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<b>let </b><font color="Maroon">S</font> be  <a href="lattice3.html#V3">complete</a> <a href="waybel_0.html#NM8">LATTICE</a>, <font color="Maroon">T</font> be  <a href="lattice3.html#V3">complete</a> <a href="waybel_0.html#NM8">LATTICE</a>;<br/><b>let </b><font color="Maroon">d</font> be  <a href="waybel_0.html#V18">sups-preserving</a> <a href="struct_0.html#NM6">Function</a> of <font color="Maroon">T</font>,<font color="Maroon">S</font>;<br/><b>let </b><font color="Maroon">s</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">S</font>;<br/>





<a NAME="E1:10"/>
<span class="p1"><a href="waybel_1.html#K1">[</a><span class="default"><span class="p2">(<span class="default"><a href="waybel34.html#K2" target="_self">UpperAdj</a> <font color="Maroon">d</font></span>)</span>,<font color="Maroon">d</font></span><a href="waybel_1.html#K1">]</a></span> is <a href="waybel_1.html#V3">Galois</a>
 
<b>by </b><i/>;<br/>
<a NAME="E2:10"/><b>then </b>
<span class="p1">(<span class="default"><a href="waybel34.html#K2" target="_self">UpperAdj</a> <font color="Maroon">d</font></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">s</font> <a href="waybel_1.html#R4">is_maximum_of</a> <font color="Maroon">d</font> <a href="relset_1.html#K11">"</a> <span class="p1">(<span class="default"><a href="waybel_0.html#K5">downarrow</a> <font color="Maroon">s</font></span>)</span>
 
<b>by </b><i><a class="ref" href="waybel_1.html#T12">WAYBEL_1:12</a></i>;<br/>
<b>hence </b><a NAME="E3:10"/>
<span class="p1">(<span class="default"><a href="waybel34.html#K2" target="_self">UpperAdj</a> <font color="Maroon">d</font></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">s</font> <a href="hidden.html#R1">=</a>  <a href="yellow_0.html#NK3" target="_self">sup</a> <span class="p1">(<span class="default"><font color="Maroon">d</font> <a href="relset_1.html#K11">"</a> <span class="p2">(<span class="default"><a href="waybel_0.html#K5">downarrow</a> <font color="Maroon">s</font></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="waybel_1.html#D7">WAYBEL_1:def 7</a></i>;<br/>


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