<?xml version="1.0"?>
<div class="add">

<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/>
<a NAME="E1:36"/>
 for <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being   <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> holds  <font color="Olive" title="b1">a</font> <a href="lattices.html#K2" title="LATTICES:func.2">"/\"</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">a</font> <a href="lattices.html#K1" title="LATTICES:func.1">"\/"</a> <font color="Olive" title="b2">b</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">a</font>
 
<div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="36_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><font color="Maroon" title="c2">a</font>, <font color="Maroon" title="c3">b</font> be   <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>; <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"> <font color="Maroon" title="c2">a</font> <a href="lattices.html#K2" title="LATTICES:func.2">"/\"</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="lattices.html#K1" title="LATTICES:func.1">"\/"</a> <font color="Maroon" title="c3">b</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">a</font></span><br/>

<span class="kw">reconsider </span><font color="Maroon" title="c4">aa</font> = <font color="Maroon" title="c2">a</font>, <font color="Maroon" title="c5">bb</font> = <font color="Maroon" title="c3">b</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/>
<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="36_1_1"><span class="kw">per </span></a><a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="kw">cases </span></a><span class="hide"><a NAME="E1:36_1_1"/>
( ( <font color="Maroon" title="c2">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ordinal1.html#K5" title="ORDINAL1:func.5">0</a>  &amp; <font color="Maroon" title="c3">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 2 ) or ( <font color="Maroon" title="c2">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 2 &amp; <font color="Maroon" title="c3">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ordinal1.html#K5" title="ORDINAL1:func.5">0</a>  ) or (  not <!--HUMANRECFAILED-->( <font color="Maroon" title="c2">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ordinal1.html#K5" title="ORDINAL1:func.5">0</a>  &amp; <font color="Maroon" title="c3">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 2 ) &amp;  not <!--HUMANRECFAILED-->( <font color="Maroon" title="c2">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 2 &amp; <font color="Maroon" title="c3">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ordinal1.html#K5" title="ORDINAL1:func.5">0</a>  ) ) )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="36_1_1_1"><span class="kw">suppose </span></a><a NAME="E1:36_1_1_1"/><span class="lab"><font color="Green" title="E20">B1</font></span>: 
( <font color="Maroon" title="c2">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ordinal1.html#K5" title="ORDINAL1:func.5">0</a>  &amp; <font color="Maroon" title="c3">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 2 )
 ; <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"> <font color="Maroon" title="c2">a</font> <a href="lattices.html#K2" title="LATTICES:func.2">"/\"</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="lattices.html#K1" title="LATTICES:func.1">"\/"</a> <font color="Maroon" title="c3">b</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">a</font></span><br/><div class="add"><a NAME="E2:36_1_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c4">aa</font> <a href="latwal_1.html#K2" title="LATWAL_1:func.2">ex123"\/"</a> <font color="Maroon" title="c5">bb</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">aa</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="latwal_1.html#D7" target="_self" onmouseover="rs('latwal_1/D7')" onmouseout="rh()">UPDef</a></span>;<br/><span class="kw">then </span><font color="Maroon" title="c2">a</font> <a href="lattices.html#K2" title="LATTICES:func.2">"/\"</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="lattices.html#K1" title="LATTICES:func.1">"\/"</a> <font color="Maroon" title="c3">b</font></span>)</span> = 
<font color="Maroon" title="c2">a</font> <a href="lattices.html#K2" title="LATTICES:func.2">"/\"</a> <font color="Maroon" title="c2">a</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="latwal_1.html#D8" target="_self" onmouseover="rs('latwal_1/D8')" onmouseout="rh()">EXUDef</a></span>
<br/>.= 
<font color="Maroon" title="c4">aa</font> <a href="latwal_1.html#K1" title="LATWAL_1:func.1">ex123"/\"</a> <font color="Maroon" title="c4">aa</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="c4">aa</font>,<font color="Maroon" title="c4">aa</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>, <a class="txt" href="#E1:36_1_1_1"><span class="lab"><font color="Green" title="E20">B1</font></span></a></span>
<br/>.= 
<font color="Maroon" title="c4">aa</font>

