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

<span class="kw">let </span><font color="Maroon" title="c1">C</font> be   <a href="conlat_1.html#NM1" title="CONLAT_1:NM.1">FormalContext</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="conlat_1.html#K11" title="CONLAT_1:func.11">ConceptLattice</a> <font color="Maroon" title="c1">C</font> is   <a href="lattices.html#NM1" title="LATTICES:NM.1">Lattice</a></span><br/>

<span class="kw">set </span><font color="Maroon" title="c2">L</font> =  <a href="lattices.html#G3" title="LATTICES:aggr.3">LattStr</a>(# <span class="p1">(<span class="default"><a href="conlat_1.html#K8" title="CONLAT_1:func.8">B-carrier</a> <font color="Maroon" title="c1">C</font></span>)</span>,<span class="p1">(<span class="default"><a href="conlat_1.html#K10" title="CONLAT_1:func.10">B-join</a> <font color="Maroon" title="c1">C</font></span>)</span>,<span class="p1">(<span class="default"><a href="conlat_1.html#K9" title="CONLAT_1:func.9">B-meet</a> <font color="Maroon" title="c1">C</font></span>)</span> #);<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c3">L</font> =  <a href="lattices.html#G3" title="LATTICES:aggr.3">LattStr</a>(# <span class="p1">(<span class="default"><a href="conlat_1.html#K8" title="CONLAT_1:func.8">B-carrier</a> <font color="Maroon" title="c1">C</font></span>)</span>,<span class="p1">(<span class="default"><a href="conlat_1.html#K10" title="CONLAT_1:func.10">B-join</a> <font color="Maroon" title="c1">C</font></span>)</span>,<span class="p1">(<span class="default"><a href="conlat_1.html#K9" title="CONLAT_1:func.9">B-meet</a> <font color="Maroon" title="c1">C</font></span>)</span> #) as   non  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>   <a href="lattices.html#V3" title="LATTICES:attr.3">strict</a>   <a href="lattices.html#L3" title="LATTICES:struct.3">LattStr</a>  ;<br/>
<a NAME="E2:84"/><span class="lab"><font color="Green" title="E47">A1</font></span>: 
 for <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font>, <font color="Olive" title="b3">c</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c3">L</font> holds  <font color="Olive" title="b1">a</font> <a href="lattices.html#K1" title="LATTICES:func.1">"\/"</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">b</font> <a href="lattices.html#K1" title="LATTICES:func.1">"\/"</a> <font color="Olive" title="b3">c</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">a</font> <a href="lattices.html#K1" title="LATTICES:func.1">"\/"</a> <font color="Olive" title="b2">b</font></span>)</span> <a href="lattices.html#K1" title="LATTICES:func.1">"\/"</a> <font color="Olive" title="b3">c</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="84_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><font color="Maroon" title="c4">a</font>, <font color="Maroon" title="c5">b</font>, <font color="Maroon" title="c6">c</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c3">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="c4">a</font> <a href="lattices.html#K1" title="LATTICES:func.1">"\/"</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">b</font> <a href="lattices.html#K1" title="LATTICES:func.1">"\/"</a> <font color="Maroon" title="c6">c</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">a</font> <a href="lattices.html#K1" title="LATTICES:func.1">"\/"</a> <font color="Maroon" title="c5">b</font></span>)</span> <a href="lattices.html#K1" title="LATTICES:func.1">"\/"</a> <font color="Maroon" title="c6">c</font></span><br/>

<span class="kw">reconsider </span><font color="Maroon" title="c7">b</font> = <font color="Maroon" title="c5">b</font>, <font color="Maroon" title="c8">c</font> = <font color="Maroon" title="c6">c</font> as    <a href="conlat_1.html#M2" title="CONLAT_1:mode.2">Element</a> of  <a href="conlat_1.html#K8" title="CONLAT_1:func.8">B-carrier</a> <font color="Maroon" title="c1">C</font> ;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c9">d</font> = <span class="p1">(<span class="default"><a href="conlat_1.html#K10" title="CONLAT_1:func.10">B-join</a> <font color="Maroon" title="c1">C</font></span>)</span> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> (<font color="Maroon" title="c7">b</font>,<font color="Maroon" title="c8">c</font>) as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c3">L</font> ;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c10">b</font> = <font color="Maroon" title="c7">b</font>, <font color="Maroon" title="c11">c</font> = <font color="Maroon" title="c8">c</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c3">L</font> ;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c12">a</font> = <font color="Maroon" title="c4">a</font>, <font color="Maroon" title="c13">b</font> = <font color="Maroon" title="c10">b</font> as    <a href="conlat_1.html#M2" title="CONLAT_1:mode.2">Element</a> of  <a href="conlat_1.html#K8" title="CONLAT_1:func.8">B-carrier</a> <font color="Maroon" title="c1">C</font> ;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c14">e</font> = <span class="p1">(<span class="default"><a href="conlat_1.html#K10" title="CONLAT_1:func.10">B-join</a> <font color="Maroon" title="c1">C</font></span>)</span> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> (<font color="Maroon" title="c12">a</font>,<font color="Maroon" title="c13">b</font>) as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c3">L</font> ;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c15">a</font> = <font color="Maroon" title="c12">a</font>, <font color="Maroon" title="c16">b</font> = <font color="Maroon" title="c13">b</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c3">L</font> ;<br/>
