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

<span class="kw">let </span><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#V10" title="ROBBINS1:attr.10">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#L4" title="ROBBINS1:struct.4">OrthoLattStr</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></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/>

<span class="kw">deffunc </span><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>) <span class="kw">-&gt; </span>   <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"><span class="kw">proof </span></a><div class="add">

<a NAME="E1:58_1_1_1"/><span class="lab"><font color="Green" title="E37">A1</font></span>: 
 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_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><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:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></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_1"/>
<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>))
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="robbins1.html#D23" title="ROBBINS1:def.23">ROBBINS1:def 23</a></span>;<br/>
<span class="kw">hence </span><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" 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 class="kw">by</span> <span class="lab"><a class="ref" href="robbins3.html#D3" title="ROBBINS3:def.3">ROBBINS3:def 3</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div>
<a NAME="E2:58_1_1_1"/><span class="lab"><font color="Green" title="E38">A2</font></span>: 
 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_2"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><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:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></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_2_1"><span class="kw">now </span></a><div class="add"><span class="kw">let </span><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:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></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_2_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>)
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:58_1_1_1"><span class="lab"><font color="Green" title="E37">A1</font></span></a></span>;<br/><span class="kw">hence </span><a NAME="E2:58_1_1_1_2_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>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:58_1_1_1"><span class="lab"><font color="Green" title="E37">A1</font></span></a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div>
<span class="kw">hence </span><a NAME="E2:58_1_1_1_2"/>
<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:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div>
<a NAME="E3:58_1_1_1"/><span class="lab"><font color="Green" title="E39">A3</font></span>: 
 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_3"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><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:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></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_3"/>
<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>))
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="robbins1.html#D23" title="ROBBINS1:def.23">ROBBINS1:def 23</a></span>;<br/>
<span class="kw">hence </span><a NAME="E2:58_1_1_1_3"/>
<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 class="kw">by</span> <span class="lab"><a class="ref" href="robbins4.html#D2" target="_self" title="ROBBINS4:def.2">Def2</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div>
<a NAME="E4:58_1_1_1"/><span class="lab"><font color="Green" title="E40">A4</font></span>: 
 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_4"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><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:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></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_4"/>
<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>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:58_1_1_1"><span class="lab"><font color="Green" title="E39">A3</font></span></a></span>;<br/>
<span class="kw">hence </span><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">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 class="kw">by</span> <span class="lab"><a class="txt" href="#E1:58_1_1_1"><span class="lab"><font color="Green" title="E37">A1</font></span></a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div>
<a NAME="E5:58_1_1_1"/><span class="lab"><font color="Green" title="E41">A5</font></span>: 
 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_5"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><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:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></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_5"/>
<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>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:58_1_1_1"><span class="lab"><font color="Green" title="E40">A4</font></span></a></span>;<br/>
<span class="kw">hence </span><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" 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 class="kw">by</span> <span class="lab"><a class="ref" href="robbins3.html#D1" title="ROBBINS3:def.1">ROBBINS3:def 1</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div>
<a NAME="E6:58_1_1_1"/><span class="lab"><font color="Green" title="E42">A6</font></span>: 
 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_6"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><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:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></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_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="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">v65</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:58_1_1_1"><span class="lab"><font color="Green" title="E38">A2</font></span></a></span>;<br/>
<span class="kw">hence </span><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>))</span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="robbins3.html#D1" title="ROBBINS3:def.1">ROBBINS3:def 1</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div>
<a NAME="E7:58_1_1_1"/><span class="lab"><font color="Green" title="E43">A7</font></span>: 
 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_7"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><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:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></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_7"/>
<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> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:58_1_1_1"><span class="lab"><font color="Green" title="E38">A2</font></span></a></span>;<br/>
<span class="kw">hence </span><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> <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 class="kw">by</span> <span class="lab"><a class="txt" href="#E6:58_1_1_1"><span class="lab"><font color="Green" title="E42">A6</font></span></a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div>
<a NAME="E8:58_1_1_1"/><span class="lab"><font color="Green" title="E44">A8</font></span>: 
 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_8"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><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:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></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_8"/>
<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>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:58_1_1_1"><span class="lab"><font color="Green" title="E38">A2</font></span></a></span>;<br/>
