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<b>let </b><font color="Maroon" title="c1">A</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/><b>let </b><font color="Maroon" title="c2">a</font>, <font color="Maroon" title="c3">b</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="lattice5.html#K1" title="LATTICE5:func.1">EqRelLATT</a> <font color="Maroon" title="c1">A</font></span>)</span>;<br/><b>let </b><font color="Maroon" title="c4">E1</font>, <font color="Maroon" title="c5">E2</font> be   <a href="eqrel_1.html#NM2" title="EQREL_1:NM.2">Equivalence_Relation</a> of <font color="Maroon" title="c1">A</font>;<br/>





<b>assume </b><b>that </b><br/><a NAME="E1:13"/><i><font color="Green" title="E11">A1</font></i>: 
<font color="Maroon" title="c2">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">E1</font>
 <b>and </b><br/><a NAME="E2:13"/><i><font color="Green" title="E12">A2</font></i>: 
<font color="Maroon" title="c3">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">E2</font>
 ;<br/>

<b>reconsider </b><font color="Maroon" title="c6">x</font> = <font color="Maroon" title="c2">a</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="lattice3.html#K3" title="LATTICE3:func.3">LattPOSet</a> <span class="p2">(<span class="default"><a href="msualg_5.html#K2" title="MSUALG_5:func.2">EqRelLatt</a> <font color="Maroon" title="c1">A</font></span>)</span></span>)</span> ;<br/>
<b>reconsider </b><font color="Maroon" title="c7">x</font> = <font color="Maroon" title="c6">x</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="msualg_5.html#K2" title="MSUALG_5:func.2">EqRelLatt</a> <font color="Maroon" title="c1">A</font></span>)</span> ;<br/>
<b>reconsider </b><font color="Maroon" title="c8">y</font> = <font color="Maroon" title="c3">b</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="lattice3.html#K3" title="LATTICE3:func.3">LattPOSet</a> <span class="p2">(<span class="default"><a href="msualg_5.html#K2" title="MSUALG_5:func.2">EqRelLatt</a> <font color="Maroon" title="c1">A</font></span>)</span></span>)</span> ;<br/>
<b>reconsider </b><font color="Maroon" title="c9">y</font> = <font color="Maroon" title="c8">y</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="msualg_5.html#K2" title="MSUALG_5:func.2">EqRelLatt</a> <font color="Maroon" title="c1">A</font></span>)</span> ;<br/>
<b>reconsider </b><font color="Maroon" title="c10">a1</font> = <font color="Maroon" title="c2">a</font>, <font color="Maroon" title="c11">b1</font> = <font color="Maroon" title="c3">b</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="lattice3.html#K3" title="LATTICE3:func.3">LattPOSet</a> <span class="p2">(<span class="default"><a href="msualg_5.html#K2" title="MSUALG_5:func.2">EqRelLatt</a> <font color="Maroon" title="c1">A</font></span>)</span></span>)</span> ;<br/>
<a NAME="E8:13"/>
( <font color="Maroon" title="c7">x</font> <a href="lattice3.html#K4" title="LATTICE3:func.4">%</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">x</font> &amp; <font color="Maroon" title="c9">y</font> <a href="lattice3.html#K4" title="LATTICE3:func.4">%</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">y</font> &amp;  <a href="lattice3.html#K5" title="LATTICE3:func.5">%</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">x</font> <a href="lattice3.html#K4" title="LATTICE3:func.4">%</a> </span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">x</font> <a href="lattice3.html#K4" title="LATTICE3:func.4">%</a>  &amp;  <a href="lattice3.html#K5" title="LATTICE3:func.5">%</a> <span class="p1">(<span class="default"><font color="Maroon" title="c9">y</font> <a href="lattice3.html#K4" title="LATTICE3:func.4">%</a> </span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">y</font> <a href="lattice3.html#K4" title="LATTICE3:func.4">%</a>  &amp;  <a href="lattice3.html#K5" title="LATTICE3:func.5">%</a> <font color="Maroon" title="c10">a1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c10">a1</font> &amp;  <a href="lattice3.html#K5" title="LATTICE3:func.5">%</a> <font color="Maroon" title="c11">b1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c11">b1</font> &amp; <span class="p1">(<span class="default"><a href="lattice3.html#K5" title="LATTICE3:func.5">%</a> <font color="Maroon" title="c10">a1</font></span>)</span> <a href="lattice3.html#K4" title="LATTICE3:func.4">%</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="lattice3.html#K5" title="LATTICE3:func.5">%</a> <font color="Maroon" title="c10">a1</font> &amp; <span class="p1">(<span class="default"><a href="lattice3.html#K5" title="LATTICE3:func.5">%</a> <font color="Maroon" title="c11">b1</font></span>)</span> <a href="lattice3.html#K4" title="LATTICE3:func.4">%</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="lattice3.html#K5" title="LATTICE3:func.5">%</a> <font color="Maroon" title="c11">b1</font> )
 
;<br/>
<b>hence </b><font color="Maroon" title="c2">a</font> <a href="lattice3.html#K13" title="LATTICE3:func.13">"\/"</a> <font color="Maroon" title="c3">b</font> = 
<font color="Maroon" title="c7">x</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon" title="c9">y</font>
<b>by </b><i><a class="ref" href="lattice5.html#T9" target="_self" title="LATTICE5:th.9">Th9</a></i>
<br/>.= 
the <a href="lattices.html#U2" title="LATTICES:sel.2">L_join</a> of <span class="p1">(<span class="default"><a href="msualg_5.html#K2" title="MSUALG_5:func.2">EqRelLatt</a> <font color="Maroon" title="c1">A</font></span>)</span> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> <font color="Maroon" title="c7">x</font>,<font color="Maroon" title="c9">y</font>
<b>by </b><i><a class="ref" href="lattices.html#D1" title="LATTICES:def.1">LATTICES:def 1</a></i>
<br/>.= 
<font color="Maroon" title="c4">E1</font> <a href="eqrel_1.html#K5" title="EQREL_1:func.5">"\/"</a> <font color="Maroon" title="c5">E2</font>
<b>by </b><i><a class="txt" href="lattice5.html#E1:13"><i><font color="Green" title="E11">A1</font></i></a>, <a class="txt" href="lattice5.html#E2:13"><i><font color="Green" title="E12">A2</font></i></a>, <a class="ref" href="msualg_5.html#D2" title="MSUALG_5:def.2">MSUALG_5:def 2</a></i>
;<br/><br/>


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