<span class="lab"><font color="Green" title="E48">A2</font></span>: <font color="Maroon" title="c15">a</font> <a href="lattices.html#K1" title="LATTICES:func.1">"\/"</a> <span class="p1">(<span class="default"><font color="Maroon" title="c16">b</font> <a href="lattices.html#K1" title="LATTICES:func.1">"\/"</a> <font color="Maroon" title="c11">c</font></span>)</span> = 
<font color="Maroon" title="c15">a</font> <a href="lattices.html#K1" title="LATTICES:func.1">"\/"</a> <font color="Maroon" title="c9">d</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="lattices.html#D1" title="LATTICES:def.1">LATTICES:def 1</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="conlat_1.html#K10" title="CONLAT_1:func.10">B-join</a> <font color="Maroon" title="c1">C</font></span>)</span> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<font color="Maroon" title="c15">a</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="conlat_1.html#K10" title="CONLAT_1:func.10">B-join</a> <font color="Maroon" title="c1">C</font></span>)</span> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<font color="Maroon" title="c16">b</font>,<font color="Maroon" title="c11">c</font>)</span>)</span>)
<span class="kw">by</span> <span class="lab"><a class="ref" href="lattices.html#D1" title="LATTICES:def.1">LATTICES:def 1</a></span>
;<br/>
<span class="lab"><font color="Green" title="E49">A3</font></span>: <span class="p1">(<span class="default"><font color="Maroon" title="c15">a</font> <a href="lattices.html#K1" title="LATTICES:func.1">"\/"</a> <font color="Maroon" title="c16">b</font></span>)</span> <a href="lattices.html#K1" title="LATTICES:func.1">"\/"</a> <font color="Maroon" title="c11">c</font> = 
<font color="Maroon" title="c14">e</font> <a href="lattices.html#K1" title="LATTICES:func.1">"\/"</a> <font color="Maroon" title="c11">c</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="lattices.html#D1" title="LATTICES:def.1">LATTICES:def 1</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="conlat_1.html#K10" title="CONLAT_1:func.10">B-join</a> <font color="Maroon" title="c1">C</font></span>)</span> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="conlat_1.html#K10" title="CONLAT_1:func.10">B-join</a> <font color="Maroon" title="c1">C</font></span>)</span> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<font color="Maroon" title="c15">a</font>,<font color="Maroon" title="c16">b</font>)</span>)</span>,<font color="Maroon" title="c11">c</font>)
<span class="kw">by</span> <span class="lab"><a class="ref" href="lattices.html#D1" title="LATTICES:def.1">LATTICES:def 1</a></span>
;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c17">a</font> = <font color="Maroon" title="c15">a</font>, <font color="Maroon" title="c18">b</font> = <font color="Maroon" title="c16">b</font>, <font color="Maroon" title="c19">c</font> = <font color="Maroon" title="c11">c</font> as   <a href="conlat_1.html#V4" title="CONLAT_1:attr.4">strict</a>  <a href="conlat_1.html#NM4" title="CONLAT_1:NM.4">FormalConcept</a> of <font color="Maroon" title="c1">C</font> <span class="kw">by</span> <span class="lab"><a class="ref" href="conlat_1.html#T31" target="_self" title="CONLAT_1:th.31">Th35</a></span>;<br/>
<a NAME="E10:84_1"/>
<span class="p1">(<span class="default"><a href="conlat_1.html#K10" title="CONLAT_1:func.10">B-join</a> <font color="Maroon" title="c1">C</font></span>)</span> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<font color="Maroon" title="c17">a</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="conlat_1.html#K10" title="CONLAT_1:func.10">B-join</a> <font color="Maroon" title="c1">C</font></span>)</span> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<font color="Maroon" title="c18">b</font>,<font color="Maroon" title="c19">c</font>)</span>)</span>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="conlat_1.html#K10" title="CONLAT_1:func.10">B-join</a> <font color="Maroon" title="c1">C</font></span>)</span> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="conlat_1.html#K10" title="CONLAT_1:func.10">B-join</a> <font color="Maroon" title="c1">C</font></span>)</span> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<font color="Maroon" title="c17">a</font>,<font color="Maroon" title="c18">b</font>)</span>)</span>,<font color="Maroon" title="c19">c</font>)
