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

<b>let </b><font color="Maroon" title="c1">C</font> be   <a href="conlat_1.html#NM1" title="CONLAT_1:NM.1">FormalContext</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">A</font> being  <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c1">C</font> holds  <span class="p1">(<span class="default"><a href="conlat_1.html#K2" title="CONLAT_1:func.2">AttributeDerivation</a> <font color="Maroon" title="c1">C</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="conlat_1.html#K1" title="CONLAT_1:func.1">ObjectDerivation</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">C</font> <a href="conlat_2.html#K7" title="CONLAT_2:func.7">.:</a> </span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">A</font></span><br/><b>let </b><font color="Maroon" title="c2">O</font> be   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c1">C</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <span class="p1">(<span class="default"><a href="conlat_1.html#K2" title="CONLAT_1:func.2">AttributeDerivation</a> <font color="Maroon" title="c1">C</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c2">O</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="conlat_1.html#K1" title="CONLAT_1:func.1">ObjectDerivation</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">C</font> <a href="conlat_2.html#K7" title="CONLAT_2:func.7">.:</a> </span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c2">O</font></span><br/>



<a NAME="E1:29"/><i><font color="Green" title="E18">A1</font></i>: 
<span class="p1">(<span class="default"><a href="conlat_1.html#K2" title="CONLAT_1:func.2">AttributeDerivation</a> <font color="Maroon" title="c1">C</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c2">O</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">{<span class="default"> <font color="Olive" title="b1">a</font> where <font color="Olive" title="b1">a</font> is   <a href="conlat_1.html#NM2" title="CONLAT_1:NM.2">Object</a> of <font color="Maroon" title="c1">C</font> : for <font color="Olive" title="b2">o</font> being  <a href="conlat_1.html#NM3" title="CONLAT_1:NM.3">Attribute</a> of <font color="Maroon" title="c1">C</font>  st <font color="Olive" title="b2">o</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">O</font> holds <br/><font color="Olive" title="b1">a</font> <a href="conlat_1.html#R1" title="CONLAT_1:pred.1">is-connected-with</a> <font color="Olive" title="b2">o</font> </span>}</span> 
 
<b>by </b><i><a class="ref" href="conlat_1.html#D7" title="CONLAT_1:def.7">CONLAT_1:def 7</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c3">O'</font> = <font color="Maroon" title="c2">O</font> as   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c1">C</font> <a href="conlat_2.html#K7" title="CONLAT_2:func.7">.:</a> </span>)</span> ;<br/>
<a NAME="E3:29"/><i><font color="Green" title="E19">A2</font></i>: 
<span class="p1">(<span class="default"><a href="conlat_1.html#K1" title="CONLAT_1:func.1">ObjectDerivation</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">C</font> <a href="conlat_2.html#K7" title="CONLAT_2:func.7">.:</a> </span>)</span></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c3">O'</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">{<span class="default"> <font color="Olive" title="b1">a</font> where <font color="Olive" title="b1">a</font> is   <a href="conlat_1.html#NM3" title="CONLAT_1:NM.3">Attribute</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c1">C</font> <a href="conlat_2.html#K7" title="CONLAT_2:func.7">.:</a> </span>)</span> : for <font color="Olive" title="b2">o</font> being  <a href="conlat_1.html#NM2" title="CONLAT_1:NM.2">Object</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c1">C</font> <a href="conlat_2.html#K7" title="CONLAT_2:func.7">.:</a> </span>)</span>  st <font color="Olive" title="b2">o</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">O'</font> holds <br/><font color="Olive" title="b2">o</font> <a href="conlat_1.html#R1" title="CONLAT_1:pred.1">is-connected-with</a> <font color="Olive" title="b1">a</font> </span>}</span> 
 
