<?xml version="1.0"?>
<div class="add">

<b>let </b><font color="Maroon">c<sub>1</sub></font> be  <a href="lattice3.html#V3">complete</a> <a href="waybel_0.html#NM6">Semilattice</a>;<br/>

<b>set </b><font color="Maroon">c<sub>2</sub></font> =  <a href="yellow_2.html#K2">SupMap</a> <font color="Maroon">c<sub>1</sub></font>;<br/>
<b>assume </b><a NAME="E1:7"/>
(  <a href="yellow_2.html#K2">SupMap</a> <font color="Maroon">c<sub>1</sub></font> is <a href="waybel_0.html#V17">infs-preserving</a> &amp;  <a href="yellow_2.html#K2">SupMap</a> <font color="Maroon">c<sub>1</sub></font> is <a href="waybel_0.html#V18">sups-preserving</a> )
 ;<br/>

<a NAME="E2:7"/><b>then </b>
ex <font color="Olive">b<sub>1</sub></font> being  <a href="struct_0.html#NM7">Function</a> of <font color="Maroon">c<sub>1</sub></font>,<span class="p1">(<span class="default"><a href="yellow_1.html#K2">InclPoset</a> <span class="p2">(<span class="default"><a href="waybel_0.html#K7">Ids</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> st <br/>( <span class="p1"><a href="waybel_1.html#K1">[</a><span class="default"><span class="p2">(<span class="default"><a href="yellow_2.html#K2">SupMap</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<font color="Olive">b<sub>1</sub></font></span><a href="waybel_1.html#K1">]</a></span> is <a href="waybel_1.html#V3">Galois</a> &amp; ( for <font color="Olive">b<sub>2</sub></font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>1</sub></font> holds <font color="Olive">b<sub>1</sub></font> <a href="yellow_6.html#K3">.</a> <font color="Olive">b<sub>2</sub></font> <a href="waybel_1.html#R3">is_minimum_of</a> <span class="p1">(<span class="default"><a href="yellow_2.html#K2">SupMap</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="relset_1.html#K11">"</a> <span class="p1">(<span class="default"><a href="waybel_0.html#K6">uparrow</a> <font color="Olive">b<sub>2</sub></font></span>)</span> ) )
 
<b>by </b><i><a class="ref" href="waybel_1.html#T15">WAYBEL_1:15</a></i>;<br/>
<b>hence </b><a NAME="E3:7"/>
 <a href="yellow_2.html#K2">SupMap</a> <font color="Maroon">c<sub>1</sub></font> is <a href="waybel_1.html#V4">upper_adjoint</a>
 <b>by </b><i><a class="ref" href="waybel_1.html#D11">WAYBEL_1:def 11</a></i>;<br/>


</div>