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="conlat_1.html#T35" target="_self" title="CONLAT_1:th.35">Th39</a></span>;<br/>
<span class="kw">hence </span><a NAME="E11:84_1"/>
<font color="Maroon" title="c4">a</font> <a href="lattices.html#K1" title="LATTICES:func.1">"\/"</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">b</font> <a href="lattices.html#K1" title="LATTICES:func.1">"\/"</a> <font color="Maroon" title="c6">c</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">a</font> <a href="lattices.html#K1" title="LATTICES:func.1">"\/"</a> <font color="Maroon" title="c5">b</font></span>)</span> <a href="lattices.html#K1" title="LATTICES:func.1">"\/"</a> <font color="Maroon" title="c6">c</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:84_1"><span class="lab"><font color="Green" title="E48">A2</font></span></a>, <a class="txt" href="#E8:84_1"><span class="lab"><font color="Green" title="E49">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="E3:84"/><span class="lab"><font color="Green" title="E48">A4</font></span>: 
 for <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c3">L</font> holds  <span class="p1">(<span class="default"><font color="Olive" title="b1">a</font> <a href="lattices.html#K2" title="LATTICES:func.2">"/\"</a> <font color="Olive" title="b2">b</font></span>)</span> <a href="lattices.html#K1" title="LATTICES:func.1">"\/"</a> <font color="Olive" title="b2">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">b</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="84_2"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><font color="Maroon" title="c4">a</font>, <font color="Maroon" title="c5">b</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c3">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="c4">a</font> <a href="lattices.html#K2" title="LATTICES:func.2">"/\"</a> <font color="Maroon" title="c5">b</font></span>)</span> <a href="lattices.html#K1" title="LATTICES:func.1">"\/"</a> <font color="Maroon" title="c5">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">b</font></span><br/>

<span class="kw">reconsider </span><font color="Maroon" title="c6">a</font> = <font color="Maroon" title="c4">a</font>, <font color="Maroon" title="c7">b</font> = <font color="Maroon" title="c5">b</font> as    <a href="conlat_1.html#M2" title="CONLAT_1:mode.2">Element</a> of  <a href="conlat_1.html#K8" title="CONLAT_1:func.8">B-carrier</a> <font color="Maroon" title="c1">C</font> ;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c8">d</font> = <span class="p1">(<span class="default"><a href="conlat_1.html#K9" title="CONLAT_1:func.9">B-meet</a> <font color="Maroon" title="c1">C</font></span>)</span> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> (<font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c7">b</font>) as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c3">L</font> ;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c9">a</font> = <font color="Maroon" title="c6">a</font>, <font color="Maroon" title="c10">b</font> = <font color="Maroon" title="c7">b</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c3">L</font> ;<br/>
<span class="lab"><font color="Green" title="E49">A5</font></span>: <span class="p1">(<span class="default"><font color="Maroon" title="c9">a</font> <a href="lattices.html#K2" title="LATTICES:func.2">"/\"</a> <font color="Maroon" title="c10">b</font></span>)</span> <a href="lattices.html#K1" title="LATTICES:func.1">"\/"</a> <font color="Maroon" title="c10">b</font> = 
<font color="Maroon" title="c8">d</font> <a href="lattices.html#K1" title="LATTICES:func.1">"\/"</a> <font color="Maroon" title="c10">b</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="lattices.html#D2" title="LATTICES:def.2">LATTICES:def 2</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="conlat_1.html#K10" title="CONLAT_1:func.10">B-join</a> <font color="Maroon" title="c1">C</font></span>)</span> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="conlat_1.html#K9" title="CONLAT_1:func.9">B-meet</a> <font color="Maroon" title="c1">C</font></span>)</span> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<font color="Maroon" title="c9">a</font>,<font color="Maroon" title="c10">b</font>)</span>)</span>,<font color="Maroon" title="c10">b</font>)
<span class="kw">by</span> <span class="lab"><a class="ref" href="lattices.html#D1" title="LATTICES:def.1">LATTICES:def 1</a></span>
;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c11">a</font> = <font color="Maroon" title="c9">a</font>, <font color="Maroon" title="c12">b</font> = <font color="Maroon" title="c10">b</font> as   <a href="conlat_1.html#V4" title="CONLAT_1:attr.4">strict</a>  <a href="conlat_1.html#NM4" title="CONLAT_1:NM.4">FormalConcept</a> of <font color="Maroon" title="c1">C</font> <span class="kw">by</span> <span class="lab"><a class="ref" href="conlat_1.html#T31" target="_self" title="CONLAT_1:th.31">Th35</a></span>;<br/>
