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<b>let </b><font color="Maroon" title="c1">L</font> be  <a href="yellow_0.html#V1" title="YELLOW_0:attr.1">lower-bounded</a> <a href="waybel_3.html#V3" title="WAYBEL_3:attr.3">continuous</a> <a href="waybel_0.html#NM7" title="WAYBEL_0:NM.7">sup-Semilattice</a>;<br/><b>let </b><font color="Maroon" title="c2">B</font> be  <a href="waybel23.html#V6" title="WAYBEL23:attr.6">with_bottom</a>  <a href="waybel23.html#M1" title="WAYBEL23:mode.1">CLbasis</a> of <font color="Maroon" title="c1">L</font>;<br/>



<a NAME="E1:105"/>
 <a href="waybel23.html#K3" title="WAYBEL23:func.3">supMap</a> <span class="p1">(<span class="default"><a href="yellow_0.html#K5" title="YELLOW_0:func.5">subrelstr</a> <font color="Maroon" title="c2">B</font></span>)</span> is <a href="waybel_1.html#V4" title="WAYBEL_1:attr.4">upper_adjoint</a>
 
<b>by </b><i><a class="ref" href="waybel23.html#T64" target="_self" title="WAYBEL23:th.64">Th64</a></i>;<br/>
<b>hence </b><a NAME="E2:105"/>
 <a href="waybel23.html#K3" title="WAYBEL23:func.3">supMap</a> <span class="p1">(<span class="default"><a href="yellow_0.html#K5" title="YELLOW_0:func.5">subrelstr</a> <font color="Maroon" title="c2">B</font></span>)</span> is <a href="waybel_0.html#V17" title="WAYBEL_0:attr.17">infs-preserving</a>
 <b>by </b><i><a class="ref" href="waybel_1.html#T13" title="WAYBEL_1:th.13">WAYBEL_1:13</a></i>;<br/>

<a NAME="E3:105"/><i><font color="Green" title="E60">A1</font></i>: 
 <a href="waybel23.html#K4" title="WAYBEL23:func.4">idsMap</a> <span class="p1">(<span class="default"><a href="yellow_0.html#K5" title="YELLOW_0:func.5">subrelstr</a> <font color="Maroon" title="c2">B</font></span>)</span> is <a href="waybel_0.html#V18" title="WAYBEL_0:attr.18">sups-preserving</a>
 
<b>by </b><i><a class="ref" href="waybel23.html#T61" target="_self" title="WAYBEL23:th.61">Th61</a></i>;<br/>
<a NAME="E4:105"/><i><font color="Green" title="E61">A2</font></i>: 
 <a href="waybel23.html#K3" title="WAYBEL23:func.3">supMap</a> <span class="p1">(<span class="default"><a href="yellow_0.html#K5" title="YELLOW_0:func.5">subrelstr</a> <font color="Maroon" title="c2">B</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="yellow_2.html#K2" title="YELLOW_2:func.2">SupMap</a> <font color="Maroon" title="c1">L</font></span>)</span> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <span class="p1">(<span class="default"><a href="waybel23.html#K4" title="WAYBEL23:func.4">idsMap</a> <span class="p2">(<span class="default"><a href="yellow_0.html#K5" title="YELLOW_0:func.5">subrelstr</a> <font color="Maroon" title="c2">B</font></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="waybel23.html#T62" target="_self" title="WAYBEL23:th.62">Th62</a></i>;<br/>
<a NAME="E5:105"/>
 <a href="yellow_2.html#K2" title="YELLOW_2:func.2">SupMap</a> <font color="Maroon" title="c1">L</font> is <a href="waybel_0.html#V18" title="WAYBEL_0:attr.18">sups-preserving</a>
 
<b>by </b><i><a class="ref" href="waybel13.html#T33" title="WAYBEL13:th.33">WAYBEL13:33</a></i>;<br/>
<b>hence </b><a NAME="E6:105"/>
 <a href="waybel23.html#K3" title="WAYBEL23:func.3">supMap</a> <span class="p1">(<span class="default"><a href="yellow_0.html#K5" title="YELLOW_0:func.5">subrelstr</a> <font color="Maroon" title="c2">B</font></span>)</span> is <a href="waybel_0.html#V18" title="WAYBEL_0:attr.18">sups-preserving</a>
 <b>by </b><i><a class="txt" href="waybel23.html#E3:105"><i><font color="Green" title="E60">A1</font></i></a>, <a class="txt" href="waybel23.html#E4:105"><i><font color="Green" title="E61">A2</font></i></a>, <a class="ref" href="waybel20.html#T28" title="WAYBEL20:th.28">WAYBEL20:28</a></i>;<br/>


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