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<b>let </b><font color="Maroon" title="c1">X</font> be  non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a>  <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">F</font> being  <a href="armstrng.html#NM2" title="ARMSTRNG:NM.2">Dependency-set</a> of <font color="Maroon" title="c1">X</font> holds   <a href="armstrng.html#K12" title="ARMSTRNG:func.12">Dependency-closure</a> <font color="Olive" title="b1">F</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <font color="Maroon" title="c1">X</font> <a href="armstrng.html#K10" title="ARMSTRNG:func.10">deps_encl_by</a> <span class="p1">(<span class="default"><a href="armstrng.html#K11" title="ARMSTRNG:func.11">enclosure_of</a> <font color="Olive" title="b1">F</font></span>)</span></span><br/><b>let </b><font color="Maroon" title="c2">F</font> be   <a href="armstrng.html#NM2" title="ARMSTRNG:NM.2">Dependency-set</a> of <font color="Maroon" title="c1">X</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  <a href="armstrng.html#K12" title="ARMSTRNG:func.12">Dependency-closure</a> <font color="Maroon" title="c2">F</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <font color="Maroon" title="c1">X</font> <a href="armstrng.html#K10" title="ARMSTRNG:func.10">deps_encl_by</a> <span class="p1">(<span class="default"><a href="armstrng.html#K11" title="ARMSTRNG:func.11">enclosure_of</a> <font color="Maroon" title="c2">F</font></span>)</span></span><br/>



<b>set </b><font color="Maroon" title="c3">B</font> =  <a href="armstrng.html#K11" title="ARMSTRNG:func.11">enclosure_of</a> <font color="Maroon" title="c2">F</font>;<br/>
<b>set </b><font color="Maroon" title="c4">H</font> = <font color="Maroon" title="c1">X</font> <a href="armstrng.html#K10" title="ARMSTRNG:func.10">deps_encl_by</a> <span class="p1">(<span class="default"><a href="armstrng.html#K11" title="ARMSTRNG:func.11">enclosure_of</a> <font color="Maroon" title="c2">F</font></span>)</span>;<br/>
<b>reconsider </b><font color="Maroon" title="c5">H</font> = <font color="Maroon" title="c1">X</font> <a href="armstrng.html#K10" title="ARMSTRNG:func.10">deps_encl_by</a> <span class="p1">(<span class="default"><a href="armstrng.html#K11" title="ARMSTRNG:func.11">enclosure_of</a> <font color="Maroon" title="c2">F</font></span>)</span> as   <a href="armstrng.html#NM5" title="ARMSTRNG:NM.5">Full-family</a> of <font color="Maroon" title="c1">X</font> <b>by </b><i><a class="ref" href="armstrng.html#T35" target="_self" title="ARMSTRNG:th.35">Th35</a></i>;<br/>
<a NAME="E2:86"/><i><font color="Green" title="E50">A1</font></i>: 
<font color="Maroon" title="c2">F</font> <a href="relset_1.html#R1" title="RELSET_1:pred.1">c=</a> <font color="Maroon" title="c5">H</font>
 
<b>by </b><i><a class="ref" href="armstrng.html#T39" target="_self" title="ARMSTRNG:th.39">Th39</a></i>;<br/>
<a NAME="E3:86"/>
for <font color="Olive" title="b1">G</font> being  <a href="armstrng.html#NM2" title="ARMSTRNG:NM.2">Dependency-set</a> of <font color="Maroon" title="c1">X</font>  st <font color="Maroon" title="c2">F</font> <a href="relset_1.html#R1" title="RELSET_1:pred.1">c=</a> <font color="Olive" title="b1">G</font> &amp; <font color="Olive" title="b1">G</font> is <a href="armstrng.html#V6" title="ARMSTRNG:attr.6">full_family</a> holds <br/><font color="Maroon" title="c5">H</font> <a href="relset_1.html#R1" title="RELSET_1:pred.1">c=</a> <font color="Olive" title="b1">G</font>
 
<b>by </b><i><a class="ref" href="armstrng.html#T39" target="_self" title="ARMSTRNG:th.39">Th39</a></i>;<br/>
<b>hence </b><a NAME="E4:86"/>
 <a href="armstrng.html#K12" title="ARMSTRNG:func.12">Dependency-closure</a> <font color="Maroon" title="c2">F</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <font color="Maroon" title="c1">X</font> <a href="armstrng.html#K10" title="ARMSTRNG:func.10">deps_encl_by</a> <span class="p1">(<span class="default"><a href="armstrng.html#K11" title="ARMSTRNG:func.11">enclosure_of</a> <font color="Maroon" title="c2">F</font></span>)</span>
 <b>by </b><i><a class="txt" href="#E2:86"><i><font color="Green" title="E50">A1</font></i></a>, <a class="ref" href="armstrng.html#D25" target="_self" title="ARMSTRNG:def.25">Def25</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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