<b>by </b><i><a class="ref" href="conlat_1.html#D6" title="CONLAT_1:def.6">CONLAT_1:def 6</a></i>;<br/>
<b>set </b><font color="Maroon" title="c4">A1</font> = <span class="p1">{<span class="default"> <font color="Olive" title="b1">a</font> where <font color="Olive" title="b1">a</font> is   <a href="conlat_1.html#NM2" title="CONLAT_1:NM.2">Object</a> of <font color="Maroon" title="c1">C</font> : for <font color="Olive" title="b2">o</font> being  <a href="conlat_1.html#NM3" title="CONLAT_1:NM.3">Attribute</a> of <font color="Maroon" title="c1">C</font>  st <font color="Olive" title="b2">o</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">O</font> holds <br/><font color="Olive" title="b1">a</font> <a href="conlat_1.html#R1" title="CONLAT_1:pred.1">is-connected-with</a> <font color="Olive" title="b2">o</font> </span>}</span> ;<br/>
<b>set </b><font color="Maroon" title="c5">A2</font> = <span class="p1">{<span class="default"> <font color="Olive" title="b1">a</font> where <font color="Olive" title="b1">a</font> is   <a href="conlat_1.html#NM3" title="CONLAT_1:NM.3">Attribute</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c1">C</font> <a href="conlat_2.html#K7" title="CONLAT_2:func.7">.:</a> </span>)</span> : for <font color="Olive" title="b2">o</font> being  <a href="conlat_1.html#NM2" title="CONLAT_1:NM.2">Object</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c1">C</font> <a href="conlat_2.html#K7" title="CONLAT_2:func.7">.:</a> </span>)</span>  st <font color="Olive" title="b2">o</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">O'</font> holds <br/><font color="Olive" title="b2">o</font> <a href="conlat_1.html#R1" title="CONLAT_1:pred.1">is-connected-with</a> <font color="Olive" title="b1">a</font> </span>}</span> ;<br/>
<a NAME="E4:29"/><i><font color="Green" title="E20">A3</font></i>: 
<span class="p1">{<span class="default"> <font color="Olive" title="b1">a</font> where <font color="Olive" title="b1">a</font> is   <a href="conlat_1.html#NM2" title="CONLAT_1:NM.2">Object</a> of <font color="Maroon" title="c1">C</font> : for <font color="Olive" title="b2">o</font> being  <a href="conlat_1.html#NM3" title="CONLAT_1:NM.3">Attribute</a> of <font color="Maroon" title="c1">C</font>  st <font color="Olive" title="b2">o</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">O</font> holds <br/><font color="Olive" title="b1">a</font> <a href="conlat_1.html#R1" title="CONLAT_1:pred.1">is-connected-with</a> <font color="Olive" title="b2">o</font> </span>}</span>  <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">{<span class="default"> <font color="Olive" title="b1">a</font> where <font color="Olive" title="b1">a</font> is   <a href="conlat_1.html#NM3" title="CONLAT_1:NM.3">Attribute</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c1">C</font> <a href="conlat_2.html#K7" title="CONLAT_2:func.7">.:</a> </span>)</span> : for <font color="Olive" title="b2">o</font> being  <a href="conlat_1.html#NM2" title="CONLAT_1:NM.2">Object</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c1">C</font> <a href="conlat_2.html#K7" title="CONLAT_2:func.7">.:</a> </span>)</span>  st <font color="Olive" title="b2">o</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">O'</font> holds <br/><font color="Olive" title="b2">o</font> <a href="conlat_1.html#R1" title="CONLAT_1:pred.1">is-connected-with</a> <font color="Olive" title="b1">a</font> </span>}</span> 
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="29_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c6">u</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3" title="TARSKI:def.3">TARSKI:def 3</a> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  not <font color="Maroon" title="c6">u</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">{<span class="default"> <font color="Olive" title="b1">a</font> where <font color="Olive" title="b1">a</font> is   <a href="conlat_1.html#NM2" title="CONLAT_1:NM.2">Object</a> of <font color="Maroon" title="c1">C</font> : for <font color="Olive" title="b2">o</font> being  <a href="conlat_1.html#NM3" title="CONLAT_1:NM.3">Attribute</a> of <font color="Maroon" title="c1">C</font>  st <font color="Olive" title="b2">o</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">O</font> holds <br/><font color="Olive" title="b1">a</font> <a href="conlat_1.html#R1" title="CONLAT_1:pred.1">is-connected-with</a> <font color="Olive" title="b2">o</font> </span>}</span>  or <font color="Maroon" title="c6">u</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">{<span class="default"> <font color="Olive" title="b1">a</font> where <font color="Olive" title="b1">a</font> is   <a href="conlat_1.html#NM3" title="CONLAT_1:NM.3">Attribute</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c1">C</font> <a href="conlat_2.html#K7" title="CONLAT_2:func.7">.:</a> </span>)</span> : for <font color="Olive" title="b2">o</font> being  <a href="conlat_1.html#NM2" title="CONLAT_1:NM.2">Object</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c1">C</font> <a href="conlat_2.html#K7" title="CONLAT_2:func.7">.:</a> </span>)</span>  st <font color="Olive" title="b2">o</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">O'</font> holds <br/><font color="Olive" title="b2">o</font> <a href="conlat_1.html#R1" title="CONLAT_1:pred.1">is-connected-with</a> <font color="Olive" title="b1">a</font> </span>}</span>  )</span><br/>

