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<b>let </b><font color="Maroon">L</font> be  <a href="lattice3.html#V2">with_infima</a> <a href="orders_2.html#NM1">Poset</a>;<br/><b>let </b><font color="Maroon">I</font> be   <a href="waybel_0.html#NM3">Ideal</a> of <font color="Maroon">L</font>, <font color="Maroon">J</font> be   <a href="waybel_0.html#NM3">Ideal</a> of <font color="Maroon">L</font>;<br/>



<b>consider </b><font color="Maroon">i</font> being    <a href="subset_1.html#M2">Element</a> of <font color="Maroon">I</font>, <font color="Maroon">j</font> being    <a href="subset_1.html#M2">Element</a> of <font color="Maroon">J</font>;<br/>
<b>set </b><font color="Maroon">a</font> = <font color="Maroon">i</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">j</font>;<br/>
<a NAME="E2:47"/>
( <font color="Maroon">i</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">j</font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">i</font> &amp; <font color="Maroon">i</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">j</font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">j</font> )
 
<b>by </b><i><a class="ref" href="yellow_0.html#T23">YELLOW_0:23</a></i>;<br/>
<a NAME="E3:47"/><b>then </b>
( <font color="Maroon">i</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">j</font> <a href="hidden.html#R2">in</a> <font color="Maroon">I</font> &amp; <font color="Maroon">i</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">j</font> <a href="hidden.html#R2">in</a> <font color="Maroon">J</font> )
 
<b>by </b><i><a class="ref" href="waybel_0.html#D19">WAYBEL_0:def 19</a></i>;<br/>
<b>hence </b><a NAME="E4:47"/>
<font color="Maroon">I</font> <a href="subset_1.html#K9">/\</a> <font color="Maroon">J</font> is   <a href="waybel_0.html#NM3">Ideal</a> of <font color="Maroon">L</font>
 <b>by </b><i><a class="ref" href="waybel_0.html#T27">WAYBEL_0:27</a>, <a class="ref" href="waybel_0.html#T44">WAYBEL_0:44</a>, <a class="ref" href="xboole_0.html#D3">XBOOLE_0:def 3</a></i>;<br/>


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