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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="binop_1.html#NM2">BinOp</a> of  <a href="zfmisc_1.html#K1">bool</a> <a href="xboole_0.html#K1">{}</a> ;<br/>

<b>set </b><font color="Maroon">c<sub>3</sub></font> =  <a href="lattices.html#G3" target="_self">LattStr</a>(# <span class="p1">(<span class="default"><a href="zfmisc_1.html#K1">bool</a> <a href="xboole_0.html#K1">{}</a> </span>)</span>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font> #);<br/>
<a NAME="E1:26"/>
for <font color="Olive">b<sub>1</sub></font>, <font color="Olive">b<sub>2</sub></font> being  <a href="struct_0.html#NM1">Element</a> of <a href="lattices.html#G3" target="_self">LattStr</a>(# <span class="p1">(<span class="default"><a href="zfmisc_1.html#K1">bool</a> <a href="xboole_0.html#K1">{}</a> </span>)</span>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font> #) holds <font color="Olive">b<sub>1</sub></font> <a href="lattices.html#K1" target="_self">"\/"</a> <font color="Olive">b<sub>2</sub></font> <a href="hidden.html#R1">=</a> <font color="Olive">b<sub>2</sub></font> <a href="lattices.html#K1" target="_self">"\/"</a> <font color="Olive">b<sub>1</sub></font>
 
<b>by </b><i><a class="txt" href="lattices.html#E4"><i><font color="Green">Lemma2</font></i></a></i>;<br/>
<a NAME="E2:26"/><b>then </b><i><font color="Green">E17</font></i>: 
 <a href="lattices.html#G3" target="_self">LattStr</a>(# <span class="p1">(<span class="default"><a href="zfmisc_1.html#K1">bool</a> <a href="xboole_0.html#K1">{}</a> </span>)</span>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font> #) is <a href="lattices.html#V4" target="_self">join-commutative</a>
 
<b>by </b><i><a class="ref" href="lattices.html#D4" target="_self">Def4</a></i>;<br/>
<a NAME="E3:26"/>
for <font color="Olive">b<sub>1</sub></font>, <font color="Olive">b<sub>2</sub></font>, <font color="Olive">b<sub>3</sub></font> being  <a href="struct_0.html#NM1">Element</a> of <a href="lattices.html#G3" target="_self">LattStr</a>(# <span class="p1">(<span class="default"><a href="zfmisc_1.html#K1">bool</a> <a href="xboole_0.html#K1">{}</a> </span>)</span>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font> #) holds <font color="Olive">b<sub>1</sub></font> <a href="lattices.html#K1" target="_self">"\/"</a> <span class="p1">(<span class="default"><font color="Olive">b<sub>2</sub></font> <a href="lattices.html#K1" target="_self">"\/"</a> <font color="Olive">b<sub>3</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Olive">b<sub>1</sub></font> <a href="lattices.html#K1" target="_self">"\/"</a> <font color="Olive">b<sub>2</sub></font></span>)</span> <a href="lattices.html#K1" target="_self">"\/"</a> <font color="Olive">b<sub>3</sub></font>
 
<b>by </b><i><a class="txt" href="lattices.html#E4"><i><font color="Green">Lemma2</font></i></a></i>;<br/>
<a NAME="E4:26"/><b>then </b><i><font color="Green">E18</font></i>: 
 <a href="lattices.html#G3" target="_self">LattStr</a>(# <span class="p1">(<span class="default"><a href="zfmisc_1.html#K1">bool</a> <a href="xboole_0.html#K1">{}</a> </span>)</span>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font> #) is <a href="lattices.html#V5" target="_self">join-associative</a>
 
<b>by </b><i><a class="ref" href="lattices.html#D5" target="_self">Def5</a></i>;<br/>
<a NAME="E5:26"/>
for <font color="Olive">b<sub>1</sub></font>, <font color="Olive">b<sub>2</sub></font> being  <a href="struct_0.html#NM1">Element</a> of <a href="lattices.html#G3" target="_self">LattStr</a>(# <span class="p1">(<span class="default"><a href="zfmisc_1.html#K1">bool</a> <a href="xboole_0.html#K1">{}</a> </span>)</span>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font> #) holds <span class="p1">(<span class="default"><font color="Olive">b<sub>1</sub></font> <a href="lattices.html#K2" target="_self">"/\"</a> <font color="Olive">b<sub>2</sub></font></span>)</span> <a href="lattices.html#K1" target="_self">"\/"</a> <font color="Olive">b<sub>2</sub></font> <a href="hidden.html#R1">=</a> <font color="Olive">b<sub>2</sub></font>
 
<b>by </b><i><a class="txt" href="lattices.html#E4"><i><font color="Green">Lemma2</font></i></a></i>;<br/>
<a NAME="E6:26"/><b>then </b><i><font color="Green">E19</font></i>: 
 <a href="lattices.html#G3" target="_self">LattStr</a>(# <span class="p1">(<span class="default"><a href="zfmisc_1.html#K1">bool</a> <a href="xboole_0.html#K1">{}</a> </span>)</span>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font> #) is <a href="lattices.html#V8" target="_self">meet-absorbing</a>
 