<a NAME="E6:84_2"/>
<span class="p1">(<span class="default"><a href="conlat_1.html#K10" title="CONLAT_1:func.10">B-join</a> <font color="Maroon" title="c1">C</font></span>)</span> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="conlat_1.html#K9" title="CONLAT_1:func.9">B-meet</a> <font color="Maroon" title="c1">C</font></span>)</span> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<font color="Maroon" title="c11">a</font>,<font color="Maroon" title="c12">b</font>)</span>)</span>,<font color="Maroon" title="c12">b</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c12">b</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="conlat_1.html#T36" target="_self" title="CONLAT_1:th.36">Th40</a></span>;<br/>
<span class="kw">hence </span><a NAME="E7:84_2"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c4">a</font> <a href="lattices.html#K2" title="LATTICES:func.2">"/\"</a> <font color="Maroon" title="c5">b</font></span>)</span> <a href="lattices.html#K1" title="LATTICES:func.1">"\/"</a> <font color="Maroon" title="c5">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">b</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:84_2"><span class="lab"><font color="Green" title="E49">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="E4:84"/><span class="lab"><font color="Green" title="E49">A6</font></span>: 
 for <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font>, <font color="Olive" title="b3">c</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c3">L</font> holds  <font color="Olive" title="b1">a</font> <a href="lattices.html#K2" title="LATTICES:func.2">"/\"</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">b</font> <a href="lattices.html#K2" title="LATTICES:func.2">"/\"</a> <font color="Olive" title="b3">c</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">a</font> <a href="lattices.html#K2" title="LATTICES:func.2">"/\"</a> <font color="Olive" title="b2">b</font></span>)</span> <a href="lattices.html#K2" title="LATTICES:func.2">"/\"</a> <font color="Olive" title="b3">c</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="84_3"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><font color="Maroon" title="c4">a</font>, <font color="Maroon" title="c5">b</font>, <font color="Maroon" title="c6">c</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c3">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="c4">a</font> <a href="lattices.html#K2" title="LATTICES:func.2">"/\"</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">b</font> <a href="lattices.html#K2" title="LATTICES:func.2">"/\"</a> <font color="Maroon" title="c6">c</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">a</font> <a href="lattices.html#K2" title="LATTICES:func.2">"/\"</a> <font color="Maroon" title="c5">b</font></span>)</span> <a href="lattices.html#K2" title="LATTICES:func.2">"/\"</a> <font color="Maroon" title="c6">c</font></span><br/>

<span class="kw">reconsider </span><font color="Maroon" title="c7">b</font> = <font color="Maroon" title="c5">b</font>, <font color="Maroon" title="c8">c</font> = <font color="Maroon" title="c6">c</font> as    <a href="conlat_1.html#M2" title="CONLAT_1:mode.2">Element</a> of  <a href="conlat_1.html#K8" title="CONLAT_1:func.8">B-carrier</a> <font color="Maroon" title="c1">C</font> ;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c9">d</font> = <span class="p1">(<span class="default"><a href="conlat_1.html#K9" title="CONLAT_1:func.9">B-meet</a> <font color="Maroon" title="c1">C</font></span>)</span> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> (<font color="Maroon" title="c7">b</font>,<font color="Maroon" title="c8">c</font>) as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c3">L</font> ;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c10">b</font> = <font color="Maroon" title="c7">b</font>, <font color="Maroon" title="c11">c</font> = <font color="Maroon" title="c8">c</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c3">L</font> ;<br/>
<span class="lab"><font color="Green" title="E50">A7</font></span>: <font color="Maroon" title="c4">a</font> <a href="lattices.html#K2" title="LATTICES:func.2">"/\"</a> <span class="p1">(<span class="default"><font color="Maroon" title="c10">b</font> <a href="lattices.html#K2" title="LATTICES:func.2">"/\"</a> <font color="Maroon" title="c11">c</font></span>)</span> = 
<font color="Maroon" title="c4">a</font> <a href="lattices.html#K2" title="LATTICES:func.2">"/\"</a> <font color="Maroon" title="c9">d</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="lattices.html#D2" title="LATTICES:def.2">LATTICES:def 2</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="conlat_1.html#K9" title="CONLAT_1:func.9">B-meet</a> <font color="Maroon" title="c1">C</font></span>)</span> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<font color="Maroon" title="c4">a</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="conlat_1.html#K9" title="CONLAT_1:func.9">B-meet</a> <font color="Maroon" title="c1">C</font></span>)</span> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<font color="Maroon" title="c10">b</font>,<font color="Maroon" title="c11">c</font>)</span>)</span>)
