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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_0.html#NM7" title="WAYBEL_0:NM.7">sup-Semilattice</a>;<br/>

<a NAME="E1:74"/>
( <span class="p1">(<span class="default"><a href="waybel_4.html#K9" title="WAYBEL_4:func.9">Rel2Map</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="waybel_4.html#K10" title="WAYBEL_4:func.10">Map2Rel</a> <font color="Maroon" title="c1">L</font></span>)</span> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a>  <a href="partfun1.html#K6" title="PARTFUN1:func.6">id</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="waybel_4.html#K8" title="WAYBEL_4:func.8">MonSet</a> <font color="Maroon" title="c1">L</font></span>)</span> implies  <a href="relset_1.html#K5" title="RELSET_1:func.5">rng</a> <span class="p1">(<span class="default"><a href="waybel_4.html#K9" title="WAYBEL_4:func.9">Rel2Map</a> <font color="Maroon" title="c1">L</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="waybel_4.html#K8" title="WAYBEL_4:func.8">MonSet</a> <font color="Maroon" title="c1">L</font></span>)</span> )
 
<b>by </b><i><a class="ref" href="funct_2.html#T24" title="FUNCT_2:th.24">FUNCT_2:24</a></i>;<br/>
<a NAME="E2:74"/><b>then </b>
(  <a href="waybel_4.html#K9" title="WAYBEL_4:func.9">Rel2Map</a> <font color="Maroon" title="c1">L</font> is <a href="funct_1.html#V2" title="FUNCT_1:attr.2">one-to-one</a> &amp;  <a href="relset_1.html#K5" title="RELSET_1:func.5">rng</a> <span class="p1">(<span class="default"><a href="waybel_4.html#K9" title="WAYBEL_4:func.9">Rel2Map</a> <font color="Maroon" title="c1">L</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <span class="p1">(<span class="default"><a href="waybel_4.html#K10" title="WAYBEL_4:func.10">Map2Rel</a> <font color="Maroon" title="c1">L</font></span>)</span> &amp; <span class="p1">(<span class="default"><a href="waybel_4.html#K10" title="WAYBEL_4:func.10">Map2Rel</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="waybel_4.html#K9" title="WAYBEL_4:func.9">Rel2Map</a> <font color="Maroon" title="c1">L</font></span>)</span> <a href="funct_2.html#R1" title="FUNCT_2:pred.1">=</a>  <a href="partfun1.html#K6" title="PARTFUN1:func.6">id</a> <span class="p1">(<span class="default"><a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <span class="p2">(<span class="default"><a href="waybel_4.html#K9" title="WAYBEL_4:func.9">Rel2Map</a> <font color="Maroon" title="c1">L</font></span>)</span></span>)</span> )
 
<b>by </b><i><a class="ref" href="waybel_4.html#T30" target="_self" title="WAYBEL_4:th.30">Th30</a>, <a class="ref" href="waybel_4.html#T31" target="_self" title="WAYBEL_4:th.31">Th31</a>, <a class="ref" href="funct_2.html#D1" title="FUNCT_2:def.1">FUNCT_2:def 1</a></i>;<br/>
<b>hence </b><a NAME="E3:74"/>
 <a href="waybel_4.html#K10" title="WAYBEL_4:func.10">Map2Rel</a> <font color="Maroon" title="c1">L</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="waybel_4.html#K9" title="WAYBEL_4:func.9">Rel2Map</a> <font color="Maroon" title="c1">L</font></span>)</span> <a href="funct_1.html#K2" title="FUNCT_1:func.2">"</a> 
 <b>by </b><i><a class="ref" href="funct_1.html#T63" title="FUNCT_1:th.63">FUNCT_1:63</a></i>;<br/>


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