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

<b>let </b><font color="Maroon" title="c1">C</font> be   <a href="conlat_1.html#NM1" title="CONLAT_1:NM.1">FormalContext</a>;<br/>

<b>set </b><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/>
<b>reconsider </b><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="E2:86"/><i><font color="Green" title="E49">A1</font></i>: 
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="86_1"><b>proof </b></a><div class="add">

<b>let </b><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>;<br/>

<a NAME="E1:86_1"/><i><font color="Green" title="E50">A2</font></i>: 
<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>
 
<b>by </b><i><a class="ref" href="lattices.html#D1" title="LATTICES:def.1">LATTICES:def 1</a></i>;<br/>
<b>reconsider </b><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#V6" title="CONLAT_1:attr.6">strict</a> <a href="conlat_1.html#NM4" title="CONLAT_1:NM.4">FormalConcept</a> of <font color="Maroon" title="c1">C</font> <b>by </b><i><a class="ref" href="conlat_1.html#T35" target="_self" title="CONLAT_1:th.35">Th35</a></i>;<br/>
<a NAME="E3:86_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="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>
 
<b>by </b><i><a class="ref" href="conlat_1.html#T37" target="_self" title="CONLAT_1:th.37">Th37</a></i>;<br/>
<b>hence </b><a NAME="E4:86_1"/>
<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>
 <b>by </b><i><a class="txt" href="conlat_1.html#E1:86_1"><i><font color="Green" title="E50">A2</font></i></a>, <a class="ref" href="lattices.html#D1" title="LATTICES:def.1">LATTICES:def 1</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E3:86"/><i><font color="Green" title="E50">A3</font></i>: 
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="86_2"><b>proof </b></a><div class="add">

<b>let </b><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>;<br/>

<b>reconsider </b><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/>
<b>reconsider </b><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/>
<b>reconsider </b><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/>
<b>reconsider </b><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/>
<b>reconsider </b><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/>
<b>reconsider </b><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/>
<i><font color="Green" title="E51">A4</font></i>: <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>
<b>by </b><i><a class="ref" href="lattices.html#D1" title="LATTICES:def.1">LATTICES:def 1</a></i>
<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>
<b>by </b><i><a class="ref" href="lattices.html#D1" title="LATTICES:def.1">LATTICES:def 1</a></i>
;<br/>
<i><font color="Green" title="E52">A5</font></i>: <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>
<b>by </b><i><a class="ref" href="lattices.html#D1" title="LATTICES:def.1">LATTICES:def 1</a></i>
<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>
<b>by </b><i><a class="ref" href="lattices.html#D1" title="LATTICES:def.1">LATTICES:def 1</a></i>
;<br/>
<b>reconsider </b><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#V6" title="CONLAT_1:attr.6">strict</a> <a href="conlat_1.html#NM4" title="CONLAT_1:NM.4">FormalConcept</a> of <font color="Maroon" title="c1">C</font> <b>by </b><i><a class="ref" href="conlat_1.html#T35" target="_self" title="CONLAT_1:th.35">Th35</a></i>;<br/>
<a NAME="E10:86_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> <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>
 
<b>by </b><i><a class="ref" href="conlat_1.html#T39" target="_self" title="CONLAT_1:th.39">Th39</a></i>;<br/>
<b>hence </b><a NAME="E11:86_2"/>
<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>
 <b>by </b><i><a class="txt" href="conlat_1.html#E7:86_2"><i><font color="Green" title="E51">A4</font></i></a>, <a class="txt" href="conlat_1.html#E8:86_2"><i><font color="Green" title="E52">A5</font></i></a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E4:86"/><i><font color="Green" title="E51">A6</font></i>: 
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="86_3"><b>proof </b></a><div class="add">

<b>let </b><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>;<br/>

<b>reconsider </b><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/>
<b>reconsider </b><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/>
<b>reconsider </b><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/>
<i><font color="Green" title="E52">A7</font></i>: <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>
<b>by </b><i><a class="ref" href="lattices.html#D2" title="LATTICES:def.2">LATTICES:def 2</a></i>
<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>
<b>by </b><i><a class="ref" href="lattices.html#D1" title="LATTICES:def.1">LATTICES:def 1</a></i>
;<br/>
<b>reconsider </b><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#V6" title="CONLAT_1:attr.6">strict</a> <a href="conlat_1.html#NM4" title="CONLAT_1:NM.4">FormalConcept</a> of <font color="Maroon" title="c1">C</font> <b>by </b><i><a class="ref" href="conlat_1.html#T35" target="_self" title="CONLAT_1:th.35">Th35</a></i>;<br/>
<a NAME="E6:86_3"/>
<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>
 
<b>by </b><i><a class="ref" href="conlat_1.html#T40" target="_self" title="CONLAT_1:th.40">Th40</a></i>;<br/>
<b>hence </b><a NAME="E7:86_3"/>
<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>
 <b>by </b><i><a class="txt" href="conlat_1.html#E4:86_3"><i><font color="Green" title="E52">A7</font></i></a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E5:86"/><i><font color="Green" title="E52">A8</font></i>: 
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="86_4"><b>proof </b></a><div class="add">

<b>let </b><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>;<br/>

<a NAME="E1:86_4"/><i><font color="Green" title="E53">A9</font></i>: 
<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>
 
