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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">O</font> be   <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>let </b><font color="Maroon">x</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="E1:19"/><i><font color="Green">E29</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">O</font>
 ;<br/>

<b>then reconsider </b><font color="Maroon">x</font> = <font color="Maroon">x</font> as   <a href="conlat_1.html#NM2">Object</a> of <font color="Maroon">C</font> ;<br/>
<b>set </b><font color="Maroon">A</font> = <span class="p1">{<span class="default"> <font color="Olive">a</font> where <font color="Olive">a</font> is   <a href="conlat_1.html#NM3">Attribute</a> of <font color="Maroon">C</font> : for <font color="Olive">o</font> being  <a href="conlat_1.html#NM2">Object</a> of <font color="Maroon">C</font>  st <font color="Olive">o</font> <a href="hidden.html#R2">in</a> <font color="Maroon">O</font> holds <br/><font color="Olive">o</font> <a href="conlat_1.html#R1" target="_self">is-connected-with</a> <font color="Olive">a</font> </span>}</span> ;<br/>
<a NAME="E3:19"/>
<span class="p1">{<span class="default"> <font color="Olive">a</font> where <font color="Olive">a</font> is   <a href="conlat_1.html#NM3">Attribute</a> of <font color="Maroon">C</font> : for <font color="Olive">o</font> being  <a href="conlat_1.html#NM2">Object</a> of <font color="Maroon">C</font>  st <font color="Olive">o</font> <a href="hidden.html#R2">in</a> <font color="Maroon">O</font> holds <br/><font color="Olive">o</font> <a href="conlat_1.html#R1" target="_self">is-connected-with</a> <font color="Olive">a</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</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="19_1"><b>proof </b></a><div class="add">

<a NAME="E1:19_1"/>
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"> <font color="Olive">a</font> where <font color="Olive">a</font> is   <a href="conlat_1.html#NM3">Attribute</a> of <font color="Maroon">C</font> : for <font color="Olive">o</font> being  <a href="conlat_1.html#NM2">Object</a> of <font color="Maroon">C</font>  st <font color="Olive">o</font> <a href="hidden.html#R2">in</a> <font color="Maroon">O</font> holds <br/><font color="Olive">o</font> <a href="conlat_1.html#R1" target="_self">is-connected-with</a> <font color="Olive">a</font> </span>}</span>  holds <br/><font color="Olive">x</font> <a href="hidden.html#R2">in</a> the <a href="conlat_1.html#U2" target="_self">Attributes</a> of <font color="Maroon">C</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="19_1_1"><b>proof </b></a><div class="add">

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

<b>assume </b><a NAME="E1:19_1_1"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <font color="Olive">a</font> where <font color="Olive">a</font> is   <a href="conlat_1.html#NM3">Attribute</a> of <font color="Maroon">C</font> : for <font color="Olive">o</font> being  <a href="conlat_1.html#NM2">Object</a> of <font color="Maroon">C</font>  st <font color="Olive">o</font> <a href="hidden.html#R2">in</a> <font color="Maroon">O</font> holds <br/><font color="Olive">o</font> <a href="conlat_1.html#R1" target="_self">is-connected-with</a> <font color="Olive">a</font> </span>}</span> 
 ;<br/>

<b>then consider </b><font color="Maroon">x'</font> being   <a href="conlat_1.html#NM3">Attribute</a> of <font color="Maroon">C</font><b> such that </b><br/><a NAME="E3:19_1_1"/><i><font color="Green">E32</font></i>: 
( <font color="Maroon">x'</font> <a href="hidden.html#R1">=</a> <font color="Maroon">x</font> &amp; ( for <font color="Olive">o</font> being  <a href="conlat_1.html#NM2">Object</a> of <font color="Maroon">C</font>  st <font color="Olive">o</font> <a href="hidden.html#R2">in</a> <font color="Maroon">O</font> holds <br/><font color="Olive">o</font> <a href="conlat_1.html#R1" target="_self">is-connected-with</a> <font color="Maroon">x'</font> ) )
 ;<br/>
<b>thus </b><a NAME="E4:19_1_1"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> the <a href="conlat_1.html#U2" target="_self">Attributes</a> of <font color="Maroon">C</font>
 <b>by </b><i/>;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E2:19_1"/>
<span class="p1">{<span class="default"> <font color="Olive">a</font> where <font color="Olive">a</font> is   <a href="conlat_1.html#NM3">Attribute</a> of <font color="Maroon">C</font> : for <font color="Olive">o</font> being  <a href="conlat_1.html#NM2">Object</a> of <font color="Maroon">C</font>  st <font color="Olive">o</font> <a href="hidden.html#R2">in</a> <font color="Maroon">O</font> holds <br/><font color="Olive">o</font> <a href="conlat_1.html#R1" target="_self">is-connected-with</a> <font color="Olive">a</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</font>
 <b>by </b><i><a class="ref" href="tarski.html#D3">TARSKI:def 3</a></i>;<br/>


