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

<b>let </b><font color="Maroon" title="c1">L</font> be  non <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a> <a href="lattices.html#V10" title="LATTICES:attr.10">Lattice-like</a> <a href="robbins1.html#V9" title="ROBBINS1:attr.9">de_Morgan</a> <a href="robbins3.html#V1" title="ROBBINS3:attr.1">join-Associative</a> <a href="robbins3.html#V3" title="ROBBINS3:attr.3">meet-Absorbing</a> <a href="robbins4.html#V1" title="ROBBINS4:attr.1">orthomodular</a>  <a href="robbins1.html#L3" title="ROBBINS1:struct.3">OrthoLattStr</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c1">L</font> is <a href="robbins3.html#V9" title="ROBBINS3:attr.9">with_Top</a></span><br/>

<b>deffunc </b><font color="Maroon">H<sub>1</sub></font>(  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">L</font>) <b>-&gt; </b>   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">L</font> = <font color="Maroon">c<sub>1</sub></font> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a> ;<br/>
<a NAME="E1:58_1_1"/>
for <font color="Olive" title="b1">x</font>, <font color="Olive" title="b2">y</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">L</font> holds  <font color="Olive" title="b1">x</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Olive" title="b1">x</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">y</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Olive" title="b2">y</font>)
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="58_1_1_1"><b>proof </b></a><div class="add">

<a NAME="E1:58_1_1_1"/><i><font color="Green" title="E37">A7</font></i>: 
for <font color="Olive" title="b1">v0</font>, <font color="Olive" title="b2">v1</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">L</font> holds  <font color="Olive" title="b1">v0</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon">H<sub>1</sub></font>(<font color="Maroon">H<sub>1</sub></font>(<font color="Olive" title="b1">v0</font>)) <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Olive" title="b1">v0</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Olive" title="b2">v1</font>)) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">v0</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Olive" title="b2">v1</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="58_1_1_1_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c2">v0</font>, <font color="Maroon" title="c3">v1</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:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c2">v0</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon">H<sub>1</sub></font>(<font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c2">v0</font>)) <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c2">v0</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon" title="c3">v1</font>)) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">v0</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon" title="c3">v1</font></span><br/>



<a NAME="E1:58_1_1_1_1"/>
<font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c2">v0</font>) <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">v0</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon" title="c3">v1</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon">H<sub>1</sub></font>(<font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c2">v0</font>)) <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c2">v0</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon" title="c3">v1</font>))
 
<b>by </b><i><a class="ref" href="robbins1.html#D23" title="ROBBINS1:def.23">ROBBINS1:def 23</a></i>;<br/>
<b>hence </b><a NAME="E2:58_1_1_1_1"/>
<font color="Maroon" title="c2">v0</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon">H<sub>1</sub></font>(<font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c2">v0</font>)) <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c2">v0</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon" title="c3">v1</font>)) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">v0</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon" title="c3">v1</font>
 <b>by </b><i><a class="ref" href="robbins4.html#D2" target="_self" title="ROBBINS4:def.2">DefMod3</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div>
<a NAME="E2:58_1_1_1"/><i><font color="Green" title="E38">A8</font></i>: 
for <font color="Olive" title="b1">v0</font>, <font color="Olive" title="b2">v1</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">L</font> holds  <font color="Olive" title="b1">v0</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon">H<sub>1</sub></font>(<font color="Olive" title="b1">v0</font>) <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Olive" title="b2">v1</font>)) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">v0</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="58_1_1_1_2"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c2">v0</font>, <font color="Maroon" title="c3">v1</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:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c2">v0</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c2">v0</font>) <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c3">v1</font>)) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">v0</font></span><br/>



<a NAME="E1:58_1_1_1_2"/>
<font color="Maroon" title="c2">v0</font> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <font color="Maroon" title="c3">v1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c2">v0</font>) <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c3">v1</font>))
 
<b>by </b><i><a class="ref" href="robbins1.html#D23" title="ROBBINS1:def.23">ROBBINS1:def 23</a></i>;<br/>
<b>hence </b><a NAME="E2:58_1_1_1_2"/>
<font color="Maroon" title="c2">v0</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c2">v0</font>) <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c3">v1</font>)) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">v0</font>
 <b>by </b><i><a class="ref" href="robbins3.html#D3" title="ROBBINS3:def.3">ROBBINS3:def 3</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div>
<a NAME="E3:58_1_1_1"/><i><font color="Green" title="E39">A11</font></i>: 
for <font color="Olive" title="b1">v64</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">L</font> holds  <font color="Olive" title="b1">v64</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon">H<sub>1</sub></font>(<font color="Olive" title="b1">v64</font>)) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">v64</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="58_1_1_1_3"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c2">v64</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:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c2">v64</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c2">v64</font>)) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">v64</font></span><br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="58_1_1_1_3_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c3">v64</font>, <font color="Maroon" title="c4">v1</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:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c3">v64</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c3">v64</font>)) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">v64</font></span><br/><a NAME="E1:58_1_1_1_3_1"/>
<font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c3">v64</font>) <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon">H<sub>1</sub></font>(<font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c3">v64</font>)) <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c4">v1</font>)) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c3">v64</font>)
 <b>by </b><i><a class="txt" href="#E2:58_1_1_1"><i><font color="Green" title="E38">A8</font></i></a></i>;<br/><b>hence </b><a NAME="E2:58_1_1_1_3_1"/>
<font color="Maroon" title="c3">v64</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c3">v64</font>)) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">v64</font>
 <b>by </b><i><a class="txt" href="#E2:58_1_1_1"><i><font color="Green" title="E38">A8</font></i></a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div>
<b>hence </b><a NAME="E2:58_1_1_1_3"/>
<font color="Maroon" title="c2">v64</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c2">v64</font>)) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">v64</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div>
<a NAME="E4:58_1_1_1"/><i><font color="Green" title="E40">A15</font></i>: 
for <font color="Olive" title="b1">v64</font>, <font color="Olive" title="b2">v65</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">L</font> holds  <font color="Olive" title="b1">v64</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Olive" title="b2">v65</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">v65</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">v64</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon">H<sub>1</sub></font>(<font color="Olive" title="b2">v65</font>))</span>)</span>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="58_1_1_1_4"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c2">v64</font>, <font color="Maroon" title="c3">v65</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:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c2">v64</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon" title="c3">v65</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">v65</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">v64</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c3">v65</font>))</span>)</span></span><br/>



<a NAME="E1:58_1_1_1_4"/>
<font color="Maroon" title="c3">v65</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c3">v65</font>)) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">v65</font>
 
<b>by </b><i><a class="txt" href="#E3:58_1_1_1"><i><font color="Green" title="E39">A11</font></i></a></i>;<br/>
<b>hence </b><a NAME="E2:58_1_1_1_4"/>
<font color="Maroon" title="c2">v64</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon" title="c3">v65</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">v65</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">v64</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c3">v65</font>))</span>)</span>
 <b>by </b><i><a class="ref" href="robbins3.html#D1" title="ROBBINS3:def.1">ROBBINS3:def 1</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div>
<a NAME="E5:58_1_1_1"/><i><font color="Green" title="E41">A20</font></i>: 
for <font color="Olive" title="b1">v64</font>, <font color="Olive" title="b2">v1</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">L</font> holds  <font color="Olive" title="b1">v64</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon">H<sub>1</sub></font>(<font color="Olive" title="b1">v64</font>) <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Olive" title="b2">v1</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">v64</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="58_1_1_1_5"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c2">v64</font>, <font color="Maroon" title="c3">v1</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:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c2">v64</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c2">v64</font>) <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon" title="c3">v1</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">v64</font></span><br/>



