href="waybel_0.html#NM8" title="WAYBEL_0:NM.8">LATTICE</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  ex <font color="Olive" title="b1">X</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>  ex <font color="Olive" title="b2">c</font> being <a href="waybel_1.html#V7" title="WAYBEL_1:attr.7">closure</a> <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <span class="p1">(<span class="default"><a href="yellow_1.html#K3" title="YELLOW_1:func.3">BoolePoset</a> <font color="Olive" title="b1">X</font></span>)</span>,<span class="p1">(<span class="default"><a href="yellow_1.html#K3" title="YELLOW_1:func.3">BoolePoset</a> <font color="Olive" title="b1">X</font></span>)</span> st <br/>( <font color="Olive" title="b2">c</font> is <a href="waybel_0.html#V22" title="WAYBEL_0:attr.22">directed-sups-preserving</a> &amp; <font color="Maroon" title="c1">L</font>, <a href="yellow_2.html#K1" title="YELLOW_2:func.1">Image</a> <font color="Olive" title="b2">c</font> <a href="waybel_1.html#R5" title="WAYBEL_1:pred.5">are_isomorphic</a>  ) implies <font color="Maroon" title="c1">L</font> is <a href="waybel_8.html#V2" title="WAYBEL_8:attr.2">algebraic</a> )</span><br/>

<b>given </b><font color="Maroon" title="c2">X</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> , <font color="Maroon" title="c3">c</font> being  <a href="waybel_1.html#V7" title="WAYBEL_1:attr.7">closure</a> <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <span class="p1">(<span class="default"><a href="yellow_1.html#K3" title="YELLOW_1:func.3">BoolePoset</a> <font color="Maroon" title="c2">X</font></span>)</span>,<span class="p1">(<span class="default"><a href="yellow_1.html#K3" title="YELLOW_1:func.3">BoolePoset</a> <font color="Maroon" title="c2">X</font></span>)</span><b> such that </b><a NAME="E2:39"/><i><font color="Green" title="E34">A1</font></i>: 
<font color="Maroon" title="c3">c</font> is <a href="waybel_0.html#V22" title="WAYBEL_0:attr.22">directed-sups-preserving</a>
 <b>and </b><br/><a NAME="E3:39"/><i><font color="Green" title="E35">A2</font></i>: 
<font color="Maroon" title="c1">L</font>, <a href="yellow_2.html#K1" title="YELLOW_2:func.1">Image</a> <font color="Maroon" title="c3">c</font> <a href="waybel_1.html#R5" title="WAYBEL_1:pred.5">are_isomorphic</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">L</font> is <a href="waybel_8.html#V2" title="WAYBEL_8:attr.2">algebraic</a></span><br/>

<a NAME="E4:39"/><i><font color="Green" title="E36">A3</font></i>: 
 <a href="yellow_2.html#K1" title="YELLOW_2:func.1">Image</a> <font color="Maroon" title="c3">c</font> is  <a href="lattice3.html#V3" title="LATTICE3:attr.3">complete</a> <a href="waybel_0.html#NM8" title="WAYBEL_0:NM.8">LATTICE</a>
 
<b>by </b><i><a class="txt" href="#E2:39"><i><font color="Green" title="E34">A1</font></i></a>, <a class="ref" href="yellow_2.html#T37" title="YELLOW_2:th.37">YELLOW_2:37</a></i>;<br/>
<a NAME="E5:39"/>
 <a href="yellow_2.html#K1" title="YELLOW_2:func.1">Image</a> <font color="Maroon" title="c3">c</font> is  <a href="waybel_8.html#V2" title="WAYBEL_8:attr.2">algebraic</a> <a href="waybel_0.html#NM8" title="WAYBEL_0:NM.8">LATTICE</a>
 
<b>by </b><i><a class="txt" href="#E2:39"><i><font color="Green" title="E34">A1</font></i></a>, <a class="ref" href="waybel_8.html#T26" title="WAYBEL_8:th.26">WAYBEL_8:26</a></i>;<br/>
<b>hence </b><a NAME="E6:39"/>
<font color="Maroon" title="c1">L</font> is <a href="waybel_8.html#V2" title="WAYBEL_8:attr.2">algebraic</a>
 <b>by </b><i><a class="txt" href="#E3:39"><i><font color="Green" title="E35">A2</font></i></a>, <a class="txt" href="#E4:39"><i><font color="Green" title="E36">A3</font></i></a>, <a class="ref" href="waybel13.html#T32" target="_self" title="WAYBEL13:th.32">Th32</a>, <a class="ref" href="waybel_1.html#T7" title="WAYBEL_1:th.7">WAYBEL_1:7</a></i>; <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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