</div><b>end;</b></div>
<b>then reconsider </b><font color="Maroon">A</font> = <span class="p1">{<span class="default"> <font color="Olive">a</font> where <font color="Olive">a</font> is   <a href="conlat_1.html#NM3">Attribute</a> of <font color="Maroon">C</font> : for <font color="Olive">o</font> being  <a href="conlat_1.html#NM2">Object</a> of <font color="Maroon">C</font>  st <font color="Olive">o</font> <a href="hidden.html#R2">in</a> <font color="Maroon">O</font> holds <br/><font color="Olive">o</font> <a href="conlat_1.html#R1" target="_self">is-connected-with</a> <font color="Olive">a</font> </span>}</span>  as   <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/>
<a NAME="E5:19"/><i><font color="Green">E33</font></i>: 
for <font color="Olive">a</font> being  <a href="conlat_1.html#NM3">Attribute</a> of <font color="Maroon">C</font>  st <font color="Olive">a</font> <a href="hidden.html#R2">in</a> <font color="Maroon">A</font> holds <br/><font color="Maroon">x</font> <a href="conlat_1.html#R1" target="_self">is-connected-with</a> <font color="Olive">a</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="19_2"><b>proof </b></a><div class="add">

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

<b>assume </b><a NAME="E1:19_2"/>
<font color="Maroon">a</font> <a href="hidden.html#R2">in</a> <font color="Maroon">A</font>
 ;<br/>

<b>then consider </b><font color="Maroon">a'</font> being   <a href="conlat_1.html#NM3">Attribute</a> of <font color="Maroon">C</font><b> such that </b><br/><a NAME="E3:19_2"/><i><font color="Green">E34</font></i>: 
( <font color="Maroon">a'</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a</font> &amp; ( for <font color="Olive">o</font> being  <a href="conlat_1.html#NM2">Object</a> of <font color="Maroon">C</font>  st <font color="Olive">o</font> <a href="hidden.html#R2">in</a> <font color="Maroon">O</font> holds <br/><font color="Olive">o</font> <a href="conlat_1.html#R1" target="_self">is-connected-with</a> <font color="Maroon">a'</font> ) )
 ;<br/>
<b>thus </b><a NAME="E4:19_2"/>
<font color="Maroon">x</font> <a href="conlat_1.html#R1" target="_self">is-connected-with</a> <font color="Maroon">a</font>
 <b>by </b><i>, </i>;<br/>


</div><b>end;</b></div>
<a NAME="E6:19"/>
<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> <a href="hidden.html#R1">=</a> <span class="p1">{<span class="default"> <font color="Olive">o</font> where <font color="Olive">o</font> is   <a href="conlat_1.html#NM2">Object</a> of <font color="Maroon">C</font> : for <font color="Olive">a</font> being  <a href="conlat_1.html#NM3">Attribute</a> of <font color="Maroon">C</font>  st <font color="Olive">a</font> <a href="hidden.html#R2">in</a> <font color="Maroon">A</font> holds <br/><font color="Olive">o</font> <a href="conlat_1.html#R1" target="_self">is-connected-with</a> <font color="Olive">a</font> </span>}</span> 
 
<b>by </b><i/>;<br/>
<a NAME="E7:19"/><b>then </b>
<font color="Maroon">x</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</font></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">A</font>
 
<b>by </b><i/>;<br/>
<b>hence </b><a NAME="E8:19"/>
<font color="Maroon">x</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</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" target="_self">ObjectDerivation</a> <font color="Maroon">C</font></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">O</font></span>)</span>
 <b>by </b><i/>;<br/>


</div>
