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



<a NAME="E1:52"/>
<span class="p1"><a href="tarski.html#K1">{</a><span class="default"><a href="xboole_0.html#K1">{}</a> </span><a href="tarski.html#K1">}</a></span> <a href="hidden.html#R2">in</a>  <a href="substlat.html#K1" target="_self">SubstitutionSet</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font>
 
<b>by </b><i><a class="ref" href="substlat.html#T2" target="_self">Th2</a></i>;<br/>
<b>then reconsider </b><font color="Maroon">c<sub>3</sub></font> = <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><a href="xboole_0.html#K1">{}</a> </span><a href="tarski.html#K1">}</a></span> as   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="substlat.html#K5" target="_self">SubstLatt</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <b>by </b><i><a class="ref" href="substlat.html#D4" target="_self">Def4</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="52_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c<sub>4</sub></font> be   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="substlat.html#K5" target="_self">SubstLatt</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span>;<br/><b>reconsider </b><font color="Maroon">c<sub>5</sub></font> = <font color="Maroon">c<sub>3</sub></font>, <font color="Maroon">c<sub>6</sub></font> = <font color="Maroon">c<sub>4</sub></font> as    <a href="subset_1.html#M2">Element</a> of  <a href="substlat.html#K1" target="_self">SubstitutionSet</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font> <b>by </b><i><a class="ref" href="substlat.html#D4" target="_self">Def4</a></i>;<br/><b>thus </b><font color="Maroon">c<sub>3</sub></font> <a href="lattices.html#K4">"/\"</a> <font color="Maroon">c<sub>4</sub></font> = 
the <a href="lattices.html#U1">L_meet</a> of <span class="p1">(<span class="default"><a href="substlat.html#K5" target="_self">SubstLatt</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="binop_1.html#K1">.</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font>

<br/>.= 
 <a href="substlat.html#K3" target="_self">mi</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="substlat.html#K4" target="_self">^</a> <font color="Maroon">c<sub>6</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="substlat.html#D4" target="_self">Def4</a></i>
<br/>.= 
 <a href="substlat.html#K3" target="_self">mi</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="substlat.html#K4" target="_self">^</a> <font color="Maroon">c<sub>5</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="substlat.html#T3" target="_self">Th3</a></i>
<br/>.= 
 <a href="substlat.html#K3" target="_self">mi</a> <font color="Maroon">c<sub>6</sub></font>
<b>by </b><i><a class="ref" href="substlat.html#T4" target="_self">Th4</a></i>
<br/>.= 
<font color="Maroon">c<sub>4</sub></font>
<b>by </b><i><a class="ref" href="substlat.html#T11" target="_self">Th11</a></i>
;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E4:52"/>
 <a href="lattices.html#K6">Top</a> <span class="p1">(<span class="default"><a href="substlat.html#K5" target="_self">SubstLatt</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><a href="xboole_0.html#K1">{}</a> </span><a href="tarski.html#K1">}</a></span>
 <b>by </b><i><a class="ref" href="lattice2.html#T24">LATTICE2:24</a></i>;<br/>


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