<span class="kw">by</span> <span class="lab"><a class="ref" href="lattices.html#D2" title="LATTICES:def.2">LATTICES:def 2</a></span>
;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c12">a</font> = <font color="Maroon" title="c4">a</font>, <font color="Maroon" title="c13">b</font> = <font color="Maroon" title="c10">b</font> as    <a href="conlat_1.html#M2" title="CONLAT_1:mode.2">Element</a> of  <a href="conlat_1.html#K8" title="CONLAT_1:func.8">B-carrier</a> <font color="Maroon" title="c1">C</font> ;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c14">e</font> = <span class="p1">(<span class="default"><a href="conlat_1.html#K9" title="CONLAT_1:func.9">B-meet</a> <font color="Maroon" title="c1">C</font></span>)</span> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> (<font color="Maroon" title="c12">a</font>,<font color="Maroon" title="c13">b</font>) as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c3">L</font> ;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c15">a</font> = <font color="Maroon" title="c12">a</font>, <font color="Maroon" title="c16">b</font> = <font color="Maroon" title="c13">b</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c3">L</font> ;<br/>
<span class="lab"><font color="Green" title="E51">A8</font></span>: <span class="p1">(<span class="default"><font color="Maroon" title="c15">a</font> <a href="lattices.html#K2" title="LATTICES:func.2">"/\"</a> <font color="Maroon" title="c16">b</font></span>)</span> <a href="lattices.html#K2" title="LATTICES:func.2">"/\"</a> <font color="Maroon" title="c11">c</font> = 
<font color="Maroon" title="c14">e</font> <a href="lattices.html#K2" title="LATTICES:func.2">"/\"</a> <font color="Maroon" title="c11">c</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="lattices.html#D2" title="LATTICES:def.2">LATTICES:def 2</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="conlat_1.html#K9" title="CONLAT_1:func.9">B-meet</a> <font color="Maroon" title="c1">C</font></span>)</span> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="conlat_1.html#K9" title="CONLAT_1:func.9">B-meet</a> <font color="Maroon" title="c1">C</font></span>)</span> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<font color="Maroon" title="c15">a</font>,<font color="Maroon" title="c16">b</font>)</span>)</span>,<font color="Maroon" title="c11">c</font>)
<span class="kw">by</span> <span class="lab"><a class="ref" href="lattices.html#D2" title="LATTICES:def.2">LATTICES:def 2</a></span>
;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c17">a</font> = <font color="Maroon" title="c15">a</font>, <font color="Maroon" title="c18">b</font> = <font color="Maroon" title="c16">b</font>, <font color="Maroon" title="c19">c</font> = <font color="Maroon" title="c11">c</font> as   <a href="conlat_1.html#V4" title="CONLAT_1:attr.4">strict</a>  <a href="conlat_1.html#NM4" title="CONLAT_1:NM.4">FormalConcept</a> of <font color="Maroon" title="c1">C</font> <span class="kw">by</span> <span class="lab"><a class="ref" href="conlat_1.html#T31" target="_self" title="CONLAT_1:th.31">Th35</a></span>;<br/>
<a NAME="E10:84_3"/>
<span class="p1">(<span class="default"><a href="conlat_1.html#K9" title="CONLAT_1:func.9">B-meet</a> <font color="Maroon" title="c1">C</font></span>)</span> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<font color="Maroon" title="c17">a</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="conlat_1.html#K9" title="CONLAT_1:func.9">B-meet</a> <font color="Maroon" title="c1">C</font></span>)</span> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<font color="Maroon" title="c18">b</font>,<font color="Maroon" title="c19">c</font>)</span>)</span>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="conlat_1.html#K9" title="CONLAT_1:func.9">B-meet</a> <font color="Maroon" title="c1">C</font></span>)</span> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="conlat_1.html#K9" title="CONLAT_1:func.9">B-meet</a> <font color="Maroon" title="c1">C</font></span>)</span> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<font color="Maroon" title="c17">a</font>,<font color="Maroon" title="c18">b</font>)</span>)</span>,<font color="Maroon" title="c19">c</font>)
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="conlat_1.html#T34" target="_self" title="CONLAT_1:th.34">Th38</a></span>;<br/>
<span class="kw">hence </span><a NAME="E11:84_3"/>