<b>by </b><i><a class="ref" href="lattices.html#D2" title="LATTICES:def.2">LATTICES:def 2</a></i>;<br/>
<b>reconsider </b><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#V6" title="CONLAT_1:attr.6">strict</a> <a href="conlat_1.html#NM4" title="CONLAT_1:NM.4">FormalConcept</a> of <font color="Maroon" title="c1">C</font> <b>by </b><i><a class="ref" href="conlat_1.html#T35" target="_self" title="CONLAT_1:th.35">Th35</a></i>;<br/>
<a NAME="E3:86_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>
 
<b>by </b><i><a class="ref" href="conlat_1.html#T36" target="_self" title="CONLAT_1:th.36">Th36</a></i>;<br/>
<b>hence </b><a NAME="E4:86_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>
 <b>by </b><i><a class="txt" href="conlat_1.html#E1:86_4"><i><font color="Green" title="E53">A9</font></i></a>, <a class="ref" href="lattices.html#D2" title="LATTICES:def.2">LATTICES:def 2</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E6:86"/><i><font color="Green" title="E53">A10</font></i>: 
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="86_5"><b>proof </b></a><div class="add">

<b>let </b><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>;<br/>

<b>reconsider </b><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/>
<b>reconsider </b><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/>
<b>reconsider </b><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/>
<i><font color="Green" title="E54">A11</font></i>: <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>
<b>by </b><i><a class="ref" href="lattices.html#D2" title="LATTICES:def.2">LATTICES:def 2</a></i>
<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>
<b>by </b><i><a class="ref" href="lattices.html#D2" title="LATTICES:def.2">LATTICES:def 2</a></i>
;<br/>
<b>reconsider </b><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/>
<b>reconsider </b><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/>
<b>reconsider </b><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/>
<i><font color="Green" title="E55">A12</font></i>: <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>
<b>by </b><i><a class="ref" href="lattices.html#D2" title="LATTICES:def.2">LATTICES:def 2</a></i>
<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>
<b>by </b><i><a class="ref" href="lattices.html#D2" title="LATTICES:def.2">LATTICES:def 2</a></i>
;<br/>
<b>reconsider </b><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#V6" title="CONLAT_1:attr.6">strict</a> <a href="conlat_1.html#NM4" title="CONLAT_1:NM.4">FormalConcept</a> of <font color="Maroon" title="c1">C</font> <b>by </b><i><a class="ref" href="conlat_1.html#T35" target="_self" title="CONLAT_1:th.35">Th35</a></i>;<br/>
<a NAME="E10:86_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="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>
 
<b>by </b><i><a class="ref" href="conlat_1.html#T38" target="_self" title="CONLAT_1:th.38">Th38</a></i>;<br/>
<b>hence </b><a NAME="E11:86_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="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>
 <b>by </b><i><a class="txt" href="conlat_1.html#E4:86_5"><i><font color="Green" title="E54">A11</font></i></a>, <a class="txt" href="conlat_1.html#E8:86_5"><i><font color="Green" title="E55">A12</font></i></a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E7:86"/>
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="86_6"><b>proof </b></a><div class="add">

<b>let </b><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>;<br/>

<b>reconsider </b><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/>
<b>reconsider </b><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/>
<b>reconsider </b><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/>
<i><font color="Green" title="E54">A13</font></i>: <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>
<b>by </b><i><a class="ref" href="lattices.html#D1" title="LATTICES:def.1">LATTICES:def 1</a></i>
<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>
<b>by </b><i><a class="ref" href="lattices.html#D2" title="LATTICES:def.2">LATTICES:def 2</a></i>
;<br/>
<b>reconsider </b><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#V6" title="CONLAT_1:attr.6">strict</a> <a href="conlat_1.html#NM4" title="CONLAT_1:NM.4">FormalConcept</a> of <font color="Maroon" title="c1">C</font> <b>by </b><i><a class="ref" href="conlat_1.html#T35" target="_self" title="CONLAT_1:th.35">Th35</a></i>;<br/>
<a NAME="E6:86_6"/>
<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>
 
<b>by </b><i><a class="ref" href="conlat_1.html#T41" target="_self" title="CONLAT_1:th.41">Th41</a></i>;<br/>
<b>hence </b><a NAME="E7:86_6"/>
<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>
 <b>by </b><i><a class="txt" href="conlat_1.html#E4:86_6"><i><font color="Green" title="E54">A13</font></i></a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E8:86"/><b>then </b>
( <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> )
 
<b>by </b><i><a class="txt" href="conlat_1.html#E2:86"><i><font color="Green" title="E49">A1</font></i></a>, <a class="txt" href="conlat_1.html#E3:86"><i><font color="Green" title="E50">A3</font></i></a>, <a class="txt" href="conlat_1.html#E4:86"><i><font color="Green" title="E51">A6</font></i></a>, <a class="txt" href="conlat_1.html#E5:86"><i><font color="Green" title="E52">A8</font></i></a>, <a class="txt" href="conlat_1.html#E6:86"><i><font color="Green" title="E53">A10</font></i></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></i>;<br/>
<b>hence </b><a NAME="E9:86"/>
 <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>
 <b>by </b><i><a class="ref" href="lattices.html#D10" title="LATTICES:def.10">LATTICES:def 10</a></i>;<br/>


</div>
