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<b>let </b><font color="Maroon">X</font> be    <a href="hidden.html#M1">set</a> , <font color="Maroon">A</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/>



<b>assume </b><a NAME="E1:113"/>
<font color="Maroon">A</font> <a href="hidden.html#R2">in</a>  <a href="armstrng.html#K14" target="_self">charact_set</a> <font color="Maroon">F</font>
 ;<br/>

<a NAME="E2:113"/><b>then </b>
<font color="Maroon">A</font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <font color="Olive">Y</font> where <font color="Olive">Y</font> is   <a href="subset_1.html#NM2">Subset</a> of <font color="Maroon">X</font> :  ex <font color="Olive">a</font>, <font color="Olive">b</font> being  <a href="subset_1.html#NM2">Subset</a> of <font color="Maroon">X</font> st <br/>( <span class="p1"><a href="armstrng.html#K6" target="_self">[</a><span class="default"><font color="Olive">a</font>,<font color="Olive">b</font></span><a href="armstrng.html#K6" target="_self">]</a></span> <a href="hidden.html#R2">in</a> <font color="Maroon">F</font> &amp; <font color="Olive">a</font> <a href="tarski.html#R1">c=</a> <font color="Olive">Y</font> &amp; not <font color="Olive">b</font> <a href="tarski.html#R1">c=</a> <font color="Olive">Y</font> ) </span>}</span> 
 
;<br/>
<a NAME="E3:113"/><b>then </b>
 ex <font color="Olive">Y</font> being  <a href="subset_1.html#NM2">Subset</a> of <font color="Maroon">X</font> st <br/>( <font color="Maroon">A</font> <a href="hidden.html#R1">=</a> <font color="Olive">Y</font> &amp;  ex <font color="Olive">a</font>, <font color="Olive">b</font> being  <a href="subset_1.html#NM2">Subset</a> of <font color="Maroon">X</font> st <br/>( <span class="p1"><a href="armstrng.html#K6" target="_self">[</a><span class="default"><font color="Olive">a</font>,<font color="Olive">b</font></span><a href="armstrng.html#K6" target="_self">]</a></span> <a href="hidden.html#R2">in</a> <font color="Maroon">F</font> &amp; <font color="Olive">a</font> <a href="tarski.html#R1">c=</a> <font color="Olive">Y</font> &amp; not <font color="Olive">b</font> <a href="tarski.html#R1">c=</a> <font color="Olive">Y</font> ) )
 
;<br/>
<b>hence </b><a NAME="E4:113"/>
( <font color="Maroon">A</font> is   <a href="subset_1.html#NM2">Subset</a> of <font color="Maroon">X</font> &amp;  ex <font color="Olive">a</font>, <font color="Olive">b</font> being  <a href="subset_1.html#NM2">Subset</a> of <font color="Maroon">X</font> st <br/>( <span class="p1"><a href="armstrng.html#K6" target="_self">[</a><span class="default"><font color="Olive">a</font>,<font color="Olive">b</font></span><a href="armstrng.html#K6" target="_self">]</a></span> <a href="hidden.html#R2">in</a> <font color="Maroon">F</font> &amp; <font color="Olive">a</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">A</font> &amp; not <font color="Olive">b</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">A</font> ) )
 ;<br/>


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