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<b>let </b><font color="Maroon" title="c1">n</font>, <font color="Maroon" title="c2">u</font> be   <a href="binop_1.html#NM2" title="BINOP_1:NM.2">BinOp</a> of  <a href="zfmisc_1.html#K1" title="ZFMISC_1:func.1">bool</a> <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> ;<br/>

<b>set </b><font color="Maroon" title="c3">G</font> =  <a href="lattices.html#G3" title="LATTICES:aggr.3">LattStr</a>(# <span class="p1">(<span class="default"><a href="zfmisc_1.html#K1" title="ZFMISC_1:func.1">bool</a> <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> </span>)</span>,<font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c2">u</font> #);<br/>
<a NAME="E1:26"/>
for <font color="Olive" title="b1">x</font>, <font color="Olive" title="b2">y</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <a href="lattices.html#G3" title="LATTICES:aggr.3">LattStr</a>(# <span class="p1">(<span class="default"><a href="zfmisc_1.html#K1" title="ZFMISC_1:func.1">bool</a> <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> </span>)</span>,<font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c2">u</font> #) holds  <font color="Olive" title="b1">x</font> <a href="lattices.html#K1" title="LATTICES:func.1">"\/"</a> <font color="Olive" title="b2">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">y</font> <a href="lattices.html#K1" title="LATTICES:func.1">"\/"</a> <font color="Olive" title="b1">x</font>
 
<b>by </b><i><a class="txt" href="lattices.html#E4"><i><font color="Green" title="E2">Lm1</font></i></a></i>;<br/>
<a NAME="E2:26"/><b>then </b><i><font color="Green" title="E17">A1</font></i>: 
 <a href="lattices.html#G3" title="LATTICES:aggr.3">LattStr</a>(# <span class="p1">(<span class="default"><a href="zfmisc_1.html#K1" title="ZFMISC_1:func.1">bool</a> <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> </span>)</span>,<font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c2">u</font> #) is <a href="lattices.html#V4" title="LATTICES:attr.4">join-commutative</a>
 
<b>by </b><i><a class="ref" href="lattices.html#D4" target="_self" title="LATTICES:def.4">Def4</a></i>;<br/>
<a NAME="E3:26"/>
for <font color="Olive" title="b1">x</font>, <font color="Olive" title="b2">y</font>, <font color="Olive" title="b3">z</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <a href="lattices.html#G3" title="LATTICES:aggr.3">LattStr</a>(# <span class="p1">(<span class="default"><a href="zfmisc_1.html#K1" title="ZFMISC_1:func.1">bool</a> <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> </span>)</span>,<font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c2">u</font> #) holds  <font color="Olive" title="b1">x</font> <a href="lattices.html#K1" title="LATTICES:func.1">"\/"</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">y</font> <a href="lattices.html#K1" title="LATTICES:func.1">"\/"</a> <font color="Olive" title="b3">z</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">x</font> <a href="lattices.html#K1" title="LATTICES:func.1">"\/"</a> <font color="Olive" title="b2">y</font></span>)</span> <a href="lattices.html#K1" title="LATTICES:func.1">"\/"</a> <font color="Olive" title="b3">z</font>
 
<b>by </b><i><a class="txt" href="lattices.html#E4"><i><font color="Green" title="E2">Lm1</font></i></a></i>;<br/>
<a NAME="E4:26"/><b>then </b><i><font color="Green" title="E18">A2</font></i>: 
 <a href="lattices.html#G3" title="LATTICES:aggr.3">LattStr</a>(# <span class="p1">(<span class="default"><a href="zfmisc_1.html#K1" title="ZFMISC_1:func.1">bool</a> <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> </span>)</span>,<font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c2">u</font> #) is <a href="lattices.html#V5" title="LATTICES:attr.5">join-associative</a>
 
<b>by </b><i><a class="ref" href="lattices.html#D5" target="_self" title="LATTICES:def.5">Def5</a></i>;<br/>
<a NAME="E5:26"/>
for <font color="Olive" title="b1">x</font>, <font color="Olive" title="b2">y</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <a href="lattices.html#G3" title="LATTICES:aggr.3">LattStr</a>(# <span class="p1">(<span class="default"><a href="zfmisc_1.html#K1" title="ZFMISC_1:func.1">bool</a> <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> </span>)</span>,<font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c2">u</font> #) holds  <span class="p1">(<span class="default"><font color="Olive" title="b1">x</font> <a href="lattices.html#K2" title="LATTICES:func.2">"/\"</a> <font color="Olive" title="b2">y</font></span>)</span> <a href="lattices.html#K1" title="LATTICES:func.1">"\/"</a> <font color="Olive" title="b2">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">y</font>
 
<b>by </b><i><a class="txt" href="lattices.html#E4"><i><font color="Green" title="E2">Lm1</font></i></a></i>;<br/>
<a NAME="E6:26"/><b>then </b><i><font color="Green" title="E19">A3</font></i>: 
 <a href="lattices.html#G3" title="LATTICES:aggr.3">LattStr</a>(# <span class="p1">(<span class="default"><a href="zfmisc_1.html#K1" title="ZFMISC_1:func.1">bool</a> <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> </span>)</span>,<font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c2">u</font> #) is <a href="lattices.html#V8" title="LATTICES:attr.8">meet-absorbing</a>
 
