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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_0.html#NM7">sup-Semilattice</a>;<br/>

<a NAME="E1:74"/>
( <span class="p1">(<span class="default"><a href="waybel_4.html#K9" target="_self">Rel2Map</a> <font color="Maroon">L</font></span>)</span> <a href="partfun1.html#K1">*</a> <span class="p1">(<span class="default"><a href="waybel_4.html#K10" target="_self">Map2Rel</a> <font color="Maroon">L</font></span>)</span> <a href="funct_2.html#R2">=</a>  <a href="partfun1.html#K6">id</a> the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="waybel_4.html#K8" target="_self">MonSet</a> <font color="Maroon">L</font></span>)</span> implies  <a href="relset_1.html#K5">rng</a> <span class="p1">(<span class="default"><a href="waybel_4.html#K9" target="_self">Rel2Map</a> <font color="Maroon">L</font></span>)</span> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="waybel_4.html#K8" target="_self">MonSet</a> <font color="Maroon">L</font></span>)</span> )
 
<b>by </b><i><a class="ref" href="funct_2.html#T24">FUNCT_2:24</a></i>;<br/>
<a NAME="E2:74"/><b>then </b>
(  <a href="waybel_4.html#K9" target="_self">Rel2Map</a> <font color="Maroon">L</font> is <a href="funct_1.html#V2">one-to-one</a> &amp;  <a href="relset_1.html#K5">rng</a> <span class="p1">(<span class="default"><a href="waybel_4.html#K9" target="_self">Rel2Map</a> <font color="Maroon">L</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="relset_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="waybel_4.html#K10" target="_self">Map2Rel</a> <font color="Maroon">L</font></span>)</span> &amp; <span class="p1">(<span class="default"><a href="waybel_4.html#K10" target="_self">Map2Rel</a> <font color="Maroon">L</font></span>)</span> <a href="partfun1.html#K1">*</a> <span class="p1">(<span class="default"><a href="waybel_4.html#K9" target="_self">Rel2Map</a> <font color="Maroon">L</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="partfun1.html#K6">id</a> <span class="p1">(<span class="default"><a href="relset_1.html#K4">dom</a> <span class="p2">(<span class="default"><a href="waybel_4.html#K9" target="_self">Rel2Map</a> <font color="Maroon">L</font></span>)</span></span>)</span> )
 
<b>by </b><i><a class="txt" href="waybel_4.html#E4"><i><font color="Green">Lemma41</font></i></a>, <a class="ref" href="waybel_4.html#D4" target="_self">Def4</a>, <a class="ref" href="funct_2.html#D1">FUNCT_2:def 1</a></i>;<br/>
<b>hence </b><a NAME="E3:74"/>
 <a href="waybel_4.html#K10" target="_self">Map2Rel</a> <font color="Maroon">L</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="waybel_4.html#K9" target="_self">Rel2Map</a> <font color="Maroon">L</font></span>)</span> <a href="funct_1.html#K2">"</a> 
 <b>by </b><i><a class="ref" href="funct_1.html#T63">FUNCT_1:63</a></i>;<br/>


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