<font color="Maroon" title="c4">a</font> <a href="lattices.html#K2" title="LATTICES:func.2">"/\"</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">b</font> <a href="lattices.html#K2" title="LATTICES:func.2">"/\"</a> <font color="Maroon" title="c6">c</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">a</font> <a href="lattices.html#K2" title="LATTICES:func.2">"/\"</a> <font color="Maroon" title="c5">b</font></span>)</span> <a href="lattices.html#K2" title="LATTICES:func.2">"/\"</a> <font color="Maroon" title="c6">c</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:84_3"><span class="lab"><font color="Green" title="E50">A7</font></span></a>, <a class="txt" href="#E8:84_3"><span class="lab"><font color="Green" title="E51">A8</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="E5:84"/><span class="lab"><font color="Green" title="E50">A9</font></span>: 
 for <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c3">L</font> holds  <font color="Olive" title="b1">a</font> <a href="lattices.html#K2" title="LATTICES:func.2">"/\"</a> <font color="Olive" title="b2">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">b</font> <a href="lattices.html#K2" title="LATTICES:func.2">"/\"</a> <font color="Olive" title="b1">a</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="84_4"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><font color="Maroon" title="c4">a</font>, <font color="Maroon" title="c5">b</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c3">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="c4">a</font> <a href="lattices.html#K2" title="LATTICES:func.2">"/\"</a> <font color="Maroon" title="c5">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">b</font> <a href="lattices.html#K2" title="LATTICES:func.2">"/\"</a> <font color="Maroon" title="c4">a</font></span><br/>

<a NAME="E1:84_4"/><span class="lab"><font color="Green" title="E51">A10</font></span>: 
<font color="Maroon" title="c5">b</font> <a href="lattices.html#K2" title="LATTICES:func.2">"/\"</a> <font color="Maroon" title="c4">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="conlat_1.html#K9" title="CONLAT_1:func.9">B-meet</a> <font color="Maroon" title="c1">C</font></span>)</span> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<font color="Maroon" title="c5">b</font>,<font color="Maroon" title="c4">a</font>)
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="lattices.html#D2" title="LATTICES:def.2">LATTICES:def 2</a></span>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c6">a</font> = <font color="Maroon" title="c4">a</font>, <font color="Maroon" title="c7">b</font> = <font color="Maroon" title="c5">b</font> as   <a href="conlat_1.html#V4" title="CONLAT_1:attr.4">strict</a>  <a href="conlat_1.html#NM4" title="CONLAT_1:NM.4">FormalConcept</a> of <font color="Maroon" title="c1">C</font> <span class="kw">by</span> <span class="lab"><a class="ref" href="conlat_1.html#T31" target="_self" title="CONLAT_1:th.31">Th35</a></span>;<br/>
<a NAME="E3:84_4"/>
<span class="p1">(<span class="default"><a href="conlat_1.html#K9" title="CONLAT_1:func.9">B-meet</a> <font color="Maroon" title="c1">C</font></span>)</span> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c7">b</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="conlat_1.html#K9" title="CONLAT_1:func.9">B-meet</a> <font color="Maroon" title="c1">C</font></span>)</span> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<font color="Maroon" title="c7">b</font>,<font color="Maroon" title="c6">a</font>)
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="conlat_1.html#T32" target="_self" title="CONLAT_1:th.32">Th36</a></span>;<br/>
<span class="kw">hence </span><a NAME="E4:84_4"/>
<font color="Maroon" title="c4">a</font> <a href="lattices.html#K2" title="LATTICES:func.2">"/\"</a> <font color="Maroon" title="c5">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">b</font> <a href="lattices.html#K2" title="LATTICES:func.2">"/\"</a> <font color="Maroon" title="c4">a</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:84_4"><span class="lab"><font color="Green" title="E51">A10</font></span></a>, <a class="ref" href="lattices.html#D2" title="LATTICES:def.2">LATTICES:def 2</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="E6:84"/><span class="lab"><font color="Green" title="E51">A11</font></span>: 
 for <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c3">L</font> holds  <font color="Olive" title="b1">a</font> <a href="lattices.html#K2" title="LATTICES:func.2">"/\"</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">a</font> <a href="lattices.html#K1" title="LATTICES:func.1">"\/"</a> <font color="Olive" title="b2">b</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">a</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="84_5"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><font color="Maroon" title="c4">a</font>, <font color="Maroon" title="c5">b</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c3">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="c4">a</font> <a href="lattices.html#K2" title="LATTICES:func.2">"/\"</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">a</font> <a href="lattices.html#K1" title="LATTICES:func.1">"\/"</a> <font color="Maroon" title="c5">b</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">a</font></span><br/>

