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<b>defpred </b><font color="Maroon">S<sub>1</sub></font>[   <a href="hidden.html#M1">set</a> ,   <a href="hidden.html#M1">set</a> ] means ex <font color="Olive">b<sub>1</sub></font> being  <a href="subset_1.html#NM2">Subset</a> of the <a href="conlat_1.html#U1">Objects</a> of <font color="Maroon">c<sub>1</sub></font>ex <font color="Olive">b<sub>2</sub></font> being  <a href="subset_1.html#NM2">Subset</a> of the <a href="conlat_1.html#U2">Attributes</a> of <font color="Maroon">c<sub>1</sub></font> st <br/>( <font color="Maroon">a<sub>2</sub></font> <a href="hidden.html#R1">=</a>  <a href="conlat_1.html#G3">ConceptStr</a>(# <font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>2</sub></font> #) &amp; <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="conlat_1.html#K2">AttributeDerivation</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="conlat_1.html#K1">ObjectDerivation</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p2"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">a<sub>1</sub></font></span><a href="tarski.html#K1">}</a></span></span>)</span> &amp; <font color="Olive">b<sub>2</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="conlat_1.html#K1">ObjectDerivation</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">a<sub>1</sub></font></span><a href="tarski.html#K1">}</a></span> );<br/>
<a NAME="E1:14_1_1"/><i><font color="Green">E7</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> the <a href="conlat_1.html#U1">Objects</a> of <font color="Maroon">c<sub>1</sub></font> holds <br/>ex <font color="Olive">b<sub>2</sub></font> being   <a href="hidden.html#M1">set</a>  st <br/>( <font color="Olive">b<sub>2</sub></font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</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> &amp; <font color="Maroon">S<sub>1</sub></font>[<font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>2</sub></font>] )
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="14_1_1_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">c<sub>2</sub></font> be    <a href="hidden.html#M1">set</a> ;<br/>

<b>assume </b><a NAME="E1:14_1_1_1"/>
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</a> the <a href="conlat_1.html#U1">Objects</a> of <font color="Maroon">c<sub>1</sub></font>
 ;<br/>

<b>then reconsider </b><font color="Maroon">c<sub>3</sub></font> = <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">c<sub>2</sub></font></span><a href="tarski.html#K1">}</a></span> as   <a href="subset_1.html#NM2">Subset</a> of the <a href="conlat_1.html#U1">Objects</a> of <font color="Maroon">c<sub>1</sub></font> <b>by </b><i><a class="ref" href="zfmisc_1.html#T37">ZFMISC_1:37</a></i>;<br/>
<b>set </b><font color="Maroon">c<sub>4</sub></font> = <span class="p1">(<span class="default"><a href="conlat_1.html#K2">AttributeDerivation</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#K1">ObjectDerivation</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>;<br/>
<b>set </b><font color="Maroon">c<sub>5</sub></font> = <span class="p1">(<span class="default"><a href="conlat_1.html#K1">ObjectDerivation</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>3</sub></font>;<br/>
<b>take </b>
 <a href="conlat_1.html#G3">ConceptStr</a>(# <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="conlat_1.html#K2">AttributeDerivation</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="funct_2.html#K3">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="conlat_1.html#K1">ObjectDerivation</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="conlat_1.html#K1">ObjectDerivation</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> #)
;<br/>

<a NAME="E3:14_1_1_1"/><i><font color="Green">E8</font></i>: 
 <a href="conlat_1.html#K11">ConceptLattice</a> <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a>  <a href="lattices.html#G3">LattStr</a>(# <span class="p1">(<span class="default"><a href="conlat_1.html#K8">B-carrier</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<span class="p1">(<span class="default"><a href="conlat_1.html#K10">B-join</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<span class="p1">(<span class="default"><a href="conlat_1.html#K9">B-meet</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> #)
 
