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<b>let </b><font color="Maroon">A</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">a</font> be   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="lattice5.html#K1" target="_self">EqRelLATT</a> <font color="Maroon">A</font></span>)</span>, <font color="Maroon">b</font> be   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="lattice5.html#K1" target="_self">EqRelLATT</a> <font color="Maroon">A</font></span>)</span>;<br/><b>let </b><font color="Maroon">E1</font> be   <a href="eqrel_1.html#NM2">Equivalence_Relation</a> of <font color="Maroon">A</font>, <font color="Maroon">E2</font> be   <a href="eqrel_1.html#NM2">Equivalence_Relation</a> of <font color="Maroon">A</font>;<br/>





<b>assume </b><b>that </b><br/><a NAME="E1:13"/><i><font color="Green">E29</font></i>: 
<font color="Maroon">a</font> <a href="hidden.html#R1">=</a> <font color="Maroon">E1</font>
 <b>and </b><br/><a NAME="E2:13"/><i><font color="Green">E37</font></i>: 
<font color="Maroon">b</font> <a href="hidden.html#R1">=</a> <font color="Maroon">E2</font>
 ;<br/>

<b>reconsider </b><font color="Maroon">x</font> = <font color="Maroon">a</font> as   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="lattice3.html#K3">LattPOSet</a> <span class="p2">(<span class="default"><a href="msualg_5.html#K2">EqRelLatt</a> <font color="Maroon">A</font></span>)</span></span>)</span> ;<br/>
<b>reconsider </b><font color="Maroon">x</font> = <font color="Maroon">x</font> as   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="msualg_5.html#K2">EqRelLatt</a> <font color="Maroon">A</font></span>)</span> ;<br/>
<b>reconsider </b><font color="Maroon">y</font> = <font color="Maroon">b</font> as   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="lattice3.html#K3">LattPOSet</a> <span class="p2">(<span class="default"><a href="msualg_5.html#K2">EqRelLatt</a> <font color="Maroon">A</font></span>)</span></span>)</span> ;<br/>
<b>reconsider </b><font color="Maroon">y</font> = <font color="Maroon">y</font> as   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="msualg_5.html#K2">EqRelLatt</a> <font color="Maroon">A</font></span>)</span> ;<br/>
<b>reconsider </b><font color="Maroon">a1</font> = <font color="Maroon">a</font>, <font color="Maroon">b1</font> = <font color="Maroon">b</font> as   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="lattice3.html#K3">LattPOSet</a> <span class="p2">(<span class="default"><a href="msualg_5.html#K2">EqRelLatt</a> <font color="Maroon">A</font></span>)</span></span>)</span> ;<br/>
<a NAME="E8:13"/><i><font color="Green">E39</font></i>: 
( <font color="Maroon">x</font> <a href="lattice3.html#K4">%</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">x</font> &amp; <font color="Maroon">y</font> <a href="lattice3.html#K4">%</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">y</font> &amp;  <a href="lattice3.html#K5">%</a> <span class="p1">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K4">%</a> </span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">x</font> <a href="lattice3.html#K4">%</a>  &amp;  <a href="lattice3.html#K5">%</a> <span class="p1">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K4">%</a> </span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">y</font> <a href="lattice3.html#K4">%</a>  &amp;  <a href="lattice3.html#K5">%</a> <font color="Maroon">a1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a1</font> &amp;  <a href="lattice3.html#K5">%</a> <font color="Maroon">b1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">b1</font> &amp; <span class="p1">(<span class="default"><a href="lattice3.html#K5">%</a> <font color="Maroon">a1</font></span>)</span> <a href="lattice3.html#K4">%</a>  <a href="hidden.html#R1">=</a>  <a href="lattice3.html#K5">%</a> <font color="Maroon">a1</font> &amp; <span class="p1">(<span class="default"><a href="lattice3.html#K5">%</a> <font color="Maroon">b1</font></span>)</span> <a href="lattice3.html#K4">%</a>  <a href="hidden.html#R1">=</a>  <a href="lattice3.html#K5">%</a> <font color="Maroon">b1</font> )
 
;<br/>
<b>thus </b><font color="Maroon">a</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">b</font> = 
<font color="Maroon">x</font> <a href="lattices.html#K3">"\/"</a> <font color="Maroon">y</font>
<b>by </b><i>, </i>
<br/>.= 
the <a href="lattices.html#U2">L_join</a> of <span class="p1">(<span class="default"><a href="msualg_5.html#K2">EqRelLatt</a> <font color="Maroon">A</font></span>)</span> <a href="binop_1.html#K2">.</a> <font color="Maroon">x</font>,<font color="Maroon">y</font>
<b>by </b><i><a class="ref" href="lattices.html#D1">LATTICES:def 1</a></i>
<br/>.= 
<font color="Maroon">E1</font> <a href="eqrel_1.html#K5">"\/"</a> <font color="Maroon">E2</font>
<b>by </b><i>, , <a class="ref" href="msualg_5.html#D2">MSUALG_5:def 2</a></i>
;<br/>


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