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

<i><font color="Green">E1</font></i>: <span class="p1">(<span class="default"><a href="conlat_2.html#K1" target="_self">@</a> <span class="p2">(<span class="default"><a href="conlat_1.html#K6">Concept-with-all-Attributes</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="conlat_1.html#K12">@</a>  = 
 <a href="conlat_2.html#K1" target="_self">@</a> <span class="p1">(<span class="default"><a href="conlat_1.html#K6">Concept-with-all-Attributes</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="conlat_1.html#D24">CONLAT_1:def 24</a></i>
<br/>.= 
 <a href="conlat_1.html#K6">Concept-with-all-Attributes</a> <font color="Maroon">c<sub>1</sub></font>

;<br/>
<a NAME="E2:2_1_1"/><i><font color="Green">E2</font></i>: 
for <font color="Olive">b<sub>1</sub></font> being  <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="conlat_1.html#K11">ConceptLattice</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> holds  <a href="conlat_2.html#K1" target="_self">@</a> <span class="p1">(<span class="default"><a href="conlat_1.html#K6">Concept-with-all-Attributes</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="lattices.html#R3">[=</a> <font color="Olive">b<sub>1</sub></font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="2_1_1_2"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">c<sub>2</sub></font> be   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="conlat_1.html#K11">ConceptLattice</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>;<br/>

<a NAME="E1:2_1_1_2"/>
<span class="p1">(<span class="default"><a href="conlat_2.html#K1" target="_self">@</a> <span class="p2">(<span class="default"><a href="conlat_1.html#K6">Concept-with-all-Attributes</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="conlat_1.html#K12">@</a>  <a href="conlat_1.html#R2">is-SubConcept-of</a> <font color="Maroon">c<sub>2</sub></font> <a href="conlat_1.html#K12">@</a> 
 
<b>by </b><i><a class="txt" href="conlat_2.html#E1:2_1_1"><i><font color="Green">E1</font></i></a>, <a class="ref" href="conlat_1.html#T34">CONLAT_1:34</a></i>;<br/>
<b>hence </b><a NAME="E2:2_1_1_2"/>
 <a href="conlat_2.html#K1" target="_self">@</a> <span class="p1">(<span class="default"><a href="conlat_1.html#K6">Concept-with-all-Attributes</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="lattices.html#R3">[=</a> <font color="Maroon">c<sub>2</sub></font>
 <b>by </b><i><a class="ref" href="conlat_1.html#T47">CONLAT_1:47</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E3:2_1_1"/>
for <font color="Olive">b<sub>1</sub></font> being  <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="conlat_1.html#K11">ConceptLattice</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> holds <br/>( <span class="p1">(<span class="default"><a href="conlat_2.html#K1" target="_self">@</a> <span class="p2">(<span class="default"><a href="conlat_1.html#K6">Concept-with-all-Attributes</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="lattices.html#K4">"/\"</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a>  <a href="conlat_2.html#K1" target="_self">@</a> <span class="p1">(<span class="default"><a href="conlat_1.html#K6">Concept-with-all-Attributes</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> &amp; <font color="Olive">b<sub>1</sub></font> <a href="lattices.html#K4">"/\"</a> <span class="p1">(<span class="default"><a href="conlat_2.html#K1" target="_self">@</a> <span class="p2">(<span class="default"><a href="conlat_1.html#K6">Concept-with-all-Attributes</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="conlat_2.html#K1" target="_self">@</a> <span class="p1">(<span class="default"><a href="conlat_1.html#K6">Concept-with-all-Attributes</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> )
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="2_1_1_3"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">c<sub>2</sub></font> be   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="conlat_1.html#K11">ConceptLattice</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>;<br/>

<a NAME="E1:2_1_1_3"/>
 <a href="conlat_2.html#K1" target="_self">@</a> <span class="p1">(<span class="default"><a href="conlat_1.html#K6">Concept-with-all-Attributes</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="lattices.html#R3">[=</a> <font color="Maroon">c<sub>2</sub></font>
 