<a NAME="E1:58_1_1_1_5"/>
<font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c2">v64</font>) <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon">H<sub>1</sub></font>(<font color="Maroon">H<sub>1</sub></font>(<font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c2">v64</font>))) <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c2">v64</font>) <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon" title="c3">v1</font>)) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c2">v64</font>) <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon" title="c3">v1</font>
 
<b>by </b><i><a class="txt" href="#E1:58_1_1_1"><i><font color="Green" title="E37">A7</font></i></a></i>;<br/>
<b>hence </b><a NAME="E2:58_1_1_1_5"/>
<font color="Maroon" title="c2">v64</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c2">v64</font>) <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon" title="c3">v1</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">v64</font>
 <b>by </b><i><a class="txt" href="#E2:58_1_1_1"><i><font color="Green" title="E38">A8</font></i></a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div>
<a NAME="E6:58_1_1_1"/><i><font color="Green" title="E42">A24</font></i>: 
for <font color="Olive" title="b1">v64</font>, <font color="Olive" title="b2">v65</font>, <font color="Olive" title="b3">v1</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">L</font> holds  <font color="Olive" title="b1">v64</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Olive" title="b2">v65</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">v65</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">v64</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon">H<sub>1</sub></font>(<font color="Olive" title="b2">v65</font>) <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Olive" title="b3">v1</font>)</span>)</span>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="58_1_1_1_6"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c2">v64</font>, <font color="Maroon" title="c3">v65</font>, <font color="Maroon" title="c4">v1</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:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c2">v64</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon" title="c3">v65</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">v65</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">v64</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c3">v65</font>) <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon" title="c4">v1</font>)</span>)</span></span><br/>





<a NAME="E1:58_1_1_1_6"/>
<font color="Maroon" title="c3">v65</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c3">v65</font>) <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon" title="c4">v1</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">v65</font>
 
<b>by </b><i><a class="txt" href="#E5:58_1_1_1"><i><font color="Green" title="E41">A20</font></i></a></i>;<br/>
<b>hence </b><a NAME="E2:58_1_1_1_6"/>
<font color="Maroon" title="c2">v64</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon" title="c3">v65</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">v65</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">v64</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c3">v65</font>) <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon" title="c4">v1</font>)</span>)</span>
 <b>by </b><i><a class="ref" href="robbins3.html#D1" title="ROBBINS3:def.1">ROBBINS3:def 1</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div>
<a NAME="E7:58_1_1_1"/><i><font color="Green" title="E43">A33</font></i>: 
for <font color="Olive" title="b1">v64</font>, <font color="Olive" title="b2">v1</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">L</font> holds  <font color="Olive" title="b1">v64</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon">H<sub>1</sub></font>(<font color="Maroon">H<sub>1</sub></font>(<font color="Olive" title="b1">v64</font>)) <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Olive" title="b2">v1</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Olive" title="b1">v64</font>)) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">v64</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">v1</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon">H<sub>1</sub></font>(<font color="Olive" title="b1">v64</font>))</span>)</span>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="58_1_1_1_7"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c2">v64</font>, <font color="Maroon" title="c3">v1</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:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c2">v64</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon">H<sub>1</sub></font>(<font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c2">v64</font>)) <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c3">v1</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon" title="c2">v64</font>)) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">v64</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">v1</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c2">v64</font>))</span>)</span></span><br/>



<a NAME="E1:58_1_1_1_7"/>
<font color="Maroon" title="c2">v64</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">v1</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c2">v64</font>))</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">v1</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon" title="c2">v64</font>
 
<b>by </b><i><a class="txt" href="#E4:58_1_1_1"><i><font color="Green" title="E40">A15</font></i></a></i>;<br/>
<b>hence </b><a NAME="E2:58_1_1_1_7"/>
<font color="Maroon" title="c2">v64</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon">H<sub>1</sub></font>(<font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c2">v64</font>)) <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c3">v1</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon" title="c2">v64</font>)) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">v64</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">v1</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c2">v64</font>))</span>)</span>
 <b>by </b><i><a class="txt" href="#E1:58_1_1_1"><i><font color="Green" title="E37">A7</font></i></a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div>
<a NAME="E8:58_1_1_1"/><i><font color="Green" title="E44">A35</font></i>: 
for <font color="Olive" title="b1">v64</font>, <font color="Olive" title="b2">v1</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">L</font> holds  <font color="Olive" title="b1">v64</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon">H<sub>1</sub></font>(<font color="Maroon">H<sub>1</sub></font>(<font color="Olive" title="b1">v64</font>)) <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Olive" title="b2">v1</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Olive" title="b1">v64</font>)) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">v1</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Olive" title="b1">v64</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="58_1_1_1_8"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c2">v64</font>, <font color="Maroon" title="c3">v1</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:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c2">v64</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon">H<sub>1</sub></font>(<font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c2">v64</font>)) <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c3">v1</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon" title="c2">v64</font>)) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">v1</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon" title="c2">v64</font></span><br/>



<a NAME="E1:58_1_1_1_8"/>
<font color="Maroon" title="c2">v64</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">v1</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c2">v64</font> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a> </span>)</span> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a> </span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">v1</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon" title="c2">v64</font>
 
<b>by </b><i><a class="txt" href="#E4:58_1_1_1"><i><font color="Green" title="E40">A15</font></i></a></i>;<br/>
<b>hence </b><a NAME="E2:58_1_1_1_8"/>
<font color="Maroon" title="c2">v64</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon">H<sub>1</sub></font>(<font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c2">v64</font>)) <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c3">v1</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon" title="c2">v64</font>)) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">v1</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon" title="c2">v64</font>
 <b>by </b><i><a class="txt" href="#E7:58_1_1_1"><i><font color="Green" title="E43">A33</font></i></a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div>
<a NAME="E9:58_1_1_1"/><i><font color="Green" title="E45">A50</font></i>: 
for <font color="Olive" title="b1">v64</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">L</font> holds  <font color="Olive" title="b1">v64</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Olive" title="b1">v64</font> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a> </span>)</span> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a> </span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Olive" title="b1">v64</font> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a> </span>)</span> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a> </span>)</span> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a> </span>)</span> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a> </span>)</span> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Olive" title="b1">v64</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="58_1_1_1_9"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c2">v64</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:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c2">v64</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">v64</font> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a> </span>)</span> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a> </span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c2">v64</font> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a> </span>)</span> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a> </span>)</span> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a> </span>)</span> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a> </span>)</span> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon" title="c2">v64</font></span><br/>