;<br/><span class="kw">hence </span><a NAME="E4:36_1_1_1"/>
<font color="Maroon" title="c2">a</font> <a href="lattices.html#K2" title="LATTICES:func.2">"/\"</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="lattices.html#K1" title="LATTICES:func.1">"\/"</a> <font color="Maroon" title="c3">b</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">a</font>
 ; <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/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="36_1_1_2"><span class="kw">suppose </span></a><a NAME="E1:36_1_1_2"/><span class="lab"><font color="Green" title="E20">B1</font></span>: 
( <font color="Maroon" title="c2">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 2 &amp; <font color="Maroon" title="c3">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ordinal1.html#K5" title="ORDINAL1:func.5">0</a>  )
 ; <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"> <font color="Maroon" title="c2">a</font> <a href="lattices.html#K2" title="LATTICES:func.2">"/\"</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="lattices.html#K1" title="LATTICES:func.1">"\/"</a> <font color="Maroon" title="c3">b</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">a</font></span><br/><div class="add"><a NAME="E2:36_1_1_2"/><span class="kw">then </span>
<font color="Maroon" title="c4">aa</font> <a href="latwal_1.html#K2" title="LATWAL_1:func.2">ex123"\/"</a> <font color="Maroon" title="c5">bb</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">bb</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="latwal_1.html#D7" target="_self" onmouseover="rs('latwal_1/D7')" onmouseout="rh()">UPDef</a></span>;<br/><span class="kw">then </span><font color="Maroon" title="c2">a</font> <a href="lattices.html#K2" title="LATTICES:func.2">"/\"</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="lattices.html#K1" title="LATTICES:func.1">"\/"</a> <font color="Maroon" title="c3">b</font></span>)</span> = 
<font color="Maroon" title="c2">a</font> <a href="lattices.html#K2" title="LATTICES:func.2">"/\"</a> <font color="Maroon" title="c3">b</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="latwal_1.html#D8" target="_self" onmouseover="rs('latwal_1/D8')" onmouseout="rh()">EXUDef</a></span>
<br/>.= 
<font color="Maroon" title="c4">aa</font> <a href="latwal_1.html#K1" title="LATWAL_1:func.1">ex123"/\"</a> <font color="Maroon" title="c5">bb</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="c4">aa</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>, <a class="txt" href="#E1:36_1_1_2"><span class="lab"><font color="Green" title="E20">B1</font></span></a></span>
;<br/><span class="kw">hence </span><a NAME="E4:36_1_1_2"/>
<font color="Maroon" title="c2">a</font> <a href="lattices.html#K2" title="LATTICES:func.2">"/\"</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="lattices.html#K1" title="LATTICES:func.1">"\/"</a> <font color="Maroon" title="c3">b</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">a</font>
 ; <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/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="36_1_1_3"><span class="kw">suppose </span></a><a NAME="E1:36_1_1_3"/><span class="lab"><font color="Green" title="E20">B1</font></span>: 
(  not <!--HUMANRECFAILED-->( <font color="Maroon" title="c2">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ordinal1.html#K5" title="ORDINAL1:func.5">0</a>  &amp; <font color="Maroon" title="c3">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 2 ) &amp;  not <!--HUMANRECFAILED-->( <font color="Maroon" title="c2">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 2 &amp; <font color="Maroon" title="c3">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ordinal1.html#K5" title="ORDINAL1:func.5">0</a>  ) )
 ; <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"> <font color="Maroon" title="c2">a</font> <a href="lattices.html#K2" title="LATTICES:func.2">"/\"</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="lattices.html#K1" title="LATTICES:func.1">"\/"</a> <font color="Maroon" title="c3">b</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">a</font></span><br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="36_1_1_3_1"><span class="kw">per </span></a><a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="kw">cases </span></a><span class="hide"><a NAME="E1:36_1_1_3_1"/>
