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<b>let </b><font color="Maroon" title="c1">L</font> be   <a href="lattices.html#NM1" title="LATTICES:NM.1">Lattice</a>;<br/>

<b>assume </b><a NAME="E1:85"/>
<font color="Maroon" title="c1">L</font> is <a href="struct_0.html#V8" title="STRUCT_0:attr.8">finite</a>
 ;<br/>

<a NAME="E2:85"/><b>then </b>
the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">L</font> is <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a>
 
<b>by </b><i><a class="ref" href="struct_0.html#D11" title="STRUCT_0:def.11">STRUCT_0:def 11</a></i>;<br/>
<b>then reconsider </b><font color="Maroon" title="c2">B</font> = the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">L</font> as   <a href="finsub_1.html#NM1" title="FINSUB_1:NM.1">Finite_Subset</a> of the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">L</font> <b>by </b><i><a class="ref" href="finsub_1.html#D5" title="FINSUB_1:def.5">FINSUB_1:def 5</a></i>;<br/>
<b>take </b><font color="Maroon" title="c3">c</font> =  <a href="lattice2.html#K2" title="LATTICE2:func.2">FinJoin</a> <font color="Maroon" title="c2">B</font>,<span class="p1">(<span class="default"><a href="partfun1.html#K6" title="PARTFUN1:func.6">id</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">L</font></span>)</span>; <i><font color="Red">:: according to </font></i><a class="ref" href="lattices.html#D14" title="LATTICES:def.14">LATTICES:def 14</a><br/>

<b>let </b><font color="Maroon" title="c4">a</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">L</font>;<br/>

<a NAME="E4:85"/>
<font color="Maroon" title="c4">a</font> <a href="lattices.html#R3" title="LATTICES:pred.3">[=</a> <span class="p1">(<span class="default"><a href="partfun1.html#K6" title="PARTFUN1:func.6">id</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">L</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c4">a</font>
 
<b>by </b><i><a class="ref" href="funct_1.html#T35" title="FUNCT_1:th.35">FUNCT_1:35</a></i>;<br/>
<a NAME="E5:85"/><b>then </b><i><font color="Green" title="E54">A1</font></i>: 
( <font color="Maroon" title="c4">a</font> <a href="lattices.html#R3" title="LATTICES:pred.3">[=</a> <font color="Maroon" title="c3">c</font> &amp; <font color="Maroon" title="c3">c</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon" title="c4">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">a</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon" title="c3">c</font> )
 
<b>by </b><i><a class="ref" href="lattice2.html#T44" target="_self" title="LATTICE2:th.44">Th44</a></i>;<br/>
<b>hence </b><a NAME="E6:85"/>
<font color="Maroon" title="c3">c</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon" title="c4">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">c</font>
 <b>by </b><i><a class="ref" href="lattices.html#D3" title="LATTICES:def.3">LATTICES:def 3</a></i>;<br/>

<b>thus </b><a NAME="E7:85"/>
<font color="Maroon" title="c4">a</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon" title="c3">c</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">c</font>
 <b>by </b><i><a class="txt" href="lattice2.html#E5:85"><i><font color="Green" title="E54">A1</font></i></a>, <a class="ref" href="lattices.html#D3" title="LATTICES:def.3">LATTICES:def 3</a></i>;<br/>


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