<b>by </b><i><a class="ref" href="conlat_1.html#D23">CONLAT_1:def 23</a></i>;<br/>
<a NAME="E4:14_1_1_1"/>
 <a href="conlat_1.html#G3">ConceptStr</a>(# <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="conlat_1.html#K2">AttributeDerivation</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="funct_2.html#K3">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="conlat_1.html#K1">ObjectDerivation</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="conlat_1.html#K1">ObjectDerivation</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> #) is   <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#T20">CONLAT_1:20</a></i>;<br/>
<b>hence </b><a NAME="E5:14_1_1_1"/>
(  <a href="conlat_1.html#G3">ConceptStr</a>(# <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="conlat_1.html#K2">AttributeDerivation</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="funct_2.html#K3">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="conlat_1.html#K1">ObjectDerivation</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="conlat_1.html#K1">ObjectDerivation</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> #) <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</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> &amp; <font color="Maroon">S<sub>1</sub></font>[<font color="Maroon">c<sub>2</sub></font>, <a href="conlat_1.html#G3">ConceptStr</a>(# <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="conlat_1.html#K2">AttributeDerivation</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="funct_2.html#K3">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="conlat_1.html#K1">ObjectDerivation</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="conlat_1.html#K1">ObjectDerivation</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> #)] )
 <b>by </b><i><a class="txt" href="conlat_2.html#E3:14_1_1_1"><i><font color="Green">E8</font></i></a>, <a class="ref" href="conlat_1.html#T35">CONLAT_1:35</a></i>;<br/>


</div><b>end;</b></div>
<b>consider </b><font color="Maroon">c<sub>2</sub></font> being   <a href="funct_2.html#NM1">Function</a> of the <a href="conlat_1.html#U1">Objects</a> of <font color="Maroon">c<sub>1</sub></font>,the <a href="struct_0.html#U1">carrier</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><b> such that </b><br/><a NAME="E3:14_1_1"/><i><font color="Green">E8</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> the <a href="conlat_1.html#U1">Objects</a> of <font color="Maroon">c<sub>1</sub></font> holds <br/><font color="Maroon">S<sub>1</sub></font>[<font color="Olive">b<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font> <a href="funct_1.html#K1">.</a> <font color="Olive">b<sub>1</sub></font>]
 <b>from </b><i><a class="ref" href="funct_2.html#S1">FUNCT_2:sch 1</a>(<a class="txt" href="conlat_2.html#E1:14_1_1"><i><font color="Green">E7</font></i></a>);<br/></i>
<b>take </b>
<font color="Maroon">c<sub>2</sub></font>
;<br/>

<b>let </b><font color="Maroon">c<sub>3</sub></font> be    <a href="subset_1.html#M1">Element</a> of the <a href="conlat_1.html#U1">Objects</a> of <font color="Maroon">c<sub>1</sub></font>;<br/>

<b>thus </b><a NAME="E4:14_1_1"/>
ex <font color="Olive">b<sub>1</sub></font> being  <a href="subset_1.html#NM2">Subset</a> of the <a href="conlat_1.html#U1">Objects</a> of <font color="Maroon">c<sub>1</sub></font>ex <font color="Olive">b<sub>2</sub></font> being  <a href="subset_1.html#NM2">Subset</a> of the <a href="conlat_1.html#U2">Attributes</a> of <font color="Maroon">c<sub>1</sub></font> st <br/>( <font color="Maroon">c<sub>2</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a>  <a href="conlat_1.html#G3">ConceptStr</a>(# <font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>2</sub></font> #) &amp; <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="conlat_1.html#K2">AttributeDerivation</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#K1">ObjectDerivation</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="funct_2.html#K3">.</a> <span class="p2"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>3</sub></font></span><a href="domain_1.html#K6">}</a></span></span>)</span> &amp; <font color="Olive">b<sub>2</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="conlat_1.html#K1">ObjectDerivation</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="funct_2.html#K3">.</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>3</sub></font></span><a href="domain_1.html#K6">}</a></span> )
 <b>by </b><i><a class="txt" href="conlat_2.html#E3:14_1_1"><i><font color="Green">E8</font></i></a></i>;<br/>


</div>
