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<span class="kw">let </span><font color="Maroon" title="c1">L</font> be   <a href="lattice3.html#V3" title="LATTICE3:attr.3">complete</a>  <a href="waybel_0.html#NM8" title="WAYBEL_0:NM.8">LATTICE</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">h</font> being  <a href="waybel_1.html#V7" title="WAYBEL_1:attr.7">closure</a>  <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <font color="Maroon" title="c1">L</font>,<font color="Maroon" title="c1">L</font> holds <br/> ( <font color="Olive" title="b1">h</font> is  <a href="waybel_0.html#V22" title="WAYBEL_0:attr.22">directed-sups-preserving</a>  iff  <a href="yellow_2.html#K1" title="YELLOW_2:func.1">Image</a> <font color="Olive" title="b1">h</font> is  <a href="waybel_0.html#V4" title="WAYBEL_0:attr.4">directed-sups-inheriting</a>  )</span><br/><span class="kw">let </span><font color="Maroon" title="c2">h</font> be   <a href="waybel_1.html#V7" title="WAYBEL_1:attr.7">closure</a>  <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <font color="Maroon" title="c1">L</font>,<font color="Maroon" title="c1">L</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">h</font> is  <a href="waybel_0.html#V22" title="WAYBEL_0:attr.22">directed-sups-preserving</a>  iff  <a href="yellow_2.html#K1" title="YELLOW_2:func.1">Image</a> <font color="Maroon" title="c2">h</font> is  <a href="waybel_0.html#V4" title="WAYBEL_0:attr.4">directed-sups-inheriting</a>  )</span><br/>



<a NAME="E1:55"/>
 <a href="waybel10.html#K7" title="WAYBEL10:func.7">closure_op</a> <span class="p1">(<span class="default"><a href="yellow_2.html#K1" title="YELLOW_2:func.1">Image</a> <font color="Maroon" title="c2">h</font></span>)</span> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Maroon" title="c2">h</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="waybel10.html#T20" target="_self" title="WAYBEL10:th.20">Th20</a></span>;<br/>
<span class="kw">hence </span><a NAME="E2:55"/>
( <font color="Maroon" title="c2">h</font> is  <a href="waybel_0.html#V22" title="WAYBEL_0:attr.22">directed-sups-preserving</a>  iff  <a href="yellow_2.html#K1" title="YELLOW_2:func.1">Image</a> <font color="Maroon" title="c2">h</font> is  <a href="waybel_0.html#V4" title="WAYBEL_0:attr.4">directed-sups-inheriting</a>  )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="waybel10.html#T25" target="_self" title="WAYBEL10:th.25">Th25</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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