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<b>consider </b><font color="Maroon" title="c1">uu</font>, <font color="Maroon" title="c2">nn</font> being   <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">GG</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">uu</font>,<font color="Maroon" title="c2">nn</font> #);<br/>
<b>reconsider </b><font color="Maroon" title="c4">GG</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">uu</font>,<font color="Maroon" title="c2">nn</font> #) as   <a href="lattices.html#NM1" title="LATTICES:NM.1">Lattice</a> <b>by </b><i><a class="txt" href="lattices.html#E18"><i><font color="Green" title="E16">Lm4</font></i></a></i>;<br/>
<a NAME="E3:27_1_1"/>
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 <font color="Maroon" title="c4">GG</font>  st <font color="Olive" title="b1">x</font> <a href="lattices.html#R1" title="LATTICES:pred.1">[=</a> <font color="Olive" title="b3">z</font> holds <br/><font color="Olive" title="b1">x</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">y</font> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</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#K3" title="LATTICES:func.3">"\/"</a> <font color="Olive" title="b2">y</font></span>)</span> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</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="E4:27_1_1"/><b>then </b><i><font color="Green" title="E17">A1</font></i>: 
<font color="Maroon" title="c4">GG</font> is <a href="lattices.html#V12" title="LATTICES:attr.12">modular</a>
 
<b>by </b><i><a class="ref" href="lattices.html#D12" target="_self" title="LATTICES:def.12">Def12</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c5">0GG</font> =  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> , <font color="Maroon" title="c6">D</font> =  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c4">GG</font> <b>by </b><i><a class="ref" href="zfmisc_1.html#D1" title="ZFMISC_1:def.1">ZFMISC_1:def 1</a></i>;<br/>
<a NAME="E6:27_1_1"/>
for <font color="Olive" title="b1">x</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c4">GG</font> holds <br/> ( <font color="Maroon" title="c5">0GG</font> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <font color="Olive" title="b1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">0GG</font> &amp; <font color="Olive" title="b1">x</font> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <font color="Maroon" title="c5">0GG</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">0GG</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="E7:27_1_1"/><b>then </b><i><font color="Green" title="E18">A2</font></i>: 
<font color="Maroon" title="c4">GG</font> is <a href="lattices.html#V13" title="LATTICES:attr.13">lower-bounded</a>
 
<b>by </b><i><a class="ref" href="lattices.html#D13" target="_self" title="LATTICES:def.13">Def13</a></i>;<br/>
<a NAME="E8:27_1_1"/><i><font color="Green" title="E19">A3</font></i>: 
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 <font color="Maroon" title="c4">GG</font> holds  <font color="Olive" title="b1">x</font> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">y</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</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#K4" title="LATTICES:func.4">"/\"</a> <font color="Olive" title="b2">y</font></span>)</span> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">x</font> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <font color="Olive" title="b3">z</font></span>)</span>
 
<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="E9:27_1_1"/><i><font color="Green" title="E20">A4</font></i>: 
for <font color="Olive" title="b1">x</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c4">GG</font> holds <br/> ( <font color="Maroon" title="c6">D</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Olive" title="b1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">D</font> &amp; <font color="Olive" title="b1">x</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon" title="c6">D</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">D</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="E10:27_1_1"/><i><font color="Green" title="E21">A5</font></i>: 
<font color="Maroon" title="c4">GG</font> is <a href="lattices.html#V11" title="LATTICES:attr.11">distributive</a>
 
<b>by </b><i><a class="txt" href="lattices.html#E8:27_1_1"><i><font color="Green" title="E19">A3</font></i></a>, <a class="ref" href="lattices.html#D11" target="_self" title="LATTICES:def.11">Def11</a></i>;<br/>
<a NAME="E11:27_1_1"/>
<font color="Maroon" title="c4">GG</font> is <a href="lattices.html#V14" title="LATTICES:attr.14">upper-bounded</a>
 
<b>by </b><i><a class="txt" href="lattices.html#E9:27_1_1"><i><font color="Green" title="E20">A4</font></i></a>, <a class="ref" href="lattices.html#D14" target="_self" title="LATTICES:def.14">Def14</a></i>;<br/>
<b>hence </b><a NAME="E12:27_1_1"/>
 ex <font color="Olive">b<sub>1</sub></font> being  <a href="lattices.html#NM1" title="LATTICES:NM.1">Lattice</a> st <br/>( <font color="Olive">b<sub>1</sub></font> is <a href="lattices.html#V3" title="LATTICES:attr.3">strict</a> &amp; <font color="Olive">b<sub>1</sub></font> is <a href="lattices.html#V11" title="LATTICES:attr.11">distributive</a> &amp; <font color="Olive">b<sub>1</sub></font> is <a href="lattices.html#V13" title="LATTICES:attr.13">lower-bounded</a> &amp; <font color="Olive">b<sub>1</sub></font> is <a href="lattices.html#V14" title="LATTICES:attr.14">upper-bounded</a> &amp; <font color="Olive">b<sub>1</sub></font> is <a href="lattices.html#V12" title="LATTICES:attr.12">modular</a> )
 <b>by </b><i><a class="txt" href="lattices.html#E4:27_1_1"><i><font color="Green" title="E17">A1</font></i></a>, <a class="txt" href="lattices.html#E7:27_1_1"><i><font color="Green" title="E18">A2</font></i></a>, <a class="txt" href="lattices.html#E10:27_1_1"><i><font color="Green" title="E21">A5</font></i></a></i>;<br/>


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