<span class="kw">hence </span><a NAME="E2:58_1_1_1_8"/>
<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 class="kw">by</span> <span class="lab"><a class="txt" href="#E7:58_1_1_1"><span class="lab"><font color="Green" title="E43">A7</font></span></a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div>
<a NAME="E9:58_1_1_1"/><span class="lab"><font color="Green" title="E45">A9</font></span>: 
 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_9"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><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:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></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_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">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>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:58_1_1_1"><span class="lab"><font color="Green" title="E44">A8</font></span></a></span>;<br/>
<span class="kw">hence </span><a NAME="E2:58_1_1_1_9"/>
<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 class="kw">by</span> <span class="lab"><a class="txt" href="#E4:58_1_1_1"><span class="lab"><font color="Green" title="E40">A4</font></span></a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div>
<a NAME="E10:58_1_1_1"/><span class="lab"><font color="Green" title="E46">A10</font></span>: 
 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_10"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><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:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></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_10"/>
<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> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:58_1_1_1"><span class="lab"><font color="Green" title="E38">A2</font></span></a></span>;<br/>
<span class="kw">hence </span><a NAME="E2:58_1_1_1_10"/>
<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 class="kw">by</span> <span class="lab"><a class="txt" href="#E9:58_1_1_1"><span class="lab"><font color="Green" title="E45">A9</font></span></a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div>
<a NAME="E11:58_1_1_1"/><span class="lab"><font color="Green" title="E47">A11</font></span>: 
 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_11"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><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:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></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_11"/>
<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>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:58_1_1_1"><span class="lab"><font color="Green" title="E44">A8</font></span></a></span>;<br/>
<span class="kw">hence </span><a NAME="E2:58_1_1_1_11"/>
<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 class="kw">by</span> <span class="lab"><a class="txt" href="#E3:58_1_1_1"><span class="lab"><font color="Green" title="E39">A3</font></span></a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div>
<a NAME="E12:58_1_1_1"/><span class="lab"><font color="Green" title="E48">A12</font></span>: 
 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_12"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><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:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></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_12"/>
<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> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E10:58_1_1_1"><span class="lab"><font color="Green" title="E46">A10</font></span></a></span>;<br/>
<span class="kw">hence </span><a NAME="E2:58_1_1_1_12"/>
<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 class="kw">by</span> <span class="lab"><a class="txt" href="#E11:58_1_1_1"><span class="lab"><font color="Green" title="E47">A11</font></span></a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div>
<a NAME="E13:58_1_1_1"/><span class="lab"><font color="Green" title="E49">A13</font></span>: 
 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_13"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><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:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></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_13"/>
<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> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E10:58_1_1_1"><span class="lab"><font color="Green" title="E46">A10</font></span></a></span>;<br/>
<span class="kw">hence </span><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" 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 class="kw">by</span> <span class="lab"><a class="txt" href="#E12:58_1_1_1"><span class="lab"><font color="Green" title="E48">A12</font></span></a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div>
<a NAME="E14:58_1_1_1"/><span class="lab"><font color="Green" title="E50">A14</font></span>: 
 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_14"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><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:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></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_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> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E10:58_1_1_1"><span class="lab"><font color="Green" title="E46">A10</font></span></a></span>;<br/>
<span class="kw">hence </span><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" 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 class="kw">by</span> <span class="lab"><a class="txt" href="#E13:58_1_1_1"><span class="lab"><font color="Green" title="E49">A13</font></span></a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div>
<a NAME="E15:58_1_1_1"/><span class="lab"><font color="Green" title="E51">A15</font></span>: 
 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_15"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><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:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></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_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> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E10:58_1_1_1"><span class="lab"><font color="Green" title="E46">A10</font></span></a></span>;<br/>
<span class="kw">hence </span><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" 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 class="kw">by</span> <span class="lab"><a class="txt" href="#E14:58_1_1_1"><span class="lab"><font color="Green" title="E50">A14</font></span></a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div>
<a NAME="E16:58_1_1_1"/><span class="lab"><font color="Green" title="E52">A16</font></span>: 
 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_16"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><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:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></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_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="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>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:58_1_1_1"><span class="lab"><font color="Green" title="E38">A2</font></span></a></span>;<br/>
<span class="kw">hence </span><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" title="c2">v65</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E15:58_1_1_1"><span class="lab"><font color="Green" title="E51">A15</font></span></a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div>
<a NAME="E17:58_1_1_1"/><span class="lab"><font color="Green" title="E53">A17</font></span>: 
