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<b>let </b><font color="Maroon">X</font> be    <a href="hidden.html#M1">set</a> , <font color="Maroon">x</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">F</font> be   <a href="armstrng.html#NM2">Dependency-set</a> of <font color="Maroon">X</font>;<br/>



<div><b>hereby </b>
<div class="add"><b>assume </b><a NAME="E1:79_1"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="armstrng.html#K9" target="_self">saturated-subsets</a> <font color="Maroon">F</font>
 ;<br/><b>then consider </b><font color="Maroon">B</font> being   <a href="subset_1.html#NM2">Subset</a> of <font color="Maroon">X</font><b> such that </b><br/><a NAME="E3:79_1"/><i><font color="Green">E33</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">B</font>
 <b>and </b><br/><a NAME="E4:79_1"/><i><font color="Green">E34</font></i>: 
 ex <font color="Olive">A</font> being  <a href="subset_1.html#NM2">Subset</a> of <font color="Maroon">X</font> st <font color="Olive">A</font> <a href="armstrng.html#R4" target="_self">^|^</a> <font color="Maroon">B</font>,<font color="Maroon">F</font>
 ;<br/><b>consider </b><font color="Maroon">A</font> being   <a href="subset_1.html#NM2">Subset</a> of <font color="Maroon">X</font><b> such that </b><br/><a NAME="E6:79_1"/><i><font color="Green">E35</font></i>: 
<font color="Maroon">A</font> <a href="armstrng.html#R4" target="_self">^|^</a> <font color="Maroon">B</font>,<font color="Maroon">F</font>
 <b>by </b><i/>;<br/><b>take </b><font color="Maroon">B</font> = <font color="Maroon">B</font>;<br/><b>take </b><font color="Maroon">A</font> = <font color="Maroon">A</font>;<br/><b>thus </b><a NAME="E7:79_1"/>
( <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">B</font> &amp; <font color="Maroon">A</font> <a href="armstrng.html#R4" target="_self">^|^</a> <font color="Maroon">B</font>,<font color="Maroon">F</font> )
 <b>by </b><i>, </i>;<br/></div>
<b>end;</b></div>

<b>given </b><font color="Maroon">B</font> being   <a href="subset_1.html#NM2">Subset</a> of <font color="Maroon">X</font>, <font color="Maroon">A</font> being   <a href="subset_1.html#NM2">Subset</a> of <font color="Maroon">X</font><b> such that </b><a NAME="E2:79"/><i><font color="Green">E38</font></i>: 
( <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">B</font> &amp; <font color="Maroon">A</font> <a href="armstrng.html#R4" target="_self">^|^</a> <font color="Maroon">B</font>,<font color="Maroon">F</font> )
 ;<br/>

<b>thus </b><a NAME="E3:79"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="armstrng.html#K9" target="_self">saturated-subsets</a> <font color="Maroon">F</font>
 <b>by </b><i/>;<br/>


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