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

<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" 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">  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 <font color="Maroon" title="c1">L</font> holds <br/> ( <font color="Olive" title="b1">a</font> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <font color="Olive" title="b2">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">a</font> <a href="lattice3.html#K4" title="LATTICE3:func.4">%</a></span>)</span> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">b</font> <a href="lattice3.html#K4" title="LATTICE3:func.4">%</a></span>)</span> &amp; <font color="Olive" title="b1">a</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Olive" title="b2">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">a</font> <a href="lattice3.html#K4" title="LATTICE3:func.4">%</a></span>)</span> <a href="lattice3.html#K13" title="LATTICE3:func.13">"\/"</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">b</font> <a href="lattice3.html#K4" title="LATTICE3:func.4">%</a></span>)</span> )</span><br/><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 <font color="Maroon" title="c1">L</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#K4" title="LATTICES:func.4">"/\"</a> <font color="Maroon" title="c3">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="lattice3.html#K4" title="LATTICE3:func.4">%</a></span>)</span> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">b</font> <a href="lattice3.html#K4" title="LATTICE3:func.4">%</a></span>)</span> &amp; <font color="Maroon" title="c2">a</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon" title="c3">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="lattice3.html#K4" title="LATTICE3:func.4">%</a></span>)</span> <a href="lattice3.html#K13" title="LATTICE3:func.13">"\/"</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">b</font> <a href="lattice3.html#K4" title="LATTICE3:func.4">%</a></span>)</span> )</span><br/>



<span class="kw">consider </span><font color="Maroon" title="c4">c</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">L</font><span class="kw"> such that </span><br/><a NAME="E2:36"/><span class="lab"><font color="Green" title="E24">A1</font></span>: 
<font color="Maroon" title="c4">c</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">a</font> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <font color="Maroon" title="c3">b</font>
 ;<br/>
<a NAME="E3:36"/><span class="lab"><font color="Green" title="E25">A2</font></span>: 
 for <font color="Olive" title="b1">d</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="lattice3.html#K3" title="LATTICE3:func.3">LattPOSet</a> <font color="Maroon" title="c1">L</font></span>)</span>  st <font color="Olive" title="b1">d</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c2">a</font> <a href="lattice3.html#K4" title="LATTICE3:func.4">%</a>  &amp; <font color="Olive" title="b1">d</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c3">b</font> <a href="lattice3.html#K4" title="LATTICE3:func.4">%</a>  holds <br/><font color="Maroon" title="c4">c</font> <a href="lattice3.html#K4" title="LATTICE3:func.4">%</a>  <a href="orders_2.html#NR2" title="ORDERS_2:NR.2">&gt;=</a> <font color="Olive" title="b1">d</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="c5">d</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="lattice3.html#K3" title="LATTICE3:func.3">LattPOSet</a> <font color="Maroon" title="c1">L</font></span>)</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"> ( <font color="Maroon" title="c5">d</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c2">a</font> <a href="lattice3.html#K4" title="LATTICE3:func.4">%</a>  &amp; <font color="Maroon" title="c5">d</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c3">b</font> <a href="lattice3.html#K4" title="LATTICE3:func.4">%</a>  implies <font color="Maroon" title="c4">c</font> <a href="lattice3.html#K4" title="LATTICE3:func.4">%</a>  <a href="orders_2.html#NR2" title="ORDERS_2:NR.2">&gt;=</a> <font color="Maroon" title="c5">d</font> )</span><br/>

<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:36_1"/><span class="lab"><font color="Green" title="E26">A3</font></span>: 
<font color="Maroon" title="c5">d</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c2">a</font> <a href="lattice3.html#K4" title="LATTICE3:func.4">%</a> 
 <span class="kw">and </span><br/><a NAME="E2:36_1"/><span class="lab"><font color="Green" title="E27">A4</font></span>: 
