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<b>let </b><font color="Maroon">T</font> be  non <a href="struct_0.html#V3">empty</a>  <a href="struct_0.html#L1">1-sorted</a> ;<br/><b>let </b><font color="Maroon">F</font> be   <a href="struct_0.html#NM3">Subset-Family</a> of <font color="Maroon">T</font>;<br/>



<b>assume </b><a NAME="E1:2"/>
<font color="Maroon">F</font> <a href="pre_topc.html#R1">is_a_cover_of</a> <font color="Maroon">T</font>
 ;<br/>

<b>then </b><i><font color="Green">E33</font></i>:  <a href="setfam_1.html#K5">union</a> <font color="Maroon">F</font> = 
 <a href="pre_topc.html#K2">[#]</a> <font color="Maroon">T</font>
<b>by </b><i><a class="ref" href="pre_topc.html#D8">PRE_TOPC:def 8</a></i>
<br/>.= 
the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">T</font>

;<br/>
<b>consider </b><font color="Maroon">x</font> being    <a href="subset_1.html#M1">Element</a> of  <a href="setfam_1.html#K5">union</a> <font color="Maroon">F</font>;<br/>
<a NAME="E4:2"/>
 ex <font color="Olive">A</font> being   <a href="hidden.html#M1">set</a>  st <br/>( <font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <font color="Olive">A</font> &amp; <font color="Olive">A</font> <a href="hidden.html#R2">in</a> <font color="Maroon">F</font> )
 
<b>by </b><i>, <a class="ref" href="tarski.html#D4">TARSKI:def 4</a></i>;<br/>
<b>hence </b><a NAME="E5:2"/>
<font color="Maroon">F</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a> 
 ;<br/>


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