 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_17"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><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:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></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_17"/>
<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> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E10:58_1_1_1"><span class="lab"><font color="Green" title="E46">A10</font></span></a></span>;<br/>
<span class="kw">hence </span><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">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 class="kw">by</span> <span class="lab"><a class="txt" href="#E4:58_1_1_1"><span class="lab"><font color="Green" title="E40">A4</font></span></a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div>
<a NAME="E18:58_1_1_1"/><span class="lab"><font color="Green" title="E54">A18</font></span>: 
 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_18"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><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:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></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_18"/>
<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> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E17:58_1_1_1"><span class="lab"><font color="Green" title="E53">A17</font></span></a></span>;<br/>
<span class="kw">hence </span><a NAME="E2:58_1_1_1_18"/>
<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 class="kw">by</span> <span class="lab"><a class="txt" href="#E16:58_1_1_1"><span class="lab"><font color="Green" title="E52">A16</font></span></a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div>
<a NAME="E19:58_1_1_1"/><span class="lab"><font color="Green" title="E55">A19</font></span>: 
 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_19"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><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:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></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_19"/>
<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>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:58_1_1_1"><span class="lab"><font color="Green" title="E42">A6</font></span></a></span>;<br/>
<span class="kw">hence </span><a NAME="E2:58_1_1_1_19"/>
<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 class="kw">by</span> <span class="lab"><a class="txt" href="#E3:58_1_1_1"><span class="lab"><font color="Green" title="E39">A3</font></span></a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div>
<a NAME="E20:58_1_1_1"/><span class="lab"><font color="Green" title="E56">A20</font></span>: 
 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_20"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><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:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></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_20"/>
<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>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:58_1_1_1"><span class="lab"><font color="Green" title="E42">A6</font></span></a></span>;<br/>
<span class="kw">hence </span><a NAME="E2:58_1_1_1_20"/>
<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 class="kw">by</span> <span class="lab"><a class="txt" href="#E19:58_1_1_1"><span class="lab"><font color="Green" title="E55">A19</font></span></a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div>
<a NAME="E21:58_1_1_1"/><span class="lab"><font color="Green" title="E57">A21</font></span>: 
 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"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><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:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></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>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E18:58_1_1_1"><span class="lab"><font color="Green" title="E54">A18</font></span></a></span>;<br/>
<span class="kw">hence </span><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>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E20:58_1_1_1"><span class="lab"><font color="Green" title="E56">A20</font></span></a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div>
<a NAME="E22:58_1_1_1"/><span class="lab"><font color="Green" title="E58">A22</font></span>: 
 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_22"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><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:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></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_22"/>
<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>)
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E21:58_1_1_1"><span class="lab"><font color="Green" title="E57">A21</font></span></a></span>;<br/>
<span class="kw">hence </span><a NAME="E2:58_1_1_1_22"/>
<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 class="kw">by</span> <span class="lab"><a class="txt" href="#E5:58_1_1_1"><span class="lab"><font color="Green" title="E41">A5</font></span></a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div>
<a NAME="E23:58_1_1_1"/><span class="lab"><font color="Green" title="E59">A23</font></span>: 
 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_23"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><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:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></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_23"/>
<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 class="kw">by</span> <span class="lab"><a class="txt" href="#E18:58_1_1_1"><span class="lab"><font color="Green" title="E54">A18</font></span></a></span>;<br/>
<span class="kw">hence </span><a NAME="E2:58_1_1_1_23"/>
<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 class="kw">by</span> <span class="lab"><a class="txt" href="#E4:58_1_1_1"><span class="lab"><font color="Green" title="E40">A4</font></span></a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div>
<a NAME="E24:58_1_1_1"/><span class="lab"><font color="Green" title="E60">A24</font></span>: 
 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"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><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:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></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>)
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E23:58_1_1_1"><span class="lab"><font color="Green" title="E59">A23</font></span></a></span>;<br/>
<span class="kw">hence </span><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>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E22:58_1_1_1"><span class="lab"><font color="Green" title="E58">A22</font></span></a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div>
<a NAME="E25:58_1_1_1"/><span class="lab"><font color="Green" title="E61">A25</font></span>: 
 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"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><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:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></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>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="robbins3.html#D1" title="ROBBINS3:def.1">ROBBINS3:def 1</a></span>;<br/>
<span class="kw">hence </span><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>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E24:58_1_1_1"><span class="lab"><font color="Green" title="E60">A24</font></span></a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div>
<a NAME="E26:58_1_1_1"/><span class="lab"><font color="Green" title="E62">A26</font></span>: 
