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

<b>let </b><font color="Maroon">c<sub>1</sub></font> be   <a href="conlat_1.html#NM1">FormalContext</a>;<br/>

<a NAME="E1:91"/>
for <font color="Olive">b<sub>1</sub></font> being  <a href="struct_0.html#NM2">Subset</a> of <span class="p1">(<span class="default"><a href="conlat_1.html#K11" target="_self">ConceptLattice</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>ex <font color="Olive">b<sub>2</sub></font> being  <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="conlat_1.html#K11" target="_self">ConceptLattice</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> st <br/>( <font color="Olive">b<sub>2</sub></font> <a href="lattice3.html#R3">is_less_than</a> <font color="Olive">b<sub>1</sub></font> &amp; ( for <font color="Olive">b<sub>3</sub></font> being  <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="conlat_1.html#K11" target="_self">ConceptLattice</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> st <font color="Olive">b<sub>3</sub></font> <a href="lattice3.html#R3">is_less_than</a> <font color="Olive">b<sub>1</sub></font> holds <br/><font color="Olive">b<sub>3</sub></font> <a href="lattices.html#R3">[=</a> <font color="Olive">b<sub>2</sub></font> ) )
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="91_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">c<sub>2</sub></font> be   <a href="struct_0.html#NM2">Subset</a> of <span class="p1">(<span class="default"><a href="conlat_1.html#K11" target="_self">ConceptLattice</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>;<br/>

<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="91_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:91_1_1"/>
( <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a>  or <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a>  )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="91_1_1_1"><b>suppose </b></a><a NAME="E1:91_1_1_1"/>
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a> 
 ;<br/><div class="add"><a NAME="E2:91_1_1_1"/><b>then </b>
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" target="_self">ConceptLattice</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> st <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>2</sub></font> holds <br/> <a href="lattices.html#K6">Top</a> <span class="p1">(<span class="default"><a href="conlat_1.html#K11" target="_self">ConceptLattice</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>
 ;<br/><a NAME="E3:91_1_1_1"/><b>then </b><i><font color="Green">E51</font></i>: 
 <a href="lattices.html#K6">Top</a> <span class="p1">(<span class="default"><a href="conlat_1.html#K11" target="_self">ConceptLattice</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="lattice3.html#R3">is_less_than</a> <font color="Maroon">c<sub>2</sub></font>
 <b>by </b><i><a class="ref" href="lattice3.html#D16">LATTICE3:def 16</a></i>;<br/><a NAME="E4:91_1_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" target="_self">ConceptLattice</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> st <font color="Olive">b<sub>1</sub></font> <a href="lattice3.html#R3">is_less_than</a> <font color="Maroon">c<sub>2</sub></font> holds <br/><font color="Olive">b<sub>1</sub></font> <a href="lattices.html#R3">[=</a>  <a href="lattices.html#K6">Top</a> <span class="p1">(<span class="default"><a href="conlat_1.html#K11" target="_self">ConceptLattice</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="91_1_1_1_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">c<sub>3</sub></font> be   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="conlat_1.html#K11" target="_self">ConceptLattice</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>;<br/>

<b>assume </b><a NAME="E1:91_1_1_1_1"/>
<font color="Maroon">c<sub>3</sub></font> <a href="lattice3.html#R3">is_less_than</a> <font color="Maroon">c<sub>2</sub></font>
 ;<br/>

<a NAME="E2:91_1_1_1_1"/>
ex <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" target="_self">ConceptLattice</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> st <br/>for <font color="Olive">b<sub>2</sub></font> being  <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="conlat_1.html#K11" target="_self">ConceptLattice</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> holds <br/>( <font color="Olive">b<sub>1</sub></font> <a href="lattices.html#K3">"\/"</a> <font color="Olive">b<sub>2</sub></font> <a href="hidden.html#R1">=</a> <font color="Olive">b<sub>1</sub></font> &amp; <font color="Olive">b<sub>2</sub></font> <a href="lattices.html#K3">"\/"</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Olive">b<sub>1</sub></font> )
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="91_1_1_1_1_1"><b>proof </b></a><div class="add">

<b>reconsider </b><font color="Maroon">c<sub>4</sub></font> =  <a href="conlat_1.html#K5" target="_self">Concept-with-all-Objects</a> <font color="Maroon">c<sub>1</sub></font> as   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="conlat_1.html#K11" target="_self">ConceptLattice</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <b>by </b><i><a class="ref" href="conlat_1.html#T35" target="_self">Th35</a></i>;<br/>
<a NAME="E2:91_1_1_1_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" target="_self">ConceptLattice</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> holds <br/>( <font color="Maroon">c<sub>4</sub></font> <a href="lattices.html#K3">"\/"</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>4</sub></font> &amp; <font color="Olive">b<sub>1</sub></font> <a href="lattices.html#K3">"\/"</a> <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>4</sub></font> )
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="91_1_1_1_1_1_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">c<sub>5</sub></font> be   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="conlat_1.html#K11" target="_self">ConceptLattice</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>;<br/>

<b>reconsider </b><font color="Maroon">c<sub>6</sub></font> = <font color="Maroon">c<sub>5</sub></font> as  <a href="conlat_1.html#V6" target="_self">strict</a> <a href="conlat_1.html#NM4">FormalConcept</a> of <font color="Maroon">c<sub>1</sub></font> <b>by </b><i><a class="ref" href="conlat_1.html#T35" target="_self">Th35</a></i>;<br/>
<b>reconsider </b><font color="Maroon">c<sub>7</sub></font> = <font color="Maroon">c<sub>4</sub></font> as  <a href="conlat_1.html#V6" target="_self">strict</a> <a href="conlat_1.html#NM4">FormalConcept</a> of <font color="Maroon">c<sub>1</sub></font> ;<br/>
<span class="p1">(<span class="default"><a href="conlat_1.html#K10" target="_self">B-join</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="binop_1.html#K1">.</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>6</sub></font> = 
<span class="p1">(<span class="default"><a href="conlat_1.html#K10" target="_self">B-join</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="binop_1.html#K1">.</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</sub></font>
<b>by </b><i><a class="ref" href="conlat_1.html#T37" target="_self">Th37</a></i>
<br/>.= 
<font color="Maroon">c<sub>7</sub></font>
<b>by </b><i><a class="ref" href="conlat_1.html#T43" target="_self">Th43</a></i>
;<br/>
<b>hence </b><a NAME="E4:91_1_1_1_1_1_1"/>
( <font color="Maroon">c<sub>4</sub></font> <a href="lattices.html#K3">"\/"</a> <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>4</sub></font> &amp; <font color="Maroon">c<sub>5</sub></font> <a href="lattices.html#K3">"\/"</a> <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>4</sub></font> )
 <b>by </b><i><a class="ref" href="lattices.html#D1">LATTICES:def 1</a></i>;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E3:91_1_1_1_1_1"/>
ex <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" target="_self">ConceptLattice</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> st <br/>for <font color="Olive">b<sub>2</sub></font> being  <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="conlat_1.html#K11" target="_self">ConceptLattice</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> holds <br/>( <font color="Olive">b<sub>1</sub></font> <a href="lattices.html#K3">"\/"</a> <font color="Olive">b<sub>2</sub></font> <a href="hidden.html#R1">=</a> <font color="Olive">b<sub>1</sub></font> &amp; <font color="Olive">b<sub>2</sub></font> <a href="lattices.html#K3">"\/"</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Olive">b<sub>1</sub></font> )
 ;<br/>


</div><b>end;</b></div>
<a NAME="E3:91_1_1_1_1"/><b>then </b>
 <a href="conlat_1.html#K11" target="_self">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/>
<a NAME="E4:91_1_1_1_1"/><b>then </b>
<span class="p1">(<span class="default"><a href="lattices.html#K6">Top</a> <span class="p2">(<span class="default"><a href="conlat_1.html#K11" target="_self">ConceptLattice</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="lattices.html#K3">"\/"</a> <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a>  <a href="lattices.html#K6">Top</a> <span class="p1">(<span class="default"><a href="conlat_1.html#K11" target="_self">ConceptLattice</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>
 
<b>by </b><i><a class="ref" href="lattices.html#D17">LATTICES:def 17</a></i>;<br/>
<b>hence </b><a NAME="E5:91_1_1_1_1"/>
<font color="Maroon">c<sub>3</sub></font> <a href="lattices.html#R3">[=</a>  <a href="lattices.html#K6">Top</a> <span class="p1">(<span class="default"><a href="conlat_1.html#K11" target="_self">ConceptLattice</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><b>hence </b><a NAME="E5:91_1_1_1"/>
ex <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" target="_self">ConceptLattice</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> st <br/>( <font color="Olive">b<sub>1</sub></font> <a href="lattice3.html#R3">is_less_than</a> <font color="Maroon">c<sub>2</sub></font> &amp; ( for <font color="Olive">b<sub>2</sub></font> being  <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="conlat_1.html#K11" target="_self">ConceptLattice</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> st <font color="Olive">b<sub>2</sub></font> <a href="lattice3.html#R3">is_less_than</a> <font color="Maroon">c<sub>2</sub></font> holds <br/><font color="Olive">b<sub>2</sub></font> <a href="lattices.html#R3">[=</a> <font color="Olive">b<sub>1</sub></font> ) )
 <b>by </b><i><a class="txt" href="conlat_1.html#E3:91_1_1_1"><i><font color="Green">E51</font></i></a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="91_1_1_2"><b>suppose </b></a><a NAME="E1:91_1_1_2"/>
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a> 
 ;<br/><div class="add"><b>then reconsider </b><font color="Maroon">c<sub>3</sub></font> = <font color="Maroon">c<sub>2</sub></font> as  non <a href="xboole_0.html#V1">empty</a> <a href="struct_0.html#NM2">Subset</a> of <span class="p1">(<span class="default"><a href="conlat_1.html#K11" target="_self">ConceptLattice</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> ;<br/><b>set </b><font color="Maroon">c<sub>4</sub></font> = <span class="p1">{<span class="default"> the <a href="conlat_1.html#U4" target="_self">Extent</a> of <font color="Olive">b<sub>1</sub></font> where B is    <a href="conlat_1.html#M2" target="_self">Element</a> of  <a href="conlat_1.html#K8" target="_self">B-carrier</a> <font color="Maroon">c<sub>1</sub></font> : <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>3</sub></font> </span>}</span> ;<br/><a NAME="E3:91_1_1_2"/><i><font color="Green">E51</font></i>: 
for <font color="Olive">b<sub>1</sub></font> being   <a href="conlat_1.html#M3" target="_self">Element</a> of <font color="Maroon">c<sub>3</sub></font> holds the <a href="conlat_1.html#U4" target="_self">Extent</a> of <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> the <a href="conlat_1.html#U4" target="_self">Extent</a> of <font color="Olive">b<sub>2</sub></font> where B is    <a href="conlat_1.html#M2" target="_self">Element</a> of  <a href="conlat_1.html#K8" target="_self">B-carrier</a> <font color="Maroon">c<sub>1</sub></font> : <font color="Olive">b<sub>2</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>3</sub></font> </span>}</span> 
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="91_1_1_2_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">c<sub>5</sub></font> be    <a href="conlat_1.html#M3" target="_self">Element</a> of <font color="Maroon">c<sub>3</sub></font>;<br/>