<a NAME="E1:58_1_1_1_9"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c2">v64</font> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a> </span>)</span> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a> </span>)</span> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a> </span>)</span> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a> </span>)</span> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">v64</font> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a> </span>)</span> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a> </span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">v64</font> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a> </span>)</span> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a> 
 
<b>by </b><i><a class="txt" href="#E3:58_1_1_1"><i><font color="Green" title="E39">A11</font></i></a></i>;<br/>
<b>hence </b><a NAME="E2:58_1_1_1_9"/>
<font color="Maroon" title="c2">v64</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">v64</font> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a> </span>)</span> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a> </span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c2">v64</font> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a> </span>)</span> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a> </span>)</span> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a> </span>)</span> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a> </span>)</span> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon" title="c2">v64</font>
 <b>by </b><i><a class="txt" href="#E4:58_1_1_1"><i><font color="Green" title="E40">A15</font></i></a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div>
<a NAME="E10:58_1_1_1"/><i><font color="Green" title="E46">A52</font></i>: 
for <font color="Olive" title="b1">v64</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">L</font> holds  <font color="Olive" title="b1">v64</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Olive" title="b1">v64</font> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a> </span>)</span> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a> </span>)</span> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a> </span>)</span> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a> </span>)</span> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Olive" title="b1">v64</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="58_1_1_1_10"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c2">v64</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:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c2">v64</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c2">v64</font> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a> </span>)</span> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a> </span>)</span> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a> </span>)</span> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a> </span>)</span> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon" title="c2">v64</font></span><br/>

<a NAME="E1:58_1_1_1_10"/>
<font color="Maroon" title="c2">v64</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">v64</font> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a> </span>)</span> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a> </span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">v64</font>
 
<b>by </b><i><a class="txt" href="#E3:58_1_1_1"><i><font color="Green" title="E39">A11</font></i></a></i>;<br/>
<b>hence </b><a NAME="E2:58_1_1_1_10"/>
<font color="Maroon" title="c2">v64</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c2">v64</font> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a> </span>)</span> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a> </span>)</span> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a> </span>)</span> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a> </span>)</span> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon" title="c2">v64</font>
 <b>by </b><i><a class="txt" href="#E9:58_1_1_1"><i><font color="Green" title="E45">A50</font></i></a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div>
<a NAME="E11:58_1_1_1"/><i><font color="Green" title="E47">A62</font></i>: 
for <font color="Olive" title="b1">v65</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">L</font> holds  <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Olive" title="b1">v65</font> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a> </span>)</span> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a> </span>)</span> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a> </span>)</span> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">v65</font> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a> </span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Olive" title="b1">v65</font> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a> </span>)</span> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a> </span>)</span> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a> 
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="58_1_1_1_11"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c2">v65</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:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c2">v65</font> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a> </span>)</span> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a> </span>)</span> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a> </span>)</span> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">v65</font> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a> </span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">v65</font> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a> </span>)</span> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a> </span>)</span> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a> </span><br/>

<a NAME="E1:58_1_1_1_11"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c2">v65</font> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a> </span>)</span> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a> </span>)</span> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a> </span>)</span> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a> </span>)</span> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon" title="c2">v65</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">v65</font>
 
<b>by </b><i><a class="txt" href="#E10:58_1_1_1"><i><font color="Green" title="E46">A52</font></i></a></i>;<br/>
<b>hence </b><a NAME="E2:58_1_1_1_11"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c2">v65</font> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a> </span>)</span> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a> </span>)</span> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a> </span>)</span> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">v65</font> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a> </span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">v65</font> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a> </span>)</span> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a> </span>)</span> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a> 
 <b>by </b><i><a class="txt" href="#E5:58_1_1_1"><i><font color="Green" title="E41">A20</font></i></a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div>
<a NAME="E12:58_1_1_1"/><i><font color="Green" title="E48">A64</font></i>: 
for <font color="Olive" title="b1">v65</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">L</font> holds  <font color="Olive" title="b1">v65</font> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Olive" title="b1">v65</font> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a> </span>)</span> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a> </span>)</span> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a> 
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="58_1_1_1_12"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c2">v65</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:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c2">v65</font> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">v65</font> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a> </span>)</span> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a> </span>)</span> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a> </span><br/>

<a NAME="E1:58_1_1_1_12"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c2">v65</font> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a> </span>)</span> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a> </span>)</span> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a> </span>)</span> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">v65</font> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a> </span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">v65</font> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a> 
 
<b>by </b><i><a class="txt" href="#E3:58_1_1_1"><i><font color="Green" title="E39">A11</font></i></a></i>;<br/>
<b>hence </b><a NAME="E2:58_1_1_1_12"/>
<font color="Maroon" title="c2">v65</font> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">v65</font> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a> </span>)</span> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a> </span>)</span> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a> 
 <b>by </b><i><a class="txt" href="#E11:58_1_1_1"><i><font color="Green" title="E47">A62</font></i></a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div>
<a NAME="E13:58_1_1_1"/><i><font color="Green" title="E49">A69</font></i>: 
for <font color="Olive" title="b1">v65</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">L</font> holds  <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon">H<sub>1</sub></font>(<font color="Maroon">H<sub>1</sub></font>(<font color="Maroon">H<sub>1</sub></font>(<font color="Olive" title="b1">v65</font>)))) <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon">H<sub>1</sub></font>(<font color="Maroon">H<sub>1</sub></font>(<font color="Maroon">H<sub>1</sub></font>(<font color="Maroon">H<sub>1</sub></font>(<font color="Maroon">H<sub>1</sub></font>(<font color="Maroon">H<sub>1</sub></font>(<font color="Olive" title="b1">v65</font>)))))) <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Olive" title="b1">v65</font>)) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon">H<sub>1</sub></font>(<font color="Maroon">H<sub>1</sub></font>(<font color="Maroon">H<sub>1</sub></font>(<font color="Olive" title="b1">v65</font>)))) <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Olive" title="b1">v65</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="58_1_1_1_13"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c2">v65</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:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon">H<sub>1</sub></font>(<font color="Maroon">H<sub>1</sub></font>(<font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c2">v65</font>)))) <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon">H<sub>1</sub></font>(<font color="Maroon">H<sub>1</sub></font>(<font color="Maroon">H<sub>1</sub></font>(<font color="Maroon">H<sub>1</sub></font>(<font color="Maroon">H<sub>1</sub></font>(<font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c2">v65</font>)))))) <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c2">v65</font>)) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon">H<sub>1</sub></font>(<font color="Maroon">H<sub>1</sub></font>(<font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c2">v65</font>)))) <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon" title="c2">v65</font></span><br/>

<a NAME="E1:58_1_1_1_13"/>
<font color="Maroon">H<sub>1</sub></font>(<font color="Maroon">H<sub>1</sub></font>(<font color="Maroon">H<sub>1</sub></font>(<font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c2">v65</font>)))) <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon" title="c2">v65</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">v65</font>
 