<b>by </b><i><a class="ref" href="lattices.html#D8" target="_self">Def8</a></i>;<br/>
<a NAME="E7:26"/>
for <font color="Olive">b<sub>1</sub></font>, <font color="Olive">b<sub>2</sub></font> being  <a href="struct_0.html#NM1">Element</a> of <a href="lattices.html#G3" target="_self">LattStr</a>(# <span class="p1">(<span class="default"><a href="zfmisc_1.html#K1">bool</a> <a href="xboole_0.html#K1">{}</a> </span>)</span>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font> #) holds <font color="Olive">b<sub>1</sub></font> <a href="lattices.html#K2" target="_self">"/\"</a> <font color="Olive">b<sub>2</sub></font> <a href="hidden.html#R1">=</a> <font color="Olive">b<sub>2</sub></font> <a href="lattices.html#K2" target="_self">"/\"</a> <font color="Olive">b<sub>1</sub></font>
 
<b>by </b><i><a class="txt" href="lattices.html#E4"><i><font color="Green">Lemma2</font></i></a></i>;<br/>
<a NAME="E8:26"/><b>then </b><i><font color="Green">E20</font></i>: 
 <a href="lattices.html#G3" target="_self">LattStr</a>(# <span class="p1">(<span class="default"><a href="zfmisc_1.html#K1">bool</a> <a href="xboole_0.html#K1">{}</a> </span>)</span>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font> #) is <a href="lattices.html#V6" target="_self">meet-commutative</a>
 
<b>by </b><i><a class="ref" href="lattices.html#D6" target="_self">Def6</a></i>;<br/>
<a NAME="E9:26"/>
for <font color="Olive">b<sub>1</sub></font>, <font color="Olive">b<sub>2</sub></font>, <font color="Olive">b<sub>3</sub></font> being  <a href="struct_0.html#NM1">Element</a> of <a href="lattices.html#G3" target="_self">LattStr</a>(# <span class="p1">(<span class="default"><a href="zfmisc_1.html#K1">bool</a> <a href="xboole_0.html#K1">{}</a> </span>)</span>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font> #) holds <font color="Olive">b<sub>1</sub></font> <a href="lattices.html#K2" target="_self">"/\"</a> <span class="p1">(<span class="default"><font color="Olive">b<sub>2</sub></font> <a href="lattices.html#K2" target="_self">"/\"</a> <font color="Olive">b<sub>3</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Olive">b<sub>1</sub></font> <a href="lattices.html#K2" target="_self">"/\"</a> <font color="Olive">b<sub>2</sub></font></span>)</span> <a href="lattices.html#K2" target="_self">"/\"</a> <font color="Olive">b<sub>3</sub></font>
 
<b>by </b><i><a class="txt" href="lattices.html#E4"><i><font color="Green">Lemma2</font></i></a></i>;<br/>
<a NAME="E10:26"/><b>then </b><i><font color="Green">E21</font></i>: 
 <a href="lattices.html#G3" target="_self">LattStr</a>(# <span class="p1">(<span class="default"><a href="zfmisc_1.html#K1">bool</a> <a href="xboole_0.html#K1">{}</a> </span>)</span>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font> #) is <a href="lattices.html#V7" target="_self">meet-associative</a>
 
<b>by </b><i><a class="ref" href="lattices.html#D7" target="_self">Def7</a></i>;<br/>
<a NAME="E11:26"/>
for <font color="Olive">b<sub>1</sub></font>, <font color="Olive">b<sub>2</sub></font> being  <a href="struct_0.html#NM1">Element</a> of <a href="lattices.html#G3" target="_self">LattStr</a>(# <span class="p1">(<span class="default"><a href="zfmisc_1.html#K1">bool</a> <a href="xboole_0.html#K1">{}</a> </span>)</span>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font> #) holds <font color="Olive">b<sub>1</sub></font> <a href="lattices.html#K2" target="_self">"/\"</a> <span class="p1">(<span class="default"><font color="Olive">b<sub>1</sub></font> <a href="lattices.html#K1" target="_self">"\/"</a> <font color="Olive">b<sub>2</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Olive">b<sub>1</sub></font>
 
<b>by </b><i><a class="txt" href="lattices.html#E4"><i><font color="Green">Lemma2</font></i></a></i>;<br/>
<a NAME="E12:26"/><b>then </b>
 <a href="lattices.html#G3" target="_self">LattStr</a>(# <span class="p1">(<span class="default"><a href="zfmisc_1.html#K1">bool</a> <a href="xboole_0.html#K1">{}</a> </span>)</span>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font> #) is <a href="lattices.html#V9" target="_self">join-absorbing</a>
 
<b>by </b><i><a class="ref" href="lattices.html#D9" target="_self">Def9</a></i>;<br/>
<b>hence </b><a NAME="E13:26"/>
 <a href="lattices.html#G3" target="_self">LattStr</a>(# <span class="p1">(<span class="default"><a href="zfmisc_1.html#K1">bool</a> <a href="xboole_0.html#K1">{}</a> </span>)</span>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font> #) is   <a href="lattices.html#NM1">Lattice</a>
 <b>by </b><i><a class="ref" href="lattices.html#D10" target="_self">Def10</a>, <a class="txt" href="lattices.html#E2:26"><i><font color="Green">E17</font></i></a>, <a class="txt" href="lattices.html#E4:26"><i><font color="Green">E18</font></i></a>, <a class="txt" href="lattices.html#E6:26"><i><font color="Green">E19</font></i></a>, <a class="txt" href="lattices.html#E8:26"><i><font color="Green">E20</font></i></a>, <a class="txt" href="lattices.html#E10:26"><i><font color="Green">E21</font></i></a></i>;<br/>


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