<a NAME="E1:91_1_1_2_1"/>
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>3</sub></font>
 
;<br/>
<b>then reconsider </b><font color="Maroon">c<sub>6</sub></font> = <font color="Maroon">c<sub>5</sub></font> as    <a href="conlat_1.html#M2" target="_self">Element</a> of  <a href="conlat_1.html#K8" target="_self">B-carrier</a> <font color="Maroon">c<sub>1</sub></font> ;<br/>
<a NAME="E3:91_1_1_2_1"/>
the <a href="conlat_1.html#U4" target="_self">Extent</a> of <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> the <a href="conlat_1.html#U4" target="_self">Extent</a> of <font color="Olive">b<sub>1</sub></font> where B is    <a href="conlat_1.html#M2" target="_self">Element</a> of  <a href="conlat_1.html#K8" target="_self">B-carrier</a> <font color="Maroon">c<sub>1</sub></font> : <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>3</sub></font> </span>}</span> 
 
;<br/>
<b>hence </b><a NAME="E4:91_1_1_2_1"/>
the <a href="conlat_1.html#U4" target="_self">Extent</a> of <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> the <a href="conlat_1.html#U4" target="_self">Extent</a> of <font color="Olive">b<sub>1</sub></font> where B is    <a href="conlat_1.html#M2" target="_self">Element</a> of  <a href="conlat_1.html#K8" target="_self">B-carrier</a> <font color="Maroon">c<sub>1</sub></font> : <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>3</sub></font> </span>}</span> 
 ;<br/>


</div><b>end;</b></div><b>then reconsider </b><font color="Maroon">c<sub>5</sub></font> = <span class="p1">{<span class="default"> the <a href="conlat_1.html#U4" target="_self">Extent</a> of <font color="Olive">b<sub>1</sub></font> where B is    <a href="conlat_1.html#M2" target="_self">Element</a> of  <a href="conlat_1.html#K8" target="_self">B-carrier</a> <font color="Maroon">c<sub>1</sub></font> : <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>3</sub></font> </span>}</span>  as  non <a href="xboole_0.html#V1">empty</a>  <a href="hidden.html#M1">set</a>  ;<br/><b>set </b><font color="Maroon">c<sub>6</sub></font> =  <a href="setfam_1.html#K1">meet</a> <font color="Maroon">c<sub>5</sub></font>;<br/><a NAME="E5:91_1_1_2"/><i><font color="Green">E52</font></i>: 
 <a href="setfam_1.html#K1">meet</a> <font color="Maroon">c<sub>5</sub></font> <a href="tarski.html#R1">c=</a> the <a href="conlat_1.html#U1" target="_self">Objects</a> of <font color="Maroon">c<sub>1</sub></font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="91_1_1_2_2"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">c<sub>7</sub></font> be    <a href="hidden.html#M1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3">TARSKI:def 3</a><br/>

<b>assume </b><a NAME="E1:91_1_1_2_2"/><i><font color="Green">E53</font></i>: 
<font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R2">in</a>  <a href="setfam_1.html#K1">meet</a> <font color="Maroon">c<sub>5</sub></font>
 ;<br/>

<b>consider </b><font color="Maroon">c<sub>8</sub></font> being    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">c<sub>5</sub></font>;<br/>
<a NAME="E3:91_1_1_2_2"/>
<font color="Maroon">c<sub>8</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>5</sub></font>
 
;<br/>
<b>then consider </b><font color="Maroon">c<sub>9</sub></font> being    <a href="conlat_1.html#M2" target="_self">Element</a> of  <a href="conlat_1.html#K8" target="_self">B-carrier</a> <font color="Maroon">c<sub>1</sub></font><b> such that </b><br/><a NAME="E5:91_1_1_2_2"/><i><font color="Green">E54</font></i>: 
( <font color="Maroon">c<sub>8</sub></font> <a href="hidden.html#R1">=</a> the <a href="conlat_1.html#U4" target="_self">Extent</a> of <font color="Maroon">c<sub>9</sub></font> &amp; <font color="Maroon">c<sub>9</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>3</sub></font> )
 ;<br/>
<a NAME="E6:91_1_1_2_2"/>
<font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R2">in</a> the <a href="conlat_1.html#U4" target="_self">Extent</a> of <font color="Maroon">c<sub>9</sub></font>
 
<b>by </b><i><a class="txt" href="conlat_1.html#E1:91_1_1_2_2"><i><font color="Green">E53</font></i></a>, <a class="txt" href="conlat_1.html#E5:91_1_1_2_2"><i><font color="Green">E54</font></i></a>, <a class="ref" href="setfam_1.html#D1">SETFAM_1:def 1</a></i>;<br/>
<b>hence </b><a NAME="E7:91_1_1_2_2"/>
<font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R2">in</a> the <a href="conlat_1.html#U1" target="_self">Objects</a> of <font color="Maroon">c<sub>1</sub></font>
 ;<br/>


</div><b>end;</b></div><a NAME="E6:91_1_1_2"/>
for <font color="Olive">b<sub>1</sub></font> being  <a href="conlat_1.html#NM2">Object</a> of <font color="Maroon">c<sub>1</sub></font> holds <br/>( <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a>  <a href="setfam_1.html#K1">meet</a> <font color="Maroon">c<sub>5</sub></font> iff for <font color="Olive">b<sub>2</sub></font> being   <a href="conlat_1.html#M3" target="_self">Element</a> of <font color="Maroon">c<sub>3</sub></font> holds <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a> the <a href="conlat_1.html#U4" target="_self">Extent</a> of <font color="Olive">b<sub>2</sub></font> )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="91_1_1_2_3"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">c<sub>7</sub></font> be   <a href="conlat_1.html#NM2">Object</a> of <font color="Maroon">c<sub>1</sub></font>;<br/>

<a NAME="E1:91_1_1_2_3"/><i><font color="Green">E53</font></i>: 
( <font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R2">in</a>  <a href="setfam_1.html#K1">meet</a> <font color="Maroon">c<sub>5</sub></font> implies for <font color="Olive">b<sub>1</sub></font> being   <a href="conlat_1.html#M3" target="_self">Element</a> of <font color="Maroon">c<sub>3</sub></font> holds <font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R2">in</a> the <a href="conlat_1.html#U4" target="_self">Extent</a> of <font color="Olive">b<sub>1</sub></font> )
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="91_1_1_2_3_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:91_1_1_2_3_1"/><i><font color="Green">E54</font></i>: 
<font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R2">in</a>  <a href="setfam_1.html#K1">meet</a> <font color="Maroon">c<sub>5</sub></font>
 ;<br/>

<b>let </b><font color="Maroon">c<sub>8</sub></font> be    <a href="conlat_1.html#M3" target="_self">Element</a> of <font color="Maroon">c<sub>3</sub></font>;<br/>

<a NAME="E2:91_1_1_2_3_1"/>
the <a href="conlat_1.html#U4" target="_self">Extent</a> of <font color="Maroon">c<sub>8</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>5</sub></font>
 
<b>by </b><i><a class="txt" href="conlat_1.html#E3:91_1_1_2"><i><font color="Green">E51</font></i></a></i>;<br/>
<b>hence </b><a NAME="E3:91_1_1_2_3_1"/>
<font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R2">in</a> the <a href="conlat_1.html#U4" target="_self">Extent</a> of <font color="Maroon">c<sub>8</sub></font>
 <b>by </b><i><a class="txt" href="conlat_1.html#E1:91_1_1_2_3_1"><i><font color="Green">E54</font></i></a>, <a class="ref" href="setfam_1.html#D1">SETFAM_1:def 1</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E2:91_1_1_2_3"/>
( ( for <font color="Olive">b<sub>1</sub></font> being   <a href="conlat_1.html#M3" target="_self">Element</a> of <font color="Maroon">c<sub>3</sub></font> holds <font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R2">in</a> the <a href="conlat_1.html#U4" target="_self">Extent</a> of <font color="Olive">b<sub>1</sub></font> ) implies <font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R2">in</a>  <a href="setfam_1.html#K1">meet</a> <font color="Maroon">c<sub>5</sub></font> )
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="91_1_1_2_3_2"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:91_1_1_2_3_2"/><i><font color="Green">E54</font></i>: 
for <font color="Olive">b<sub>1</sub></font> being   <a href="conlat_1.html#M3" target="_self">Element</a> of <font color="Maroon">c<sub>3</sub></font> holds <font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R2">in</a> the <a href="conlat_1.html#U4" target="_self">Extent</a> of <font color="Olive">b<sub>1</sub></font>
 ;<br/>

