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<span class="kw">let </span><font color="Maroon" title="c1">L</font> be   <a href="lattices.html#NM1" title="LATTICES:NM.1">Lattice</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">p</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">L</font>  st <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Olive" title="b1">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> is   <a href="filter_2.html#NM1" title="FILTER_2:NM.1">Ideal</a> of <font color="Maroon" title="c1">L</font> holds <br/><font color="Maroon" title="c1">L</font> is  <a href="lattices.html#V13" title="LATTICES:attr.13">lower-bounded</a> </span><br/><span class="kw">let </span><font color="Maroon" title="c2">p</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">L</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c2">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> is   <a href="filter_2.html#NM1" title="FILTER_2:NM.1">Ideal</a> of <font color="Maroon" title="c1">L</font> implies <font color="Maroon" title="c1">L</font> is  <a href="lattices.html#V13" title="LATTICES:attr.13">lower-bounded</a>  )</span><br/>



<span class="kw">assume </span><a NAME="E1:42"/>
<span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c2">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> is   <a href="filter_2.html#NM1" title="FILTER_2:NM.1">Ideal</a> of <font color="Maroon" title="c1">L</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c1">L</font> is  <a href="lattices.html#V13" title="LATTICES:attr.13">lower-bounded</a> </span><br/>

<a NAME="E2:42"/><span class="kw">then </span>
<span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c2">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> is   <a href="filter_0.html#NM1" title="FILTER_0:NM.1">Filter</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c1">L</font> <a href="lattice2.html#K1" title="LATTICE2:func.1">.:</a> </span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="filter_2.html#T21" target="_self" title="FILTER_2:th.21">Th21</a></span>;<br/>
<a NAME="E3:42"/><span class="kw">then </span>
<font color="Maroon" title="c1">L</font> <a href="lattice2.html#K1" title="LATTICE2:func.1">.:</a>  is  <a href="lattices.html#V14" title="LATTICES:attr.14">upper-bounded</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="filter_0.html#T14" title="FILTER_0:th.14">FILTER_0:14</a></span>;<br/>
<span class="kw">hence </span><a NAME="E4:42"/>
<font color="Maroon" title="c1">L</font> is  <a href="lattices.html#V13" title="LATTICES:attr.13">lower-bounded</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="lattice2.html#T63" title="LATTICE2:th.63">LATTICE2:63</a></span>; <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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