<b>assume </b><a NAME="E1:29_1"/>
<font color="Maroon" title="c6">u</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">{<span class="default"> <font color="Olive" title="b1">a</font> where <font color="Olive" title="b1">a</font> is   <a href="conlat_1.html#NM2" title="CONLAT_1:NM.2">Object</a> of <font color="Maroon" title="c1">C</font> : for <font color="Olive" title="b2">o</font> being  <a href="conlat_1.html#NM3" title="CONLAT_1:NM.3">Attribute</a> of <font color="Maroon" title="c1">C</font>  st <font color="Olive" title="b2">o</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">O</font> holds <br/><font color="Olive" title="b1">a</font> <a href="conlat_1.html#R1" title="CONLAT_1:pred.1">is-connected-with</a> <font color="Olive" title="b2">o</font> </span>}</span> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c6">u</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">{<span class="default"> <font color="Olive" title="b1">a</font> where <font color="Olive" title="b1">a</font> is   <a href="conlat_1.html#NM3" title="CONLAT_1:NM.3">Attribute</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c1">C</font> <a href="conlat_2.html#K7" title="CONLAT_2:func.7">.:</a> </span>)</span> : for <font color="Olive" title="b2">o</font> being  <a href="conlat_1.html#NM2" title="CONLAT_1:NM.2">Object</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c1">C</font> <a href="conlat_2.html#K7" title="CONLAT_2:func.7">.:</a> </span>)</span>  st <font color="Olive" title="b2">o</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">O'</font> holds <br/><font color="Olive" title="b2">o</font> <a href="conlat_1.html#R1" title="CONLAT_1:pred.1">is-connected-with</a> <font color="Olive" title="b1">a</font> </span>}</span> </span><br/>

<b>then consider </b><font color="Maroon" title="c7">a</font> being   <a href="conlat_1.html#NM2" title="CONLAT_1:NM.2">Object</a> of <font color="Maroon" title="c1">C</font><b> such that </b><br/><a NAME="E3:29_1"/><i><font color="Green" title="E21">A4</font></i>: 
( <font color="Maroon" title="c7">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">u</font> &amp; ( for <font color="Olive" title="b1">o</font> being  <a href="conlat_1.html#NM3" title="CONLAT_1:NM.3">Attribute</a> of <font color="Maroon" title="c1">C</font>  st <font color="Olive" title="b1">o</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">O</font> holds <br/><font color="Maroon" title="c7">a</font> <a href="conlat_1.html#R1" title="CONLAT_1:pred.1">is-connected-with</a> <font color="Olive" title="b1">o</font> ) )
 ;<br/>
<b>reconsider </b><font color="Maroon" title="c8">u'</font> = <font color="Maroon" title="c6">u</font> as   <a href="conlat_1.html#NM3" title="CONLAT_1:NM.3">Attribute</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c1">C</font> <a href="conlat_2.html#K7" title="CONLAT_2:func.7">.:</a> </span>)</span> <b>by </b><i><a class="txt" href="#E3:29_1"><i><font color="Green" title="E21">A4</font></i></a></i>;<br/>
<a NAME="E5:29_1"/>
for <font color="Olive" title="b1">o</font> being  <a href="conlat_1.html#NM2" title="CONLAT_1:NM.2">Object</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c1">C</font> <a href="conlat_2.html#K7" title="CONLAT_2:func.7">.:</a> </span>)</span>  st <font color="Olive" title="b1">o</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">O'</font> holds <br/><font color="Olive" title="b1">o</font> <a href="conlat_1.html#R1" title="CONLAT_1:pred.1">is-connected-with</a> <font color="Maroon" title="c8">u'</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="29_1_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c9">o'</font> be   <a href="conlat_1.html#NM2" title="CONLAT_1:NM.2">Object</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c1">C</font> <a href="conlat_2.html#K7" title="CONLAT_2:func.7">.:</a> </span>)</span>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c9">o'</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">O'</font> implies <font color="Maroon" title="c9">o'</font> <a href="conlat_1.html#R1" title="CONLAT_1:pred.1">is-connected-with</a> <font color="Maroon" title="c8">u'</font> )</span><br/>