<a NAME="E2:91_1_1_2_3_2"/>
for <font color="Olive">b<sub>1</sub></font> being   <a href="hidden.html#M1">set</a>  st <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>5</sub></font> holds <br/><font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R2">in</a> <font color="Olive">b<sub>1</sub></font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="91_1_1_2_3_2_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">c<sub>8</sub></font> be    <a href="hidden.html#M1">set</a> ;<br/>

<b>assume </b><a NAME="E1:91_1_1_2_3_2_1"/>
<font color="Maroon">c<sub>8</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>5</sub></font>
 ;<br/>

<a NAME="E2:91_1_1_2_3_2_1"/><b>then </b>
ex <font color="Olive">b<sub>1</sub></font> being   <a href="conlat_1.html#M2" target="_self">Element</a> of  <a href="conlat_1.html#K8" target="_self">B-carrier</a> <font color="Maroon">c<sub>1</sub></font> st <br/>( <font color="Maroon">c<sub>8</sub></font> <a href="hidden.html#R1">=</a> the <a href="conlat_1.html#U4" target="_self">Extent</a> of <font color="Olive">b<sub>1</sub></font> &amp; <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>3</sub></font> )
 
;<br/>
<b>hence </b><a NAME="E3:91_1_1_2_3_2_1"/>
<font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>8</sub></font>
 <b>by </b><i><a class="txt" href="conlat_1.html#E1:91_1_1_2_3_2"><i><font color="Green">E54</font></i></a></i>;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E3:91_1_1_2_3_2"/>
<font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R2">in</a>  <a href="setfam_1.html#K1">meet</a> <font color="Maroon">c<sub>5</sub></font>
 <b>by </b><i><a class="ref" href="setfam_1.html#D1">SETFAM_1:def 1</a></i>;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E3:91_1_1_2_3"/>
( <font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R2">in</a>  <a href="setfam_1.html#K1">meet</a> <font color="Maroon">c<sub>5</sub></font> iff for <font color="Olive">b<sub>1</sub></font> being   <a href="conlat_1.html#M3" target="_self">Element</a> of <font color="Maroon">c<sub>3</sub></font> holds <font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R2">in</a> the <a href="conlat_1.html#U4" target="_self">Extent</a> of <font color="Olive">b<sub>1</sub></font> )
 <b>by </b><i><a class="txt" href="conlat_1.html#E1:91_1_1_2_3"><i><font color="Green">E53</font></i></a></i>;<br/>


</div><b>end;</b></div><b>then consider </b><font color="Maroon">c<sub>7</sub></font> being   <a href="subset_1.html#NM2">Subset</a> of the <a href="conlat_1.html#U1" target="_self">Objects</a> of <font color="Maroon">c<sub>1</sub></font><b> such that </b><br/><a NAME="E8:91_1_1_2"/><i><font color="Green">E53</font></i>: 
for <font color="Olive">b<sub>1</sub></font> being  <a href="conlat_1.html#NM2">Object</a> of <font color="Maroon">c<sub>1</sub></font> holds <br/>( <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>7</sub></font> iff for <font color="Olive">b<sub>2</sub></font> being   <a href="conlat_1.html#M3" target="_self">Element</a> of <font color="Maroon">c<sub>3</sub></font> holds <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a> the <a href="conlat_1.html#U4" target="_self">Extent</a> of <font color="Olive">b<sub>2</sub></font> )
 <b>by </b><i><a class="txt" href="conlat_1.html#E5:91_1_1_2"><i><font color="Green">E52</font></i></a></i>;<br/><b>set </b><font color="Maroon">c<sub>8</sub></font> = <span class="p1">{<span class="default"> the <a href="conlat_1.html#U5" target="_self">Intent</a> of <font color="Olive">b<sub>1</sub></font> where B is    <a href="conlat_1.html#M2" target="_self">Element</a> of  <a href="conlat_1.html#K8" target="_self">B-carrier</a> <font color="Maroon">c<sub>1</sub></font> : <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>3</sub></font> </span>}</span> ;<br/><b>set </b><font color="Maroon">c<sub>9</sub></font> =  <a href="tarski.html#K3">union</a> <span class="p1">{<span class="default"> the <a href="conlat_1.html#U5" target="_self">Intent</a> of <font color="Olive">b<sub>1</sub></font> where B is    <a href="conlat_1.html#M2" target="_self">Element</a> of  <a href="conlat_1.html#K8" target="_self">B-carrier</a> <font color="Maroon">c<sub>1</sub></font> : <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>3</sub></font> </span>}</span> ;<br/><a NAME="E9:91_1_1_2"/><i><font color="Green">E54</font></i>: 
 <a href="tarski.html#K3">union</a> <span class="p1">{<span class="default"> the <a href="conlat_1.html#U5" target="_self">Intent</a> of <font color="Olive">b<sub>1</sub></font> where B is    <a href="conlat_1.html#M2" target="_self">Element</a> of  <a href="conlat_1.html#K8" target="_self">B-carrier</a> <font color="Maroon">c<sub>1</sub></font> : <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>3</sub></font> </span>}</span>  <a href="tarski.html#R1">c=</a> the <a href="conlat_1.html#U2" target="_self">Attributes</a> of <font color="Maroon">c<sub>1</sub></font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="91_1_1_2_4"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">c<sub>10</sub></font> be    <a href="hidden.html#M1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3">TARSKI:def 3</a><br/>

<b>assume </b><a NAME="E1:91_1_1_2_4"/>
<font color="Maroon">c<sub>10</sub></font> <a href="hidden.html#R2">in</a>  <a href="tarski.html#K3">union</a> <span class="p1">{<span class="default"> the <a href="conlat_1.html#U5" target="_self">Intent</a> of <font color="Olive">b<sub>1</sub></font> where B is    <a href="conlat_1.html#M2" target="_self">Element</a> of  <a href="conlat_1.html#K8" target="_self">B-carrier</a> <font color="Maroon">c<sub>1</sub></font> : <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>3</sub></font> </span>}</span> 
 ;<br/>

<b>then consider </b><font color="Maroon">c<sub>11</sub></font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E3:91_1_1_2_4"/><i><font color="Green">E55</font></i>: 
( <font color="Maroon">c<sub>10</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>11</sub></font> &amp; <font color="Maroon">c<sub>11</sub></font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> the <a href="conlat_1.html#U5" target="_self">Intent</a> of <font color="Olive">b<sub>1</sub></font> where B is    <a href="conlat_1.html#M2" target="_self">Element</a> of  <a href="conlat_1.html#K8" target="_self">B-carrier</a> <font color="Maroon">c<sub>1</sub></font> : <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>3</sub></font> </span>}</span>  )
 <b>by </b><i><a class="ref" href="tarski.html#D4">TARSKI:def 4</a></i>;<br/>
<b>consider </b><font color="Maroon">c<sub>12</sub></font> being    <a href="conlat_1.html#M2" target="_self">Element</a> of  <a href="conlat_1.html#K8" target="_self">B-carrier</a> <font color="Maroon">c<sub>1</sub></font><b> such that </b><br/><a NAME="E5:91_1_1_2_4"/><i><font color="Green">E56</font></i>: 
( <font color="Maroon">c<sub>11</sub></font> <a href="hidden.html#R1">=</a> the <a href="conlat_1.html#U5" target="_self">Intent</a> of <font color="Maroon">c<sub>12</sub></font> &amp; <font color="Maroon">c<sub>12</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>3</sub></font> )
 <b>by </b><i><a class="txt" href="conlat_1.html#E3:91_1_1_2_4"><i><font color="Green">E55</font></i></a></i>;<br/>
<b>thus </b><a NAME="E6:91_1_1_2_4"/>
<font color="Maroon">c<sub>10</sub></font> <a href="hidden.html#R2">in</a> the <a href="conlat_1.html#U2" target="_self">Attributes</a> of <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="conlat_1.html#E3:91_1_1_2_4"><i><font color="Green">E55</font></i></a>, <a class="txt" href="conlat_1.html#E5:91_1_1_2_4"><i><font color="Green">E56</font></i></a></i>;<br/>


</div><b>end;</b></div><a NAME="E10:91_1_1_2"/>
for <font color="Olive">b<sub>1</sub></font> being  <a href="conlat_1.html#NM3">Attribute</a> of <font color="Maroon">c<sub>1</sub></font> holds <br/>( <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a>  <a href="tarski.html#K3">union</a> <span class="p1">{<span class="default"> the <a href="conlat_1.html#U5" target="_self">Intent</a> of <font color="Olive">b<sub>2</sub></font> where B is    <a href="conlat_1.html#M2" target="_self">Element</a> of  <a href="conlat_1.html#K8" target="_self">B-carrier</a> <font color="Maroon">c<sub>1</sub></font> : <font color="Olive">b<sub>2</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>3</sub></font> </span>}</span>  iff ex <font color="Olive">b<sub>2</sub></font> being   <a href="conlat_1.html#M3" target="_self">Element</a> of <font color="Maroon">c<sub>3</sub></font> st <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a> the <a href="conlat_1.html#U5" target="_self">Intent</a> of <font color="Olive">b<sub>2</sub></font> )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="91_1_1_2_5"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">c<sub>10</sub></font> be   <a href="conlat_1.html#NM3">Attribute</a> of <font color="Maroon">c<sub>1</sub></font>;<br/>

