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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 <font color="Maroon" title="c1">L</font> is  <a href="lattices.html#V13" title="LATTICES:attr.13">lower-bounded</a>  holds <br/> <a href="filter_2.html#K15" title="FILTER_2:func.15">latt</a> <font color="Maroon" title="c1">L</font>,<span class="p1"><a href="filter_2.html#K10" title="FILTER_2:func.10">(.</a><span class="default"><font color="Olive" title="b1">p</font></span><a href="filter_2.html#K10" title="FILTER_2:func.10">.&gt;</a></span> is  <a href="lattices.html#V15" title="LATTICES:attr.15">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"> ( <font color="Maroon" title="c1">L</font> is  <a href="lattices.html#V13" title="LATTICES:attr.13">lower-bounded</a>  implies  <a href="filter_2.html#K15" title="FILTER_2:func.15">latt</a> <font color="Maroon" title="c1">L</font>,<span class="p1"><a href="filter_2.html#K10" title="FILTER_2:func.10">(.</a><span class="default"><font color="Maroon" title="c2">p</font></span><a href="filter_2.html#K10" title="FILTER_2:func.10">.&gt;</a></span> is  <a href="lattices.html#V15" title="LATTICES:attr.15">bounded</a>  )</span><br/>



<span class="kw">assume </span><a NAME="E1:113"/>
<font color="Maroon" title="c1">L</font> is  <a href="lattices.html#V13" title="LATTICES:attr.13">lower-bounded</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide">  <a href="filter_2.html#K15" title="FILTER_2:func.15">latt</a> <font color="Maroon" title="c1">L</font>,<span class="p1"><a href="filter_2.html#K10" title="FILTER_2:func.10">(.</a><span class="default"><font color="Maroon" title="c2">p</font></span><a href="filter_2.html#K10" title="FILTER_2:func.10">.&gt;</a></span> is  <a href="lattices.html#V15" title="LATTICES:attr.15">bounded</a> </span><br/>

<a NAME="E2:113"/><span class="kw">then </span>
 <a href="filter_2.html#K15" title="FILTER_2:func.15">latt</a> <font color="Maroon" title="c1">L</font>,<span class="p1"><a href="filter_2.html#K10" title="FILTER_2:func.10">(.</a><span class="default"><font color="Maroon" title="c2">p</font></span><a href="filter_2.html#K10" title="FILTER_2:func.10">.&gt;</a></span> is   <a href="lattices.html#V13" title="LATTICES:attr.13">lower-bounded</a>   <a href="lattices.html#V14" title="LATTICES:attr.14">upper-bounded</a>  <a href="lattices.html#NM1" title="LATTICES:NM.1">Lattice</a>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="filter_2.html#T80" target="_self" title="FILTER_2:th.80">Th80</a>, <a class="ref" href="filter_2.html#T82" target="_self" title="FILTER_2:th.82">Th82</a></span>;<br/>
<span class="kw">hence </span><a NAME="E3:113"/>
 <a href="filter_2.html#K15" title="FILTER_2:func.15">latt</a> <font color="Maroon" title="c1">L</font>,<span class="p1"><a href="filter_2.html#K10" title="FILTER_2:func.10">(.</a><span class="default"><font color="Maroon" title="c2">p</font></span><a href="filter_2.html#K10" title="FILTER_2:func.10">.&gt;</a></span> is  <a href="lattices.html#V15" title="LATTICES:attr.15">bounded</a> 
 ; <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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