<b>by </b><i><a class="txt" href="#E10:58_1_1_1"><i><font color="Green" title="E46">A52</font></i></a></i>;<br/>
<b>hence </b><a NAME="E2:58_1_1_1_13"/>
<font color="Maroon">H<sub>1</sub></font>(<font color="Maroon">H<sub>1</sub></font>(<font color="Maroon">H<sub>1</sub></font>(<font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c2">v65</font>)))) <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon">H<sub>1</sub></font>(<font color="Maroon">H<sub>1</sub></font>(<font color="Maroon">H<sub>1</sub></font>(<font color="Maroon">H<sub>1</sub></font>(<font color="Maroon">H<sub>1</sub></font>(<font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c2">v65</font>)))))) <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c2">v65</font>)) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon">H<sub>1</sub></font>(<font color="Maroon">H<sub>1</sub></font>(<font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c2">v65</font>)))) <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon" title="c2">v65</font>
 <b>by </b><i><a class="txt" href="#E1:58_1_1_1"><i><font color="Green" title="E37">A7</font></i></a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div>
<a NAME="E14:58_1_1_1"/><i><font color="Green" title="E50">A71</font></i>: 
for <font color="Olive" title="b1">v65</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">L</font> holds  <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon">H<sub>1</sub></font>(<font color="Olive" title="b1">v65</font>)) <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon">H<sub>1</sub></font>(<font color="Maroon">H<sub>1</sub></font>(<font color="Maroon">H<sub>1</sub></font>(<font color="Maroon">H<sub>1</sub></font>(<font color="Maroon">H<sub>1</sub></font>(<font color="Maroon">H<sub>1</sub></font>(<font color="Olive" title="b1">v65</font>)))))) <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Olive" title="b1">v65</font>)) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon">H<sub>1</sub></font>(<font color="Maroon">H<sub>1</sub></font>(<font color="Maroon">H<sub>1</sub></font>(<font color="Olive" title="b1">v65</font>)))) <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Olive" title="b1">v65</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="58_1_1_1_14"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c2">v65</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:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c2">v65</font>)) <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon">H<sub>1</sub></font>(<font color="Maroon">H<sub>1</sub></font>(<font color="Maroon">H<sub>1</sub></font>(<font color="Maroon">H<sub>1</sub></font>(<font color="Maroon">H<sub>1</sub></font>(<font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c2">v65</font>)))))) <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c2">v65</font>)) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon">H<sub>1</sub></font>(<font color="Maroon">H<sub>1</sub></font>(<font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c2">v65</font>)))) <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon" title="c2">v65</font></span><br/>

<a NAME="E1:58_1_1_1_14"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">v65</font> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a> </span>)</span> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a> </span>)</span> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">v65</font> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a> 
 
<b>by </b><i><a class="txt" href="#E12:58_1_1_1"><i><font color="Green" title="E48">A64</font></i></a></i>;<br/>
<b>hence </b><a NAME="E2:58_1_1_1_14"/>
<font color="Maroon">H<sub>1</sub></font>(<font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c2">v65</font>)) <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon">H<sub>1</sub></font>(<font color="Maroon">H<sub>1</sub></font>(<font color="Maroon">H<sub>1</sub></font>(<font color="Maroon">H<sub>1</sub></font>(<font color="Maroon">H<sub>1</sub></font>(<font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c2">v65</font>)))))) <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c2">v65</font>)) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon">H<sub>1</sub></font>(<font color="Maroon">H<sub>1</sub></font>(<font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c2">v65</font>)))) <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon" title="c2">v65</font>
 <b>by </b><i><a class="txt" href="#E13:58_1_1_1"><i><font color="Green" title="E49">A69</font></i></a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div>
<a NAME="E15:58_1_1_1"/><i><font color="Green" title="E51">A73</font></i>: 
for <font color="Olive" title="b1">v65</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">L</font> holds  <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon">H<sub>1</sub></font>(<font color="Olive" title="b1">v65</font>)) <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon">H<sub>1</sub></font>(<font color="Maroon">H<sub>1</sub></font>(<font color="Maroon">H<sub>1</sub></font>(<font color="Maroon">H<sub>1</sub></font>(<font color="Olive" title="b1">v65</font>)))) <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Olive" title="b1">v65</font>)) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon">H<sub>1</sub></font>(<font color="Maroon">H<sub>1</sub></font>(<font color="Maroon">H<sub>1</sub></font>(<font color="Olive" title="b1">v65</font>)))) <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Olive" title="b1">v65</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="58_1_1_1_15"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c2">v65</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:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c2">v65</font>)) <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon">H<sub>1</sub></font>(<font color="Maroon">H<sub>1</sub></font>(<font color="Maroon">H<sub>1</sub></font>(<font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c2">v65</font>)))) <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c2">v65</font>)) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon">H<sub>1</sub></font>(<font color="Maroon">H<sub>1</sub></font>(<font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c2">v65</font>)))) <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon" title="c2">v65</font></span><br/>

<a NAME="E1:58_1_1_1_15"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">v65</font> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a> </span>)</span> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a> </span>)</span> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">v65</font> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a> 
 
<b>by </b><i><a class="txt" href="#E12:58_1_1_1"><i><font color="Green" title="E48">A64</font></i></a></i>;<br/>
<b>hence </b><a NAME="E2:58_1_1_1_15"/>
<font color="Maroon">H<sub>1</sub></font>(<font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c2">v65</font>)) <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon">H<sub>1</sub></font>(<font color="Maroon">H<sub>1</sub></font>(<font color="Maroon">H<sub>1</sub></font>(<font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c2">v65</font>)))) <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c2">v65</font>)) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon">H<sub>1</sub></font>(<font color="Maroon">H<sub>1</sub></font>(<font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c2">v65</font>)))) <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon" title="c2">v65</font>
 <b>by </b><i><a class="txt" href="#E14:58_1_1_1"><i><font color="Green" title="E50">A71</font></i></a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div>
<a NAME="E16:58_1_1_1"/><i><font color="Green" title="E52">A75</font></i>: 
for <font color="Olive" title="b1">v65</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">L</font> holds  <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon">H<sub>1</sub></font>(<font color="Olive" title="b1">v65</font>)) <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon">H<sub>1</sub></font>(<font color="Maroon">H<sub>1</sub></font>(<font color="Olive" title="b1">v65</font>)) <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Olive" title="b1">v65</font>)) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon">H<sub>1</sub></font>(<font color="Maroon">H<sub>1</sub></font>(<font color="Maroon">H<sub>1</sub></font>(<font color="Olive" title="b1">v65</font>)))) <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Olive" title="b1">v65</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="58_1_1_1_16"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c2">v65</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:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c2">v65</font>)) <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon">H<sub>1</sub></font>(<font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c2">v65</font>)) <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c2">v65</font>)) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon">H<sub>1</sub></font>(<font color="Maroon">H<sub>1</sub></font>(<font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c2">v65</font>)))) <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon" title="c2">v65</font></span><br/>

<a NAME="E1:58_1_1_1_16"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">v65</font> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a> </span>)</span> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a> </span>)</span> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">v65</font> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a> 
 
