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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>let </b><font color="Maroon" title="c2">u</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">L</font>;<br/><b>let </b><font color="Maroon" title="c3">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="c4">B</font> be   <a href="finsub_1.html#NM1" title="FINSUB_1:NM.1">Finite_Subset</a> of <font color="Maroon" title="c3">A</font>;<br/><b>let </b><font color="Maroon" title="c5">f</font> be   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <font color="Maroon" title="c3">A</font>,the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">L</font>;<br/>









<b>given </b><font color="Maroon" title="c6">x</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c3">A</font><b> such that </b><a NAME="E2:53"/><i><font color="Green" title="E40">A1</font></i>: 
<font color="Maroon" title="c6">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">B</font>
 <b>and </b><br/><a NAME="E3:53"/><i><font color="Green" title="E41">A2</font></i>: 
<font color="Maroon" title="c5">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="c2">u</font>
 ;<br/>

<b>reconsider </b><font color="Maroon" title="c7">f'</font> = <font color="Maroon" title="c5">f</font> as   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <font color="Maroon" title="c3">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="c1">L</font> <a href="lattice2.html#K1" title="LATTICE2:func.1">.:</a> </span>)</span> ;<br/>
<b>reconsider </b><font color="Maroon" title="c8">u'</font> = <font color="Maroon" title="c2">u</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c1">L</font> <a href="lattice2.html#K1" title="LATTICE2:func.1">.:</a> </span>)</span> ;<br/>
<a NAME="E6:53"/>
<font color="Maroon" title="c8">u'</font> <a href="lattices.html#R3" title="LATTICES:pred.3">[=</a> <font color="Maroon" title="c7">f'</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#E3:53"><i><font color="Green" title="E41">A2</font></i></a>, <a class="ref" href="lattice2.html#T53" target="_self" title="LATTICE2:th.53">Th53</a></i>;<br/>
<a NAME="E7:53"/><b>then </b>
<font color="Maroon" title="c8">u'</font> <a href="lattices.html#R3" title="LATTICES:pred.3">[=</a>  <a href="lattice2.html#K2" title="LATTICE2:func.2">FinJoin</a> <font color="Maroon" title="c4">B</font>,<font color="Maroon" title="c7">f'</font>
 
<b>by </b><i><a class="txt" href="lattice2.html#E2:53"><i><font color="Green" title="E40">A1</font></i></a>, <a class="ref" href="lattice2.html#T44" target="_self" title="LATTICE2:th.44">Th44</a></i>;<br/>
<b>hence </b><a NAME="E8:53"/>
 <a href="lattice2.html#K3" title="LATTICE2:func.3">FinMeet</a> <font color="Maroon" title="c4">B</font>,<font color="Maroon" title="c5">f</font> <a href="lattices.html#R3" title="LATTICES:pred.3">[=</a> <font color="Maroon" title="c2">u</font>
 <b>by </b><i><a class="ref" href="lattice2.html#T54" target="_self" title="LATTICE2:th.54">Th54</a></i>;<br/>


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