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<b>let </b><font color="Maroon" title="c1">X</font> be    <a href="struct_0.html#L1" title="STRUCT_0:struct.1">1-sorted</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="struct_0.html#NM3" title="STRUCT_0:NM.3">Subset-Family</a> of <font color="Maroon" title="c1">X</font> holds   <a href="setfam_1.html#K5" title="SETFAM_1:func.5">union</a> <span class="p1">(<span class="default"><a href="setfam_1.html#K7" title="SETFAM_1:func.7">COMPLEMENT</a> <font color="Olive" title="b1">F</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="setfam_1.html#K8" title="SETFAM_1:func.8">Intersect</a> <font color="Olive" title="b1">F</font></span>)</span> <a href="subset_1.html#K3" title="SUBSET_1:func.3">`</a> </span><br/><b>let </b><font color="Maroon" title="c2">F</font> be   <a href="struct_0.html#NM3" title="STRUCT_0:NM.3">Subset-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">  <a href="setfam_1.html#K5" title="SETFAM_1:func.5">union</a> <span class="p1">(<span class="default"><a href="setfam_1.html#K7" title="SETFAM_1:func.7">COMPLEMENT</a> <font color="Maroon" title="c2">F</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="setfam_1.html#K8" title="SETFAM_1:func.8">Intersect</a> <font color="Maroon" title="c2">F</font></span>)</span> <a href="subset_1.html#K3" title="SUBSET_1:func.3">`</a> </span><br/>



<b>thus </b> <a href="setfam_1.html#K5" title="SETFAM_1:func.5">union</a> <span class="p1">(<span class="default"><a href="setfam_1.html#K7" title="SETFAM_1:func.7">COMPLEMENT</a> <font color="Maroon" title="c2">F</font></span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="setfam_1.html#K5" title="SETFAM_1:func.5">union</a> <span class="p3">(<span class="default"><a href="setfam_1.html#K7" title="SETFAM_1:func.7">COMPLEMENT</a> <font color="Maroon" title="c2">F</font></span>)</span></span>)</span> <a href="subset_1.html#K3" title="SUBSET_1:func.3">`</a> </span>)</span> <a href="subset_1.html#K3" title="SUBSET_1:func.3">`</a> 

<br/>.= 
<span class="p1">(<span class="default"><a href="setfam_1.html#K8" title="SETFAM_1:func.8">Intersect</a> <span class="p2">(<span class="default"><a href="setfam_1.html#K7" title="SETFAM_1:func.7">COMPLEMENT</a> <span class="p3">(<span class="default"><a href="setfam_1.html#K7" title="SETFAM_1:func.7">COMPLEMENT</a> <font color="Maroon" title="c2">F</font></span>)</span></span>)</span></span>)</span> <a href="subset_1.html#K3" title="SUBSET_1:func.3">`</a> 
<b>by </b><i><a class="ref" href="yellow_8.html#T15" target="_self" title="YELLOW_8:th.15">Th15</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="setfam_1.html#K8" title="SETFAM_1:func.8">Intersect</a> <font color="Maroon" title="c2">F</font></span>)</span> <a href="subset_1.html#K3" title="SUBSET_1:func.3">`</a> 

; <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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