<b>assume </b><a NAME="E1:29_1_1"/><i><font color="Green" title="E22">A5</font></i>: 
<font color="Maroon" title="c9">o'</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">O'</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c9">o'</font> <a href="conlat_1.html#R1" title="CONLAT_1:pred.1">is-connected-with</a> <font color="Maroon" title="c8">u'</font></span><br/>

<b>reconsider </b><font color="Maroon" title="c10">o</font> = <font color="Maroon" title="c9">o'</font> as   <a href="conlat_1.html#NM3" title="CONLAT_1:NM.3">Attribute</a> of <font color="Maroon" title="c1">C</font> ;<br/>
<a NAME="E3:29_1_1"/>
<font color="Maroon" title="c7">a</font> <a href="conlat_1.html#R1" title="CONLAT_1:pred.1">is-connected-with</a> <font color="Maroon" title="c10">o</font>
 
<b>by </b><i><a class="txt" href="#E3:29_1"><i><font color="Green" title="E21">A4</font></i></a>, <a class="txt" href="#E1:29_1_1"><i><font color="Green" title="E22">A5</font></i></a></i>;<br/>
<a NAME="E4:29_1_1"/><b>then </b>
<span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c7">a</font>,<font color="Maroon" title="c10">o</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="conlat_1.html#U1" title="CONLAT_1:sel.1">Information</a> of <font color="Maroon" title="c1">C</font>
 
<b>by </b><i><a class="ref" href="conlat_1.html#D5" title="CONLAT_1:def.5">CONLAT_1:def 5</a></i>;<br/>
<a NAME="E5:29_1_1"/><b>then </b>
<span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c9">o'</font>,<font color="Maroon" title="c8">u'</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="conlat_1.html#U1" title="CONLAT_1:sel.1">Information</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c1">C</font> <a href="conlat_2.html#K7" title="CONLAT_2:func.7">.:</a> </span>)</span>
 
