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<b>let </b><font color="Maroon">L</font> be   <a href="lattices.html#NM1">Lattice</a>;<br/>

<b>assume </b><a NAME="E1:89"/>
<font color="Maroon">L</font> is <a href="group_1.html#V6">finite</a>
 ;<br/>

<a NAME="E2:89"/><b>then </b>
the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">L</font> is <a href="finset_1.html#V1">finite</a>
 
<b>by </b><i><a class="ref" href="group_1.html#D14">GROUP_1:def 14</a></i>;<br/>
<b>then reconsider </b><font color="Maroon">B</font> = the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">L</font> as   <a href="finsub_1.html#NM1">Finite_Subset</a> of the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">L</font> <b>by </b><i><a class="ref" href="finsub_1.html#D5">FINSUB_1:def 5</a></i>;<br/>
<b>take </b><font color="Maroon">c</font> =  <a href="lattice2.html#K2" target="_self">FinJoin</a> <font color="Maroon">B</font>,<span class="p1">(<span class="default"><a href="partfun1.html#K6">id</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">L</font></span>)</span>; <i><font color="Red">:: according to </font></i><a class="ref" href="lattices.html#D14">LATTICES:def 14</a><br/>

<b>let </b><font color="Maroon">a</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L</font>;<br/>

<a NAME="E4:89"/>
<font color="Maroon">a</font> <a href="lattices.html#R3">[=</a> <span class="p1">(<span class="default"><a href="partfun1.html#K6">id</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">L</font></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">a</font>
 
<b>by </b><i><a class="ref" href="funct_1.html#T35">FUNCT_1:35</a></i>;<br/>
<a NAME="E5:89"/><b>then </b><i><font color="Green">E17</font></i>: 
( <font color="Maroon">a</font> <a href="lattices.html#R3">[=</a> <font color="Maroon">c</font> &amp; <font color="Maroon">c</font> <a href="lattices.html#K3">"\/"</a> <font color="Maroon">a</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a</font> <a href="lattices.html#K3">"\/"</a> <font color="Maroon">c</font> )
 
<b>by </b><i/>;<br/>
<b>hence </b><a NAME="E6:89"/>
<font color="Maroon">c</font> <a href="lattices.html#K3">"\/"</a> <font color="Maroon">a</font> <a href="hidden.html#R1">=</a> <font color="Maroon">c</font>
 <b>by </b><i><a class="ref" href="lattices.html#D3">LATTICES:def 3</a></i>;<br/>

<b>thus </b><a NAME="E7:89"/>
<font color="Maroon">a</font> <a href="lattices.html#K3">"\/"</a> <font color="Maroon">c</font> <a href="hidden.html#R1">=</a> <font color="Maroon">c</font>
 <b>by </b><i><a class="ref" href="lattice2.html#T30" target="_self">Th30</a>, <a class="ref" href="lattices.html#D3">LATTICES:def 3</a></i>;<br/>


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