<font color="Maroon" title="c5">d</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c3">b</font> <a href="lattice3.html#K4" title="LATTICE3:func.4">%</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="c4">c</font> <a href="lattice3.html#K4" title="LATTICE3:func.4">%</a>  <a href="orders_2.html#NR2" title="ORDERS_2:NR.2">&gt;=</a> <font color="Maroon" title="c5">d</font></span><br/>

<span class="lab"><font color="Green" title="E28">A5</font></span>: <span class="p1">(<span class="default"><a href="lattice3.html#K5" title="LATTICE3:func.5">%</a> <font color="Maroon" title="c5">d</font></span>)</span> <a href="lattice3.html#K4" title="LATTICE3:func.4">%</a>  = 
 <a href="lattice3.html#K5" title="LATTICE3:func.5">%</a> <font color="Maroon" title="c5">d</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="lattice3.html#D3" onmouseover="rs('lattice3/D3')" onmouseout="rh()">LATTICE3:def 3</a></span>
<br/>.= 
<font color="Maroon" title="c5">d</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="lattice3.html#D4" onmouseover="rs('lattice3/D4')" onmouseout="rh()">LATTICE3:def 4</a></span>
;<br/>
<a NAME="E4:36_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E29">A6</font></span>: 
 <a href="lattice3.html#K5" title="LATTICE3:func.5">%</a> <font color="Maroon" title="c5">d</font> <a href="lattices.html#R3" title="LATTICES:pred.3">[=</a> <font color="Maroon" title="c2">a</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:36_1"><span class="lab"><font color="Green" title="E26">A3</font></span></a>, <a class="ref" href="lattice3.html#T7" onmouseover="rs('lattice3/T7')" onmouseout="rh()">LATTICE3:7</a></span>;<br/>
<a NAME="E5:36_1"/><span class="lab"><font color="Green" title="E30">A7</font></span>: 
 <a href="lattice3.html#K5" title="LATTICE3:func.5">%</a> <font color="Maroon" title="c5">d</font> <a href="lattices.html#R3" title="LATTICES:pred.3">[=</a> <font color="Maroon" title="c3">b</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:36_1"><span class="lab"><font color="Green" title="E27">A4</font></span></a>, <a class="txt" href="#E3:36_1"><span class="lab"><font color="Green" title="E28">A5</font></span></a>, <a class="ref" href="lattice3.html#T7" onmouseover="rs('lattice3/T7')" onmouseout="rh()">LATTICE3:7</a></span>;<br/>
<span class="p1">(<span class="default"><a href="lattice3.html#K5" title="LATTICE3:func.5">%</a> <font color="Maroon" title="c5">d</font></span>)</span> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <font color="Maroon" title="c4">c</font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="lattice3.html#K5" title="LATTICE3:func.5">%</a> <font color="Maroon" title="c5">d</font></span>)</span> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <font color="Maroon" title="c2">a</font></span>)</span> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <font color="Maroon" title="c3">b</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:36"><span class="lab"><font color="Green" title="E24">A1</font></span></a>, <a class="ref" href="lattices.html#D7" onmouseover="rs('lattices/D7')" onmouseout="rh()">LATTICES:def 7</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="lattice3.html#K5" title="LATTICE3:func.5">%</a> <font color="Maroon" title="c5">d</font></span>)</span> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <font color="Maroon" title="c3">b</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:36_1"><span class="lab"><font color="Green" title="E29">A6</font></span></a>, <a class="ref" href="lattices.html#T4" onmouseover="rs('lattices/T4')" onmouseout="rh()">LATTICES:4</a></span>
<br/>.= 
 <a href="lattice3.html#K5" title="LATTICE3:func.5">%</a> <font color="Maroon" title="c5">d</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:36_1"><span class="lab"><font color="Green" title="E30">A7</font></span></a>, <a class="ref" href="lattices.html#T4" onmouseover="rs('lattices/T4')" onmouseout="rh()">LATTICES:4</a></span>
;<br/>
<a NAME="E7:36_1"/><span class="kw">then </span>
 <a href="lattice3.html#K5" title="LATTICE3:func.5">%</a> <font color="Maroon" title="c5">d</font> <a href="lattices.html#R3" title="LATTICES:pred.3">[=</a> <font color="Maroon" title="c4">c</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="lattices.html#T4" onmouseover="rs('lattices/T4')" onmouseout="rh()">LATTICES:4</a></span>;<br/>
<span class="kw">hence </span><a NAME="E8:36_1"/>
<font color="Maroon" title="c4">c</font> <a href="lattice3.html#K4" title="LATTICE3:func.4">%</a>  <a href="orders_2.html#NR2" title="ORDERS_2:NR.2">&gt;=</a> <font color="Maroon" title="c5">d</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:36_1"><span class="lab"><font color="Green" title="E28">A5</font></span></a>, <a class="ref" href="lattice3.html#T7" onmouseover="rs('lattice3/T7')" onmouseout="rh()">LATTICE3:7</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>
