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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="E1:75"/><i><font color="Green" title="E51">A1</font></i>: 
for <font color="Olive" title="b1">x</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">A</font>  st <font color="Olive" title="b1">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">B</font> holds <br/><font color="Maroon" title="c4">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">x</font> <a href="lattices.html#R3" title="LATTICES:pred.3">[=</a> <font color="Maroon" title="c5">g</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">x</font>
 ;<br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="75_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c6">x</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">A</font>;<br/><b>assume </b><a NAME="E1:75_1"/><i><font color="Green" title="E52">A2</font></i>: 
<font color="Maroon" title="c6">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">B</font>
 ;<br/><a NAME="E2:75_1"/><b>then </b>
<font color="Maroon" title="c4">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c6">x</font> <a href="lattices.html#R3" title="LATTICES:pred.3">[=</a> <font color="Maroon" title="c5">g</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c6">x</font>
 <b>by </b><i><a class="txt" href="lattice2.html#E1:75"><i><font color="Green" title="E51">A1</font></i></a></i>;<br/><b>hence </b><a NAME="E3:75_1"/>
 <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="lattices.html#R3" title="LATTICES:pred.3">[=</a> <font color="Maroon" title="c5">g</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c6">x</font>
 <b>by </b><i><a class="txt" href="lattice2.html#E1:75_1"><i><font color="Green" title="E52">A2</font></i></a>, <a class="ref" href="lattice2.html#T56" target="_self" title="LATTICE2:th.56">Th56</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E3:75"/>
 <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="lattices.html#R3" title="LATTICES:pred.3">[=</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="ref" href="lattice2.html#T76" target="_self" title="LATTICE2:th.76">Th76</a></i>;<br/>


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