<b>by </b><i><a class="txt" href="#E3:29_1"><i><font color="Green" title="E21">A4</font></i></a>, <a class="ref" href="relat_1.html#D7" title="RELAT_1:def.7">RELAT_1:def 7</a></i>;<br/>
<b>hence </b><a NAME="E6:29_1_1"/>
<font color="Maroon" title="c9">o'</font> <a href="conlat_1.html#R1" title="CONLAT_1:pred.1">is-connected-with</a> <font color="Maroon" title="c8">u'</font>
 <b>by </b><i><a class="ref" href="conlat_1.html#D5" title="CONLAT_1:def.5">CONLAT_1:def 5</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E6:29_1"/>
<font color="Maroon" title="c6">u</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">{<span class="default"> <font color="Olive" title="b1">a</font> where <font color="Olive" title="b1">a</font> is   <a href="conlat_1.html#NM3" title="CONLAT_1:NM.3">Attribute</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c1">C</font> <a href="conlat_2.html#K7" title="CONLAT_2:func.7">.:</a> </span>)</span> : for <font color="Olive" title="b2">o</font> being  <a href="conlat_1.html#NM2" title="CONLAT_1:NM.2">Object</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c1">C</font> <a href="conlat_2.html#K7" title="CONLAT_2:func.7">.:</a> </span>)</span>  st <font color="Olive" title="b2">o</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">O'</font> holds <br/><font color="Olive" title="b2">o</font> <a href="conlat_1.html#R1" title="CONLAT_1:pred.1">is-connected-with</a> <font color="Olive" title="b1">a</font> </span>}</span> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div>
<a NAME="E5:29"/>
<span class="p1">{<span class="default"> <font color="Olive" title="b1">a</font> where <font color="Olive" title="b1">a</font> is   <a href="conlat_1.html#NM3" title="CONLAT_1:NM.3">Attribute</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c1">C</font> <a href="conlat_2.html#K7" title="CONLAT_2:func.7">.:</a> </span>)</span> : for <font color="Olive" title="b2">o</font> being  <a href="conlat_1.html#NM2" title="CONLAT_1:NM.2">Object</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c1">C</font> <a href="conlat_2.html#K7" title="CONLAT_2:func.7">.:</a> </span>)</span>  st <font color="Olive" title="b2">o</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">O'</font> holds <br/><font color="Olive" title="b2">o</font> <a href="conlat_1.html#R1" title="CONLAT_1:pred.1">is-connected-with</a> <font color="Olive" title="b1">a</font> </span>}</span>  <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">{<span class="default"> <font color="Olive" title="b1">a</font> where <font color="Olive" title="b1">a</font> is   <a href="conlat_1.html#NM2" title="CONLAT_1:NM.2">Object</a> of <font color="Maroon" title="c1">C</font> : for <font color="Olive" title="b2">o</font> being  <a href="conlat_1.html#NM3" title="CONLAT_1:NM.3">Attribute</a> of <font color="Maroon" title="c1">C</font>  st <font color="Olive" title="b2">o</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">O</font> holds <br/><font color="Olive" title="b1">a</font> <a href="conlat_1.html#R1" title="CONLAT_1:pred.1">is-connected-with</a> <font color="Olive" title="b2">o</font> </span>}</span> 
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="29_2"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c6">u</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3" title="TARSKI:def.3">TARSKI:def 3</a> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  not <font color="Maroon" title="c6">u</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">{<span class="default"> <font color="Olive" title="b1">a</font> where <font color="Olive" title="b1">a</font> is   <a href="conlat_1.html#NM3" title="CONLAT_1:NM.3">Attribute</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c1">C</font> <a href="conlat_2.html#K7" title="CONLAT_2:func.7">.:</a> </span>)</span> : for <font color="Olive" title="b2">o</font> being  <a href="conlat_1.html#NM2" title="CONLAT_1:NM.2">Object</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c1">C</font> <a href="conlat_2.html#K7" title="CONLAT_2:func.7">.:</a> </span>)</span>  st <font color="Olive" title="b2">o</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">O'</font> holds <br/><font color="Olive" title="b2">o</font> <a href="conlat_1.html#R1" title="CONLAT_1:pred.1">is-connected-with</a> <font color="Olive" title="b1">a</font> </span>}</span>  or <font color="Maroon" title="c6">u</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">{<span class="default"> <font color="Olive" title="b1">a</font> where <font color="Olive" title="b1">a</font> is   <a href="conlat_1.html#NM2" title="CONLAT_1:NM.2">Object</a> of <font color="Maroon" title="c1">C</font> : for <font color="Olive" title="b2">o</font> being  <a href="conlat_1.html#NM3" title="CONLAT_1:NM.3">Attribute</a> of <font color="Maroon" title="c1">C</font>  st <font color="Olive" title="b2">o</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">O</font> holds <br/><font color="Olive" title="b1">a</font> <a href="conlat_1.html#R1" title="CONLAT_1:pred.1">is-connected-with</a> <font color="Olive" title="b2">o</font> </span>}</span>  )</span><br/>