<a NAME="E1:91_1_1_2_5"/><i><font color="Green">E55</font></i>: 
( <font color="Maroon">c<sub>10</sub></font> <a href="hidden.html#R2">in</a>  <a href="tarski.html#K3">union</a> <span class="p1">{<span class="default"> the <a href="conlat_1.html#U5" target="_self">Intent</a> of <font color="Olive">b<sub>1</sub></font> where B is    <a href="conlat_1.html#M2" target="_self">Element</a> of  <a href="conlat_1.html#K8" target="_self">B-carrier</a> <font color="Maroon">c<sub>1</sub></font> : <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>3</sub></font> </span>}</span>  implies ex <font color="Olive">b<sub>1</sub></font> being   <a href="conlat_1.html#M3" target="_self">Element</a> of <font color="Maroon">c<sub>3</sub></font> st <font color="Maroon">c<sub>10</sub></font> <a href="hidden.html#R2">in</a> the <a href="conlat_1.html#U5" target="_self">Intent</a> of <font color="Olive">b<sub>1</sub></font> )
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="91_1_1_2_5_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:91_1_1_2_5_1"/>
<font color="Maroon">c<sub>10</sub></font> <a href="hidden.html#R2">in</a>  <a href="tarski.html#K3">union</a> <span class="p1">{<span class="default"> the <a href="conlat_1.html#U5" target="_self">Intent</a> of <font color="Olive">b<sub>1</sub></font> where B is    <a href="conlat_1.html#M2" target="_self">Element</a> of  <a href="conlat_1.html#K8" target="_self">B-carrier</a> <font color="Maroon">c<sub>1</sub></font> : <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>3</sub></font> </span>}</span> 
 ;<br/>

<b>then consider </b><font color="Maroon">c<sub>11</sub></font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E3:91_1_1_2_5_1"/><i><font color="Green">E56</font></i>: 
( <font color="Maroon">c<sub>10</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>11</sub></font> &amp; <font color="Maroon">c<sub>11</sub></font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> the <a href="conlat_1.html#U5" target="_self">Intent</a> of <font color="Olive">b<sub>1</sub></font> where B is    <a href="conlat_1.html#M2" target="_self">Element</a> of  <a href="conlat_1.html#K8" target="_self">B-carrier</a> <font color="Maroon">c<sub>1</sub></font> : <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>3</sub></font> </span>}</span>  )
 <b>by </b><i><a class="ref" href="tarski.html#D4">TARSKI:def 4</a></i>;<br/>
<b>consider </b><font color="Maroon">c<sub>12</sub></font> being    <a href="conlat_1.html#M2" target="_self">Element</a> of  <a href="conlat_1.html#K8" target="_self">B-carrier</a> <font color="Maroon">c<sub>1</sub></font><b> such that </b><br/><a NAME="E5:91_1_1_2_5_1"/><i><font color="Green">E57</font></i>: 
( <font color="Maroon">c<sub>11</sub></font> <a href="hidden.html#R1">=</a> the <a href="conlat_1.html#U5" target="_self">Intent</a> of <font color="Maroon">c<sub>12</sub></font> &amp; <font color="Maroon">c<sub>12</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>3</sub></font> )
 <b>by </b><i><a class="txt" href="conlat_1.html#E3:91_1_1_2_5_1"><i><font color="Green">E56</font></i></a></i>;<br/>
<b>thus </b><a NAME="E6:91_1_1_2_5_1"/>
ex <font color="Olive">b<sub>1</sub></font> being   <a href="conlat_1.html#M3" target="_self">Element</a> of <font color="Maroon">c<sub>3</sub></font> st <font color="Maroon">c<sub>10</sub></font> <a href="hidden.html#R2">in</a> the <a href="conlat_1.html#U5" target="_self">Intent</a> of <font color="Olive">b<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="conlat_1.html#E3:91_1_1_2_5_1"><i><font color="Green">E56</font></i></a>, <a class="txt" href="conlat_1.html#E5:91_1_1_2_5_1"><i><font color="Green">E57</font></i></a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E2:91_1_1_2_5"/>
( ex <font color="Olive">b<sub>1</sub></font> being   <a href="conlat_1.html#M3" target="_self">Element</a> of <font color="Maroon">c<sub>3</sub></font> st <font color="Maroon">c<sub>10</sub></font> <a href="hidden.html#R2">in</a> the <a href="conlat_1.html#U5" target="_self">Intent</a> of <font color="Olive">b<sub>1</sub></font> implies <font color="Maroon">c<sub>10</sub></font> <a href="hidden.html#R2">in</a>  <a href="tarski.html#K3">union</a> <span class="p1">{<span class="default"> the <a href="conlat_1.html#U5" target="_self">Intent</a> of <font color="Olive">b<sub>1</sub></font> where B is    <a href="conlat_1.html#M2" target="_self">Element</a> of  <a href="conlat_1.html#K8" target="_self">B-carrier</a> <font color="Maroon">c<sub>1</sub></font> : <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>3</sub></font> </span>}</span>  )
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="91_1_1_2_5_2"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:91_1_1_2_5_2"/><i><font color="Green">E56</font></i>: 
ex <font color="Olive">b<sub>1</sub></font> being   <a href="conlat_1.html#M3" target="_self">Element</a> of <font color="Maroon">c<sub>3</sub></font> st <font color="Maroon">c<sub>10</sub></font> <a href="hidden.html#R2">in</a> the <a href="conlat_1.html#U5" target="_self">Intent</a> of <font color="Olive">b<sub>1</sub></font>
 ;<br/>

<a NAME="E2:91_1_1_2_5_2"/>
ex <font color="Olive">b<sub>1</sub></font> being   <a href="hidden.html#M1">set</a>  st <br/>( <font color="Maroon">c<sub>10</sub></font> <a href="hidden.html#R2">in</a> <font color="Olive">b<sub>1</sub></font> &amp; <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> the <a href="conlat_1.html#U5" target="_self">Intent</a> of <font color="Olive">b<sub>2</sub></font> where B is    <a href="conlat_1.html#M2" target="_self">Element</a> of  <a href="conlat_1.html#K8" target="_self">B-carrier</a> <font color="Maroon">c<sub>1</sub></font> : <font color="Olive">b<sub>2</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>3</sub></font> </span>}</span>  )
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="91_1_1_2_5_2_1"><b>proof </b></a><div class="add">

<b>consider </b><font color="Maroon">c<sub>11</sub></font> being    <a href="conlat_1.html#M3" target="_self">Element</a> of <font color="Maroon">c<sub>3</sub></font><b> such that </b><br/><a NAME="E2:91_1_1_2_5_2_1"/><i><font color="Green">E57</font></i>: 
<font color="Maroon">c<sub>10</sub></font> <a href="hidden.html#R2">in</a> the <a href="conlat_1.html#U5" target="_self">Intent</a> of <font color="Maroon">c<sub>11</sub></font>
 <b>by </b><i><a class="txt" href="conlat_1.html#E1:91_1_1_2_5_2"><i><font color="Green">E56</font></i></a></i>;<br/>
<a NAME="E3:91_1_1_2_5_2_1"/>
<font color="Maroon">c<sub>11</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>3</sub></font>
 
;<br/>
<a NAME="E4:91_1_1_2_5_2_1"/><b>then </b>
the <a href="conlat_1.html#U5" target="_self">Intent</a> of <font color="Maroon">c<sub>11</sub></font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> the <a href="conlat_1.html#U5" target="_self">Intent</a> of <font color="Olive">b<sub>1</sub></font> where B is    <a href="conlat_1.html#M2" target="_self">Element</a> of  <a href="conlat_1.html#K8" target="_self">B-carrier</a> <font color="Maroon">c<sub>1</sub></font> : <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>3</sub></font> </span>}</span> 
 
;<br/>
<b>hence </b><a NAME="E5:91_1_1_2_5_2_1"/>
ex <font color="Olive">b<sub>1</sub></font> being   <a href="hidden.html#M1">set</a>  st <br/>( <font color="Maroon">c<sub>10</sub></font> <a href="hidden.html#R2">in</a> <font color="Olive">b<sub>1</sub></font> &amp; <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> the <a href="conlat_1.html#U5" target="_self">Intent</a> of <font color="Olive">b<sub>2</sub></font> where B is    <a href="conlat_1.html#M2" target="_self">Element</a> of  <a href="conlat_1.html#K8" target="_self">B-carrier</a> <font color="Maroon">c<sub>1</sub></font> : <font color="Olive">b<sub>2</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>3</sub></font> </span>}</span>  )
 <b>by </b><i><a class="txt" href="conlat_1.html#E2:91_1_1_2_5_2_1"><i><font color="Green">E57</font></i></a></i>;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E3:91_1_1_2_5_2"/>
<font color="Maroon">c<sub>10</sub></font> <a href="hidden.html#R2">in</a>  <a href="tarski.html#K3">union</a> <span class="p1">{<span class="default"> the <a href="conlat_1.html#U5" target="_self">Intent</a> of <font color="Olive">b<sub>1</sub></font> where B is    <a href="conlat_1.html#M2" target="_self">Element</a> of  <a href="conlat_1.html#K8" target="_self">B-carrier</a> <font color="Maroon">c<sub>1</sub></font> : <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>3</sub></font> </span>}</span> 
 <b>by </b><i><a class="ref" href="tarski.html#D4">TARSKI:def 4</a></i>;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E3:91_1_1_2_5"/>
( <font color="Maroon">c<sub>10</sub></font> <a href="hidden.html#R2">in</a>  <a href="tarski.html#K3">union</a> <span class="p1">{<span class="default"> the <a href="conlat_1.html#U5" target="_self">Intent</a> of <font color="Olive">b<sub>1</sub></font> where B is    <a href="conlat_1.html#M2" target="_self">Element</a> of  <a href="conlat_1.html#K8" target="_self">B-carrier</a> <font color="Maroon">c<sub>1</sub></font> : <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>3</sub></font> </span>}</span>  iff ex <font color="Olive">b<sub>1</sub></font> being   <a href="conlat_1.html#M3" target="_self">Element</a> of <font color="Maroon">c<sub>3</sub></font> st <font color="Maroon">c<sub>10</sub></font> <a href="hidden.html#R2">in</a> the <a href="conlat_1.html#U5" target="_self">Intent</a> of <font color="Olive">b<sub>1</sub></font> )
 <b>by </b><i><a class="txt" href="conlat_1.html#E1:91_1_1_2_5"><i><font color="Green">E55</font></i></a></i>;<br/>


