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<b>let </b><font color="Maroon" title="c3">it1</font>, <font color="Maroon" title="c4">it2</font> be   <a href="armstrng.html#NM5" title="ARMSTRNG:NM.5">Full-family</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"> ( <font color="Maroon" title="c2">F</font> <a href="relset_1.html#R1" title="RELSET_1:pred.1">c=</a> <font color="Maroon" title="c3">it1</font> &amp; ( 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="c3">it1</font> <a href="relset_1.html#R1" title="RELSET_1:pred.1">c=</a> <font color="Olive" title="b1">G</font> ) &amp; <font color="Maroon" title="c2">F</font> <a href="relset_1.html#R1" title="RELSET_1:pred.1">c=</a> <font color="Maroon" title="c4">it2</font> &amp; ( 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="c4">it2</font> <a href="relset_1.html#R1" title="RELSET_1:pred.1">c=</a> <font color="Olive" title="b1">G</font> ) implies <font color="Maroon" title="c3">it1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">it2</font> )</span><br/>

<b>assume </b><a NAME="E1:85_1_2"/>
( <font color="Maroon" title="c2">F</font> <a href="relset_1.html#R1" title="RELSET_1:pred.1">c=</a> <font color="Maroon" title="c3">it1</font> &amp; ( 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="c3">it1</font> <a href="relset_1.html#R1" title="RELSET_1:pred.1">c=</a> <font color="Olive" title="b1">G</font> ) &amp; <font color="Maroon" title="c2">F</font> <a href="relset_1.html#R1" title="RELSET_1:pred.1">c=</a> <font color="Maroon" title="c4">it2</font> &amp; ( 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="c4">it2</font> <a href="relset_1.html#R1" title="RELSET_1:pred.1">c=</a> <font color="Olive" title="b1">G</font> ) )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c3">it1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">it2</font></span><br/>

<a NAME="E2:85_1_2"/><b>then </b>
( <font color="Maroon" title="c3">it1</font> <a href="relset_1.html#R1" title="RELSET_1:pred.1">c=</a> <font color="Maroon" title="c4">it2</font> &amp; <font color="Maroon" title="c4">it2</font> <a href="relset_1.html#R1" title="RELSET_1:pred.1">c=</a> <font color="Maroon" title="c3">it1</font> )
 
;<br/>
<b>hence </b><a NAME="E3:85_1_2"/>
<font color="Maroon" title="c3">it1</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <font color="Maroon" title="c4">it2</font>
 <b>by </b><i><a class="ref" href="xboole_0.html#D10" title="XBOOLE_0:def.10">XBOOLE_0:def 10</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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