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<span class="kw">let </span><font color="Maroon" title="c1">E</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">sE</font> being  <a href="setfam_1.html#NM1" title="SETFAM_1:NM.1">Subset-Family</a> of <font color="Maroon" title="c1">E</font> holds <br/> ( <font color="Olive" title="b1">sE</font> is  <a href="abian.html#V2" title="ABIAN:attr.2">covering</a>  iff  <a href="setfam_1.html#K5" title="SETFAM_1:func.5">union</a> <font color="Olive" title="b1">sE</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">E</font> )</span><br/><span class="kw">let </span><font color="Maroon" title="c2">sE</font> be   <a href="setfam_1.html#NM1" title="SETFAM_1:NM.1">Subset-Family</a> of <font color="Maroon" title="c1">E</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c2">sE</font> is  <a href="abian.html#V2" title="ABIAN:attr.2">covering</a>  iff  <a href="setfam_1.html#K5" title="SETFAM_1:func.5">union</a> <font color="Maroon" title="c2">sE</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">E</font> )</span><br/>



 <a href="setfam_1.html#K5" title="SETFAM_1:func.5">union</a> <span class="p1">(<span class="default"><a href="setfam_1.html#K5" title="SETFAM_1:func.5">union</a> <span class="p2">(<span class="default"><a href="setfam_1.html#K9" title="SETFAM_1:func.9">bool</a> <span class="p3">(<span class="default"><a href="setfam_1.html#K9" title="SETFAM_1:func.9">bool</a> <font color="Maroon" title="c1">E</font></span>)</span></span>)</span></span>)</span> = 
 <a href="setfam_1.html#K5" title="SETFAM_1:func.5">union</a> <span class="p1">(<span class="default"><a href="setfam_1.html#K9" title="SETFAM_1:func.9">bool</a> <font color="Maroon" title="c1">E</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="zfmisc_1.html#T99" title="ZFMISC_1:th.99">ZFMISC_1:99</a></span>
<br/>.= 
<font color="Maroon" title="c1">E</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="zfmisc_1.html#T99" title="ZFMISC_1:th.99">ZFMISC_1:99</a></span>
;<br/>
<span class="kw">hence </span><a NAME="E2:29"/>
( <font color="Maroon" title="c2">sE</font> is  <a href="abian.html#V2" title="ABIAN:attr.2">covering</a>  iff  <a href="setfam_1.html#K5" title="SETFAM_1:func.5">union</a> <font color="Maroon" title="c2">sE</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">E</font> )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="abian.html#D6" target="_self" title="ABIAN:def.6">Def6</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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