(  <a href="xxreal_0.html#K4" title="XXREAL_0:func.4">max</a> (<font color="Maroon" title="c4">aa</font>,<font color="Maroon" title="c5">bb</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">aa</font> or  <a href="xxreal_0.html#K4" title="XXREAL_0:func.4">max</a> (<font color="Maroon" title="c4">aa</font>,<font color="Maroon" title="c5">bb</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">bb</font> )
 </span><span class="kw">by</span> <span class="lab"><a class="ref" href="xxreal_0.html#T16" onmouseover="rs('xxreal_0/T16')" onmouseout="rh()">XXREAL_0:16</a></span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="36_1_1_3_1_1"><span class="kw">suppose </span></a><a NAME="E1:36_1_1_3_1_1"/><span class="lab"><font color="Green" title="E21">E</font></span>: 
 <a href="xxreal_0.html#K4" title="XXREAL_0:func.4">max</a> (<font color="Maroon" title="c4">aa</font>,<font color="Maroon" title="c5">bb</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">aa</font>
 ; <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"> <font color="Maroon" title="c2">a</font> <a href="lattices.html#K2" title="LATTICES:func.2">"/\"</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="lattices.html#K1" title="LATTICES:func.1">"\/"</a> <font color="Maroon" title="c3">b</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">a</font></span><br/><div class="add"><span class="lab"><font color="Green" title="E22">A3</font></span>: <font color="Maroon" title="c2">a</font> <a href="lattices.html#K1" title="LATTICES:func.1">"\/"</a> <font color="Maroon" title="c3">b</font> = 
<font color="Maroon" title="c4">aa</font> <a href="latwal_1.html#K2" title="LATWAL_1:func.2">ex123"\/"</a> <font color="Maroon" title="c5">bb</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="latwal_1.html#D8" target="_self" onmouseover="rs('latwal_1/D8')" onmouseout="rh()">EXUDef</a></span>
<br/>.= 
<font color="Maroon" title="c4">aa</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:36_1_1_3"><span class="lab"><font color="Green" title="E20">B1</font></span></a>, <a class="ref" href="latwal_1.html#D7" target="_self" onmouseover="rs('latwal_1/D7')" onmouseout="rh()">UPDef</a>, <a class="txt" href="#E1:36_1_1_3_1_1"><span class="lab"><font color="Green" title="E21">E</font></span></a></span>
;<br/><a NAME="E3:36_1_1_3_1_1"/><span class="lab"><font color="Green" title="E23">WW</font></span>: 
(  not <!--HUMANRECFAILED-->( <font color="Maroon" title="c2">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ordinal1.html#K5" title="ORDINAL1:func.5">0</a>  &amp; <font color="Maroon" title="c2">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 2 ) &amp;  not <!--HUMANRECFAILED-->( <font color="Maroon" title="c2">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 2 &amp; <font color="Maroon" title="c2">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ordinal1.html#K5" title="ORDINAL1:func.5">0</a>  ) )
 ;<br/><font color="Maroon" title="c2">a</font> <a href="lattices.html#K2" title="LATTICES:func.2">"/\"</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="lattices.html#K1" title="LATTICES:func.1">"\/"</a> <font color="Maroon" title="c3">b</font></span>)</span> = 
<font color="Maroon" title="c4">aa</font> <a href="latwal_1.html#K1" title="LATWAL_1:func.1">ex123"/\"</a> <font color="Maroon" title="c4">aa</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>, <a class="txt" href="#E2:36_1_1_3_1_1"><span class="lab"><font color="Green" title="E22">A3</font></span></a></span>
<br/>.= 
 <a href="xxreal_0.html#K3" title="XXREAL_0:func.3">min</a> (<font color="Maroon" title="c4">aa</font>,<font color="Maroon" title="c4">aa</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>, <a class="txt" href="#E3:36_1_1_3_1_1"><span class="lab"><font color="Green" title="E23">WW</font></span></a></span>
<br/>.= 
<font color="Maroon" title="c4">aa</font>