<b>assume </b><a NAME="E1:29_2"/>
<font color="Maroon" title="c6">u</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">{<span class="default"> <font color="Olive" title="b1">a</font> where <font color="Olive" title="b1">a</font> is   <a href="conlat_1.html#NM3" title="CONLAT_1:NM.3">Attribute</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c1">C</font> <a href="conlat_2.html#K7" title="CONLAT_2:func.7">.:</a> </span>)</span> : for <font color="Olive" title="b2">o</font> being  <a href="conlat_1.html#NM2" title="CONLAT_1:NM.2">Object</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c1">C</font> <a href="conlat_2.html#K7" title="CONLAT_2:func.7">.:</a> </span>)</span>  st <font color="Olive" title="b2">o</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">O'</font> holds <br/><font color="Olive" title="b2">o</font> <a href="conlat_1.html#R1" title="CONLAT_1:pred.1">is-connected-with</a> <font color="Olive" title="b1">a</font> </span>}</span> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c6">u</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">{<span class="default"> <font color="Olive" title="b1">a</font> where <font color="Olive" title="b1">a</font> is   <a href="conlat_1.html#NM2" title="CONLAT_1:NM.2">Object</a> of <font color="Maroon" title="c1">C</font> : for <font color="Olive" title="b2">o</font> being  <a href="conlat_1.html#NM3" title="CONLAT_1:NM.3">Attribute</a> of <font color="Maroon" title="c1">C</font>  st <font color="Olive" title="b2">o</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">O</font> holds <br/><font color="Olive" title="b1">a</font> <a href="conlat_1.html#R1" title="CONLAT_1:pred.1">is-connected-with</a> <font color="Olive" title="b2">o</font> </span>}</span> </span><br/>

<b>then consider </b><font color="Maroon" title="c7">a</font> being   <a href="conlat_1.html#NM3" title="CONLAT_1:NM.3">Attribute</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c1">C</font> <a href="conlat_2.html#K7" title="CONLAT_2:func.7">.:</a> </span>)</span><b> such that </b><br/><a NAME="E3:29_2"/><i><font color="Green" title="E21">A6</font></i>: 
( <font color="Maroon" title="c7">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">u</font> &amp; ( for <font color="Olive" title="b1">o</font> being  <a href="conlat_1.html#NM2" title="CONLAT_1:NM.2">Object</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c1">C</font> <a href="conlat_2.html#K7" title="CONLAT_2:func.7">.:</a> </span>)</span>  st <font color="Olive" title="b1">o</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">O'</font> holds <br/><font color="Olive" title="b1">o</font> <a href="conlat_1.html#R1" title="CONLAT_1:pred.1">is-connected-with</a> <font color="Maroon" title="c7">a</font> ) )
 ;<br/>
<b>reconsider </b><font color="Maroon" title="c8">u'</font> = <font color="Maroon" title="c6">u</font> as   <a href="conlat_1.html#NM2" title="CONLAT_1:NM.2">Object</a> of <font color="Maroon" title="c1">C</font> <b>by </b><i><a class="txt" href="#E3:29_2"><i><font color="Green" title="E21">A6</font></i></a></i>;<br/>
<a NAME="E5:29_2"/>
for <font color="Olive" title="b1">o</font> being  <a href="conlat_1.html#NM3" title="CONLAT_1:NM.3">Attribute</a> of <font color="Maroon" title="c1">C</font>  st <font color="Olive" title="b1">o</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">O</font> holds <br/><font color="Maroon" title="c8">u'</font> <a href="conlat_1.html#R1" title="CONLAT_1:pred.1">is-connected-with</a> <font color="Olive" title="b1">o</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="29_2_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c9">o'</font> be   <a href="conlat_1.html#NM3" title="CONLAT_1:NM.3">Attribute</a> of <font color="Maroon" title="c1">C</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c9">o'</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">O</font> implies <font color="Maroon" title="c8">u'</font> <a href="conlat_1.html#R1" title="CONLAT_1:pred.1">is-connected-with</a> <font color="Maroon" title="c9">o'</font> )</span><br/>

<b>assume </b><a NAME="E1:29_2_1"/><i><font color="Green" title="E22">A7</font></i>: 
<font color="Maroon" title="c9">o'</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">O</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c8">u'</font> <a href="conlat_1.html#R1" title="CONLAT_1:pred.1">is-connected-with</a> <font color="Maroon" title="c9">o'</font></span><br/>

