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<b>reconsider </b><font color="Maroon">c<sub>3</sub></font> = <font color="Maroon">H<sub>2</sub></font>(<font color="Maroon">c<sub>1</sub></font>) <a href="realset1.html#K1">||</a> <font color="Maroon">c<sub>2</sub></font>, <font color="Maroon">c<sub>4</sub></font> = <font color="Maroon">H<sub>3</sub></font>(<font color="Maroon">c<sub>1</sub></font>) <a href="realset1.html#K1">||</a> <font color="Maroon">c<sub>2</sub></font> as   <a href="binop_1.html#NM2">BinOp</a> of <font color="Maroon">c<sub>2</sub></font> <b>by </b><i><a class="ref" href="filter_2.html#T61" target="_self">Th61</a></i>;<br/>
<a NAME="E2:97_1_1"/>
( <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">H<sub>2</sub></font>(<font color="Maroon">c<sub>1</sub></font>) <a href="realset1.html#K1">||</a> <font color="Maroon">c<sub>2</sub></font> &amp; <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">H<sub>3</sub></font>(<font color="Maroon">c<sub>1</sub></font>) <a href="realset1.html#K1">||</a> <font color="Maroon">c<sub>2</sub></font> )
 
;<br/>
<a NAME="E3:97_1_1"/><b>then </b>
( <font color="Maroon">c<sub>3</sub></font> is <a href="binop_1.html#V1">commutative</a> &amp; <font color="Maroon">c<sub>3</sub></font> is <a href="binop_1.html#V2">associative</a> &amp; <font color="Maroon">c<sub>4</sub></font> is <a href="binop_1.html#V1">commutative</a> &amp; <font color="Maroon">c<sub>4</sub></font> is <a href="binop_1.html#V2">associative</a> &amp; <font color="Maroon">c<sub>3</sub></font> <a href="lattice2.html#R1">absorbs</a> <font color="Maroon">c<sub>4</sub></font> &amp; <font color="Maroon">c<sub>4</sub></font> <a href="lattice2.html#R1">absorbs</a> <font color="Maroon">c<sub>3</sub></font> )
 
<b>by </b><i><a class="ref" href="filter_2.html#T62" target="_self">Th62</a></i>;<br/>
<b>then reconsider </b><font color="Maroon">c<sub>5</sub></font> =  <a href="lattices.html#G3">LattStr</a>(# <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font> #) as  <a href="lattices.html#V3">strict</a> <a href="lattices.html#NM1">Lattice</a> <b>by </b><i><a class="ref" href="lattice2.html#T17">LATTICE2:17</a></i>;<br/>
<b>reconsider </b><font color="Maroon">c<sub>6</sub></font> = <font color="Maroon">c<sub>5</sub></font> as  <a href="lattices.html#V3">strict</a>  <a href="nat_lat.html#M2">Sublattice</a> of <font color="Maroon">c<sub>1</sub></font> <b>by </b><i><a class="ref" href="nat_lat.html#D16">NAT_LAT:def 16</a></i>;<br/>
<b>take </b>
<font color="Maroon">c<sub>6</sub></font>
;<br/>

<b>take </b>
<font color="Maroon">c<sub>3</sub></font>
;<br/>

<b>take </b>
<font color="Maroon">c<sub>4</sub></font>
;<br/>

<b>thus </b><a NAME="E6:97_1_1"/>
( <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> the <a href="lattices.html#U2">L_join</a> of <font color="Maroon">c<sub>1</sub></font> <a href="realset1.html#K1">||</a> <font color="Maroon">c<sub>2</sub></font> &amp; <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> the <a href="lattices.html#U1">L_meet</a> of <font color="Maroon">c<sub>1</sub></font> <a href="realset1.html#K1">||</a> <font color="Maroon">c<sub>2</sub></font> &amp; <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R1">=</a>  <a href="lattices.html#G3">LattStr</a>(# <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font> #) )
 ;<br/>


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