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<b>let </b><font color="Maroon">F1</font> be   <a href="binop_1.html#NM2">BinOp</a> of  <a href="conlat_1.html#K8" target="_self">B-carrier</a> <font color="Maroon">C</font>, <font color="Maroon">F2</font> be   <a href="binop_1.html#NM2">BinOp</a> of  <a href="conlat_1.html#K8" target="_self">B-carrier</a> <font color="Maroon">C</font>;<br/>

<b>assume </b><a NAME="E1:71_1_2"/><i><font color="Green">E39</font></i>: 
for <font color="Olive">CP1</font>, <font color="Olive">CP2</font> being <a href="conlat_1.html#V6" target="_self">strict</a> <a href="conlat_1.html#NM4">FormalConcept</a> of <font color="Maroon">C</font>  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> ex <font color="Olive">A</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</font> st <br/>( <font color="Maroon">F1</font> <a href="binop_1.html#K1">.</a> <font color="Olive">CP1</font>,<font color="Olive">CP2</font> <a href="hidden.html#R1">=</a>  <a href="conlat_1.html#G3" target="_self">ConceptStr</a>(# <font color="Olive">O</font>,<font color="Olive">A</font> #) &amp; <font color="Olive">O</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</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> <span class="p2">(<span class="default">the <a href="conlat_1.html#U4" target="_self">Extent</a> of <font color="Olive">CP1</font> <a href="subset_1.html#K4">\/</a> the <a href="conlat_1.html#U4" target="_self">Extent</a> of <font color="Olive">CP2</font></span>)</span></span>)</span> &amp; <font color="Olive">A</font> <a href="hidden.html#R1">=</a> the <a href="conlat_1.html#U5" target="_self">Intent</a> of <font color="Olive">CP1</font> <a href="subset_1.html#K9">/\</a> the <a href="conlat_1.html#U5" target="_self">Intent</a> of <font color="Olive">CP2</font> )
 ;<br/>

<b>assume </b><a NAME="E2:71_1_2"/><i><font color="Green">E42</font></i>: 
for <font color="Olive">CP1</font>, <font color="Olive">CP2</font> being <a href="conlat_1.html#V6" target="_self">strict</a> <a href="conlat_1.html#NM4">FormalConcept</a> of <font color="Maroon">C</font>  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> ex <font color="Olive">A</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</font> st <br/>( <font color="Maroon">F2</font> <a href="binop_1.html#K1">.</a> <font color="Olive">CP1</font>,<font color="Olive">CP2</font> <a href="hidden.html#R1">=</a>  <a href="conlat_1.html#G3" target="_self">ConceptStr</a>(# <font color="Olive">O</font>,<font color="Olive">A</font> #) &amp; <font color="Olive">O</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</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> <span class="p2">(<span class="default">the <a href="conlat_1.html#U4" target="_self">Extent</a> of <font color="Olive">CP1</font> <a href="subset_1.html#K4">\/</a> the <a href="conlat_1.html#U4" target="_self">Extent</a> of <font color="Olive">CP2</font></span>)</span></span>)</span> &amp; <font color="Olive">A</font> <a href="hidden.html#R1">=</a> the <a href="conlat_1.html#U5" target="_self">Intent</a> of <font color="Olive">CP1</font> <a href="subset_1.html#K9">/\</a> the <a href="conlat_1.html#U5" target="_self">Intent</a> of <font color="Olive">CP2</font> )
 ;<br/>

<a NAME="E3:71_1_2"/><i><font color="Green">E43</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"><a href="zfmisc_1.html#K2">[:</a><span class="default"><span class="p2">(<span class="default"><a href="conlat_1.html#K8" target="_self">B-carrier</a> <font color="Maroon">C</font></span>)</span>,<span class="p2">(<span class="default"><a href="conlat_1.html#K8" target="_self">B-carrier</a> <font color="Maroon">C</font></span>)</span></span><a href="zfmisc_1.html#K2">:]</a></span> holds <br/><font color="Maroon">F1</font> <a href="funct_1.html#K1">.</a> <font color="Olive">X</font> <a href="hidden.html#R1">=</a> <font color="Maroon">F2</font> <a href="funct_1.html#K1">.</a> <font color="Olive">X</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="71_1_2_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="E1:71_1_2_1"/>
<font color="Maroon">X</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><span class="p2">(<span class="default"><a href="conlat_1.html#K8" target="_self">B-carrier</a> <font color="Maroon">C</font></span>)</span>,<span class="p2">(<span class="default"><a href="conlat_1.html#K8" target="_self">B-carrier</a> <font color="Maroon">C</font></span>)</span></span><a href="zfmisc_1.html#K2">:]</a></span>
 ;<br/>

