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<b>let </b><font color="Maroon" title="c1">S</font>, <font color="Maroon" title="c2">T</font> be  <a href="lattice3.html#V3" title="LATTICE3:attr.3">complete</a> <a href="waybel_0.html#NM8" title="WAYBEL_0:NM.8">LATTICE</a>;<br/><b>let </b><font color="Maroon" title="c3">d</font> be  <a href="waybel_0.html#V18" title="WAYBEL_0:attr.18">sups-preserving</a> <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <font color="Maroon" title="c2">T</font>,<font color="Maroon" title="c1">S</font>;<br/><b>let </b><font color="Maroon" title="c4">s</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">S</font>;<br/>





<a NAME="E1:10"/>
<span class="p1"><a href="waybel_1.html#K1" title="WAYBEL_1:func.1">[</a><span class="default"><span class="p2">(<span class="default"><a href="waybel34.html#K2" title="WAYBEL34:func.2">UpperAdj</a> <font color="Maroon" title="c3">d</font></span>)</span>,<font color="Maroon" title="c3">d</font></span><a href="waybel_1.html#K1" title="WAYBEL_1:func.1">]</a></span> is <a href="waybel_1.html#V3" title="WAYBEL_1:attr.3">Galois</a>
 
<b>by </b><i><a class="ref" href="waybel34.html#D2" target="_self" title="WAYBEL34:def.2">Def2</a></i>;<br/>
<a NAME="E2:10"/><b>then </b>
<span class="p1">(<span class="default"><a href="waybel34.html#K2" title="WAYBEL34:func.2">UpperAdj</a> <font color="Maroon" title="c3">d</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c4">s</font> <a href="waybel_1.html#R4" title="WAYBEL_1:pred.4">is_maximum_of</a> <font color="Maroon" title="c3">d</font> <a href="relset_1.html#K11" title="RELSET_1:func.11">"</a> <span class="p1">(<span class="default"><a href="waybel_0.html#K5" title="WAYBEL_0:func.5">downarrow</a> <font color="Maroon" title="c4">s</font></span>)</span>
 
<b>by </b><i><a class="ref" href="waybel_1.html#T12" title="WAYBEL_1:th.12">WAYBEL_1:12</a></i>;<br/>
<b>hence </b><a NAME="E3:10"/>
<span class="p1">(<span class="default"><a href="waybel34.html#K2" title="WAYBEL34:func.2">UpperAdj</a> <font color="Maroon" title="c3">d</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c4">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="yellow_0.html#NK3" title="YELLOW_0:NK.3">sup</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">d</font> <a href="relset_1.html#K11" title="RELSET_1:func.11">"</a> <span class="p2">(<span class="default"><a href="waybel_0.html#K5" title="WAYBEL_0:func.5">downarrow</a> <font color="Maroon" title="c4">s</font></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="waybel_1.html#D7" title="WAYBEL_1:def.7">WAYBEL_1:def 7</a></i>;<br/>


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