<b>by </b><i><a class="txt" href="conlat_2.html#E2:2_1_1"><i><font color="Green">E2</font></i></a></i>;<br/>
<b>hence </b><a NAME="E2:2_1_1_3"/>
( <span class="p1">(<span class="default"><a href="conlat_2.html#K1" target="_self">@</a> <span class="p2">(<span class="default"><a href="conlat_1.html#K6">Concept-with-all-Attributes</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="lattices.html#K4">"/\"</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a>  <a href="conlat_2.html#K1" target="_self">@</a> <span class="p1">(<span class="default"><a href="conlat_1.html#K6">Concept-with-all-Attributes</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> &amp; <font color="Maroon">c<sub>2</sub></font> <a href="lattices.html#K4">"/\"</a> <span class="p1">(<span class="default"><a href="conlat_2.html#K1" target="_self">@</a> <span class="p2">(<span class="default"><a href="conlat_1.html#K6">Concept-with-all-Attributes</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="conlat_2.html#K1" target="_self">@</a> <span class="p1">(<span class="default"><a href="conlat_1.html#K6">Concept-with-all-Attributes</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> )
 <b>by </b><i><a class="ref" href="lattices.html#T21">LATTICES:21</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E4:2_1_1"/><b>then </b><i><font color="Green">E3</font></i>: 
 <a href="conlat_1.html#K11">ConceptLattice</a> <font color="Maroon">c<sub>1</sub></font> is <a href="lattices.html#V13">lower-bounded</a>
 
<b>by </b><i><a class="ref" href="lattices.html#D13">LATTICES:def 13</a></i>;<br/>
<i><font color="Green">E4</font></i>: <span class="p1">(<span class="default"><a href="conlat_2.html#K1" target="_self">@</a> <span class="p2">(<span class="default"><a href="conlat_1.html#K5">Concept-with-all-Objects</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="conlat_1.html#K12">@</a>  = 
 <a href="conlat_2.html#K1" target="_self">@</a> <span class="p1">(<span class="default"><a href="conlat_1.html#K5">Concept-with-all-Objects</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="conlat_1.html#D24">CONLAT_1:def 24</a></i>
<br/>.= 
 <a href="conlat_1.html#K5">Concept-with-all-Objects</a> <font color="Maroon">c<sub>1</sub></font>

;<br/>
<a NAME="E6:2_1_1"/><i><font color="Green">E5</font></i>: 
for <font color="Olive">b<sub>1</sub></font> being  <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="conlat_1.html#K11">ConceptLattice</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> holds <font color="Olive">b<sub>1</sub></font> <a href="lattices.html#R3">[=</a>  <a href="conlat_2.html#K1" target="_self">@</a> <span class="p1">(<span class="default"><a href="conlat_1.html#K5">Concept-with-all-Objects</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="2_1_1_5"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">c<sub>2</sub></font> be   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="conlat_1.html#K11">ConceptLattice</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>;<br/>

<a NAME="E1:2_1_1_5"/>
<font color="Maroon">c<sub>2</sub></font> <a href="conlat_1.html#K12">@</a>  <a href="conlat_1.html#R2">is-SubConcept-of</a> <span class="p1">(<span class="default"><a href="conlat_2.html#K1" target="_self">@</a> <span class="p2">(<span class="default"><a href="conlat_1.html#K5">Concept-with-all-Objects</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="conlat_1.html#K12">@</a> 
 