</div><b>end;</b></div><b>then consider </b><font color="Maroon">c<sub>10</sub></font> being   <a href="subset_1.html#NM2">Subset</a> of the <a href="conlat_1.html#U2" target="_self">Attributes</a> of <font color="Maroon">c<sub>1</sub></font><b> such that </b><br/><a NAME="E12:91_1_1_2"/><i><font color="Green">E55</font></i>: 
for <font color="Olive">b<sub>1</sub></font> being  <a href="conlat_1.html#NM3">Attribute</a> of <font color="Maroon">c<sub>1</sub></font> holds <br/>( <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>10</sub></font> iff ex <font color="Olive">b<sub>2</sub></font> being   <a href="conlat_1.html#M3" target="_self">Element</a> of <font color="Maroon">c<sub>3</sub></font> st <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a> the <a href="conlat_1.html#U5" target="_self">Intent</a> of <font color="Olive">b<sub>2</sub></font> )
 <b>by </b><i><a class="txt" href="conlat_1.html#E9:91_1_1_2"><i><font color="Green">E54</font></i></a></i>;<br/><b>consider </b><font color="Maroon">c<sub>11</sub></font> being   <a href="subset_1.html#NM2">Subset</a> of the <a href="conlat_1.html#U2" target="_self">Attributes</a> of <font color="Maroon">c<sub>1</sub></font><b> such that </b><br/><a NAME="E14:91_1_1_2"/><i><font color="Green">E56</font></i>: 
<font color="Maroon">c<sub>11</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="conlat_1.html#K1" target="_self">ObjectDerivation</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="funct_2.html#K3">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="conlat_1.html#K2" target="_self">AttributeDerivation</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>10</sub></font></span>)</span>
 ;<br/><b>set </b><font color="Maroon">c<sub>12</sub></font> =  <a href="conlat_1.html#G3" target="_self">ConceptStr</a>(# <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>11</sub></font> #);<br/><a NAME="E15:91_1_1_2"/>
 <a href="conlat_1.html#G3" target="_self">ConceptStr</a>(# <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>11</sub></font> #) is   <a href="conlat_1.html#NM4">FormalConcept</a> of <font color="Maroon">c<sub>1</sub></font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="91_1_1_2_6"><b>proof </b></a><div class="add">

<a NAME="E1:91_1_1_2_6"/>
<font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="conlat_1.html#K2" target="_self">AttributeDerivation</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>10</sub></font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="91_1_1_2_6_1"><b>proof </b></a><div class="add">

<a NAME="E1:91_1_1_2_6_1"/><i><font color="Green">E57</font></i>: 
for <font color="Olive">b<sub>1</sub></font> being  <a href="conlat_1.html#NM2">Object</a> of <font color="Maroon">c<sub>1</sub></font> holds <br/>( <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>7</sub></font> iff for <font color="Olive">b<sub>2</sub></font> being   <a href="conlat_1.html#M3" target="_self">Element</a> of <font color="Maroon">c<sub>3</sub></font> holds <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="conlat_1.html#K2" target="_self">AttributeDerivation</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="funct_2.html#K3">.</a> the <a href="conlat_1.html#U5" target="_self">Intent</a> of <font color="Olive">b<sub>2</sub></font> )
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="91_1_1_2_6_1_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">c<sub>13</sub></font> be   <a href="conlat_1.html#NM2">Object</a> of <font color="Maroon">c<sub>1</sub></font>;<br/>

<a NAME="E1:91_1_1_2_6_1_1"/><i><font color="Green">E58</font></i>: 
( <font color="Maroon">c<sub>13</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>7</sub></font> implies for <font color="Olive">b<sub>1</sub></font> being   <a href="conlat_1.html#M3" target="_self">Element</a> of <font color="Maroon">c<sub>3</sub></font> holds <font color="Maroon">c<sub>13</sub></font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="conlat_1.html#K2" target="_self">AttributeDerivation</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="funct_2.html#K3">.</a> the <a href="conlat_1.html#U5" target="_self">Intent</a> of <font color="Olive">b<sub>1</sub></font> )
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="91_1_1_2_6_1_1_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:91_1_1_2_6_1_1_1"/><i><font color="Green">E59</font></i>: 
<font color="Maroon">c<sub>13</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>7</sub></font>
 ;<br/>

<a NAME="E2:91_1_1_2_6_1_1_1"/>
for <font color="Olive">b<sub>1</sub></font> being   <a href="conlat_1.html#M3" target="_self">Element</a> of <font color="Maroon">c<sub>3</sub></font> holds <font color="Maroon">c<sub>13</sub></font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="conlat_1.html#K2" target="_self">AttributeDerivation</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="funct_2.html#K3">.</a> the <a href="conlat_1.html#U5" target="_self">Intent</a> of <font color="Olive">b<sub>1</sub></font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="91_1_1_2_6_1_1_1_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">c<sub>14</sub></font> be    <a href="conlat_1.html#M3" target="_self">Element</a> of <font color="Maroon">c<sub>3</sub></font>;<br/>

<a NAME="E1:91_1_1_2_6_1_1_1_1"/>
<font color="Maroon">c<sub>13</sub></font> <a href="hidden.html#R2">in</a> the <a href="conlat_1.html#U4" target="_self">Extent</a> of <font color="Maroon">c<sub>14</sub></font>
 
<b>by </b><i><a class="txt" href="conlat_1.html#E8:91_1_1_2"><i><font color="Green">E53</font></i></a>, <a class="txt" href="conlat_1.html#E1:91_1_1_2_6_1_1_1"><i><font color="Green">E59</font></i></a></i>;<br/>
<b>hence </b><a NAME="E2:91_1_1_2_6_1_1_1_1"/>
<font color="Maroon">c<sub>13</sub></font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="conlat_1.html#K2" target="_self">AttributeDerivation</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="funct_2.html#K3">.</a> the <a href="conlat_1.html#U5" target="_self">Intent</a> of <font color="Maroon">c<sub>14</sub></font>
 <b>by </b><i><a class="ref" href="conlat_1.html#D13" target="_self">Def13</a></i>;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E3:91_1_1_2_6_1_1_1"/>
for <font color="Olive">b<sub>1</sub></font> being   <a href="conlat_1.html#M3" target="_self">Element</a> of <font color="Maroon">c<sub>3</sub></font> holds <font color="Maroon">c<sub>13</sub></font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="conlat_1.html#K2" target="_self">AttributeDerivation</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="funct_2.html#K3">.</a> the <a href="conlat_1.html#U5" target="_self">Intent</a> of <font color="Olive">b<sub>1</sub></font>
 ;<br/>


</div><b>end;</b></div>
<a NAME="E2:91_1_1_2_6_1_1"/>
( ( for <font color="Olive">b<sub>1</sub></font> being   <a href="conlat_1.html#M3" target="_self">Element</a> of <font color="Maroon">c<sub>3</sub></font> holds <font color="Maroon">c<sub>13</sub></font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="conlat_1.html#K2" target="_self">AttributeDerivation</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="funct_2.html#K3">.</a> the <a href="conlat_1.html#U5" target="_self">Intent</a> of <font color="Olive">b<sub>1</sub></font> ) implies <font color="Maroon">c<sub>13</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>7</sub></font> )
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="91_1_1_2_6_1_1_2"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:91_1_1_2_6_1_1_2"/><i><font color="Green">E59</font></i>: 
for <font color="Olive">b<sub>1</sub></font> being   <a href="conlat_1.html#M3" target="_self">Element</a> of <font color="Maroon">c<sub>3</sub></font> holds <font color="Maroon">c<sub>13</sub></font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="conlat_1.html#K2" target="_self">AttributeDerivation</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="funct_2.html#K3">.</a> the <a href="conlat_1.html#U5" target="_self">Intent</a> of <font color="Olive">b<sub>1</sub></font>
 ;<br/>

<a NAME="E2:91_1_1_2_6_1_1_2"/>
for <font color="Olive">b<sub>1</sub></font> being   <a href="conlat_1.html#M3" target="_self">Element</a> of <font color="Maroon">c<sub>3</sub></font> holds <font color="Maroon">c<sub>13</sub></font> <a href="hidden.html#R2">in</a> the <a href="conlat_1.html#U4" target="_self">Extent</a> of <font color="Olive">b<sub>1</sub></font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="91_1_1_2_6_1_1_2_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">c<sub>14</sub></font> be    <a href="conlat_1.html#M3" target="_self">Element</a> of <font color="Maroon">c<sub>3</sub></font>;<br/>

<a NAME="E1:91_1_1_2_6_1_1_2_1"/>
<font color="Maroon">c<sub>13</sub></font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="conlat_1.html#K2" target="_self">AttributeDerivation</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="funct_2.html#K3">.</a> the <a href="conlat_1.html#U5" target="_self">Intent</a> of <font color="Maroon">c<sub>14</sub></font>
 