<b>reconsider </b><font color="Maroon" title="c10">o</font> = <font color="Maroon" title="c9">o'</font> as   <a href="conlat_1.html#NM2" title="CONLAT_1:NM.2">Object</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c1">C</font> <a href="conlat_2.html#K7" title="CONLAT_2:func.7">.:</a> </span>)</span> ;<br/>
<a NAME="E3:29_2_1"/>
<font color="Maroon" title="c10">o</font> <a href="conlat_1.html#R1" title="CONLAT_1:pred.1">is-connected-with</a> <font color="Maroon" title="c7">a</font>
 
<b>by </b><i><a class="txt" href="#E3:29_2"><i><font color="Green" title="E21">A6</font></i></a>, <a class="txt" href="#E1:29_2_1"><i><font color="Green" title="E22">A7</font></i></a></i>;<br/>
<a NAME="E4:29_2_1"/><b>then </b>
<span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c10">o</font>,<font color="Maroon" title="c7">a</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="conlat_1.html#U1" title="CONLAT_1:sel.1">Information</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c1">C</font> <a href="conlat_2.html#K7" title="CONLAT_2:func.7">.:</a> </span>)</span>
 
<b>by </b><i><a class="ref" href="conlat_1.html#D5" title="CONLAT_1:def.5">CONLAT_1:def 5</a></i>;<br/>
<a NAME="E5:29_2_1"/><b>then </b>
<span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c8">u'</font>,<font color="Maroon" title="c9">o'</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="conlat_1.html#U1" title="CONLAT_1:sel.1">Information</a> of <font color="Maroon" title="c1">C</font>
 
<b>by </b><i><a class="txt" href="#E3:29_2"><i><font color="Green" title="E21">A6</font></i></a>, <a class="ref" href="relat_1.html#D7" title="RELAT_1:def.7">RELAT_1:def 7</a></i>;<br/>
<b>hence </b><a NAME="E6:29_2_1"/>
<font color="Maroon" title="c8">u'</font> <a href="conlat_1.html#R1" title="CONLAT_1:pred.1">is-connected-with</a> <font color="Maroon" title="c9">o'</font>
 <b>by </b><i><a class="ref" href="conlat_1.html#D5" title="CONLAT_1:def.5">CONLAT_1:def 5</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E6:29_2"/>
<font color="Maroon" title="c6">u</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">{<span class="default"> <font color="Olive" title="b1">a</font> where <font color="Olive" title="b1">a</font> is   <a href="conlat_1.html#NM2" title="CONLAT_1:NM.2">Object</a> of <font color="Maroon" title="c1">C</font> : for <font color="Olive" title="b2">o</font> being  <a href="conlat_1.html#NM3" title="CONLAT_1:NM.3">Attribute</a> of <font color="Maroon" title="c1">C</font>  st <font color="Olive" title="b2">o</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">O</font> holds <br/><font color="Olive" title="b1">a</font> <a href="conlat_1.html#R1" title="CONLAT_1:pred.1">is-connected-with</a> <font color="Olive" title="b2">o</font> </span>}</span> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E6:29"/>
<span class="p1">(<span class="default"><a href="conlat_1.html#K2" title="CONLAT_1:func.2">AttributeDerivation</a> <font color="Maroon" title="c1">C</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c2">O</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="conlat_1.html#K1" title="CONLAT_1:func.1">ObjectDerivation</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">C</font> <a href="conlat_2.html#K7" title="CONLAT_2:func.7">.:</a> </span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c2">O</font>
 <b>by </b><i><a class="txt" href="#E1:29"><i><font color="Green" title="E18">A1</font></i></a>, <a class="txt" href="#E3:29"><i><font color="Green" title="E19">A2</font></i></a>, <a class="txt" href="#E4:29"><i><font color="Green" title="E20">A3</font></i></a>, <a class="ref" href="xboole_0.html#D10" title="XBOOLE_0:def.10">XBOOLE_0:def 10</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div>