<b>by </b><i><a class="txt" href="#E12:58_1_1_1"><i><font color="Green" title="E48">A64</font></i></a></i>;<br/>
<b>hence </b><a NAME="E2:58_1_1_1_16"/>
<font color="Maroon">H<sub>1</sub></font>(<font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c2">v65</font>)) <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon">H<sub>1</sub></font>(<font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c2">v65</font>)) <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c2">v65</font>)) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon">H<sub>1</sub></font>(<font color="Maroon">H<sub>1</sub></font>(<font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c2">v65</font>)))) <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon" title="c2">v65</font>
 <b>by </b><i><a class="txt" href="#E15:58_1_1_1"><i><font color="Green" title="E51">A73</font></i></a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div>
<a NAME="E17:58_1_1_1"/><i><font color="Green" title="E53">A77</font></i>: 
for <font color="Olive" title="b1">v65</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">L</font> holds  <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon">H<sub>1</sub></font>(<font color="Olive" title="b1">v65</font>)) <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon">H<sub>1</sub></font>(<font color="Maroon">H<sub>1</sub></font>(<font color="Olive" title="b1">v65</font>)) <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Olive" title="b1">v65</font>)) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon">H<sub>1</sub></font>(<font color="Olive" title="b1">v65</font>)) <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Olive" title="b1">v65</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="58_1_1_1_17"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c2">v65</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:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c2">v65</font>)) <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon">H<sub>1</sub></font>(<font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c2">v65</font>)) <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c2">v65</font>)) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c2">v65</font>)) <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon" title="c2">v65</font></span><br/>

<a NAME="E1:58_1_1_1_17"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">v65</font> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a> </span>)</span> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a> </span>)</span> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">v65</font> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a> 
 
<b>by </b><i><a class="txt" href="#E12:58_1_1_1"><i><font color="Green" title="E48">A64</font></i></a></i>;<br/>
<b>hence </b><a NAME="E2:58_1_1_1_17"/>
<font color="Maroon">H<sub>1</sub></font>(<font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c2">v65</font>)) <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon">H<sub>1</sub></font>(<font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c2">v65</font>)) <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c2">v65</font>)) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c2">v65</font>)) <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon" title="c2">v65</font>
 <b>by </b><i><a class="txt" href="#E16:58_1_1_1"><i><font color="Green" title="E52">A75</font></i></a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div>
<a NAME="E18:58_1_1_1"/><i><font color="Green" title="E54">A79</font></i>: 
for <font color="Olive" title="b1">v65</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">L</font> holds  <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon">H<sub>1</sub></font>(<font color="Olive" title="b1">v65</font>)) <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon">H<sub>1</sub></font>(<font color="Maroon">H<sub>1</sub></font>(<font color="Olive" title="b1">v65</font>)) <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Olive" title="b1">v65</font>)) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">v65</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="58_1_1_1_18"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c2">v65</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:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c2">v65</font>)) <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon">H<sub>1</sub></font>(<font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c2">v65</font>)) <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c2">v65</font>)) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">v65</font></span><br/>

<a NAME="E1:58_1_1_1_18"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">v65</font> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a> </span>)</span> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a> </span>)</span> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon" title="c2">v65</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">v65</font>
 
<b>by </b><i><a class="txt" href="#E3:58_1_1_1"><i><font color="Green" title="E39">A11</font></i></a></i>;<br/>
<b>hence </b><a NAME="E2:58_1_1_1_18"/>
<font color="Maroon">H<sub>1</sub></font>(<font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c2">v65</font>)) <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon">H<sub>1</sub></font>(<font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c2">v65</font>)) <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c2">v65</font>)) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">v65</font>
 <b>by </b><i><a class="txt" href="#E17:58_1_1_1"><i><font color="Green" title="E53">A77</font></i></a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div>
<a NAME="E19:58_1_1_1"/><i><font color="Green" title="E55">A82</font></i>: 
for <font color="Olive" title="b1">v0</font>, <font color="Olive" title="b2">v65</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">L</font> holds  <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon">H<sub>1</sub></font>(<font color="Olive" title="b1">v0</font>)) <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Olive" title="b2">v65</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Olive" title="b1">v0</font>)) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">v0</font> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a> </span>)</span> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a> 
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="58_1_1_1_19"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c2">v0</font>, <font color="Maroon" title="c3">v65</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:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c2">v0</font>)) <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c3">v65</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c2">v0</font>)) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">v0</font> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a> </span>)</span> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a> </span><br/>



<a NAME="E1:58_1_1_1_19"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">v0</font> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a> </span>)</span> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a> </span>)</span> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">v0</font> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a> 
 
<b>by </b><i><a class="txt" href="#E12:58_1_1_1"><i><font color="Green" title="E48">A64</font></i></a></i>;<br/>
<b>hence </b><a NAME="E2:58_1_1_1_19"/>
<font color="Maroon">H<sub>1</sub></font>(<font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c2">v0</font>)) <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c3">v65</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c2">v0</font>)) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">v0</font> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a> </span>)</span> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a> 
 <b>by </b><i><a class="txt" href="#E5:58_1_1_1"><i><font color="Green" title="E41">A20</font></i></a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div>
<a NAME="E20:58_1_1_1"/><i><font color="Green" title="E56">A85</font></i>: 
for <font color="Olive" title="b1">v0</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">L</font> holds  <span class="p1">(<span class="default"><font color="Olive" title="b1">v0</font> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a> </span>)</span> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">v0</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="58_1_1_1_20"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c2">v0</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:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <span class="p1">(<span class="default"><font color="Maroon" title="c2">v0</font> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a> </span>)</span> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">v0</font></span><br/>

<a NAME="E1:58_1_1_1_20"/>
<font color="Maroon">H<sub>1</sub></font>(<font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c2">v0</font>)) <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon">H<sub>1</sub></font>(<font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c2">v0</font>)) <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c2">v0</font>)) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">v0</font> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a> </span>)</span> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a> 
 
<b>by </b><i><a class="txt" href="#E19:58_1_1_1"><i><font color="Green" title="E55">A82</font></i></a></i>;<br/>
<b>hence </b><a NAME="E2:58_1_1_1_20"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c2">v0</font> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a> </span>)</span> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">v0</font>
 <b>by </b><i><a class="txt" href="#E18:58_1_1_1"><i><font color="Green" title="E54">A79</font></i></a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div>
<a NAME="E21:58_1_1_1"/><i><font color="Green" title="E57">A87</font></i>: 
for <font color="Olive" title="b1">v0</font>, <font color="Olive" title="b2">v1</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">L</font> holds  <font color="Olive" title="b1">v0</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Olive" title="b1">v0</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Olive" title="b2">v1</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Olive" title="b1">v0</font>)) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">v1</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Olive" title="b1">v0</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="58_1_1_1_21"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c2">v0</font>, <font color="Maroon" title="c3">v1</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:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c2">v0</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c2">v0</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c3">v1</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon" title="c2">v0</font>)) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">v1</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon" title="c2">v0</font></span><br/>



<a NAME="E1:58_1_1_1_21"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c2">v0</font> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a> </span>)</span> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">v0</font>
 
