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<b>let </b><font color="Maroon" title="c1">A</font> be  non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/><b>let </b><font color="Maroon" title="c2">B</font> be   <a href="finsub_1.html#NM1" title="FINSUB_1:NM.1">Finite_Subset</a> of <font color="Maroon" title="c1">A</font>;<br/><b>let </b><font color="Maroon" title="c3">L</font> be   <a href="lattices.html#NM5" title="LATTICES:NM.5">1_Lattice</a>;<br/><b>let </b><font color="Maroon" title="c4">f</font>, <font color="Maroon" title="c5">g</font> be   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <font color="Maroon" title="c1">A</font>,the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c3">L</font>;<br/>









<b>assume </b><a NAME="E1:69"/><i><font color="Green" title="E49">A1</font></i>: 
<font color="Maroon" title="c4">f</font> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <font color="Maroon" title="c2">B</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">g</font> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <font color="Maroon" title="c2">B</font>
 ;<br/>

<b>reconsider </b><font color="Maroon" title="c6">f'</font> = <font color="Maroon" title="c4">f</font>, <font color="Maroon" title="c7">g'</font> = <font color="Maroon" title="c5">g</font> as   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <font color="Maroon" title="c1">A</font>,the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c3">L</font> <a href="lattice2.html#K1" title="LATTICE2:func.1">.:</a> </span>)</span> ;<br/>
<a NAME="E3:69"/><i><font color="Green" title="E50">A2</font></i>: 
<font color="Maroon" title="c3">L</font> <a href="lattice2.html#K1" title="LATTICE2:func.1">.:</a>  is   <a href="lattices.html#NM4" title="LATTICES:NM.4">0_Lattice</a>
 
<b>by </b><i><a class="ref" href="lattice2.html#T64" target="_self" title="LATTICE2:th.64">Th64</a></i>;<br/>
<a NAME="E4:69"/>
(  <a href="lattice2.html#K3" title="LATTICE2:func.3">FinMeet</a> <font color="Maroon" title="c2">B</font>,<font color="Maroon" title="c4">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="lattice2.html#K2" title="LATTICE2:func.2">FinJoin</a> <font color="Maroon" title="c2">B</font>,<font color="Maroon" title="c6">f'</font> &amp;  <a href="lattice2.html#K3" title="LATTICE2:func.3">FinMeet</a> <font color="Maroon" title="c2">B</font>,<font color="Maroon" title="c5">g</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="lattice2.html#K2" title="LATTICE2:func.2">FinJoin</a> <font color="Maroon" title="c2">B</font>,<font color="Maroon" title="c7">g'</font> )
 
;<br/>
<b>hence </b><a NAME="E5:69"/>
 <a href="lattice2.html#K3" title="LATTICE2:func.3">FinMeet</a> <font color="Maroon" title="c2">B</font>,<font color="Maroon" title="c4">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="lattice2.html#K3" title="LATTICE2:func.3">FinMeet</a> <font color="Maroon" title="c2">B</font>,<font color="Maroon" title="c5">g</font>
 <b>by </b><i><a class="txt" href="lattice2.html#E1:69"><i><font color="Green" title="E49">A1</font></i></a>, <a class="txt" href="lattice2.html#E3:69"><i><font color="Green" title="E50">A2</font></i></a>, <a class="ref" href="lattice2.html#T69" target="_self" title="LATTICE2:th.69">Th69</a></i>;<br/>


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