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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="lattices.html#NM5">1_Lattice</a>;<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="E1:74"/><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">u</font> <a href="lattices.html#R3">[=</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Olive">x</font>
 ;<br/>

<b>reconsider </b><font color="Maroon">f'</font> = <font color="Maroon">f</font> 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 <span class="p1">(<span class="default"><font color="Maroon">L</font> <a href="lattice2.html#K1" target="_self">.:</a> </span>)</span> ;<br/>
<b>reconsider </b><font color="Maroon">u'</font> = <font color="Maroon">u</font> as   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><font color="Maroon">L</font> <a href="lattice2.html#K1" target="_self">.:</a> </span>)</span> ;<br/>
<a NAME="E4:74"/><i><font color="Green">E18</font></i>: 
<font color="Maroon">L</font> <a href="lattice2.html#K1" target="_self">.:</a>  is   <a href="lattices.html#NM4">0_Lattice</a>
 
<b>by </b><i/>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="74_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="E1:74_1"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">B</font>
 ;<br/><a NAME="E2:74_1"/><b>then </b>
<font color="Maroon">u</font> <a href="lattices.html#R3">[=</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">x</font>
 <b>by </b><i><a class="ref" href="lattice2.html#T26" target="_self">Th26</a></i>;<br/><b>hence </b><a NAME="E3:74_1"/>
<font color="Maroon">f'</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">x</font> <a href="lattices.html#R3">[=</a> <font color="Maroon">u'</font>
 <b>by </b><i/>;<br/></div><b>end;</b></div>
<a NAME="E6:74"/><b>then </b>
 <a href="lattice2.html#K2" target="_self">FinJoin</a> <font color="Maroon">B</font>,<font color="Maroon">f'</font> <a href="lattices.html#R3">[=</a> <font color="Maroon">u'</font>
 
<b>by </b><i><a class="ref" href="lattice2.html#T27" target="_self">Th27</a>, <a class="ref" href="lattice2.html#T21" target="_self">Th21</a></i>;<br/>
<b>hence </b><a NAME="E7:74"/>
<font color="Maroon">u</font> <a href="lattices.html#R3">[=</a>  <a href="lattice2.html#K3" target="_self">FinMeet</a> <font color="Maroon">B</font>,<font color="Maroon">f</font>
 <b>by </b><i/>;<br/>


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