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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>, <font color="Maroon">c<sub>4</sub></font> be    <a href="subset_1.html#M2">Element</a> of  <a href="normform.html#K8" target="_self">Normal_forms_on</a> <font color="Maroon">c<sub>1</sub></font>;<br/>







<a NAME="E1:74"/>
( the <a href="lattices.html#U2">L_join</a> of <span class="p1">(<span class="default"><a href="normform.html#K12" target="_self">NormForm</a> <font color="Maroon">c<sub>1</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="normform.html#K9" target="_self">mi</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="setwiseo.html#K5">\/</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="normform.html#K12" target="_self">NormForm</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="binop_1.html#K1">.</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a>  <a href="normform.html#K9" target="_self">mi</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="normform.html#K10" target="_self">^</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> &amp; the <a href="lattices.html#U1">L_meet</a> of <span class="p1">(<span class="default"><a href="normform.html#K12" target="_self">NormForm</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="binop_1.html#K1">.</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a>  <a href="normform.html#K9" target="_self">mi</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="normform.html#K10" target="_self">^</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> )
 
<b>by </b><i><a class="ref" href="normform.html#D14" target="_self">Def14</a></i>;<br/>
<b>then reconsider </b><font color="Maroon">c<sub>5</sub></font> = the <a href="lattices.html#U2">L_join</a> of <span class="p1">(<span class="default"><a href="normform.html#K12" target="_self">NormForm</a> <font color="Maroon">c<sub>1</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>6</sub></font> = the <a href="lattices.html#U1">L_meet</a> of <span class="p1">(<span class="default"><a href="normform.html#K12" target="_self">NormForm</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="binop_1.html#K1">.</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</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="normform.html#K12" target="_self">NormForm</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="binop_1.html#K1">.</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>4</sub></font> as    <a href="subset_1.html#M2">Element</a> of  <a href="normform.html#K8" target="_self">Normal_forms_on</a> <font color="Maroon">c<sub>1</sub></font> ;<br/>
the <a href="lattices.html#U1">L_meet</a> of <span class="p1">(<span class="default"><a href="normform.html#K12" target="_self">NormForm</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="binop_1.html#K1">.</a> <font color="Maroon">c<sub>2</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="normform.html#K12" target="_self">NormForm</a> <font color="Maroon">c<sub>1</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> = 
 <a href="normform.html#K9" target="_self">mi</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="normform.html#K10" target="_self">^</a> <font color="Maroon">c<sub>5</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="normform.html#D14" target="_self">Def14</a></i>
<br/>.= 
 <a href="normform.html#K9" target="_self">mi</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="normform.html#K10" target="_self">^</a> <span class="p2">(<span class="default"><a href="normform.html#K9" target="_self">mi</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="setwiseo.html#K5">\/</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="normform.html#D14" target="_self">Def14</a></i>
<br/>.= 
 <a href="normform.html#K9" target="_self">mi</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="normform.html#K10" target="_self">^</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="setwiseo.html#K5">\/</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="normform.html#T75" target="_self">Th75</a></i>
<br/>.= 
 <a href="normform.html#K9" target="_self">mi</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="normform.html#K10" target="_self">^</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="setwiseo.html#K5">\/</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="normform.html#K10" target="_self">^</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="normform.html#T77" target="_self">Th77</a></i>
<br/>.= 
 <a href="normform.html#K9" target="_self">mi</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="normform.html#K9" target="_self">mi</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="normform.html#K10" target="_self">^</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span> <a href="setwiseo.html#K5">\/</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="normform.html#K10" target="_self">^</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="normform.html#T68" target="_self">Th68</a></i>
<br/>.= 
 <a href="normform.html#K9" target="_self">mi</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="normform.html#K9" target="_self">mi</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="normform.html#K10" target="_self">^</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span> <a href="setwiseo.html#K5">\/</a> <span class="p2">(<span class="default"><a href="normform.html#K9" target="_self">mi</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="normform.html#K10" target="_self">^</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="normform.html#T68" target="_self">Th68</a></i>
<br/>.= 
 <a href="normform.html#K9" target="_self">mi</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="setwiseo.html#K5">\/</a> <span class="p2">(<span class="default"><a href="normform.html#K9" target="_self">mi</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="normform.html#K10" target="_self">^</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="normform.html#D14" target="_self">Def14</a></i>
<br/>.= 
 <a href="normform.html#K9" target="_self">mi</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="setwiseo.html#K5">\/</a> <font color="Maroon">c<sub>7</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="normform.html#D14" target="_self">Def14</a></i>
;<br/>
<b>hence </b><a NAME="E4:74"/>
the <a href="lattices.html#U1">L_meet</a> of <span class="p1">(<span class="default"><a href="normform.html#K12" target="_self">NormForm</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="binop_1.html#K1">.</a> <font color="Maroon">c<sub>2</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="normform.html#K12" target="_self">NormForm</a> <font color="Maroon">c<sub>1</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> <a href="hidden.html#R1">=</a> the <a href="lattices.html#U2">L_join</a> of <span class="p1">(<span class="default"><a href="normform.html#K12" target="_self">NormForm</a> <font color="Maroon">c<sub>1</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="normform.html#K12" target="_self">NormForm</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="binop_1.html#K1">.</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</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="normform.html#K12" target="_self">NormForm</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="binop_1.html#K1">.</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span>
 <b>by </b><i><a class="ref" href="normform.html#D14" target="_self">Def14</a></i>;<br/>


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