<b>then consider </b><font color="Maroon">A</font> being    <a href="hidden.html#M1">set</a> , <font color="Maroon">B</font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E3:71_1_2_1"/><i><font color="Green">E44</font></i>: 
( <font color="Maroon">A</font> <a href="hidden.html#R2">in</a>  <a href="conlat_1.html#K8" target="_self">B-carrier</a> <font color="Maroon">C</font> &amp; <font color="Maroon">B</font> <a href="hidden.html#R2">in</a>  <a href="conlat_1.html#K8" target="_self">B-carrier</a> <font color="Maroon">C</font> &amp; <font color="Maroon">X</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">A</font>,<font color="Maroon">B</font></span><a href="tarski.html#K4">]</a></span> )
 <b>by </b><i><a class="ref" href="zfmisc_1.html#D2">ZFMISC_1:def 2</a></i>;<br/>
<b>reconsider </b><font color="Maroon">A</font> = <font color="Maroon">A</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</font> <b>by </b><i>, </i>;<br/>
<b>reconsider </b><font color="Maroon">B</font> = <font color="Maroon">B</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</font> <b>by </b><i>, </i>;<br/>
<b>consider </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>, <font color="Maroon">At</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</font><b> such that </b><br/><a NAME="E7:71_1_2_1"/><i><font color="Green">E45</font></i>: 
( <font color="Maroon">F1</font> <a href="binop_1.html#K1">.</a> <font color="Maroon">A</font>,<font color="Maroon">B</font> <a href="hidden.html#R1">=</a>  <a href="conlat_1.html#G3" target="_self">ConceptStr</a>(# <font color="Maroon">O</font>,<font color="Maroon">At</font> #) &amp; <font color="Maroon">O</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</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> <span class="p2">(<span class="default">the <a href="conlat_1.html#U4" target="_self">Extent</a> of <font color="Maroon">A</font> <a href="subset_1.html#K4">\/</a> the <a href="conlat_1.html#U4" target="_self">Extent</a> of <font color="Maroon">B</font></span>)</span></span>)</span> &amp; <font color="Maroon">At</font> <a href="hidden.html#R1">=</a> the <a href="conlat_1.html#U5" target="_self">Intent</a> of <font color="Maroon">A</font> <a href="subset_1.html#K9">/\</a> the <a href="conlat_1.html#U5" target="_self">Intent</a> of <font color="Maroon">B</font> )
 <b>by </b><i/>;<br/>
<b>consider </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>, <font color="Maroon">At'</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</font><b> such that </b><br/><a NAME="E9:71_1_2_1"/><i><font color="Green">E46</font></i>: 
( <font color="Maroon">F2</font> <a href="binop_1.html#K1">.</a> <font color="Maroon">A</font>,<font color="Maroon">B</font> <a href="hidden.html#R1">=</a>  <a href="conlat_1.html#G3" target="_self">ConceptStr</a>(# <font color="Maroon">O'</font>,<font color="Maroon">At'</font> #) &amp; <font color="Maroon">O'</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</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> <span class="p2">(<span class="default">the <a href="conlat_1.html#U4" target="_self">Extent</a> of <font color="Maroon">A</font> <a href="subset_1.html#K4">\/</a> the <a href="conlat_1.html#U4" target="_self">Extent</a> of <font color="Maroon">B</font></span>)</span></span>)</span> &amp; <font color="Maroon">At'</font> <a href="hidden.html#R1">=</a> the <a href="conlat_1.html#U5" target="_self">Intent</a> of <font color="Maroon">A</font> <a href="subset_1.html#K9">/\</a> the <a href="conlat_1.html#U5" target="_self">Intent</a> of <font color="Maroon">B</font> )
 <b>by </b><i/>;<br/>
<b>thus </b><a NAME="E10:71_1_2_1"/>
<font color="Maroon">F1</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">X</font> <a href="hidden.html#R1">=</a> <font color="Maroon">F2</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">X</font>
 <b>by </b><i>, , <a class="txt" href="conlat_1.html#E2:71_1_2"><i><font color="Green">E42</font></i></a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E4:71_1_2"/><i><font color="Green">E48</font></i>: 
 <a href="relset_1.html#K4">dom</a> <font color="Maroon">F1</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><span class="p2">(<span class="default"><a href="conlat_1.html#K8" target="_self">B-carrier</a> <font color="Maroon">C</font></span>)</span>,<span class="p2">(<span class="default"><a href="conlat_1.html#K8" target="_self">B-carrier</a> <font color="Maroon">C</font></span>)</span></span><a href="zfmisc_1.html#K2">:]</a></span>
 
<b>by </b><i><a class="ref" href="funct_2.html#D1">FUNCT_2:def 1</a></i>;<br/>
<a NAME="E5:71_1_2"/>
 <a href="relset_1.html#K4">dom</a> <font color="Maroon">F2</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><span class="p2">(<span class="default"><a href="conlat_1.html#K8" target="_self">B-carrier</a> <font color="Maroon">C</font></span>)</span>,<span class="p2">(<span class="default"><a href="conlat_1.html#K8" target="_self">B-carrier</a> <font color="Maroon">C</font></span>)</span></span><a href="zfmisc_1.html#K2">:]</a></span>
 
<b>by </b><i><a class="ref" href="funct_2.html#D1">FUNCT_2:def 1</a></i>;<br/>
<b>hence </b><a NAME="E6:71_1_2"/>
<font color="Maroon">F1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">F2</font>
 <b>by </b><i><a class="txt" href="conlat_1.html#E1:71_1_2"><i><font color="Green">E39</font></i></a>, , <a class="ref" href="funct_1.html#T9">FUNCT_1:9</a></i>;<br/>


</div>
