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<b>let </b><font color="Maroon">c<sub>1</sub></font> be    <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font>, <font color="Maroon">c<sub>3</sub></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">c<sub>1</sub></font></span>)</span>;<br/>



<div><i><font color="Green">E9</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="11_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c<sub>4</sub></font>, <font color="Maroon">c<sub>5</sub></font> be   <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">c<sub>1</sub></font></span>)</span>;<br/><b>reconsider </b><font color="Maroon">c<sub>6</sub></font> = <font color="Maroon">c<sub>4</sub></font> as   <a href="eqrel_1.html#NM2">Equivalence_Relation</a> of <font color="Maroon">c<sub>1</sub></font> <b>by </b><i><a class="ref" href="msualg_7.html#T1">MSUALG_7:1</a></i>;<br/><b>reconsider </b><font color="Maroon">c<sub>7</sub></font> = <font color="Maroon">c<sub>5</sub></font> as   <a href="eqrel_1.html#NM2">Equivalence_Relation</a> of <font color="Maroon">c<sub>1</sub></font> <b>by </b><i><a class="ref" href="msualg_7.html#T1">MSUALG_7:1</a></i>;<br/><b>thus </b><font color="Maroon">c<sub>4</sub></font> <a href="lattices.html#K4">"/\"</a> <font color="Maroon">c<sub>5</sub></font> = 
the <a href="lattices.html#U1">L_meet</a> of <span class="p1">(<span class="default"><a href="msualg_5.html#K2">EqRelLatt</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="binop_1.html#K1">.</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</sub></font>
<b>by </b><i><a class="ref" href="lattices.html#D2">LATTICES:def 2</a></i>
<br/>.= 
<font color="Maroon">c<sub>4</sub></font> <a href="xboole_0.html#K3">/\</a> <font color="Maroon">c<sub>5</sub></font>
<b>by </b><i><a class="ref" href="msualg_5.html#D2">MSUALG_5:def 2</a></i>
;<br/></div><b>end;</b></div>
<b>reconsider </b><font color="Maroon">c<sub>4</sub></font> = <font color="Maroon">c<sub>2</sub></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">c<sub>1</sub></font></span>)</span></span>)</span> ;<br/>
<b>reconsider </b><font color="Maroon">c<sub>5</sub></font> = <font color="Maroon">c<sub>4</sub></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">c<sub>1</sub></font></span>)</span> ;<br/>
<b>reconsider </b><font color="Maroon">c<sub>6</sub></font> = <font color="Maroon">c<sub>3</sub></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">c<sub>1</sub></font></span>)</span></span>)</span> ;<br/>
<b>reconsider </b><font color="Maroon">c<sub>7</sub></font> = <font color="Maroon">c<sub>6</sub></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">c<sub>1</sub></font></span>)</span> ;<br/>
<b>reconsider </b><font color="Maroon">c<sub>8</sub></font> = <font color="Maroon">c<sub>2</sub></font>, <font color="Maroon">c<sub>9</sub></font> = <font color="Maroon">c<sub>3</sub></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">c<sub>1</sub></font></span>)</span></span>)</span> ;<br/>
<a NAME="E7:11"/><i><font color="Green">E10</font></i>: 
( <font color="Maroon">c<sub>5</sub></font> <a href="lattice3.html#K4">%</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>5</sub></font> &amp; <font color="Maroon">c<sub>7</sub></font> <a href="lattice3.html#K4">%</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>7</sub></font> &amp;  <a href="lattice3.html#K5">%</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="lattice3.html#K4">%</a> </span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>5</sub></font> <a href="lattice3.html#K4">%</a>  &amp;  <a href="lattice3.html#K5">%</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="lattice3.html#K4">%</a> </span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>7</sub></font> <a href="lattice3.html#K4">%</a>  &amp;  <a href="lattice3.html#K5">%</a> <font color="Maroon">c<sub>8</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>8</sub></font> &amp;  <a href="lattice3.html#K5">%</a> <font color="Maroon">c<sub>9</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>9</sub></font> &amp; <span class="p1">(<span class="default"><a href="lattice3.html#K5">%</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="lattice3.html#K4">%</a>  <a href="hidden.html#R1">=</a>  <a href="lattice3.html#K5">%</a> <font color="Maroon">c<sub>8</sub></font> &amp; <span class="p1">(<span class="default"><a href="lattice3.html#K5">%</a> <font color="Maroon">c<sub>9</sub></font></span>)</span> <a href="lattice3.html#K4">%</a>  <a href="hidden.html#R1">=</a>  <a href="lattice3.html#K5">%</a> <font color="Maroon">c<sub>9</sub></font> )
 
;<br/>
<b>thus </b><font color="Maroon">c<sub>2</sub></font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">c<sub>3</sub></font> = 
<font color="Maroon">c<sub>8</sub></font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">c<sub>9</sub></font>

<br/>.= 
<font color="Maroon">c<sub>5</sub></font> <a href="lattices.html#K4">"/\"</a> <font color="Maroon">c<sub>7</sub></font>
<b>by </b><i><a class="txt" href="lattice5.html#E7:11"><i><font color="Green">E10</font></i></a>, <a class="ref" href="lattice5.html#T7" target="_self">Th7</a></i>
<br/>.= 
<font color="Maroon">c<sub>2</sub></font> <a href="xboole_0.html#K3">/\</a> <font color="Maroon">c<sub>3</sub></font>
<b>by </b><i><a class="txt" href="lattice5.html#E1:11"><i><font color="Green">E9</font></i></a></i>
;<br/>


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