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<b>let </b><font color="Maroon" title="c1">S</font>, <font color="Maroon" title="c2">T</font> be  non <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a> <a href="waybel19.html#NM1" title="WAYBEL19:NM.1">TopPoset</a>;<br/><b>let </b><font color="Maroon" title="c3">X</font> be  non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> <a href="waybel_0.html#V2" title="WAYBEL_0:attr.2">filtered</a> <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">S</font>;<br/><b>let </b><font color="Maroon" title="c4">f</font> be  <a href="orders_3.html#V5" title="ORDERS_3:attr.5">monotone</a> <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <font color="Maroon" title="c1">S</font>,<font color="Maroon" title="c2">T</font>;<br/><b>let </b><font color="Maroon" title="c5">Y</font> be  non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> <a href="waybel_0.html#V2" title="WAYBEL_0:attr.2">filtered</a> <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c2">T</font>;<br/>







<b>assume </b><a NAME="E1:40"/>
<font color="Maroon" title="c5">Y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">f</font> <a href="relset_1.html#K10" title="RELSET_1:func.10">.:</a> <font color="Maroon" title="c3">X</font>
 ;<br/>

<a NAME="E2:40"/><b>then </b>
<font color="Maroon" title="c4">f</font> <a href="waybel_9.html#K7" title="WAYBEL_9:func.7">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">X</font> <a href="yellow_9.html#K3" title="YELLOW_9:func.3">opp+id</a> </span>)</span> is    <a href="yellow_6.html#M2" title="YELLOW_6:mode.2">subnet</a> of <font color="Maroon" title="c5">Y</font> <a href="yellow_9.html#K3" title="YELLOW_9:func.3">opp+id</a> 
 
<b>by </b><i><a class="ref" href="waybel21.html#T30" target="_self" title="WAYBEL21:th.30">Th30</a></i>;<br/>
<b>hence </b><a NAME="E3:40"/>
 <a href="yellow_6.html#K11" title="YELLOW_6:func.11">Lim</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">Y</font> <a href="yellow_9.html#K3" title="YELLOW_9:func.3">opp+id</a> </span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="yellow_6.html#K11" title="YELLOW_6:func.11">Lim</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="waybel_9.html#K7" title="WAYBEL_9:func.7">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">X</font> <a href="yellow_9.html#K3" title="YELLOW_9:func.3">opp+id</a> </span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="yellow_6.html#T41" title="YELLOW_6:th.41">YELLOW_6:41</a></i>;<br/>


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