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<span class="kw">let </span><font color="Maroon" title="c1">x</font>, <font color="Maroon" title="c2">y</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"> <a href="latwal_1.html#K3" title="LATWAL_1:func.3">ex123\/</a> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c2">y</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <a href="latwal_1.html#K3" title="LATWAL_1:func.3">ex123\/</a> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<font color="Maroon" title="c2">y</font>,<font color="Maroon" title="c1">x</font>)</span><br/>

<span class="kw">reconsider </span><font color="Maroon" title="c3">xx</font> = <font color="Maroon" title="c1">x</font>, <font color="Maroon" title="c4">yy</font> = <font color="Maroon" title="c2">y</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="39_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="E1:39_1"/>
( (  not <!--HUMANRECFAILED-->( <font color="Maroon" title="c1">x</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">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 2 ) &amp;  not <!--HUMANRECFAILED-->( <font color="Maroon" title="c1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 2 &amp; <font color="Maroon" title="c2">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ordinal1.html#K5" title="ORDINAL1:func.5">0</a>  ) ) or ( <font color="Maroon" title="c1">x</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">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 2 ) or ( <font color="Maroon" title="c1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 2 &amp; <font color="Maroon" title="c2">y</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="39_1_1"><span class="kw">suppose </span></a><a NAME="E1:39_1_1"/><span class="lab"><font color="Green" title="E23">V1</font></span>: 
(  not <!--HUMANRECFAILED-->( <font color="Maroon" title="c1">x</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">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 2 ) &amp;  not <!--HUMANRECFAILED-->( <font color="Maroon" title="c1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 2 &amp; <font color="Maroon" title="c2">y</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"> <a href="latwal_1.html#K3" title="LATWAL_1:func.3">ex123\/</a> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c2">y</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <a href="latwal_1.html#K3" title="LATWAL_1:func.3">ex123\/</a> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<font color="Maroon" title="c2">y</font>,<font color="Maroon" title="c1">x</font>)</span><br/><div class="add"><a NAME="E2:39_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c3">xx</font> <a href="latwal_1.html#K2" title="LATWAL_1:func.2">ex123"\/"</a> <font color="Maroon" title="c4">yy</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xxreal_0.html#K4" title="XXREAL_0:func.4">max</a> (<font color="Maroon" title="c3">xx</font>,<font color="Maroon" title="c4">yy</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/><a NAME="E3:39_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E24">V3</font></span>: 
<a href="latwal_1.html#K3" title="LATWAL_1:func.3">ex123\/</a> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c2">y</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xxreal_0.html#K4" title="XXREAL_0:func.4">max</a> (<font color="Maroon" title="c3">xx</font>,<font color="Maroon" title="c4">yy</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/><a NAME="E4:39_1_1"/>
<font color="Maroon" title="c4">yy</font> <a href="latwal_1.html#K2" title="LATWAL_1:func.2">ex123"\/"</a> <font color="Maroon" title="c3">xx</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xxreal_0.html#K4" title="XXREAL_0:func.4">max</a> (<font color="Maroon" title="c4">yy</font>,<font color="Maroon" title="c3">xx</font>)
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:39_1_1"><span class="lab"><font color="Green" title="E23">V1</font></span></a>, <a class="ref" href="latwal_1.html#D7" target="_self" onmouseover="rs('latwal_1/D7')" onmouseout="rh()">UPDef</a></span>;<br/><span class="kw">hence </span><a NAME="E5:39_1_1"/>
<a href="latwal_1.html#K3" title="LATWAL_1:func.3">ex123\/</a> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c2">y</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <a href="latwal_1.html#K3" title="LATWAL_1:func.3">ex123\/</a> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<font color="Maroon" title="c2">y</font>,<font color="Maroon" title="c1">x</font>)
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:39_1_1"><span class="lab"><font color="Green" title="E24">V3</font></span></a>, <a class="ref" href="latwal_1.html#D8" target="_self" onmouseover="rs('latwal_1/D8')" onmouseout="rh()">EXUDef</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><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="39_1_2"><span class="kw">suppose </span></a><a NAME="E1:39_1_2"/><span class="lab"><font color="Green" title="E23">V1</font></span>: 
( ( <font color="Maroon" title="c1">x</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">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 2 ) or ( <font color="Maroon" title="c1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 2 &amp; <font color="Maroon" title="c2">y</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"> <a href="latwal_1.html#K3" title="LATWAL_1:func.3">ex123\/</a> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c2">y</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <a href="latwal_1.html#K3" title="LATWAL_1:func.3">ex123\/</a> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<font color="Maroon" title="c2">y</font>,<font color="Maroon" title="c1">x</font>)</span><br/><div class="add"><a NAME="E2:39_1_2"/><span class="kw">then </span>
<font color="Maroon" title="c3">xx</font> <a href="latwal_1.html#K2" title="LATWAL_1:func.2">ex123"\/"</a> <font color="Maroon" title="c4">yy</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ordinal1.html#K5" title="ORDINAL1:func.5">0</a> 
 <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/><a NAME="E3:39_1_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E24">V3</font></span>: 
<a href="latwal_1.html#K3" title="LATWAL_1:func.3">ex123\/</a> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c2">y</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ordinal1.html#K5" title="ORDINAL1:func.5">0</a> 
 <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/><a NAME="E4:39_1_2"/>
<font color="Maroon" title="c4">yy</font> <a href="latwal_1.html#K2" title="LATWAL_1:func.2">ex123"\/"</a> <font color="Maroon" title="c3">xx</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ordinal1.html#K5" title="ORDINAL1:func.5">0</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:39_1_2"><span class="lab"><font color="Green" title="E23">V1</font></span></a>, <a class="ref" href="latwal_1.html#D7" target="_self" onmouseover="rs('latwal_1/D7')" onmouseout="rh()">UPDef</a></span>;<br/><span class="kw">hence </span><a NAME="E5:39_1_2"/>
<a href="latwal_1.html#K3" title="LATWAL_1:func.3">ex123\/</a> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c2">y</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <a href="latwal_1.html#K3" title="LATWAL_1:func.3">ex123\/</a> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<font color="Maroon" title="c2">y</font>,<font color="Maroon" title="c1">x</font>)
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:39_1_2"><span class="lab"><font color="Green" title="E24">V3</font></span></a>, <a class="ref" href="latwal_1.html#D8" target="_self" onmouseover="rs('latwal_1/D8')" onmouseout="rh()">EXUDef</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><span class="kw">end;</span></div></div><span class="kw">end;</span></div>

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