 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"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><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:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></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>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="robbins3.html#D1" title="ROBBINS3:def.1">ROBBINS3:def 1</a></span>;<br/>
<span class="kw">hence </span><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>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E22:58_1_1_1"><span class="lab"><font color="Green" title="E58">A22</font></span></a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div>
<a NAME="E27:58_1_1_1"/><span class="lab"><font color="Green" title="E63">A27</font></span>: 
 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"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><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:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></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>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E25:58_1_1_1"><span class="lab"><font color="Green" title="E61">A25</font></span></a></span>;<br/>
<span class="kw">hence </span><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>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E26:58_1_1_1"><span class="lab"><font color="Green" title="E62">A26</font></span></a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div>
<a NAME="E28:58_1_1_1"/><span class="lab"><font color="Green" title="E64">A28</font></span>: 
 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"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><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:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></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>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="robbins3.html#D1" title="ROBBINS3:def.1">ROBBINS3:def 1</a></span>;<br/>
<span class="kw">hence </span><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>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E22:58_1_1_1"><span class="lab"><font color="Green" title="E58">A22</font></span></a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div>
<a NAME="E29:58_1_1_1"/><span class="lab"><font color="Green" title="E65">A29</font></span>: 
 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"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><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:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></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"><span class="kw">now </span></a><div class="add"><span class="kw">let </span><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:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></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>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E27:58_1_1_1"><span class="lab"><font color="Green" title="E63">A27</font></span></a></span>;<br/><span class="kw">hence </span><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>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E28:58_1_1_1"><span class="lab"><font color="Green" title="E64">A28</font></span></a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div>
<span class="kw">hence </span><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:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div>
<a NAME="E30:58_1_1_1"/><span class="lab"><font color="Green" title="E66">A30</font></span>: 
 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"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><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:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></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>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E29:58_1_1_1"><span class="lab"><font color="Green" title="E65">A29</font></span></a></span>;<br/>
<span class="kw">hence </span><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>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E22:58_1_1_1"><span class="lab"><font color="Green" title="E58">A22</font></span></a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div>
<a NAME="E31:58_1_1_1"/><span class="lab"><font color="Green" title="E67">A31</font></span>: 
 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"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><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:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></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>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="robbins3.html#D1" title="ROBBINS3:def.1">ROBBINS3:def 1</a></span>;<br/>
<span class="kw">hence </span><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>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E30:58_1_1_1"><span class="lab"><font color="Green" title="E66">A30</font></span></a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div>
<a NAME="E32:58_1_1_1"/><span class="lab"><font color="Green" title="E68">A32</font></span>: 
 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"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><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:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></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"><span class="kw">now </span></a><div class="add"><span class="kw">let </span><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:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></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>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E27:58_1_1_1"><span class="lab"><font color="Green" title="E63">A27</font></span></a></span>;<br/><span class="kw">hence </span><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>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E31:58_1_1_1"><span class="lab"><font color="Green" title="E67">A31</font></span></a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div>
<span class="kw">hence </span><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:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div>
<a NAME="E33:58_1_1_1"/><span class="lab"><font color="Green" title="E69">A33</font></span>: 
 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"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><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:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></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>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E22:58_1_1_1"><span class="lab"><font color="Green" title="E58">A22</font></span></a></span>;<br/>
<span class="kw">hence </span><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>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E32:58_1_1_1"><span class="lab"><font color="Green" title="E68">A32</font></span></a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div>
<span class="kw">let </span><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:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></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>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E22:58_1_1_1"><span class="lab"><font color="Green" title="E58">A22</font></span></a></span>;<br/>
<span class="kw">hence </span><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>)
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E33:58_1_1_1"><span class="lab"><font color="Green" title="E69">A33</font></span></a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div>
<span class="kw">hence </span><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> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="robbins3.html#D7" title="ROBBINS3:def.7">ROBBINS3:def 7</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div>