<b>by </b><i><a class="txt" href="conlat_1.html#E1:91_1_1_2_6_1_1_2"><i><font color="Green">E59</font></i></a></i>;<br/>
<b>hence </b><a NAME="E2:91_1_1_2_6_1_1_2_1"/>
<font color="Maroon">c<sub>13</sub></font> <a href="hidden.html#R2">in</a> the <a href="conlat_1.html#U4" target="_self">Extent</a> of <font color="Maroon">c<sub>14</sub></font>
 <b>by </b><i><a class="ref" href="conlat_1.html#D13" target="_self">Def13</a></i>;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E3:91_1_1_2_6_1_1_2"/>
<font color="Maroon">c<sub>13</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>7</sub></font>
 <b>by </b><i><a class="txt" href="conlat_1.html#E8:91_1_1_2"><i><font color="Green">E53</font></i></a></i>;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E3:91_1_1_2_6_1_1"/>
( <font color="Maroon">c<sub>13</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>7</sub></font> iff for <font color="Olive">b<sub>1</sub></font> being   <a href="conlat_1.html#M3" target="_self">Element</a> of <font color="Maroon">c<sub>3</sub></font> holds <font color="Maroon">c<sub>13</sub></font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="conlat_1.html#K2" target="_self">AttributeDerivation</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="funct_2.html#K3">.</a> the <a href="conlat_1.html#U5" target="_self">Intent</a> of <font color="Olive">b<sub>1</sub></font> )
 <b>by </b><i><a class="txt" href="conlat_1.html#E1:91_1_1_2_6_1_1"><i><font color="Green">E58</font></i></a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E2:91_1_1_2_6_1"/><i><font color="Green">E58</font></i>: 
for <font color="Olive">b<sub>1</sub></font> being   <a href="hidden.html#M1">set</a>  st <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>7</sub></font> holds <br/><font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="conlat_1.html#K2" target="_self">AttributeDerivation</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>10</sub></font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="91_1_1_2_6_1_2"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">c<sub>13</sub></font> be    <a href="hidden.html#M1">set</a> ;<br/>

<b>assume </b><a NAME="E1:91_1_1_2_6_1_2"/><i><font color="Green">E59</font></i>: 
<font color="Maroon">c<sub>13</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>7</sub></font>
 ;<br/>

<b>then reconsider </b><font color="Maroon">c<sub>14</sub></font> = <font color="Maroon">c<sub>13</sub></font> as   <a href="conlat_1.html#NM2">Object</a> of <font color="Maroon">c<sub>1</sub></font> ;<br/>
<a NAME="E3:91_1_1_2_6_1_2"/>
for <font color="Olive">b<sub>1</sub></font> being  <a href="conlat_1.html#NM3">Attribute</a> of <font color="Maroon">c<sub>1</sub></font> st <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>10</sub></font> holds <br/><font color="Maroon">c<sub>14</sub></font> <a href="conlat_1.html#R1" target="_self">is-connected-with</a> <font color="Olive">b<sub>1</sub></font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="91_1_1_2_6_1_2_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">c<sub>15</sub></font> be   <a href="conlat_1.html#NM3">Attribute</a> of <font color="Maroon">c<sub>1</sub></font>;<br/>

<b>assume </b><a NAME="E1:91_1_1_2_6_1_2_1"/>
<font color="Maroon">c<sub>15</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>10</sub></font>
 ;<br/>

<b>then consider </b><font color="Maroon">c<sub>16</sub></font> being    <a href="conlat_1.html#M3" target="_self">Element</a> of <font color="Maroon">c<sub>3</sub></font><b> such that </b><br/><a NAME="E3:91_1_1_2_6_1_2_1"/><i><font color="Green">E60</font></i>: 
<font color="Maroon">c<sub>15</sub></font> <a href="hidden.html#R2">in</a> the <a href="conlat_1.html#U5" target="_self">Intent</a> of <font color="Maroon">c<sub>16</sub></font>
 <b>by </b><i><a class="txt" href="conlat_1.html#E12:91_1_1_2"><i><font color="Green">E55</font></i></a></i>;<br/>
<a NAME="E4:91_1_1_2_6_1_2_1"/>
<font color="Maroon">c<sub>14</sub></font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="conlat_1.html#K2" target="_self">AttributeDerivation</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="funct_2.html#K3">.</a> the <a href="conlat_1.html#U5" target="_self">Intent</a> of <font color="Maroon">c<sub>16</sub></font>
 
<b>by </b><i><a class="txt" href="conlat_1.html#E1:91_1_1_2_6_1"><i><font color="Green">E57</font></i></a>, <a class="txt" href="conlat_1.html#E1:91_1_1_2_6_1_2"><i><font color="Green">E59</font></i></a></i>;<br/>
<a NAME="E5:91_1_1_2_6_1_2_1"/><b>then </b>
<font color="Maroon">c<sub>14</sub></font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <font color="Olive">b<sub>1</sub></font> where B is   <a href="conlat_1.html#NM2">Object</a> of <font color="Maroon">c<sub>1</sub></font> : for <font color="Olive">b<sub>1</sub></font> being  <a href="conlat_1.html#NM3">Attribute</a> of <font color="Maroon">c<sub>1</sub></font> st <font color="Olive">b<sub>2</sub></font> <a href="hidden.html#R2">in</a> the <a href="conlat_1.html#U5" target="_self">Intent</a> of <font color="Maroon">c<sub>16</sub></font> holds <br/><font color="Olive">b<sub>1</sub></font> <a href="conlat_1.html#R1" target="_self">is-connected-with</a> <font color="Olive">b<sub>2</sub></font> </span>}</span> 
 
<b>by </b><i><a class="ref" href="conlat_1.html#D7" target="_self">Def7</a></i>;<br/>
<b>then consider </b><font color="Maroon">c<sub>17</sub></font> being   <a href="conlat_1.html#NM2">Object</a> of <font color="Maroon">c<sub>1</sub></font><b> such that </b><br/><a NAME="E7:91_1_1_2_6_1_2_1"/><i><font color="Green">E61</font></i>: 
( <font color="Maroon">c<sub>17</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>14</sub></font> &amp; ( for <font color="Olive">b<sub>1</sub></font> being  <a href="conlat_1.html#NM3">Attribute</a> of <font color="Maroon">c<sub>1</sub></font> st <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a> the <a href="conlat_1.html#U5" target="_self">Intent</a> of <font color="Maroon">c<sub>16</sub></font> holds <br/><font color="Maroon">c<sub>17</sub></font> <a href="conlat_1.html#R1" target="_self">is-connected-with</a> <font color="Olive">b<sub>1</sub></font> ) )
 ;<br/>
<b>thus </b><a NAME="E8:91_1_1_2_6_1_2_1"/>
<font color="Maroon">c<sub>14</sub></font> <a href="conlat_1.html#R1" target="_self">is-connected-with</a> <font color="Maroon">c<sub>15</sub></font>
 <b>by </b><i><a class="txt" href="conlat_1.html#E3:91_1_1_2_6_1_2_1"><i><font color="Green">E60</font></i></a>, <a class="txt" href="conlat_1.html#E7:91_1_1_2_6_1_2_1"><i><font color="Green">E61</font></i></a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E4:91_1_1_2_6_1_2"/><b>then </b>
<font color="Maroon">c<sub>14</sub></font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <font color="Olive">b<sub>1</sub></font> where B is   <a href="conlat_1.html#NM2">Object</a> of <font color="Maroon">c<sub>1</sub></font> : for <font color="Olive">b<sub>1</sub></font> being  <a href="conlat_1.html#NM3">Attribute</a> of <font color="Maroon">c<sub>1</sub></font> st <font color="Olive">b<sub>2</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>10</sub></font> holds <br/><font color="Olive">b<sub>1</sub></font> <a href="conlat_1.html#R1" target="_self">is-connected-with</a> <font color="Olive">b<sub>2</sub></font> </span>}</span> 
 
;<br/>
<b>hence </b><a NAME="E5:91_1_1_2_6_1_2"/>
<font color="Maroon">c<sub>13</sub></font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="conlat_1.html#K2" target="_self">AttributeDerivation</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>10</sub></font>
 <b>by </b><i><a class="ref" href="conlat_1.html#D7" target="_self">Def7</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E3:91_1_1_2_6_1"/>
for <font color="Olive">b<sub>1</sub></font> being   <a href="hidden.html#M1">set</a>  st <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="conlat_1.html#K2" target="_self">AttributeDerivation</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>10</sub></font> holds <br/><font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>7</sub></font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="91_1_1_2_6_1_3"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">c<sub>13</sub></font> be    <a href="hidden.html#M1">set</a> ;<br/>

<b>assume </b><a NAME="E1:91_1_1_2_6_1_3"/>
<font color="Maroon">c<sub>13</sub></font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="conlat_1.html#K2" target="_self">AttributeDerivation</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>10</sub></font>
 ;<br/>

<a NAME="E2:91_1_1_2_6_1_3"/><b>then </b>
<font color="Maroon">c<sub>13</sub></font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <font color="Olive">b<sub>1</sub></font> where B is   <a href="conlat_1.html#NM2">Object</a> of <font color="Maroon">c<sub>1</sub></font> : for <font color="Olive">b<sub>1</sub></font> being  <a href="conlat_1.html#NM3">Attribute</a> of <font color="Maroon">c<sub>1</sub></font> st <font color="Olive">b<sub>2</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>10</sub></font> holds <br/><font color="Olive">b<sub>1</sub></font> <a href="conlat_1.html#R1" target="_self">is-connected-with</a> <font color="Olive">b<sub>2</sub></font> </span>}</span> 
 