<a NAME="E4:36"/>
<font color="Maroon" title="c4">c</font> <a href="lattices.html#R3" title="LATTICES:pred.3">[=</a> <font color="Maroon" title="c3">b</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:36"><span class="lab"><font color="Green" title="E24">A1</font></span></a>, <a class="ref" href="lattices.html#T6" onmouseover="rs('lattices/T6')" onmouseout="rh()">LATTICES:6</a></span>;<br/>
<a NAME="E5:36"/><span class="kw">then </span><span class="lab"><font color="Green" title="E26">A8</font></span>: 
<font color="Maroon" title="c4">c</font> <a href="lattice3.html#K4" title="LATTICE3:func.4">%</a>  <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c3">b</font> <a href="lattice3.html#K4" title="LATTICE3:func.4">%</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="lattice3.html#T7" onmouseover="rs('lattice3/T7')" onmouseout="rh()">LATTICE3:7</a></span>;<br/>
<a NAME="E6:36"/>
<font color="Maroon" title="c4">c</font> <a href="lattices.html#R3" title="LATTICES:pred.3">[=</a> <font color="Maroon" title="c2">a</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:36"><span class="lab"><font color="Green" title="E24">A1</font></span></a>, <a class="ref" href="lattices.html#T6" onmouseover="rs('lattices/T6')" onmouseout="rh()">LATTICES:6</a></span>;<br/>
<a NAME="E7:36"/><span class="kw">then </span>
<font color="Maroon" title="c4">c</font> <a href="lattice3.html#K4" title="LATTICE3:func.4">%</a>  <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c2">a</font> <a href="lattice3.html#K4" title="LATTICE3:func.4">%</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="lattice3.html#T7" onmouseover="rs('lattice3/T7')" onmouseout="rh()">LATTICE3:7</a></span>;<br/>
<a NAME="E8:36"/><span class="kw">then </span><span class="lab"><font color="Green" title="E27">A9</font></span>: 
<font color="Maroon" title="c4">c</font> <a href="lattice3.html#K4" title="LATTICE3:func.4">%</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="lattice3.html#K4" title="LATTICE3:func.4">%</a></span>)</span> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">b</font> <a href="lattice3.html#K4" title="LATTICE3:func.4">%</a></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:36"><span class="lab"><font color="Green" title="E26">A8</font></span></a>, <a class="txt" href="#E3:36"><span class="lab"><font color="Green" title="E25">A2</font></span></a>, <a class="ref" href="yellow_0.html#T23" onmouseover="rs('yellow_0/T23')" onmouseout="rh()">YELLOW_0:23</a></span>;<br/>
<span class="kw">consider </span><font color="Maroon" title="c5">c</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">L</font><span class="kw"> such that </span><br/><a NAME="E10:36"/><span class="lab"><font color="Green" title="E28">A10</font></span>: 
<font color="Maroon" title="c5">c</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">a</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon" title="c3">b</font>
 ;<br/>
<a NAME="E11:36"/><span class="lab"><font color="Green" title="E29">A11</font></span>: 
 for <font color="Olive" title="b1">d</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="lattice3.html#K3" title="LATTICE3:func.3">LattPOSet</a> <font color="Maroon" title="c1">L</font></span>)</span>  st <font color="Maroon" title="c2">a</font> <a href="lattice3.html#K4" title="LATTICE3:func.4">%</a>  <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Olive" title="b1">d</font> &amp; <font color="Maroon" title="c3">b</font> <a href="lattice3.html#K4" title="LATTICE3:func.4">%</a>  <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Olive" title="b1">d</font> holds <br/><font color="Olive" title="b1">d</font> <a href="orders_2.html#NR2" title="ORDERS_2:NR.2">&gt;=</a> <font color="Maroon" title="c5">c</font> <a href="lattice3.html#K4" title="LATTICE3:func.4">%</a> 
 
<div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="36_2"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><font color="Maroon" title="c6">d</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="lattice3.html#K3" title="LATTICE3:func.3">LattPOSet</a> <font color="Maroon" title="c1">L</font></span>)</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"> ( <font color="Maroon" title="c2">a</font> <a href="lattice3.html#K4" title="LATTICE3:func.4">%</a>  <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c6">d</font> &amp; <font color="Maroon" title="c3">b</font> <a href="lattice3.html#K4" title="LATTICE3:func.4">%</a>  <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c6">d</font> implies <font color="Maroon" title="c6">d</font> <a href="orders_2.html#NR2" title="ORDERS_2:NR.2">&gt;=</a> <font color="Maroon" title="c5">c</font> <a href="lattice3.html#K4" title="LATTICE3:func.4">%</a>  )</span><br/>