<b>by </b><i><a class="txt" href="#E20:58_1_1_1"><i><font color="Green" title="E56">A85</font></i></a></i>;<br/>
<b>hence </b><a NAME="E2:58_1_1_1_21"/>
<font color="Maroon" title="c2">v0</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c2">v0</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c3">v1</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon" title="c2">v0</font>)) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">v1</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon" title="c2">v0</font>
 <b>by </b><i><a class="txt" href="#E8:58_1_1_1"><i><font color="Green" title="E44">A35</font></i></a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div>
<a NAME="E22:58_1_1_1"/><i><font color="Green" title="E58">A89</font></i>: 
for <font color="Olive" title="b1">v0</font>, <font color="Olive" title="b2">v65</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">L</font> holds  <font color="Maroon">H<sub>1</sub></font>(<font color="Olive" title="b1">v0</font>) <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Olive" title="b1">v0</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Olive" title="b2">v65</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">v0</font> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a> 
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="58_1_1_1_22"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c2">v0</font>, <font color="Maroon" title="c3">v65</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:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c2">v0</font>) <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c2">v0</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon" title="c3">v65</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">v0</font> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a> </span><br/>



<a NAME="E1:58_1_1_1_22"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c2">v0</font> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a> </span>)</span> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">v0</font>
 
<b>by </b><i><a class="txt" href="#E20:58_1_1_1"><i><font color="Green" title="E56">A85</font></i></a></i>;<br/>
<b>hence </b><a NAME="E2:58_1_1_1_22"/>
<font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c2">v0</font>) <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c2">v0</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon" title="c3">v65</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">v0</font> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a> 
 <b>by </b><i><a class="txt" href="#E5:58_1_1_1"><i><font color="Green" title="E41">A20</font></i></a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div>
<a NAME="E23:58_1_1_1"/><i><font color="Green" title="E59">A148</font></i>: 
for <font color="Olive" title="b1">v64</font>, <font color="Olive" title="b2">v1</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">L</font> holds  <font color="Olive" title="b1">v64</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">v1</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Olive" title="b1">v64</font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Olive" title="b1">v64</font>) <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Olive" title="b1">v64</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="58_1_1_1_23"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c2">v64</font>, <font color="Maroon" title="c3">v1</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:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c2">v64</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">v1</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c2">v64</font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c2">v64</font>) <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon" title="c2">v64</font></span><br/>



<a NAME="E1:58_1_1_1_23"/>
<font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c2">v64</font>) <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c2">v64</font>) <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c3">v1</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c2">v64</font>))) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">v1</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c2">v64</font>)
 
<b>by </b><i><a class="txt" href="#E21:58_1_1_1"><i><font color="Green" title="E57">A87</font></i></a></i>;<br/>
<b>hence </b><a NAME="E2:58_1_1_1_23"/>
<font color="Maroon" title="c2">v64</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">v1</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c2">v64</font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c2">v64</font>) <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon" title="c2">v64</font>
 <b>by </b><i><a class="txt" href="#E6:58_1_1_1"><i><font color="Green" title="E42">A24</font></i></a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div>
<a NAME="E24:58_1_1_1"/><i><font color="Green" title="E60">A152</font></i>: 
for <font color="Olive" title="b1">v0</font>, <font color="Olive" title="b2">v1</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">L</font> holds  <span class="p1">(<span class="default"><font color="Olive" title="b1">v0</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Olive" title="b2">v1</font></span>)</span> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Olive" title="b1">v0</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Olive" title="b1">v0</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Olive" title="b2">v1</font>) <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">v0</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Olive" title="b2">v1</font></span>)</span>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="58_1_1_1_24"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c2">v0</font>, <font color="Maroon" title="c3">v1</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:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <span class="p1">(<span class="default"><font color="Maroon" title="c2">v0</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon" title="c3">v1</font></span>)</span> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c2">v0</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c2">v0</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon" title="c3">v1</font>) <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">v0</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon" title="c3">v1</font></span>)</span></span><br/>



<a NAME="E1:58_1_1_1_24"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c2">v0</font> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a> </span>)</span> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c2">v0</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon" title="c3">v1</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c2">v0</font>)
 
<b>by </b><i><a class="txt" href="#E22:58_1_1_1"><i><font color="Green" title="E58">A89</font></i></a></i>;<br/>
<b>hence </b><a NAME="E2:58_1_1_1_24"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c2">v0</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon" title="c3">v1</font></span>)</span> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c2">v0</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c2">v0</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon" title="c3">v1</font>) <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">v0</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon" title="c3">v1</font></span>)</span>
 <b>by </b><i><a class="txt" href="#E23:58_1_1_1"><i><font color="Green" title="E59">A148</font></i></a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div>
<a NAME="E25:58_1_1_1"/><i><font color="Green" title="E61">A154</font></i>: 
for <font color="Olive" title="b1">v0</font>, <font color="Olive" title="b2">v1</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">L</font> holds  <font color="Olive" title="b1">v0</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">v1</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Olive" title="b1">v0</font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Olive" title="b1">v0</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Olive" title="b2">v1</font>) <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">v0</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Olive" title="b2">v1</font></span>)</span>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="58_1_1_1_25"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c2">v0</font>, <font color="Maroon" title="c3">v1</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:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c2">v0</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">v1</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c2">v0</font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c2">v0</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon" title="c3">v1</font>) <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">v0</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon" title="c3">v1</font></span>)</span></span><br/>



<a NAME="E1:58_1_1_1_25"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c2">v0</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon" title="c3">v1</font></span>)</span> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c2">v0</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">v0</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">v1</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c2">v0</font>)</span>)</span>
 
<b>by </b><i><a class="ref" href="robbins3.html#D1" title="ROBBINS3:def.1">ROBBINS3:def 1</a></i>;<br/>
<b>hence </b><a NAME="E2:58_1_1_1_25"/>
<font color="Maroon" title="c2">v0</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">v1</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c2">v0</font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c2">v0</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon" title="c3">v1</font>) <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">v0</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon" title="c3">v1</font></span>)</span>
 <b>by </b><i><a class="txt" href="#E24:58_1_1_1"><i><font color="Green" title="E60">A152</font></i></a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div>
<a NAME="E26:58_1_1_1"/><i><font color="Green" title="E62">A158</font></i>: 
for <font color="Olive" title="b1">v0</font>, <font color="Olive" title="b2">v1</font>, <font color="Olive" title="b3">v65</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">L</font> holds  <font color="Olive" title="b1">v0</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">v1</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <span class="p2">(<span class="default"><font color="Olive" title="b3">v65</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Olive" title="b1">v0</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Olive" title="b2">v1</font>)</span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Olive" title="b1">v0</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Olive" title="b2">v1</font>) <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">v0</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Olive" title="b2">v1</font></span>)</span>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="58_1_1_1_26"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c2">v0</font>, <font color="Maroon" title="c3">v1</font>, <font color="Maroon" title="c4">v65</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:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c2">v0</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">v1</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">v65</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c2">v0</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon" title="c3">v1</font>)</span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c2">v0</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon" title="c3">v1</font>) <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">v0</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon" title="c3">v1</font></span>)</span></span><br/>





