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<b>let </b><font color="Maroon">A</font> be  non <a href="xboole_0.html#V1">empty</a>  <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">B</font> be   <a href="finsub_1.html#NM1">Finite_Subset</a> of <font color="Maroon">A</font>;<br/><b>let </b><font color="Maroon">L</font> be   <a href="lattice2.html#NM1">D0_Lattice</a>;<br/><b>let </b><font color="Maroon">g</font> be   <a href="funct_2.html#NM1">Function</a> of <font color="Maroon">A</font>,the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">L</font>;<br/><b>let </b><font color="Maroon">f</font> be   <a href="funct_2.html#NM1">Function</a> of <font color="Maroon">A</font>,the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">L</font>;<br/><b>let </b><font color="Maroon">u</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L</font>;<br/>











<b>assume </b><a NAME="E1:80"/><i><font color="Green">E17</font></i>: 
for <font color="Olive">x</font> being   <a href="subset_1.html#M1">Element</a> of <font color="Maroon">A</font>  st <font color="Olive">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">B</font> holds <br/><font color="Maroon">g</font> <a href="funct_2.html#K3">.</a> <font color="Olive">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">u</font> <a href="lattices.html#K4">"/\"</a> <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Olive">x</font></span>)</span>
 ;<br/>

<b>reconsider </b><font color="Maroon">G</font> = <span class="p1">(<span class="default">the <a href="lattices.html#U1">L_meet</a> of <font color="Maroon">L</font> <a href="funcop_1.html#K8">[;]</a> <font color="Maroon">u</font>,<font color="Maroon">f</font></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p1">(<span class="default"><font color="Maroon">g</font> <a href="partfun1.html#K2">|</a> <font color="Maroon">B</font></span>)</span> as   <a href="funct_2.html#NM1">Function</a> of <font color="Maroon">A</font>,the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">L</font> <b>by </b><i/>;<br/>
<a NAME="E3:80"/>
 <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><font color="Maroon">g</font> <a href="partfun1.html#K2">|</a> <font color="Maroon">B</font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">B</font>
 
<b>by </b><i/>;<br/>
<a NAME="E4:80"/><b>then </b><i><font color="Green">E18</font></i>: 
<font color="Maroon">G</font> <a href="partfun1.html#K2">|</a> <font color="Maroon">B</font> <a href="hidden.html#R1">=</a> <font color="Maroon">g</font> <a href="partfun1.html#K2">|</a> <font color="Maroon">B</font>
 
<b>by </b><i><a class="ref" href="funct_4.html#T24">FUNCT_4:24</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="80_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">x</font> be    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">A</font>;<br/><b>assume </b><a NAME="E1:80_1"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">B</font>
 ;<br/><b>hence </b><font color="Maroon">g</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">x</font> = 
<font color="Maroon">u</font> <a href="lattices.html#K4">"/\"</a> <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">x</font></span>)</span>
<b>by </b><i><a class="ref" href="lattice2.html#T27" target="_self">Th27</a></i>
<br/>.= 
<span class="p1">(<span class="default">the <a href="lattices.html#U1">L_meet</a> of <font color="Maroon">L</font> <a href="funcop_1.html#K8">[;]</a> <font color="Maroon">u</font>,<font color="Maroon">f</font></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">x</font>
<b>by </b><i><a class="ref" href="funcop_1.html#T66">FUNCOP_1:66</a></i>
;<br/><br/></div><b>end;</b></div>
<a NAME="E6:80"/><b>then </b><i><font color="Green">E19</font></i>: 
<font color="Maroon">G</font> <a href="funct_2.html#R2">=</a> the <a href="lattices.html#U1">L_meet</a> of <font color="Maroon">L</font> <a href="funcop_1.html#K8">[;]</a> <font color="Maroon">u</font>,<font color="Maroon">f</font>
 
<b>by </b><i/>;<br/>
<b>thus </b><font color="Maroon">u</font> <a href="lattices.html#K4">"/\"</a> <span class="p1">(<span class="default"><a href="lattice2.html#K2" target="_self">FinJoin</a> <font color="Maroon">B</font>,<font color="Maroon">f</font></span>)</span> = 
 <a href="lattice2.html#K2" target="_self">FinJoin</a> <font color="Maroon">B</font>,<font color="Maroon">G</font>
<b>by </b><i>, <a class="ref" href="lattice2.html#T26" target="_self">Th26</a></i>
<br/>.= 
 <a href="lattice2.html#K2" target="_self">FinJoin</a> <font color="Maroon">B</font>,<font color="Maroon">g</font>
<b>by </b><i><a class="ref" href="lattice2.html#T28" target="_self">Th28</a>, </i>
;<br/>


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