<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:36_2"/><span class="lab"><font color="Green" title="E30">A12</font></span>: 
<font color="Maroon" title="c2">a</font> <a href="lattice3.html#K4" title="LATTICE3:func.4">%</a>  <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c6">d</font>
 <span class="kw">and </span><br/><a NAME="E2:36_2"/><span class="lab"><font color="Green" title="E31">A13</font></span>: 
<font color="Maroon" title="c3">b</font> <a href="lattice3.html#K4" title="LATTICE3:func.4">%</a>  <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c6">d</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="c6">d</font> <a href="orders_2.html#NR2" title="ORDERS_2:NR.2">&gt;=</a> <font color="Maroon" title="c5">c</font> <a href="lattice3.html#K4" title="LATTICE3:func.4">%</a> </span><br/>

<span class="lab"><font color="Green" title="E32">A14</font></span>: <span class="p1">(<span class="default"><a href="lattice3.html#K5" title="LATTICE3:func.5">%</a> <font color="Maroon" title="c6">d</font></span>)</span> <a href="lattice3.html#K4" title="LATTICE3:func.4">%</a>  = 
 <a href="lattice3.html#K5" title="LATTICE3:func.5">%</a> <font color="Maroon" title="c6">d</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="lattice3.html#D3" onmouseover="rs('lattice3/D3')" onmouseout="rh()">LATTICE3:def 3</a></span>
<br/>.= 
<font color="Maroon" title="c6">d</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="lattice3.html#D4" onmouseover="rs('lattice3/D4')" onmouseout="rh()">LATTICE3:def 4</a></span>
;<br/>
<a NAME="E4:36_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E33">A15</font></span>: 
<font color="Maroon" title="c2">a</font> <a href="lattices.html#R3" title="LATTICES:pred.3">[=</a>  <a href="lattice3.html#K5" title="LATTICE3:func.5">%</a> <font color="Maroon" title="c6">d</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:36_2"><span class="lab"><font color="Green" title="E30">A12</font></span></a>, <a class="ref" href="lattice3.html#T7" onmouseover="rs('lattice3/T7')" onmouseout="rh()">LATTICE3:7</a></span>;<br/>
<a NAME="E5:36_2"/><span class="lab"><font color="Green" title="E34">A16</font></span>: 
<font color="Maroon" title="c3">b</font> <a href="lattices.html#R3" title="LATTICES:pred.3">[=</a>  <a href="lattice3.html#K5" title="LATTICE3:func.5">%</a> <font color="Maroon" title="c6">d</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:36_2"><span class="lab"><font color="Green" title="E31">A13</font></span></a>, <a class="txt" href="#E3:36_2"><span class="lab"><font color="Green" title="E32">A14</font></span></a>, <a class="ref" href="lattice3.html#T7" onmouseover="rs('lattice3/T7')" onmouseout="rh()">LATTICE3:7</a></span>;<br/>
<span class="p1">(<span class="default"><a href="lattice3.html#K5" title="LATTICE3:func.5">%</a> <font color="Maroon" title="c6">d</font></span>)</span> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon" title="c5">c</font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="lattice3.html#K5" title="LATTICE3:func.5">%</a> <font color="Maroon" title="c6">d</font></span>)</span> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon" title="c2">a</font></span>)</span> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon" title="c3">b</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E10:36"><span class="lab"><font color="Green" title="E28">A10</font></span></a>, <a class="ref" href="lattices.html#D5" onmouseover="rs('lattices/D5')" onmouseout="rh()">LATTICES:def 5</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="lattice3.html#K5" title="LATTICE3:func.5">%</a> <font color="Maroon" title="c6">d</font></span>)</span> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon" title="c3">b</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:36_2"><span class="lab"><font color="Green" title="E33">A15</font></span></a>, <a class="ref" href="lattices.html#D3" onmouseover="rs('lattices/D3')" onmouseout="rh()">LATTICES:def 3</a></span>
<br/>.= 
 <a href="lattice3.html#K5" title="LATTICE3:func.5">%</a> <font color="Maroon" title="c6">d</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:36_2"><span class="lab"><font color="Green" title="E34">A16</font></span></a>, <a class="ref" href="lattices.html#D3" onmouseover="rs('lattices/D3')" onmouseout="rh()">LATTICES:def 3</a></span>
;<br/>
<a NAME="E7:36_2"/><span class="kw">then </span>