<a NAME="E1:58_1_1_1_26"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c2">v0</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon" title="c3">v1</font></span>)</span> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">v65</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c2">v0</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon" title="c3">v1</font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">v0</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">v1</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">v65</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c2">v0</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon" title="c3">v1</font>)</span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="robbins3.html#D1" title="ROBBINS3:def.1">ROBBINS3:def 1</a></i>;<br/>
<b>hence </b><a NAME="E2:58_1_1_1_26"/>
<font color="Maroon" title="c2">v0</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">v1</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">v65</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c2">v0</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon" title="c3">v1</font>)</span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c2">v0</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon" title="c3">v1</font>) <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">v0</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon" title="c3">v1</font></span>)</span>
 <b>by </b><i><a class="txt" href="#E23:58_1_1_1"><i><font color="Green" title="E59">A148</font></i></a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div>
<a NAME="E27:58_1_1_1"/><i><font color="Green" title="E63">A159</font></i>: 
for <font color="Olive" title="b1">v0</font>, <font color="Olive" title="b2">v1</font>, <font color="Olive" title="b3">v65</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">L</font> holds  <font color="Olive" title="b1">v0</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">v1</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <span class="p2">(<span class="default"><font color="Olive" title="b3">v65</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Olive" title="b1">v0</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Olive" title="b2">v1</font>)</span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">v0</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">v1</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Olive" title="b1">v0</font>)</span>)</span>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="58_1_1_1_27"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c2">v0</font>, <font color="Maroon" title="c3">v1</font>, <font color="Maroon" title="c4">v65</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:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c2">v0</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">v1</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">v65</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c2">v0</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon" title="c3">v1</font>)</span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">v0</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">v1</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c2">v0</font>)</span>)</span></span><br/>





<a NAME="E1:58_1_1_1_27"/>
<font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c2">v0</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon" title="c3">v1</font>) <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">v0</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon" title="c3">v1</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">v0</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">v1</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c2">v0</font>)</span>)</span>
 
<b>by </b><i><a class="txt" href="#E25:58_1_1_1"><i><font color="Green" title="E61">A154</font></i></a></i>;<br/>
<b>hence </b><a NAME="E2:58_1_1_1_27"/>
<font color="Maroon" title="c2">v0</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">v1</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">v65</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c2">v0</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon" title="c3">v1</font>)</span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">v0</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">v1</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c2">v0</font>)</span>)</span>
 <b>by </b><i><a class="txt" href="#E26:58_1_1_1"><i><font color="Green" title="E62">A158</font></i></a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div>
<a NAME="E28:58_1_1_1"/><i><font color="Green" title="E64">A164</font></i>: 
for <font color="Olive" title="b1">v1</font>, <font color="Olive" title="b2">v0</font>, <font color="Olive" title="b3">v65</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">L</font> holds  <font color="Maroon">H<sub>1</sub></font>(<font color="Olive" title="b1">v1</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Olive" title="b2">v0</font>) <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">v0</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Olive" title="b1">v1</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">v0</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">v1</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <span class="p2">(<span class="default"><font color="Olive" title="b3">v65</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Olive" title="b2">v0</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Olive" title="b1">v1</font>)</span>)</span></span>)</span>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="58_1_1_1_28"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c2">v1</font>, <font color="Maroon" title="c3">v0</font>, <font color="Maroon" title="c4">v65</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:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c2">v1</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon" title="c3">v0</font>) <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">v0</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon" title="c2">v1</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">v0</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">v1</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">v65</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c3">v0</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon" title="c2">v1</font>)</span>)</span></span>)</span></span><br/>





<a NAME="E1:58_1_1_1_28"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c3">v0</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon" title="c2">v1</font></span>)</span> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">v65</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c3">v0</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon" title="c2">v1</font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">v0</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">v1</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">v65</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c3">v0</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon" title="c2">v1</font>)</span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="robbins3.html#D1" title="ROBBINS3:def.1">ROBBINS3:def 1</a></i>;<br/>
<b>hence </b><a NAME="E2:58_1_1_1_28"/>
<font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c2">v1</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon" title="c3">v0</font>) <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">v0</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon" title="c2">v1</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">v0</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">v1</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">v65</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c3">v0</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon" title="c2">v1</font>)</span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="#E23:58_1_1_1"><i><font color="Green" title="E59">A148</font></i></a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div>
<a NAME="E29:58_1_1_1"/><i><font color="Green" title="E65">A166</font></i>: 
for <font color="Olive" title="b1">v1</font>, <font color="Olive" title="b2">v0</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">L</font> holds  <font color="Maroon">H<sub>1</sub></font>(<font color="Olive" title="b1">v1</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Olive" title="b2">v0</font>) <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">v0</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Olive" title="b1">v1</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">v0</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">v1</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Olive" title="b2">v0</font>)</span>)</span>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="58_1_1_1_29"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c2">v1</font>, <font color="Maroon" title="c3">v0</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:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c2">v1</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon" title="c3">v0</font>) <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">v0</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon" title="c2">v1</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">v0</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">v1</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c3">v0</font>)</span>)</span></span><br/>



<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="58_1_1_1_29_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c4">v65</font>, <font color="Maroon" title="c5">v1</font>, <font color="Maroon" title="c6">v0</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:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c5">v1</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon" title="c6">v0</font>) <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">v0</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon" title="c5">v1</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">v0</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">v1</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c6">v0</font>)</span>)</span></span><br/><a NAME="E1:58_1_1_1_29_1"/>
<font color="Maroon" title="c6">v0</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">v1</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">v65</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c6">v0</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon" title="c5">v1</font>)</span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">v0</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">v1</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c6">v0</font>)</span>)</span>
 <b>by </b><i><a class="txt" href="#E27:58_1_1_1"><i><font color="Green" title="E63">A159</font></i></a></i>;<br/><b>hence </b><a NAME="E2:58_1_1_1_29_1"/>
<font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c5">v1</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon" title="c6">v0</font>) <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">v0</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon" title="c5">v1</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">v0</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">v1</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c6">v0</font>)</span>)</span>
 <b>by </b><i><a class="txt" href="#E28:58_1_1_1"><i><font color="Green" title="E64">A164</font></i></a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div>
<b>hence </b><a NAME="E2:58_1_1_1_29"/>
<font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c2">v1</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon" title="c3">v0</font>) <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">v0</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon" title="c2">v1</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">v0</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">v1</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c3">v0</font>)</span>)</span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div>
<a NAME="E30:58_1_1_1"/><i><font color="Green" title="E66">A172</font></i>: 
for <font color="Olive" title="b1">v2</font>, <font color="Olive" title="b2">v1</font>, <font color="Olive" title="b3">v65</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">L</font> holds  <font color="Olive" title="b1">v2</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">v1</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Olive" title="b1">v2</font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">v1</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Olive" title="b1">v2</font></span>)</span> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <span class="p1">(<span class="default"><font color="Olive" title="b3">v65</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Olive" title="b2">v1</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Olive" title="b1">v2</font>)</span>)</span>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="58_1_1_1_30"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c2">v2</font>, <font color="Maroon" title="c3">v1</font>, <font color="Maroon" title="c4">v65</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:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c2">v2</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">v1</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c2">v2</font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">v1</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon" title="c2">v2</font></span>)</span> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">v65</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c3">v1</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon" title="c2">v2</font>)</span>)</span></span><br/>





