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<span class="kw">set </span><font color="Maroon" title="c1">L</font> =  <a href="latwal_1.html#K5" title="LATWAL_1:func.5">ExNearLattice</a> ;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c2">x</font> =  <a href="ordinal1.html#K5" title="ORDINAL1:func.5">0</a> , <font color="Maroon" title="c3">y</font> = 1, <font color="Maroon" title="c4">z</font> = 2 as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <a href="latwal_1.html#K5" title="LATWAL_1:func.5">ExNearLattice</a> <span class="kw">by</span> <span class="lab"><a class="ref" href="enumset1.html#D1" onmouseover="rs('enumset1/D1')" onmouseout="rh()">ENUMSET1:def 1</a></span>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c5">xx</font> = <font color="Maroon" title="c2">x</font>, <font color="Maroon" title="c6">yy</font> = <font color="Maroon" title="c3">y</font>, <font color="Maroon" title="c7">zz</font> = <font color="Maroon" title="c4">z</font> as    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <span class="p1"><a href="enumset1.html#K1" title="ENUMSET1:func.1">{</a><span class="default"><a href="ordinal1.html#K5" title="ORDINAL1:func.5">0</a>,1,2</span><a href="enumset1.html#K1" title="ENUMSET1:func.1">}</a></span> ;<br/>
<font color="Maroon" title="c6">yy</font> <a href="latwal_1.html#K1" title="LATWAL_1:func.1">ex123"/\"</a> <font color="Maroon" title="c7">zz</font> = 
 <a href="xxreal_0.html#K3" title="XXREAL_0:func.3">min</a> (<font color="Maroon" title="c6">yy</font>,<font color="Maroon" title="c7">zz</font>)
<span class="kw">by</span> <span class="lab"><a class="ref" href="latwal_1.html#D6" target="_self" onmouseover="rs('latwal_1/D6')" onmouseout="rh()">ExMeetDef</a></span>
<br/>.= 
1
<span class="kw">by</span> <span class="lab"><a class="ref" href="xxreal_0.html#D9" onmouseover="rs('xxreal_0/D9')" onmouseout="rh()">XXREAL_0:def 9</a></span>
;<br/>
<span class="kw">then </span><span class="lab"><font color="Green" title="E25">t1</font></span>: <font color="Maroon" title="c2">x</font> <a href="lattices.html#K2" title="LATTICES:func.2">"/\"</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">y</font> <a href="lattices.html#K2" title="LATTICES:func.2">"/\"</a> <font color="Maroon" title="c4">z</font></span>)</span> = 
<font color="Maroon" title="c2">x</font> <a href="lattices.html#K2" title="LATTICES:func.2">"/\"</a> <font color="Maroon" title="c3">y</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="latwal_1.html#D9" target="_self" onmouseover="rs('latwal_1/D9')" onmouseout="rh()">EXNDef</a></span>
<br/>.= 
<font color="Maroon" title="c5">xx</font> <a href="latwal_1.html#K1" title="LATWAL_1:func.1">ex123"/\"</a> <font color="Maroon" title="c6">yy</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="latwal_1.html#D9" target="_self" onmouseover="rs('latwal_1/D9')" onmouseout="rh()">EXNDef</a></span>
<br/>.= 
 <a href="xxreal_0.html#K3" title="XXREAL_0:func.3">min</a> (<font color="Maroon" title="c5">xx</font>,<font color="Maroon" title="c6">yy</font>)
<span class="kw">by</span> <span class="lab"><a class="ref" href="latwal_1.html#D6" target="_self" onmouseover="rs('latwal_1/D6')" onmouseout="rh()">ExMeetDef</a></span>
<br/>.= 
 <a href="ordinal1.html#K5" title="ORDINAL1:func.5">0</a> 
<span class="kw">by</span> <span class="lab"><a class="ref" href="xxreal_0.html#D9" onmouseover="rs('xxreal_0/D9')" onmouseout="rh()">XXREAL_0:def 9</a></span>
;<br/>
<font color="Maroon" title="c5">xx</font> <a href="latwal_1.html#K1" title="LATWAL_1:func.1">ex123"/\"</a> <font color="Maroon" title="c6">yy</font> = 
 <a href="xxreal_0.html#K3" title="XXREAL_0:func.3">min</a> (<font color="Maroon" title="c5">xx</font>,<font color="Maroon" title="c6">yy</font>)
<span class="kw">by</span> <span class="lab"><a class="ref" href="latwal_1.html#D6" target="_self" onmouseover="rs('latwal_1/D6')" onmouseout="rh()">ExMeetDef</a></span>
<br/>.= 
 <a href="ordinal1.html#K5" title="ORDINAL1:func.5">0</a> 
<span class="kw">by</span> <span class="lab"><a class="ref" href="xxreal_0.html#D9" onmouseover="rs('xxreal_0/D9')" onmouseout="rh()">XXREAL_0:def 9</a></span>
;<br/>
<span class="kw">then </span><span class="p1">(<span class="default"><font color="Maroon" title="c2">x</font> <a href="lattices.html#K2" title="LATTICES:func.2">"/\"</a> <font color="Maroon" title="c3">y</font></span>)</span> <a href="lattices.html#K2" title="LATTICES:func.2">"/\"</a> <font color="Maroon" title="c4">z</font> = 
<font color="Maroon" title="c2">x</font> <a href="lattices.html#K2" title="LATTICES:func.2">"/\"</a> <font color="Maroon" title="c4">z</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="latwal_1.html#D9" target="_self" onmouseover="rs('latwal_1/D9')" onmouseout="rh()">EXNDef</a></span>
<br/>.= 
<font color="Maroon" title="c5">xx</font> <a href="latwal_1.html#K1" title="LATWAL_1:func.1">ex123"/\"</a> <font color="Maroon" title="c7">zz</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="latwal_1.html#D9" target="_self" onmouseover="rs('latwal_1/D9')" onmouseout="rh()">EXNDef</a></span>
<br/>.= 
2
<span class="kw">by</span> <span class="lab"><a class="ref" href="latwal_1.html#D6" target="_self" onmouseover="rs('latwal_1/D6')" onmouseout="rh()">ExMeetDef</a></span>
;<br/>
<span class="kw">hence </span><a NAME="E7:41"/>
 not  <a href="latwal_1.html#K5" title="LATWAL_1:func.5">ExNearLattice</a>  is  <a href="lattices.html#V7" title="LATTICES:attr.7">meet-associative</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="lattices.html#D7" onmouseover="rs('lattices/D7')" onmouseout="rh()">LATTICES:def 7</a>, <a class="txt" href="#E4:41"><span class="lab"><font color="Green" title="E25">t1</font></span></a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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