<?xml version="1.0"?>
<div class="add">

<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/><b>let </b><font color="Maroon">c<sub>3</sub></font>, <font color="Maroon">c<sub>4</sub></font>, <font color="Maroon">c<sub>5</sub></font> be    <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>;<br/>









<a NAME="E1:47"/>
( the <a href="lattices.html#U2">L_join</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>4</sub></font>,<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a>  <a href="substlat.html#K3" target="_self">mi</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="substlat.html#K2" target="_self">\/</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> &amp; 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>3</sub></font>,<font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a>  <a href="substlat.html#K3" target="_self">mi</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="substlat.html#K4" target="_self">^</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> &amp; 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>3</sub></font>,<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a>  <a href="substlat.html#K3" target="_self">mi</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</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#D4" target="_self">Def4</a></i>;<br/>
<b>then reconsider </b><font color="Maroon">c<sub>6</sub></font> = the <a href="lattices.html#U2">L_join</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>4</sub></font>,<font color="Maroon">c<sub>5</sub></font>, <font color="Maroon">c<sub>7</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>3</sub></font>,<font color="Maroon">c<sub>4</sub></font>, <font color="Maroon">c<sub>8</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>3</sub></font>,<font color="Maroon">c<sub>5</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> ;<br/>
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>3</sub></font>,<span class="p1">(<span class="default">the <a href="lattices.html#U2">L_join</a> of <span class="p2">(<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>4</sub></font>,<font color="Maroon">c<sub>5</sub></font></span>)</span> = 
 <a href="substlat.html#K3" target="_self">mi</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</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>3</sub></font> <a href="substlat.html#K4" target="_self">^</a> <span class="p2">(<span class="default"><a href="substlat.html#K3" target="_self">mi</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="substlat.html#K2" target="_self">\/</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span></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>3</sub></font> <a href="substlat.html#K4" target="_self">^</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="substlat.html#K2" target="_self">\/</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="substlat.html#T20" target="_self">Th20</a></i>
<br/>.= 
 <a href="substlat.html#K3" target="_self">mi</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="substlat.html#K4" target="_self">^</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="finsub_1.html#K1">\/</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="substlat.html#K4" target="_self">^</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="substlat.html#T22" target="_self">Th22</a></i>
<br/>.= 
 <a href="substlat.html#K3" target="_self">mi</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="substlat.html#K3" target="_self">mi</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="substlat.html#K4" target="_self">^</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span> <a href="finsub_1.html#K1">\/</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="substlat.html#K4" target="_self">^</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="substlat.html#T13" target="_self">Th13</a></i>
<br/>.= 
 <a href="substlat.html#K3" target="_self">mi</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="substlat.html#K3" target="_self">mi</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="substlat.html#K4" target="_self">^</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span> <a href="substlat.html#K2" target="_self">\/</a> <span class="p2">(<span class="default"><a href="substlat.html#K3" target="_self">mi</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="substlat.html#K4" target="_self">^</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="substlat.html#T13" target="_self">Th13</a></i>
<br/>.= 
 <a href="substlat.html#K3" target="_self">mi</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="substlat.html#K2" target="_self">\/</a> <span class="p2">(<span class="default"><a href="substlat.html#K3" target="_self">mi</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="substlat.html#K4" target="_self">^</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span></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>7</sub></font> <a href="substlat.html#K2" target="_self">\/</a> <font color="Maroon">c<sub>8</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="substlat.html#D4" target="_self">Def4</a></i>
;<br/>
<b>hence </b><a NAME="E4:47"/>
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>3</sub></font>,<span class="p1">(<span class="default">the <a href="lattices.html#U2">L_join</a> of <span class="p2">(<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>4</sub></font>,<font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="hidden.html#R1">=</a> the <a href="lattices.html#U2">L_join</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> <span class="p1">(<span class="default">the <a href="lattices.html#U1">L_meet</a> of <span class="p2">(<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>3</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span>,<span class="p1">(<span class="default">the <a href="lattices.html#U1">L_meet</a> of <span class="p2">(<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>3</sub></font>,<font color="Maroon">c<sub>5</sub></font></span>)</span>
 <b>by </b><i><a class="ref" href="substlat.html#D4" target="_self">Def4</a></i>;<br/>


</div>
