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<b>consider </b><font color="Maroon">uu</font> being   <a href="binop_1.html#NM2">BinOp</a> of  <a href="zfmisc_1.html#K1">bool</a> <a href="xboole_0.html#K1">{}</a> , <font color="Maroon">nn</font> being   <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">GG</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">uu</font>,<font color="Maroon">nn</font> #);<br/>
<b>reconsider </b><font color="Maroon">GG</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">uu</font>,<font color="Maroon">nn</font> #) as   <a href="lattices.html#NM1">Lattice</a> <b>by </b><i/>;<br/>
<a NAME="E3:27_1_1"/><i><font color="Green">E34</font></i>: 
for <font color="Olive">x</font>, <font color="Olive">y</font>, <font color="Olive">z</font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">GG</font>  st <font color="Olive">x</font> <a href="lattices.html#R1" target="_self">[=</a> <font color="Olive">z</font> holds <br/><font color="Olive">x</font> <a href="lattices.html#K3" target="_self">"\/"</a> <span class="p1">(<span class="default"><font color="Olive">y</font> <a href="lattices.html#K4" target="_self">"/\"</a> <font color="Olive">z</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Olive">x</font> <a href="lattices.html#K3" target="_self">"\/"</a> <font color="Olive">y</font></span>)</span> <a href="lattices.html#K4" target="_self">"/\"</a> <font color="Olive">z</font>
 
<b>by </b><i/>;<br/>
<a NAME="E4:27_1_1"/><i><font color="Green">E37</font></i>: 
<font color="Maroon">GG</font> is <a href="lattices.html#V12" target="_self">modular</a>
 
<b>by </b><i>, </i>;<br/>
<b>reconsider </b><font color="Maroon">0GG</font> =  <a href="xboole_0.html#K1">{}</a> , <font color="Maroon">D</font> =  <a href="xboole_0.html#K1">{}</a>  as   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">GG</font> <b>by </b><i><a class="ref" href="zfmisc_1.html#D1">ZFMISC_1:def 1</a></i>;<br/>
<a NAME="E6:27_1_1"/><i><font color="Green">E39</font></i>: 
for <font color="Olive">x</font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">GG</font> holds <br/> ( <font color="Maroon">0GG</font> <a href="lattices.html#K4" target="_self">"/\"</a> <font color="Olive">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">0GG</font> &amp; <font color="Olive">x</font> <a href="lattices.html#K4" target="_self">"/\"</a> <font color="Maroon">0GG</font> <a href="hidden.html#R1">=</a> <font color="Maroon">0GG</font> )
 
<b>by </b><i/>;<br/>
<a NAME="E7:27_1_1"/><i><font color="Green">E40</font></i>: 
<font color="Maroon">GG</font> is <a href="lattices.html#V13" target="_self">lower-bounded</a>
 
<b>by </b><i><a class="ref" href="lattices.html#D3" target="_self">Def3</a>, </i>;<br/>
<a NAME="E8:27_1_1"/><i><font color="Green">E41</font></i>: 
for <font color="Olive">x</font>, <font color="Olive">y</font>, <font color="Olive">z</font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">GG</font> holds  <font color="Olive">x</font> <a href="lattices.html#K4" target="_self">"/\"</a> <span class="p1">(<span class="default"><font color="Olive">y</font> <a href="lattices.html#K3" target="_self">"\/"</a> <font color="Olive">z</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Olive">x</font> <a href="lattices.html#K4" target="_self">"/\"</a> <font color="Olive">y</font></span>)</span> <a href="lattices.html#K3" target="_self">"\/"</a> <span class="p1">(<span class="default"><font color="Olive">x</font> <a href="lattices.html#K4" target="_self">"/\"</a> <font color="Olive">z</font></span>)</span>
 
<b>by </b><i/>;<br/>
<a NAME="E9:27_1_1"/><i><font color="Green">E42</font></i>: 
for <font color="Olive">x</font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">GG</font> holds <br/> ( <font color="Maroon">D</font> <a href="lattices.html#K3" target="_self">"\/"</a> <font color="Olive">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">D</font> &amp; <font color="Olive">x</font> <a href="lattices.html#K3" target="_self">"\/"</a> <font color="Maroon">D</font> <a href="hidden.html#R1">=</a> <font color="Maroon">D</font> )
 
<b>by </b><i/>;<br/>
<a NAME="E10:27_1_1"/><i><font color="Green">E43</font></i>: 
<font color="Maroon">GG</font> is <a href="lattices.html#V11" target="_self">distributive</a>
 
<b>by </b><i>, <a class="txt" href="lattices.html#E6"><i><font color="Green">Lemma21</font></i></a></i>;<br/>
<a NAME="E11:27_1_1"/>
<font color="Maroon">GG</font> is <a href="lattices.html#V14" target="_self">upper-bounded</a>
 
<b>by </b><i><a class="txt" href="lattices.html#E4"><i><font color="Green">Lemma15</font></i></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">Lattice</a> st <br/>( <font color="Olive">b<sub>1</sub></font> is <a href="lattices.html#V3" target="_self">strict</a> &amp; <font color="Olive">b<sub>1</sub></font> is <a href="lattices.html#V11" target="_self">distributive</a> &amp; <font color="Olive">b<sub>1</sub></font> is <a href="lattices.html#V13" target="_self">lower-bounded</a> &amp; <font color="Olive">b<sub>1</sub></font> is <a href="lattices.html#V14" target="_self">upper-bounded</a> &amp; <font color="Olive">b<sub>1</sub></font> is <a href="lattices.html#V12" target="_self">modular</a> )
 <b>by </b><i>, <a class="txt" href="lattices.html#E5"><i><font color="Green">Lemma20</font></i></a>, <a class="ref" href="lattices.html#D4" target="_self">Def4</a></i>;<br/>


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