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<b>let </b><font color="Maroon">X</font> be  non <a href="xboole_0.html#V1">empty</a> <a href="finset_1.html#V1">finite</a>  <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>set </b><font color="Maroon">B</font> =  <a href="armstrng.html#K11" target="_self">enclosure_of</a> <font color="Maroon">F</font>;<br/>
<b>set </b><font color="Maroon">H</font> = <font color="Maroon">X</font> <a href="armstrng.html#K10" target="_self">deps_encl_by</a> <span class="p1">(<span class="default"><a href="armstrng.html#K11" target="_self">enclosure_of</a> <font color="Maroon">F</font></span>)</span>;<br/>
<b>reconsider </b><font color="Maroon">H</font> = <font color="Maroon">X</font> <a href="armstrng.html#K10" target="_self">deps_encl_by</a> <span class="p1">(<span class="default"><a href="armstrng.html#K11" target="_self">enclosure_of</a> <font color="Maroon">F</font></span>)</span> as   <a href="armstrng.html#NM5">Full-family</a> of <font color="Maroon">X</font> <b>by </b><i/>;<br/>
<a NAME="E2:89"/><i><font color="Green">E33</font></i>: 
<font color="Maroon">F</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">H</font>
 
<b>by </b><i/>;<br/>
<a NAME="E3:89"/>
for <font color="Olive">G</font> being  <a href="armstrng.html#NM2">Dependency-set</a> of <font color="Maroon">X</font>  st <font color="Maroon">F</font> <a href="tarski.html#R1">c=</a> <font color="Olive">G</font> &amp; <font color="Olive">G</font> is <a href="armstrng.html#V6" target="_self">full_family</a> holds <br/><font color="Maroon">H</font> <a href="tarski.html#R1">c=</a> <font color="Olive">G</font>
 
<b>by </b><i/>;<br/>
<b>hence </b><a NAME="E4:89"/>
 <a href="armstrng.html#K12" target="_self">Dependency-closure</a> <font color="Maroon">F</font> <a href="hidden.html#R1">=</a> <font color="Maroon">X</font> <a href="armstrng.html#K10" target="_self">deps_encl_by</a> <span class="p1">(<span class="default"><a href="armstrng.html#K11" target="_self">enclosure_of</a> <font color="Maroon">F</font></span>)</span>
 <b>by </b><i>, </i>;<br/>


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