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



<div><i><font color="Green">E29</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="49_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:49_1"/><i><font color="Green">E32</font></i>: 
<span class="p1">(<span class="default"><a href="conlat_1.html#K1" target="_self">ObjectDerivation</a> <font color="Maroon">C</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</font></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">A</font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">A</font>
 ;<br/><b>reconsider </b><font color="Maroon">O</font> = <span class="p1">(<span class="default"><a href="conlat_1.html#K2" target="_self">AttributeDerivation</a> <font color="Maroon">C</font></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">A</font> as   <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</font> ;<br/><b>set </b><font color="Maroon">M'</font> =  <a href="conlat_1.html#G3" target="_self">ConceptStr</a>(# <font color="Maroon">O</font>,<font color="Maroon">A</font> #);<br/><a NAME="E3:49_1"/>
 <a href="conlat_1.html#G3" target="_self">ConceptStr</a>(# <font color="Maroon">O</font>,<font color="Maroon">A</font> #) is   <a href="conlat_1.html#NM4">FormalConcept</a> of <font color="Maroon">C</font>
 <b>by </b><i>, <a class="ref" href="conlat_1.html#D5" target="_self">Def5</a>, </i>;<br/><b>hence </b><a NAME="E4:49_1"/>
 ex <font color="Olive">O</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</font> st  <a href="conlat_1.html#G3" target="_self">ConceptStr</a>(# <font color="Olive">O</font>,<font color="Maroon">A</font> #) is   <a href="conlat_1.html#NM4">FormalConcept</a> of <font color="Maroon">C</font>
 ;<br/></div><b>end;</b></div>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="49_2"><b>now </b></a><div class="add"><b>given </b><font color="Maroon">O</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</font><b> such that </b><a NAME="E1:49_2"/><i><font color="Green">E33</font></i>: 
 <a href="conlat_1.html#G3" target="_self">ConceptStr</a>(# <font color="Maroon">O</font>,<font color="Maroon">A</font> #) is   <a href="conlat_1.html#NM4">FormalConcept</a> of <font color="Maroon">C</font>
 ;<br/><a NAME="E2:49_2"/>
<span class="p1">(<span class="default"><a href="conlat_1.html#K1" target="_self">ObjectDerivation</a> <font color="Maroon">C</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</font></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">A</font></span>)</span> <a href="tarski.html#R1">c=</a> <font color="Maroon">A</font>
 <b>by </b><i>, </i>;<br/><a NAME="E3:49_2"/><b>then </b><i><font color="Green">E34</font></i>: 
for <font color="Olive">x</font> being   <a href="hidden.html#M1">set</a>   st <font color="Olive">x</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="conlat_1.html#K1" target="_self">ObjectDerivation</a> <font color="Maroon">C</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</font></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">A</font></span>)</span> holds <br/><font color="Olive">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">A</font>
 ;<br/><a NAME="E4:49_2"/>
<font color="Maroon">A</font> <a href="tarski.html#R1">c=</a> <span class="p1">(<span class="default"><a href="conlat_1.html#K1" target="_self">ObjectDerivation</a> <font color="Maroon">C</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</font></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">A</font></span>)</span>
 <b>by </b><i/>;<br/><a NAME="E5:49_2"/><b>then </b>
for <font color="Olive">x</font> being   <a href="hidden.html#M1">set</a>   st <font color="Olive">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">A</font> holds <br/><font color="Olive">x</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="conlat_1.html#K1" target="_self">ObjectDerivation</a> <font color="Maroon">C</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</font></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">A</font></span>)</span>
 ;<br/><b>hence </b><a NAME="E6:49_2"/>
<span class="p1">(<span class="default"><a href="conlat_1.html#K1" target="_self">ObjectDerivation</a> <font color="Maroon">C</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</font></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">A</font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">A</font>
 <b>by </b><i>, <a class="ref" href="tarski.html#T2">TARSKI:2</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E3:49"/>
(  ex <font color="Olive">O</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</font> st  <a href="conlat_1.html#G3" target="_self">ConceptStr</a>(# <font color="Olive">O</font>,<font color="Maroon">A</font> #) is   <a href="conlat_1.html#NM4">FormalConcept</a> of <font color="Maroon">C</font> iff <span class="p1">(<span class="default"><a href="conlat_1.html#K1" target="_self">ObjectDerivation</a> <font color="Maroon">C</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</font></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">A</font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">A</font> )
 <b>by </b><i/>;<br/>


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