;<br/><span class="kw">hence </span><a NAME="E5:36_1_1_3_1_1"/>
<font color="Maroon" title="c2">a</font> <a href="lattices.html#K2" title="LATTICES:func.2">"/\"</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="lattices.html#K1" title="LATTICES:func.1">"\/"</a> <font color="Maroon" title="c3">b</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">a</font>
 ; <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/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="36_1_1_3_1_2"><span class="kw">suppose </span></a><a NAME="E1:36_1_1_3_1_2"/><span class="lab"><font color="Green" title="E21">E</font></span>: 
 <a href="xxreal_0.html#K4" title="XXREAL_0:func.4">max</a> (<font color="Maroon" title="c4">aa</font>,<font color="Maroon" title="c5">bb</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">bb</font>
 ; <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"> <font color="Maroon" title="c2">a</font> <a href="lattices.html#K2" title="LATTICES:func.2">"/\"</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="lattices.html#K1" title="LATTICES:func.1">"\/"</a> <font color="Maroon" title="c3">b</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">a</font></span><br/><div class="add"><span class="lab"><font color="Green" title="E22">A3</font></span>: <font color="Maroon" title="c2">a</font> <a href="lattices.html#K1" title="LATTICES:func.1">"\/"</a> <font color="Maroon" title="c3">b</font> = 
<font color="Maroon" title="c4">aa</font> <a href="latwal_1.html#K2" title="LATWAL_1:func.2">ex123"\/"</a> <font color="Maroon" title="c5">bb</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="latwal_1.html#D8" target="_self" onmouseover="rs('latwal_1/D8')" onmouseout="rh()">EXUDef</a></span>
<br/>.= 
<font color="Maroon" title="c5">bb</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:36_1_1_3_1_2"><span class="lab"><font color="Green" title="E21">E</font></span></a>, <a class="txt" href="#E1:36_1_1_3"><span class="lab"><font color="Green" title="E20">B1</font></span></a>, <a class="ref" href="latwal_1.html#D7" target="_self" onmouseover="rs('latwal_1/D7')" onmouseout="rh()">UPDef</a></span>
;<br/><font color="Maroon" title="c2">a</font> <a href="lattices.html#K2" title="LATTICES:func.2">"/\"</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="lattices.html#K1" title="LATTICES:func.1">"\/"</a> <font color="Maroon" title="c3">b</font></span>)</span> = 
<font color="Maroon" title="c4">aa</font> <a href="latwal_1.html#K1" title="LATWAL_1:func.1">ex123"/\"</a> <font color="Maroon" title="c5">bb</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>, <a class="txt" href="#E2:36_1_1_3_1_2"><span class="lab"><font color="Green" title="E22">A3</font></span></a></span>
<br/>.= 
 <a href="xxreal_0.html#K3" title="XXREAL_0:func.3">min</a> (<font color="Maroon" title="c4">aa</font>,<font color="Maroon" title="c5">bb</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>, <a class="txt" href="#E1:36_1_1_3"><span class="lab"><font color="Green" title="E20">B1</font></span></a></span>
<br/>.= 
<font color="Maroon" title="c4">aa</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:36_1_1_3_1_2"><span class="lab"><font color="Green" title="E21">E</font></span></a>, <a class="ref" href="xxreal_0.html#D9" onmouseover="rs('xxreal_0/D9')" onmouseout="rh()">XXREAL_0:def 9</a>, <a class="ref" href="xxreal_0.html#T25" onmouseover="rs('xxreal_0/T25')" onmouseout="rh()">XXREAL_0:25</a></span>
;<br/><span class="kw">hence </span><a NAME="E4:36_1_1_3_1_2"/>
<font color="Maroon" title="c2">a</font> <a href="lattices.html#K2" title="LATTICES:func.2">"/\"</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="lattices.html#K1" title="LATTICES:func.1">"\/"</a> <font color="Maroon" title="c3">b</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">a</font>
 ; <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/></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div>

</div><span class="kw">end;</span></div>
<span class="kw">hence </span><a NAME="E2:36"/>
 <a href="latwal_1.html#K5" title="LATWAL_1:func.5">ExNearLattice</a>  is  <a href="lattices.html#V9" title="LATTICES:attr.9">join-absorbing</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="lattices.html#D9" onmouseover="rs('lattices/D9')" onmouseout="rh()">LATTICES:def 9</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/>


</div>