<b>by </b><i><a class="ref" href="conlat_1.html#D7" target="_self">Def7</a></i>;<br/>
<b>then consider </b><font color="Maroon">c<sub>14</sub></font> being   <a href="conlat_1.html#NM2">Object</a> of <font color="Maroon">c<sub>1</sub></font><b> such that </b><br/><a NAME="E4:91_1_1_2_6_1_3"/><i><font color="Green">E59</font></i>: 
( <font color="Maroon">c<sub>14</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>13</sub></font> &amp; ( for <font color="Olive">b<sub>1</sub></font> being  <a href="conlat_1.html#NM3">Attribute</a> of <font color="Maroon">c<sub>1</sub></font> st <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>10</sub></font> holds <br/><font color="Maroon">c<sub>14</sub></font> <a href="conlat_1.html#R1" target="_self">is-connected-with</a> <font color="Olive">b<sub>1</sub></font> ) )
 ;<br/>
<a NAME="E5:91_1_1_2_6_1_3"/>
for <font color="Olive">b<sub>1</sub></font> being   <a href="conlat_1.html#M3" target="_self">Element</a> of <font color="Maroon">c<sub>3</sub></font> holds <font color="Maroon">c<sub>14</sub></font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="conlat_1.html#K2" target="_self">AttributeDerivation</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="funct_2.html#K3">.</a> the <a href="conlat_1.html#U5" target="_self">Intent</a> of <font color="Olive">b<sub>1</sub></font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="91_1_1_2_6_1_3_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">c<sub>15</sub></font> be    <a href="conlat_1.html#M3" target="_self">Element</a> of <font color="Maroon">c<sub>3</sub></font>;<br/>

<a NAME="E1:91_1_1_2_6_1_3_1"/>
for <font color="Olive">b<sub>1</sub></font> being  <a href="conlat_1.html#NM3">Attribute</a> of <font color="Maroon">c<sub>1</sub></font> st <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a> the <a href="conlat_1.html#U5" target="_self">Intent</a> of <font color="Maroon">c<sub>15</sub></font> holds <br/><font color="Maroon">c<sub>14</sub></font> <a href="conlat_1.html#R1" target="_self">is-connected-with</a> <font color="Olive">b<sub>1</sub></font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="91_1_1_2_6_1_3_1_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">c<sub>16</sub></font> be   <a href="conlat_1.html#NM3">Attribute</a> of <font color="Maroon">c<sub>1</sub></font>;<br/>

<b>assume </b><a NAME="E1:91_1_1_2_6_1_3_1_1"/>
<font color="Maroon">c<sub>16</sub></font> <a href="hidden.html#R2">in</a> the <a href="conlat_1.html#U5" target="_self">Intent</a> of <font color="Maroon">c<sub>15</sub></font>
 ;<br/>

<a NAME="E2:91_1_1_2_6_1_3_1_1"/><b>then </b>
<font color="Maroon">c<sub>16</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>10</sub></font>
 
<b>by </b><i><a class="txt" href="conlat_1.html#E12:91_1_1_2"><i><font color="Green">E55</font></i></a></i>;<br/>
<b>hence </b><a NAME="E3:91_1_1_2_6_1_3_1_1"/>
<font color="Maroon">c<sub>14</sub></font> <a href="conlat_1.html#R1" target="_self">is-connected-with</a> <font color="Maroon">c<sub>16</sub></font>
 <b>by </b><i><a class="txt" href="conlat_1.html#E4:91_1_1_2_6_1_3"><i><font color="Green">E59</font></i></a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E2:91_1_1_2_6_1_3_1"/><b>then </b>
<font color="Maroon">c<sub>14</sub></font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <font color="Olive">b<sub>1</sub></font> where B is   <a href="conlat_1.html#NM2">Object</a> of <font color="Maroon">c<sub>1</sub></font> : for <font color="Olive">b<sub>1</sub></font> being  <a href="conlat_1.html#NM3">Attribute</a> of <font color="Maroon">c<sub>1</sub></font> st <font color="Olive">b<sub>2</sub></font> <a href="hidden.html#R2">in</a> the <a href="conlat_1.html#U5" target="_self">Intent</a> of <font color="Maroon">c<sub>15</sub></font> holds <br/><font color="Olive">b<sub>1</sub></font> <a href="conlat_1.html#R1" target="_self">is-connected-with</a> <font color="Olive">b<sub>2</sub></font> </span>}</span> 
 
;<br/>
<b>hence </b><a NAME="E3:91_1_1_2_6_1_3_1"/>
<font color="Maroon">c<sub>14</sub></font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="conlat_1.html#K2" target="_self">AttributeDerivation</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="funct_2.html#K3">.</a> the <a href="conlat_1.html#U5" target="_self">Intent</a> of <font color="Maroon">c<sub>15</sub></font>
 <b>by </b><i><a class="ref" href="conlat_1.html#D7" target="_self">Def7</a></i>;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E6:91_1_1_2_6_1_3"/>
<font color="Maroon">c<sub>13</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>7</sub></font>
 <b>by </b><i><a class="txt" href="conlat_1.html#E1:91_1_1_2_6_1"><i><font color="Green">E57</font></i></a>, <a class="txt" href="conlat_1.html#E4:91_1_1_2_6_1_3"><i><font color="Green">E59</font></i></a></i>;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E4:91_1_1_2_6_1"/>
<font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="conlat_1.html#K2" target="_self">AttributeDerivation</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>10</sub></font>
 <b>by </b><i><a class="txt" href="conlat_1.html#E2:91_1_1_2_6_1"><i><font color="Green">E58</font></i></a>, <a class="ref" href="tarski.html#T2">TARSKI:2</a></i>;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E2:91_1_1_2_6"/>
 <a href="conlat_1.html#G3" target="_self">ConceptStr</a>(# <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>11</sub></font> #) is   <a href="conlat_1.html#NM4">FormalConcept</a> of <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="conlat_1.html#E14:91_1_1_2"><i><font color="Green">E56</font></i></a>, <a class="ref" href="conlat_1.html#T22" target="_self">Th22</a></i>;<br/>


</div><b>end;</b></div><b>then reconsider </b><font color="Maroon">c<sub>13</sub></font> =  <a href="conlat_1.html#G3" target="_self">ConceptStr</a>(# <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>11</sub></font> #) as   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="conlat_1.html#K11" target="_self">ConceptLattice</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <b>by </b><i><a class="ref" href="conlat_1.html#T35" target="_self">Th35</a></i>;<br/><a NAME="E17:91_1_1_2"/><i><font color="Green">E57</font></i>: 
<font color="Maroon">c<sub>13</sub></font> <a href="lattice3.html#R3">is_less_than</a> <font color="Maroon">c<sub>3</sub></font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="91_1_1_2_7"><b>proof </b></a><div class="add">

<a NAME="E1:91_1_1_2_7"/>
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" target="_self">ConceptLattice</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> st <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>3</sub></font> holds <br/><font color="Maroon">c<sub>13</sub></font> <a href="lattices.html#R3">[=</a> <font color="Olive">b<sub>1</sub></font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="91_1_1_2_7_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">c<sub>14</sub></font> be   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="conlat_1.html#K11" target="_self">ConceptLattice</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>;<br/>

<b>assume </b><a NAME="E1:91_1_1_2_7_1"/>
<font color="Maroon">c<sub>14</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>3</sub></font>
 ;<br/>

<a NAME="E2:91_1_1_2_7_1"/><b>then </b><i><font color="Green">E58</font></i>: 
<font color="Maroon">c<sub>14</sub></font> <a href="conlat_1.html#K12" target="_self">@</a>  <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>3</sub></font>
 
;<br/>
<a NAME="E3:91_1_1_2_7_1"/>
the <a href="conlat_1.html#U4" target="_self">Extent</a> of <span class="p1">(<span class="default"><font color="Maroon">c<sub>13</sub></font> <a href="conlat_1.html#K12" target="_self">@</a> </span>)</span> <a href="tarski.html#R1">c=</a> the <a href="conlat_1.html#U4" target="_self">Extent</a> of <span class="p1">(<span class="default"><font color="Maroon">c<sub>14</sub></font> <a href="conlat_1.html#K12" target="_self">@</a> </span>)</span>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="91_1_1_2_7_1_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">c<sub>15</sub></font> be    <a href="hidden.html#M1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3">TARSKI:def 3</a><br/>

<b>assume </b><a NAME="E1:91_1_1_2_7_1_1"/>
<font color="Maroon">c<sub>15</sub></font> <a href="hidden.html#R2">in</a> the <a href="conlat_1.html#U4" target="_self">Extent</a> of <span class="p1">(<span class="default"><font color="Maroon">c<sub>13</sub></font> <a href="conlat_1.html#K12" target="_self">@</a> </span>)</span>
 ;<br/>

<a NAME="E2:91_1_1_2_7_1_1"/><b>then </b>
<font color="Maroon">c<sub>15</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>7</sub></font>
 
;<br/>
<b>hence </b><a NAME="E3:91_1_1_2_7_1_1"/>
<font color="Maroon">c<sub>15</sub></font> <a href="hidden.html#R2">in</a> the <a href="conlat_1.html#U4" target="_self">Extent</a> of <span class="p1">(<span class="default"><font color="Maroon">c<sub>14</sub></font> <a href="conlat_1.html#K12" target="_self">@</a> </span>)</span>
 <b>by </b><i><a class="txt" href="conlat_1.html#E8:91_1_1_2"><i><font color="Green">E53</font></i></a>, <a class="txt" href="conlat_1.html#E2:91_1_1_2_7_1"><i><font color="Green">E58</font></i></a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E4:91_1_1_2_7_1"/><b>then </b>
<font color="Maroon">c<sub>13</sub></font> <a href="conlat_1.html#K12" target="_self">@</a>  <a href="conlat_1.html#R2" target="_self">is-SubConcept-of</a> <font color="Maroon">c<sub>14</sub></font> <a href="conlat_1.html#K12" target="_self">@</a> 
 