<span class="kw">reconsider </span><font color="Maroon" title="c6">a</font> = <font color="Maroon" title="c4">a</font>, <font color="Maroon" title="c7">b</font> = <font color="Maroon" title="c5">b</font> as    <a href="conlat_1.html#M2" title="CONLAT_1:mode.2">Element</a> of  <a href="conlat_1.html#K8" title="CONLAT_1:func.8">B-carrier</a> <font color="Maroon" title="c1">C</font> ;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c8">d</font> = <span class="p1">(<span class="default"><a href="conlat_1.html#K10" title="CONLAT_1:func.10">B-join</a> <font color="Maroon" title="c1">C</font></span>)</span> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> (<font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c7">b</font>) as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c3">L</font> ;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c9">a</font> = <font color="Maroon" title="c6">a</font>, <font color="Maroon" title="c10">b</font> = <font color="Maroon" title="c7">b</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c3">L</font> ;<br/>
<span class="lab"><font color="Green" title="E52">A12</font></span>: <font color="Maroon" title="c9">a</font> <a href="lattices.html#K2" title="LATTICES:func.2">"/\"</a> <span class="p1">(<span class="default"><font color="Maroon" title="c9">a</font> <a href="lattices.html#K1" title="LATTICES:func.1">"\/"</a> <font color="Maroon" title="c10">b</font></span>)</span> = 
<font color="Maroon" title="c9">a</font> <a href="lattices.html#K2" title="LATTICES:func.2">"/\"</a> <font color="Maroon" title="c8">d</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="lattices.html#D1" title="LATTICES:def.1">LATTICES:def 1</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="conlat_1.html#K9" title="CONLAT_1:func.9">B-meet</a> <font color="Maroon" title="c1">C</font></span>)</span> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<font color="Maroon" title="c9">a</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="conlat_1.html#K10" title="CONLAT_1:func.10">B-join</a> <font color="Maroon" title="c1">C</font></span>)</span> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<font color="Maroon" title="c9">a</font>,<font color="Maroon" title="c10">b</font>)</span>)</span>)
<span class="kw">by</span> <span class="lab"><a class="ref" href="lattices.html#D2" title="LATTICES:def.2">LATTICES:def 2</a></span>
;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c11">a</font> = <font color="Maroon" title="c9">a</font>, <font color="Maroon" title="c12">b</font> = <font color="Maroon" title="c10">b</font> as   <a href="conlat_1.html#V4" title="CONLAT_1:attr.4">strict</a>  <a href="conlat_1.html#NM4" title="CONLAT_1:NM.4">FormalConcept</a> of <font color="Maroon" title="c1">C</font> <span class="kw">by</span> <span class="lab"><a class="ref" href="conlat_1.html#T31" target="_self" title="CONLAT_1:th.31">Th35</a></span>;<br/>
<a NAME="E6:84_5"/>
<span class="p1">(<span class="default"><a href="conlat_1.html#K9" title="CONLAT_1:func.9">B-meet</a> <font color="Maroon" title="c1">C</font></span>)</span> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<font color="Maroon" title="c11">a</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="conlat_1.html#K10" title="CONLAT_1:func.10">B-join</a> <font color="Maroon" title="c1">C</font></span>)</span> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<font color="Maroon" title="c11">a</font>,<font color="Maroon" title="c12">b</font>)</span>)</span>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c11">a</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="conlat_1.html#T37" target="_self" title="CONLAT_1:th.37">Th41</a></span>;<br/>
<span class="kw">hence </span><a NAME="E7:84_5"/>
<font color="Maroon" title="c4">a</font> <a href="lattices.html#K2" title="LATTICES:func.2">"/\"</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">a</font> <a href="lattices.html#K1" title="LATTICES:func.1">"\/"</a> <font color="Maroon" title="c5">b</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">a</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:84_5"><span class="lab"><font color="Green" title="E52">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="E7:84"/>
 for <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c3">L</font> holds  <font color="Olive" title="b1">a</font> <a href="lattices.html#K1" title="LATTICES:func.1">"\/"</a> <font color="Olive" title="b2">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">b</font> <a href="lattices.html#K1" title="LATTICES:func.1">"\/"</a> <font color="Olive" title="b1">a</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="84_6"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><font color="Maroon" title="c4">a</font>, <font color="Maroon" title="c5">b</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c3">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="c4">a</font> <a href="lattices.html#K1" title="LATTICES:func.1">"\/"</a> <font color="Maroon" title="c5">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">b</font> <a href="lattices.html#K1" title="LATTICES:func.1">"\/"</a> <font color="Maroon" title="c4">a</font></span><br/>

