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<b>let </b><font color="Maroon">L</font> be  <a href="yellow_0.html#V1">lower-bounded</a> <a href="waybel_3.html#V3">continuous</a> <a href="waybel_0.html#NM7">sup-Semilattice</a>;<br/><b>let </b><font color="Maroon">B</font> be  <a href="waybel23.html#V6" target="_self">with_bottom</a>  <a href="waybel23.html#M1" target="_self">CLbasis</a> of <font color="Maroon">L</font>;<br/>



<a NAME="E1:105"/>
 <a href="waybel23.html#K3" target="_self">supMap</a> <span class="p1">(<span class="default"><a href="yellow_0.html#K5">subrelstr</a> <font color="Maroon">B</font></span>)</span> is <a href="waybel_1.html#V4">upper_adjoint</a>
 
<b>by </b><i/>;<br/>
<b>hence </b><a NAME="E2:105"/>
 <a href="waybel23.html#K3" target="_self">supMap</a> <span class="p1">(<span class="default"><a href="yellow_0.html#K5">subrelstr</a> <font color="Maroon">B</font></span>)</span> is <a href="waybel_0.html#V17">infs-preserving</a>
 <b>by </b><i><a class="ref" href="waybel_1.html#T13">WAYBEL_1:13</a></i>;<br/>

<a NAME="E3:105"/><i><font color="Green">E31</font></i>: 
 <a href="waybel23.html#K4" target="_self">idsMap</a> <span class="p1">(<span class="default"><a href="yellow_0.html#K5">subrelstr</a> <font color="Maroon">B</font></span>)</span> is <a href="waybel_0.html#V18">sups-preserving</a>
 
<b>by </b><i/>;<br/>
<a NAME="E4:105"/><i><font color="Green">E33</font></i>: 
 <a href="waybel23.html#K3" target="_self">supMap</a> <span class="p1">(<span class="default"><a href="yellow_0.html#K5">subrelstr</a> <font color="Maroon">B</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="yellow_2.html#K2">SupMap</a> <font color="Maroon">L</font></span>)</span> <a href="partfun1.html#K1">*</a> <span class="p1">(<span class="default"><a href="waybel23.html#K4" target="_self">idsMap</a> <span class="p2">(<span class="default"><a href="yellow_0.html#K5">subrelstr</a> <font color="Maroon">B</font></span>)</span></span>)</span>
 
<b>by </b><i/>;<br/>
<a NAME="E5:105"/>
 <a href="yellow_2.html#K2">SupMap</a> <font color="Maroon">L</font> is <a href="waybel_0.html#V18">sups-preserving</a>
 
<b>by </b><i><a class="ref" href="waybel13.html#T33">WAYBEL13:33</a></i>;<br/>
<b>hence </b><a NAME="E6:105"/>
 <a href="waybel23.html#K3" target="_self">supMap</a> <span class="p1">(<span class="default"><a href="yellow_0.html#K5">subrelstr</a> <font color="Maroon">B</font></span>)</span> is <a href="waybel_0.html#V18">sups-preserving</a>
 <b>by </b><i>, , <a class="ref" href="waybel20.html#T28">WAYBEL20:28</a></i>;<br/>


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