<b>by </b><i><a class="ref" href="conlat_1.html#D19" target="_self">Def19</a></i>;<br/>
<b>hence </b><a NAME="E5:91_1_1_2_7_1"/>
<font color="Maroon">c<sub>13</sub></font> <a href="lattices.html#R3">[=</a> <font color="Maroon">c<sub>14</sub></font>
 <b>by </b><i><a class="ref" href="conlat_1.html#T47" target="_self">Th47</a></i>;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E2:91_1_1_2_7"/>
<font color="Maroon">c<sub>13</sub></font> <a href="lattice3.html#R3">is_less_than</a> <font color="Maroon">c<sub>3</sub></font>
 <b>by </b><i><a class="ref" href="lattice3.html#D16">LATTICE3:def 16</a></i>;<br/>


</div><b>end;</b></div><a NAME="E18:91_1_1_2"/>
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" target="_self">ConceptLattice</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> st <font color="Olive">b<sub>1</sub></font> <a href="lattice3.html#R3">is_less_than</a> <font color="Maroon">c<sub>3</sub></font> holds <br/><font color="Olive">b<sub>1</sub></font> <a href="lattices.html#R3">[=</a> <font color="Maroon">c<sub>13</sub></font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="91_1_1_2_8"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">c<sub>14</sub></font> be   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="conlat_1.html#K11" target="_self">ConceptLattice</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>;<br/>

<b>assume </b><a NAME="E1:91_1_1_2_8"/><i><font color="Green">E58</font></i>: 
<font color="Maroon">c<sub>14</sub></font> <a href="lattice3.html#R3">is_less_than</a> <font color="Maroon">c<sub>3</sub></font>
 ;<br/>

<a NAME="E2:91_1_1_2_8"/>
the <a href="conlat_1.html#U4" target="_self">Extent</a> of <span class="p1">(<span class="default"><font color="Maroon">c<sub>14</sub></font> <a href="conlat_1.html#K12" target="_self">@</a> </span>)</span> <a href="tarski.html#R1">c=</a> the <a href="conlat_1.html#U4" target="_self">Extent</a> of <span class="p1">(<span class="default"><font color="Maroon">c<sub>13</sub></font> <a href="conlat_1.html#K12" target="_self">@</a> </span>)</span>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="91_1_1_2_8_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">c<sub>15</sub></font> be    <a href="hidden.html#M1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3">TARSKI:def 3</a><br/>

<b>assume </b><a NAME="E1:91_1_1_2_8_1"/><i><font color="Green">E59</font></i>: 
<font color="Maroon">c<sub>15</sub></font> <a href="hidden.html#R2">in</a> the <a href="conlat_1.html#U4" target="_self">Extent</a> of <span class="p1">(<span class="default"><font color="Maroon">c<sub>14</sub></font> <a href="conlat_1.html#K12" target="_self">@</a> </span>)</span>
 ;<br/>

<b>then reconsider </b><font color="Maroon">c<sub>16</sub></font> = <font color="Maroon">c<sub>15</sub></font> as   <a href="conlat_1.html#NM2">Object</a> of <font color="Maroon">c<sub>1</sub></font> ;<br/>
<a NAME="E3:91_1_1_2_8_1"/>
for <font color="Olive">b<sub>1</sub></font> being   <a href="conlat_1.html#M3" target="_self">Element</a> of <font color="Maroon">c<sub>3</sub></font> holds <font color="Maroon">c<sub>16</sub></font> <a href="hidden.html#R2">in</a> the <a href="conlat_1.html#U4" target="_self">Extent</a> of <font color="Olive">b<sub>1</sub></font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="91_1_1_2_8_1_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">c<sub>17</sub></font> be    <a href="conlat_1.html#M3" target="_self">Element</a> of <font color="Maroon">c<sub>3</sub></font>;<br/>

<a NAME="E1:91_1_1_2_8_1_1"/>
<font color="Maroon">c<sub>17</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>3</sub></font>
 
;<br/>
<b>then reconsider </b><font color="Maroon">c<sub>18</sub></font> = <font color="Maroon">c<sub>17</sub></font> as   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="conlat_1.html#K11" target="_self">ConceptLattice</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> ;<br/>
<a NAME="E3:91_1_1_2_8_1_1"/>
<font color="Maroon">c<sub>14</sub></font> <a href="lattices.html#R3">[=</a> <font color="Maroon">c<sub>18</sub></font>
 
<b>by </b><i><a class="txt" href="conlat_1.html#E1:91_1_1_2_8"><i><font color="Green">E58</font></i></a>, <a class="ref" href="lattice3.html#D16">LATTICE3:def 16</a></i>;<br/>
<a NAME="E4:91_1_1_2_8_1_1"/><b>then </b>
<font color="Maroon">c<sub>14</sub></font> <a href="conlat_1.html#K12" target="_self">@</a>  <a href="conlat_1.html#R2" target="_self">is-SubConcept-of</a> <font color="Maroon">c<sub>18</sub></font> <a href="conlat_1.html#K12" target="_self">@</a> 
 
<b>by </b><i><a class="ref" href="conlat_1.html#T47" target="_self">Th47</a></i>;<br/>
<a NAME="E5:91_1_1_2_8_1_1"/><b>then </b><i><font color="Green">E60</font></i>: 
the <a href="conlat_1.html#U4" target="_self">Extent</a> of <span class="p1">(<span class="default"><font color="Maroon">c<sub>14</sub></font> <a href="conlat_1.html#K12" target="_self">@</a> </span>)</span> <a href="tarski.html#R1">c=</a> the <a href="conlat_1.html#U4" target="_self">Extent</a> of <span class="p1">(<span class="default"><font color="Maroon">c<sub>18</sub></font> <a href="conlat_1.html#K12" target="_self">@</a> </span>)</span>
 
<b>by </b><i><a class="ref" href="conlat_1.html#D19" target="_self">Def19</a></i>;<br/>
<b>reconsider </b><font color="Maroon">c<sub>19</sub></font> = <font color="Maroon">c<sub>18</sub></font> as    <a href="conlat_1.html#M3" target="_self">Element</a> of <font color="Maroon">c<sub>3</sub></font> ;<br/>
<b>thus </b><a NAME="E7:91_1_1_2_8_1_1"/>
<font color="Maroon">c<sub>16</sub></font> <a href="hidden.html#R2">in</a> the <a href="conlat_1.html#U4" target="_self">Extent</a> of <font color="Maroon">c<sub>17</sub></font>
 <b>by </b><i><a class="txt" href="conlat_1.html#E1:91_1_1_2_8_1"><i><font color="Green">E59</font></i></a>, <a class="txt" href="conlat_1.html#E5:91_1_1_2_8_1_1"><i><font color="Green">E60</font></i></a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E4:91_1_1_2_8_1"/><b>then </b>
<font color="Maroon">c<sub>16</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>7</sub></font>
 
<b>by </b><i><a class="txt" href="conlat_1.html#E8:91_1_1_2"><i><font color="Green">E53</font></i></a></i>;<br/>
<b>hence </b><a NAME="E5:91_1_1_2_8_1"/>
<font color="Maroon">c<sub>15</sub></font> <a href="hidden.html#R2">in</a> the <a href="conlat_1.html#U4" target="_self">Extent</a> of <span class="p1">(<span class="default"><font color="Maroon">c<sub>13</sub></font> <a href="conlat_1.html#K12" target="_self">@</a> </span>)</span>
 ;<br/>


</div><b>end;</b></div>
<a NAME="E3:91_1_1_2_8"/><b>then </b>
<font color="Maroon">c<sub>14</sub></font> <a href="conlat_1.html#K12" target="_self">@</a>  <a href="conlat_1.html#R2" target="_self">is-SubConcept-of</a> <font color="Maroon">c<sub>13</sub></font> <a href="conlat_1.html#K12" target="_self">@</a> 
 
<b>by </b><i><a class="ref" href="conlat_1.html#D19" target="_self">Def19</a></i>;<br/>
<b>hence </b><a NAME="E4:91_1_1_2_8"/>
<font color="Maroon">c<sub>14</sub></font> <a href="lattices.html#R3">[=</a> <font color="Maroon">c<sub>13</sub></font>
 <b>by </b><i><a class="ref" href="conlat_1.html#T47" target="_self">Th47</a></i>;<br/>


</div><b>end;</b></div><b>hence </b><a NAME="E19:91_1_1_2"/>
ex <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" target="_self">ConceptLattice</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> st <br/>( <font color="Olive">b<sub>1</sub></font> <a href="lattice3.html#R3">is_less_than</a> <font color="Maroon">c<sub>2</sub></font> &amp; ( for <font color="Olive">b<sub>2</sub></font> being  <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="conlat_1.html#K11" target="_self">ConceptLattice</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> st <font color="Olive">b<sub>2</sub></font> <a href="lattice3.html#R3">is_less_than</a> <font color="Maroon">c<sub>2</sub></font> holds <br/><font color="Olive">b<sub>2</sub></font> <a href="lattices.html#R3">[=</a> <font color="Olive">b<sub>1</sub></font> ) )
 <b>by </b><i><a class="txt" href="conlat_1.html#E17:91_1_1_2"><i><font color="Green">E57</font></i></a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div>

</div><b>end;</b></div>
<b>hence </b><a NAME="E2:91"/>
 <a href="conlat_1.html#K11" target="_self">ConceptLattice</a> <font color="Maroon">c<sub>1</sub></font> is  <a href="lattice3.html#V4">complete</a> <a href="lattices.html#NM1">Lattice</a>
 <b>by </b><i><a class="ref" href="vectsp_8.html#D6">VECTSP_8:def 6</a></i>;<br/>


</div>