<a NAME="E1:58_1_1_1_30"/>
<font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c3">v1</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon" title="c2">v2</font>) <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">v2</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon" title="c3">v1</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">v2</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">v1</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c2">v2</font>)</span>)</span>
 
<b>by </b><i><a class="txt" href="#E29:58_1_1_1"><i><font color="Green" title="E65">A166</font></i></a></i>;<br/>
<b>hence </b><a NAME="E2:58_1_1_1_30"/>
<font color="Maroon" title="c2">v2</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">v1</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c2">v2</font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">v1</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon" title="c2">v2</font></span>)</span> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">v65</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c3">v1</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon" title="c2">v2</font>)</span>)</span>
 <b>by </b><i><a class="txt" href="#E23:58_1_1_1"><i><font color="Green" title="E59">A148</font></i></a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div>
<a NAME="E31:58_1_1_1"/><i><font color="Green" title="E67">A174</font></i>: 
for <font color="Olive" title="b1">v2</font>, <font color="Olive" title="b2">v1</font>, <font color="Olive" title="b3">v65</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">L</font> holds  <font color="Olive" title="b1">v2</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">v1</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <span class="p2">(<span class="default"><font color="Olive" title="b1">v2</font> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a> </span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">v1</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">v2</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <span class="p2">(<span class="default"><font color="Olive" title="b3">v65</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Olive" title="b2">v1</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Olive" title="b1">v2</font>)</span>)</span></span>)</span>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="58_1_1_1_31"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c2">v2</font>, <font color="Maroon" title="c3">v1</font>, <font color="Maroon" title="c4">v65</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:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c2">v2</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">v1</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">v2</font> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a> </span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">v1</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">v2</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">v65</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c3">v1</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon" title="c2">v2</font>)</span>)</span></span>)</span></span><br/>





<a NAME="E1:58_1_1_1_31"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c3">v1</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon" title="c2">v2</font></span>)</span> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">v65</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c3">v1</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon" title="c2">v2</font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">v1</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">v2</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">v65</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c3">v1</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon" title="c2">v2</font>)</span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="robbins3.html#D1" title="ROBBINS3:def.1">ROBBINS3:def 1</a></i>;<br/>
<b>hence </b><a NAME="E2:58_1_1_1_31"/>
<font color="Maroon" title="c2">v2</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">v1</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">v2</font> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a> </span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">v1</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">v2</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">v65</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c3">v1</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon" title="c2">v2</font>)</span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="#E30:58_1_1_1"><i><font color="Green" title="E66">A172</font></i></a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div>
<a NAME="E32:58_1_1_1"/><i><font color="Green" title="E68">A176</font></i>: 
for <font color="Olive" title="b1">v2</font>, <font color="Olive" title="b2">v1</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">L</font> holds  <font color="Olive" title="b1">v2</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">v1</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <span class="p2">(<span class="default"><font color="Olive" title="b1">v2</font> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a> </span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">v1</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">v2</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <span class="p2">(<span class="default"><font color="Olive" title="b2">v1</font> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a> </span>)</span></span>)</span>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="58_1_1_1_32"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c2">v2</font>, <font color="Maroon" title="c3">v1</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:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c2">v2</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">v1</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">v2</font> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a> </span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">v1</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">v2</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">v1</font> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a> </span>)</span></span>)</span></span><br/>



<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="58_1_1_1_32_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c4">v65</font>, <font color="Maroon" title="c5">v2</font>, <font color="Maroon" title="c6">v1</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:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c5">v2</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">v1</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c5">v2</font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">v1</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">v2</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c6">v1</font>)</span>)</span></span><br/><a NAME="E1:58_1_1_1_32_1"/>
<font color="Maroon" title="c6">v1</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">v2</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">v65</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c6">v1</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon" title="c5">v2</font>)</span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">v1</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">v2</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c6">v1</font>)</span>)</span>
 <b>by </b><i><a class="txt" href="#E27:58_1_1_1"><i><font color="Green" title="E63">A159</font></i></a></i>;<br/><b>hence </b><a NAME="E2:58_1_1_1_32_1"/>
<font color="Maroon" title="c5">v2</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">v1</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c5">v2</font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">v1</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">v2</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c6">v1</font>)</span>)</span>
 <b>by </b><i><a class="txt" href="#E31:58_1_1_1"><i><font color="Green" title="E67">A174</font></i></a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div>
<b>hence </b><a NAME="E2:58_1_1_1_32"/>
<font color="Maroon" title="c2">v2</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">v1</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">v2</font> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a> </span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">v1</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">v2</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">v1</font> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a> </span>)</span></span>)</span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div>
<a NAME="E33:58_1_1_1"/><i><font color="Green" title="E69">A183</font></i>: 
for <font color="Olive" title="b1">v0</font>, <font color="Olive" title="b2">v1</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">L</font> holds  <font color="Olive" title="b1">v0</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">v0</font> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a> </span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">v1</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">v0</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <span class="p2">(<span class="default"><font color="Olive" title="b2">v1</font> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a> </span>)</span></span>)</span>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="58_1_1_1_33"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c2">v0</font>, <font color="Maroon" title="c3">v1</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:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c2">v0</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">v0</font> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a> </span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">v1</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">v0</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">v1</font> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a> </span>)</span></span>)</span></span><br/>



<a NAME="E1:58_1_1_1_33"/>
<font color="Maroon" title="c2">v0</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">v1</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">v0</font> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a> </span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">v0</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">v0</font> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a> </span>)</span>
 
<b>by </b><i><a class="txt" href="#E23:58_1_1_1"><i><font color="Green" title="E59">A148</font></i></a></i>;<br/>
<b>hence </b><a NAME="E2:58_1_1_1_33"/>
<font color="Maroon" title="c2">v0</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">v0</font> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a> </span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">v1</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">v0</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">v1</font> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a> </span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="#E32:58_1_1_1"><i><font color="Green" title="E68">A176</font></i></a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div>
<b>let </b><font color="Maroon" title="c2">v1</font>, <font color="Maroon" title="c3">v0</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:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c2">v1</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c2">v1</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">v0</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c3">v0</font>)</span><br/>



<a NAME="E34:58_1_1_1"/>
<font color="Maroon" title="c2">v1</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">v0</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">v1</font> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a> </span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">v1</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">v1</font> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a> </span>)</span>
 
<b>by </b><i><a class="txt" href="#E23:58_1_1_1"><i><font color="Green" title="E59">A148</font></i></a></i>;<br/>
<b>hence </b><a NAME="E35:58_1_1_1"/>
<font color="Maroon" title="c2">v1</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c2">v1</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">v0</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c3">v0</font>)
 <b>by </b><i><a class="txt" href="#E33:58_1_1_1"><i><font color="Green" title="E69">A183</font></i></a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E2:58_1_1"/>
<font color="Maroon" title="c1">L</font> is <a href="robbins3.html#V9" title="ROBBINS3:attr.9">with_Top</a>
 <b>by </b><i><a class="ref" href="robbins3.html#D7" title="ROBBINS3:def.7">ROBBINS3:def 7</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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