<b>by </b><i><a class="txt" href="conlat_2.html#E5:2_1_1"><i><font color="Green">E4</font></i></a>, <a class="ref" href="conlat_1.html#T34">CONLAT_1:34</a></i>;<br/>
<b>hence </b><a NAME="E2:2_1_1_5"/>
<font color="Maroon">c<sub>2</sub></font> <a href="lattices.html#R3">[=</a>  <a href="conlat_2.html#K1" target="_self">@</a> <span class="p1">(<span class="default"><a href="conlat_1.html#K5">Concept-with-all-Objects</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>
 <b>by </b><i><a class="ref" href="conlat_1.html#T47">CONLAT_1:47</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E7:2_1_1"/>
for <font color="Olive">b<sub>1</sub></font> being  <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="conlat_1.html#K11">ConceptLattice</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> holds <br/>( <span class="p1">(<span class="default"><a href="conlat_2.html#K1" target="_self">@</a> <span class="p2">(<span class="default"><a href="conlat_1.html#K5">Concept-with-all-Objects</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="lattices.html#K3">"\/"</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a>  <a href="conlat_2.html#K1" target="_self">@</a> <span class="p1">(<span class="default"><a href="conlat_1.html#K5">Concept-with-all-Objects</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> &amp; <font color="Olive">b<sub>1</sub></font> <a href="lattices.html#K3">"\/"</a> <span class="p1">(<span class="default"><a href="conlat_2.html#K1" target="_self">@</a> <span class="p2">(<span class="default"><a href="conlat_1.html#K5">Concept-with-all-Objects</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="conlat_2.html#K1" target="_self">@</a> <span class="p1">(<span class="default"><a href="conlat_1.html#K5">Concept-with-all-Objects</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> )
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="2_1_1_6"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">c<sub>2</sub></font> be   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="conlat_1.html#K11">ConceptLattice</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>;<br/>

<a NAME="E1:2_1_1_6"/>
<font color="Maroon">c<sub>2</sub></font> <a href="lattices.html#R3">[=</a>  <a href="conlat_2.html#K1" target="_self">@</a> <span class="p1">(<span class="default"><a href="conlat_1.html#K5">Concept-with-all-Objects</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>
 
<b>by </b><i><a class="txt" href="conlat_2.html#E6:2_1_1"><i><font color="Green">E5</font></i></a></i>;<br/>
<b>hence </b><a NAME="E2:2_1_1_6"/>
( <span class="p1">(<span class="default"><a href="conlat_2.html#K1" target="_self">@</a> <span class="p2">(<span class="default"><a href="conlat_1.html#K5">Concept-with-all-Objects</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="lattices.html#K3">"\/"</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a>  <a href="conlat_2.html#K1" target="_self">@</a> <span class="p1">(<span class="default"><a href="conlat_1.html#K5">Concept-with-all-Objects</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> &amp; <font color="Maroon">c<sub>2</sub></font> <a href="lattices.html#K3">"\/"</a> <span class="p1">(<span class="default"><a href="conlat_2.html#K1" target="_self">@</a> <span class="p2">(<span class="default"><a href="conlat_1.html#K5">Concept-with-all-Objects</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="conlat_2.html#K1" target="_self">@</a> <span class="p1">(<span class="default"><a href="conlat_1.html#K5">Concept-with-all-Objects</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> )
 <b>by </b><i><a class="ref" href="lattices.html#D3">LATTICES:def 3</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E8:2_1_1"/><b>then </b>
 <a href="conlat_1.html#K11">ConceptLattice</a> <font color="Maroon">c<sub>1</sub></font> is <a href="lattices.html#V14">upper-bounded</a>
 
<b>by </b><i><a class="ref" href="lattices.html#D14">LATTICES:def 14</a></i>;<br/>
<b>hence </b><a NAME="E9:2_1_1"/>
 <a href="conlat_1.html#K11">ConceptLattice</a> <font color="Maroon">c<sub>1</sub></font> is <a href="lattices.html#V15">bounded</a>
 <b>by </b><i><a class="txt" href="conlat_2.html#E4:2_1_1"><i><font color="Green">E3</font></i></a>, <a class="ref" href="lattices.html#D15">LATTICES:def 15</a></i>;<br/>


</div>