<a NAME="E1:84_6"/><span class="lab"><font color="Green" title="E52">A13</font></span>: 
<font color="Maroon" title="c5">b</font> <a href="lattices.html#K1" title="LATTICES:func.1">"\/"</a> <font color="Maroon" title="c4">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="conlat_1.html#K10" title="CONLAT_1:func.10">B-join</a> <font color="Maroon" title="c1">C</font></span>)</span> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<font color="Maroon" title="c5">b</font>,<font color="Maroon" title="c4">a</font>)
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="lattices.html#D1" title="LATTICES:def.1">LATTICES:def 1</a></span>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c6">a</font> = <font color="Maroon" title="c4">a</font>, <font color="Maroon" title="c7">b</font> = <font color="Maroon" title="c5">b</font> as   <a href="conlat_1.html#V4" title="CONLAT_1:attr.4">strict</a>  <a href="conlat_1.html#NM4" title="CONLAT_1:NM.4">FormalConcept</a> of <font color="Maroon" title="c1">C</font> <span class="kw">by</span> <span class="lab"><a class="ref" href="conlat_1.html#T31" target="_self" title="CONLAT_1:th.31">Th35</a></span>;<br/>
<a NAME="E3:84_6"/>
<span class="p1">(<span class="default"><a href="conlat_1.html#K10" title="CONLAT_1:func.10">B-join</a> <font color="Maroon" title="c1">C</font></span>)</span> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c7">b</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="conlat_1.html#K10" title="CONLAT_1:func.10">B-join</a> <font color="Maroon" title="c1">C</font></span>)</span> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<font color="Maroon" title="c7">b</font>,<font color="Maroon" title="c6">a</font>)
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="conlat_1.html#T33" target="_self" title="CONLAT_1:th.33">Th37</a></span>;<br/>
<span class="kw">hence </span><a NAME="E4:84_6"/>
<font color="Maroon" title="c4">a</font> <a href="lattices.html#K1" title="LATTICES:func.1">"\/"</a> <font color="Maroon" title="c5">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">b</font> <a href="lattices.html#K1" title="LATTICES:func.1">"\/"</a> <font color="Maroon" title="c4">a</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:84_6"><span class="lab"><font color="Green" title="E52">A13</font></span></a>, <a class="ref" href="lattices.html#D1" title="LATTICES:def.1">LATTICES: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="E8:84"/><span class="kw">then </span>
( <font color="Maroon" title="c3">L</font> is  <a href="lattices.html#V4" title="LATTICES:attr.4">join-commutative</a>  &amp; <font color="Maroon" title="c3">L</font> is  <a href="lattices.html#V5" title="LATTICES:attr.5">join-associative</a>  &amp; <font color="Maroon" title="c3">L</font> is  <a href="lattices.html#V8" title="LATTICES:attr.8">meet-absorbing</a>  &amp; <font color="Maroon" title="c3">L</font> is  <a href="lattices.html#V6" title="LATTICES:attr.6">meet-commutative</a>  &amp; <font color="Maroon" title="c3">L</font> is  <a href="lattices.html#V7" title="LATTICES:attr.7">meet-associative</a>  &amp; <font color="Maroon" title="c3">L</font> is  <a href="lattices.html#V9" title="LATTICES:attr.9">join-absorbing</a>  )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:84"><span class="lab"><font color="Green" title="E47">A1</font></span></a>, <a class="txt" href="#E3:84"><span class="lab"><font color="Green" title="E48">A4</font></span></a>, <a class="txt" href="#E5:84"><span class="lab"><font color="Green" title="E50">A9</font></span></a>, <a class="txt" href="#E4:84"><span class="lab"><font color="Green" title="E49">A6</font></span></a>, <a class="txt" href="#E6:84"><span class="lab"><font color="Green" title="E51">A11</font></span></a>, <a class="ref" href="lattices.html#D4" title="LATTICES:def.4">LATTICES:def 4</a>, <a class="ref" href="lattices.html#D5" title="LATTICES:def.5">LATTICES:def 5</a>, <a class="ref" href="lattices.html#D6" title="LATTICES:def.6">LATTICES:def 6</a>, <a class="ref" href="lattices.html#D7" title="LATTICES:def.7">LATTICES:def 7</a>, <a class="ref" href="lattices.html#D8" title="LATTICES:def.8">LATTICES:def 8</a>, <a class="ref" href="lattices.html#D9" title="LATTICES:def.9">LATTICES:def 9</a></span>;<br/>
<span class="kw">hence </span><a NAME="E9:84"/>
 <a href="conlat_1.html#K11" title="CONLAT_1:func.11">ConceptLattice</a> <font color="Maroon" title="c1">C</font> is   <a href="lattices.html#NM1" title="LATTICES:NM.1">Lattice</a>
 ; <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>
