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<b>let </b><font color="Maroon">c<sub>1</sub></font> be  <a href="waybel_0.html#V24">up-complete</a> <a href="waybel_0.html#NM8">LATTICE</a>;<br/>

<div><b>hereby </b>
<div class="add"><b>assume </b><a NAME="E1:75_1"/>
<font color="Maroon">c<sub>1</sub></font> is <a href="waybel_2.html#V2" target="_self">meet-continuous</a>
 ;<br/><a NAME="E2:75_1"/><b>then </b>
for <font color="Olive">b<sub>1</sub></font>, <font color="Olive">b<sub>2</sub></font> being  <a href="waybel_0.html#NM3">Ideal</a> of <font color="Maroon">c<sub>1</sub></font> holds <span class="p1">(<span class="default"><a href="yellow_0.html#NK3" target="_self">sup</a> <font color="Olive">b<sub>1</sub></font></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p1">(<span class="default"><a href="yellow_0.html#NK3" target="_self">sup</a> <font color="Olive">b<sub>2</sub></font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="yellow_0.html#NK3" target="_self">sup</a> <span class="p1">(<span class="default"><font color="Olive">b<sub>1</sub></font> <a href="yellow_4.html#K4">"/\"</a> <font color="Olive">b<sub>2</sub></font></span>)</span>
 <b>by </b><i><a class="ref" href="waybel_2.html#T50" target="_self">Th50</a></i>;<br/><b>hence </b><a NAME="E3:75_1"/>
for <font color="Olive">b<sub>1</sub></font>, <font color="Olive">b<sub>2</sub></font> being non <a href="xboole_0.html#V1">empty</a> <a href="waybel_0.html#V1">directed</a> <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">c<sub>1</sub></font> holds <span class="p1">(<span class="default"><a href="yellow_0.html#NK3" target="_self">sup</a> <font color="Olive">b<sub>1</sub></font></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p1">(<span class="default"><a href="yellow_0.html#NK3" target="_self">sup</a> <font color="Olive">b<sub>2</sub></font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="yellow_0.html#NK3" target="_self">sup</a> <span class="p1">(<span class="default"><font color="Olive">b<sub>1</sub></font> <a href="yellow_4.html#K4">"/\"</a> <font color="Olive">b<sub>2</sub></font></span>)</span>
 <b>by </b><i><a class="ref" href="waybel_2.html#T40" target="_self">Th40</a></i>;<br/></div>
<b>end;</b></div>

<b>assume </b><a NAME="E2:75"/>
for <font color="Olive">b<sub>1</sub></font>, <font color="Olive">b<sub>2</sub></font> being non <a href="xboole_0.html#V1">empty</a> <a href="waybel_0.html#V1">directed</a> <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">c<sub>1</sub></font> holds <span class="p1">(<span class="default"><a href="yellow_0.html#NK3" target="_self">sup</a> <font color="Olive">b<sub>1</sub></font></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p1">(<span class="default"><a href="yellow_0.html#NK3" target="_self">sup</a> <font color="Olive">b<sub>2</sub></font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="yellow_0.html#NK3" target="_self">sup</a> <span class="p1">(<span class="default"><font color="Olive">b<sub>1</sub></font> <a href="yellow_4.html#K4">"/\"</a> <font color="Olive">b<sub>2</sub></font></span>)</span>
 ;<br/>

<b>hence </b><a NAME="E3:75"/>
( <font color="Maroon">c<sub>1</sub></font> is <a href="waybel_0.html#V24">up-complete</a> &amp; <font color="Maroon">c<sub>1</sub></font> is <a href="waybel_2.html#V1" target="_self">satisfying_MC</a> )
 <b>by </b><i><a class="ref" href="waybel_2.html#T44" target="_self">Th44</a></i>; <i><font color="Red">:: according to </font></i><a class="ref" href="waybel_2.html#D7" target="_self">WAYBEL_2:def 7</a><br/>


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