<font color="Maroon" title="c5">c</font> <a href="lattices.html#R3" title="LATTICES:pred.3">[=</a>  <a href="lattice3.html#K5" title="LATTICE3:func.5">%</a> <font color="Maroon" title="c6">d</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="lattices.html#D3" onmouseover="rs('lattices/D3')" onmouseout="rh()">LATTICES:def 3</a></span>;<br/>
<span class="kw">hence </span><a NAME="E8:36_2"/>
<font color="Maroon" title="c6">d</font> <a href="orders_2.html#NR2" title="ORDERS_2:NR.2">&gt;=</a> <font color="Maroon" title="c5">c</font> <a href="lattice3.html#K4" title="LATTICE3:func.4">%</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:36_2"><span class="lab"><font color="Green" title="E32">A14</font></span></a>, <a class="ref" href="lattice3.html#T7" onmouseover="rs('lattice3/T7')" onmouseout="rh()">LATTICE3:7</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>
<a NAME="E12:36"/>
<font color="Maroon" title="c3">b</font> <a href="lattices.html#R3" title="LATTICES:pred.3">[=</a> <font color="Maroon" title="c5">c</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E10:36"><span class="lab"><font color="Green" title="E28">A10</font></span></a>, <a class="ref" href="lattices.html#T5" onmouseover="rs('lattices/T5')" onmouseout="rh()">LATTICES:5</a></span>;<br/>
<a NAME="E13:36"/><span class="kw">then </span><span class="lab"><font color="Green" title="E30">A17</font></span>: 
<font color="Maroon" title="c3">b</font> <a href="lattice3.html#K4" title="LATTICE3:func.4">%</a>  <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c5">c</font> <a href="lattice3.html#K4" title="LATTICE3:func.4">%</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="lattice3.html#T7" onmouseover="rs('lattice3/T7')" onmouseout="rh()">LATTICE3:7</a></span>;<br/>
<a NAME="E14:36"/>
<font color="Maroon" title="c2">a</font> <a href="lattices.html#R3" title="LATTICES:pred.3">[=</a> <font color="Maroon" title="c5">c</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E10:36"><span class="lab"><font color="Green" title="E28">A10</font></span></a>, <a class="ref" href="lattices.html#T5" onmouseover="rs('lattices/T5')" onmouseout="rh()">LATTICES:5</a></span>;<br/>
<a NAME="E15:36"/><span class="kw">then </span>
<font color="Maroon" title="c2">a</font> <a href="lattice3.html#K4" title="LATTICE3:func.4">%</a>  <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c5">c</font> <a href="lattice3.html#K4" title="LATTICE3:func.4">%</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="lattice3.html#T7" onmouseover="rs('lattice3/T7')" onmouseout="rh()">LATTICE3:7</a></span>;<br/>
<a NAME="E16:36"/><span class="kw">then </span>
<font color="Maroon" title="c5">c</font> <a href="lattice3.html#K4" title="LATTICE3:func.4">%</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="lattice3.html#K4" title="LATTICE3:func.4">%</a></span>)</span> <a href="lattice3.html#K13" title="LATTICE3:func.13">"\/"</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">b</font> <a href="lattice3.html#K4" title="LATTICE3:func.4">%</a></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E13:36"><span class="lab"><font color="Green" title="E30">A17</font></span></a>, <a class="txt" href="#E11:36"><span class="lab"><font color="Green" title="E29">A11</font></span></a>, <a class="ref" href="yellow_0.html#T22" onmouseover="rs('yellow_0/T22')" onmouseout="rh()">YELLOW_0:22</a></span>;<br/>
<span class="kw">hence </span><a NAME="E17:36"/>
( <font color="Maroon" title="c2">a</font> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <font color="Maroon" title="c3">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="lattice3.html#K4" title="LATTICE3:func.4">%</a></span>)</span> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">b</font> <a href="lattice3.html#K4" title="LATTICE3:func.4">%</a></span>)</span> &amp; <font color="Maroon" title="c2">a</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon" title="c3">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="lattice3.html#K4" title="LATTICE3:func.4">%</a></span>)</span> <a href="lattice3.html#K13" title="LATTICE3:func.13">"\/"</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">b</font> <a href="lattice3.html#K4" title="LATTICE3:func.4">%</a></span>)</span> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:36"><span class="lab"><font color="Green" title="E24">A1</font></span></a>, <a class="txt" href="#E8:36"><span class="lab"><font color="Green" title="E27">A9</font></span></a>, <a class="txt" href="#E10:36"><span class="lab"><font color="Green" title="E28">A10</font></span></a>, <a class="ref" href="lattice3.html#D3" onmouseover="rs('lattice3/D3')" onmouseout="rh()">LATTICE3:def 3</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>
