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<b>let </b><font color="Maroon" title="c1">X</font>, <font color="Maroon" title="c2">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/><b>let </b><font color="Maroon" title="c3">F</font> be   <a href="armstrng.html#NM2" title="ARMSTRNG:NM.2">Dependency-set</a> of <font color="Maroon" title="c1">X</font>;<br/>



<div><b>hereby </b>
<div class="add"><b>assume </b><a NAME="E1:79_1"/>
<font color="Maroon" title="c2">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="armstrng.html#K9" title="ARMSTRNG:func.9">saturated-subsets</a> <font color="Maroon" title="c3">F</font>
 ;<br/><b>then consider </b><font color="Maroon" title="c4">B</font> being   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <font color="Maroon" title="c1">X</font><b> such that </b><br/><a NAME="E3:79_1"/><i><font color="Green" title="E45">A1</font></i>: 
<font color="Maroon" title="c2">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">B</font>
 <b>and </b><br/><a NAME="E4:79_1"/><i><font color="Green" title="E46">A2</font></i>: 
 ex <font color="Olive" title="b1">A</font> being  <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <font color="Maroon" title="c1">X</font> st <font color="Olive" title="b1">A</font> <a href="armstrng.html#R4" title="ARMSTRNG:pred.4">^|^</a> <font color="Maroon" title="c4">B</font>,<font color="Maroon" title="c3">F</font>
 ;<br/><b>consider </b><font color="Maroon" title="c5">A</font> being   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <font color="Maroon" title="c1">X</font><b> such that </b><br/><a NAME="E6:79_1"/><i><font color="Green" title="E47">A3</font></i>: 
<font color="Maroon" title="c5">A</font> <a href="armstrng.html#R4" title="ARMSTRNG:pred.4">^|^</a> <font color="Maroon" title="c4">B</font>,<font color="Maroon" title="c3">F</font>
 <b>by </b><i><a class="txt" href="armstrng.html#E4:79_1"><i><font color="Green" title="E46">A2</font></i></a></i>;<br/><b>take </b><font color="Maroon" title="c6">B</font> = <font color="Maroon" title="c4">B</font>;<br/><b>take </b><font color="Maroon" title="c7">A</font> = <font color="Maroon" title="c5">A</font>;<br/><b>thus </b><a NAME="E7:79_1"/>
( <font color="Maroon" title="c2">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">B</font> &amp; <font color="Maroon" title="c7">A</font> <a href="armstrng.html#R4" title="ARMSTRNG:pred.4">^|^</a> <font color="Maroon" title="c6">B</font>,<font color="Maroon" title="c3">F</font> )
 <b>by </b><i><a class="txt" href="armstrng.html#E3:79_1"><i><font color="Green" title="E45">A1</font></i></a>, <a class="txt" href="armstrng.html#E6:79_1"><i><font color="Green" title="E47">A3</font></i></a></i>;<br/></div>
<b>end;</b></div>

<b>given </b><font color="Maroon" title="c4">B</font>, <font color="Maroon" title="c5">A</font> being   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <font color="Maroon" title="c1">X</font><b> such that </b><a NAME="E3:79"/><i><font color="Green" title="E45">A4</font></i>: 
( <font color="Maroon" title="c2">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">B</font> &amp; <font color="Maroon" title="c5">A</font> <a href="armstrng.html#R4" title="ARMSTRNG:pred.4">^|^</a> <font color="Maroon" title="c4">B</font>,<font color="Maroon" title="c3">F</font> )
 ;<br/>

<b>thus </b><a NAME="E4:79"/>
<font color="Maroon" title="c2">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="armstrng.html#K9" title="ARMSTRNG:func.9">saturated-subsets</a> <font color="Maroon" title="c3">F</font>
 <b>by </b><i><a class="txt" href="armstrng.html#E3:79"><i><font color="Green" title="E45">A4</font></i></a></i>;<br/>


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