<b>by </b><i><a class="ref" href="lattices.html#D8" target="_self" title="LATTICES:def.8">Def8</a></i>;<br/>
<a NAME="E7:26"/>
for <font color="Olive" title="b1">x</font>, <font color="Olive" title="b2">y</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <a href="lattices.html#G3" title="LATTICES:aggr.3">LattStr</a>(# <span class="p1">(<span class="default"><a href="zfmisc_1.html#K1" title="ZFMISC_1:func.1">bool</a> <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> </span>)</span>,<font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c2">u</font> #) holds  <font color="Olive" title="b1">x</font> <a href="lattices.html#K2" title="LATTICES:func.2">"/\"</a> <font color="Olive" title="b2">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">y</font> <a href="lattices.html#K2" title="LATTICES:func.2">"/\"</a> <font color="Olive" title="b1">x</font>
 
<b>by </b><i><a class="txt" href="lattices.html#E4"><i><font color="Green" title="E2">Lm1</font></i></a></i>;<br/>
<a NAME="E8:26"/><b>then </b><i><font color="Green" title="E20">A4</font></i>: 
 <a href="lattices.html#G3" title="LATTICES:aggr.3">LattStr</a>(# <span class="p1">(<span class="default"><a href="zfmisc_1.html#K1" title="ZFMISC_1:func.1">bool</a> <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> </span>)</span>,<font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c2">u</font> #) is <a href="lattices.html#V6" title="LATTICES:attr.6">meet-commutative</a>
 
<b>by </b><i><a class="ref" href="lattices.html#D6" target="_self" title="LATTICES:def.6">Def6</a></i>;<br/>
<a NAME="E9:26"/>
for <font color="Olive" title="b1">x</font>, <font color="Olive" title="b2">y</font>, <font color="Olive" title="b3">z</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <a href="lattices.html#G3" title="LATTICES:aggr.3">LattStr</a>(# <span class="p1">(<span class="default"><a href="zfmisc_1.html#K1" title="ZFMISC_1:func.1">bool</a> <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> </span>)</span>,<font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c2">u</font> #) holds  <font color="Olive" title="b1">x</font> <a href="lattices.html#K2" title="LATTICES:func.2">"/\"</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">y</font> <a href="lattices.html#K2" title="LATTICES:func.2">"/\"</a> <font color="Olive" title="b3">z</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">x</font> <a href="lattices.html#K2" title="LATTICES:func.2">"/\"</a> <font color="Olive" title="b2">y</font></span>)</span> <a href="lattices.html#K2" title="LATTICES:func.2">"/\"</a> <font color="Olive" title="b3">z</font>
 
<b>by </b><i><a class="txt" href="lattices.html#E4"><i><font color="Green" title="E2">Lm1</font></i></a></i>;<br/>
<a NAME="E10:26"/><b>then </b><i><font color="Green" title="E21">A5</font></i>: 
 <a href="lattices.html#G3" title="LATTICES:aggr.3">LattStr</a>(# <span class="p1">(<span class="default"><a href="zfmisc_1.html#K1" title="ZFMISC_1:func.1">bool</a> <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> </span>)</span>,<font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c2">u</font> #) is <a href="lattices.html#V7" title="LATTICES:attr.7">meet-associative</a>
 
<b>by </b><i><a class="ref" href="lattices.html#D7" target="_self" title="LATTICES:def.7">Def7</a></i>;<br/>
<a NAME="E11:26"/>
for <font color="Olive" title="b1">x</font>, <font color="Olive" title="b2">y</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <a href="lattices.html#G3" title="LATTICES:aggr.3">LattStr</a>(# <span class="p1">(<span class="default"><a href="zfmisc_1.html#K1" title="ZFMISC_1:func.1">bool</a> <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> </span>)</span>,<font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c2">u</font> #) holds  <font color="Olive" title="b1">x</font> <a href="lattices.html#K2" title="LATTICES:func.2">"/\"</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">x</font> <a href="lattices.html#K1" title="LATTICES:func.1">"\/"</a> <font color="Olive" title="b2">y</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">x</font>
 
<b>by </b><i><a class="txt" href="lattices.html#E4"><i><font color="Green" title="E2">Lm1</font></i></a></i>;<br/>
<a NAME="E12:26"/><b>then </b>
 <a href="lattices.html#G3" title="LATTICES:aggr.3">LattStr</a>(# <span class="p1">(<span class="default"><a href="zfmisc_1.html#K1" title="ZFMISC_1:func.1">bool</a> <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> </span>)</span>,<font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c2">u</font> #) is <a href="lattices.html#V9" title="LATTICES:attr.9">join-absorbing</a>
 
<b>by </b><i><a class="ref" href="lattices.html#D9" target="_self" title="LATTICES:def.9">Def9</a></i>;<br/>
<b>hence </b><a NAME="E13:26"/>
 <a href="lattices.html#G3" title="LATTICES:aggr.3">LattStr</a>(# <span class="p1">(<span class="default"><a href="zfmisc_1.html#K1" title="ZFMISC_1:func.1">bool</a> <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> </span>)</span>,<font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c2">u</font> #) is   <a href="lattices.html#NM1" title="LATTICES:NM.1">Lattice</a>
 <b>by </b><i><a class="ref" href="lattices.html#D10" target="_self" title="LATTICES:def.10">Def10</a>, <a class="txt" href="lattices.html#E2:26"><i><font color="Green" title="E17">A1</font></i></a>, <a class="txt" href="lattices.html#E4:26"><i><font color="Green" title="E18">A2</font></i></a>, <a class="txt" href="lattices.html#E6:26"><i><font color="Green" title="E19">A3</font></i></a>, <a class="txt" href="lattices.html#E8:26"><i><font color="Green" title="E20">A4</font></i></a>, <a class="txt" href="lattices.html#E10:26"><i><font color="Green" title="E21">A5</font></i></a></i>;<br/>


</div>
