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<b>consider </b><font color="Maroon">u</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">n</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>take </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">u</font>,<font color="Maroon">n</font> #);<br/>

<a NAME="E2:18_3_1"/><i><font color="Green">E39</font></i>: 
for <font color="Olive">x</font>, <font color="Olive">y</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#K1" target="_self">"\/"</a> <font color="Olive">y</font> <a href="hidden.html#R1">=</a> <font color="Olive">y</font> <a href="lattices.html#K1" target="_self">"\/"</a> <font color="Olive">x</font>
 
<b>by </b><i/>;<br/>
<a NAME="E3:18_3_1"/><i><font color="Green">E40</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#K1" target="_self">"\/"</a> <span class="p1">(<span class="default"><font color="Olive">y</font> <a href="lattices.html#K1" 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#K1" target="_self">"\/"</a> <font color="Olive">y</font></span>)</span> <a href="lattices.html#K1" target="_self">"\/"</a> <font color="Olive">z</font>
 
<b>by </b><i/>;<br/>
<a NAME="E4:18_3_1"/><i><font color="Green">E41</font></i>: 
for <font color="Olive">x</font>, <font color="Olive">y</font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">GG</font> holds  <span class="p1">(<span class="default"><font color="Olive">x</font> <a href="lattices.html#K2" target="_self">"/\"</a> <font color="Olive">y</font></span>)</span> <a href="lattices.html#K1" target="_self">"\/"</a> <font color="Olive">y</font> <a href="hidden.html#R1">=</a> <font color="Olive">y</font>
 
<b>by </b><i/>;<br/>
<a NAME="E5:18_3_1"/><i><font color="Green">E42</font></i>: 
for <font color="Olive">x</font>, <font color="Olive">y</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#K2" target="_self">"/\"</a> <font color="Olive">y</font> <a href="hidden.html#R1">=</a> <font color="Olive">y</font> <a href="lattices.html#K2" target="_self">"/\"</a> <font color="Olive">x</font>
 
<b>by </b><i/>;<br/>
<a NAME="E6:18_3_1"/><i><font color="Green">E43</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#K2" target="_self">"/\"</a> <span class="p1">(<span class="default"><font color="Olive">y</font> <a href="lattices.html#K2" 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#K2" target="_self">"/\"</a> <font color="Olive">y</font></span>)</span> <a href="lattices.html#K2" target="_self">"/\"</a> <font color="Olive">z</font>
 
<b>by </b><i/>;<br/>
<a NAME="E7:18_3_1"/><i><font color="Green">E44</font></i>: 
for <font color="Olive">x</font>, <font color="Olive">y</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#K2" target="_self">"/\"</a> <span class="p1">(<span class="default"><font color="Olive">x</font> <a href="lattices.html#K1" target="_self">"\/"</a> <font color="Olive">y</font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Olive">x</font>
 
<b>by </b><i/>;<br/>
<a NAME="E8:18_3_1"/>
( <font color="Maroon">GG</font> is <a href="lattices.html#V4" target="_self">join-commutative</a> &amp; <font color="Maroon">GG</font> is <a href="lattices.html#V5" target="_self">join-associative</a> &amp; <font color="Maroon">GG</font> is <a href="lattices.html#V8" target="_self">meet-absorbing</a> &amp; <font color="Maroon">GG</font> is <a href="lattices.html#V6" target="_self">meet-commutative</a> &amp; <font color="Maroon">GG</font> is <a href="lattices.html#V7" target="_self">meet-associative</a> &amp; <font color="Maroon">GG</font> is <a href="lattices.html#V9" target="_self">join-absorbing</a> )
 
<b>by </b><i>, , , , , , , , <a class="ref" href="lattices.html#D3" target="_self">Def3</a>, <a class="txt" href="lattices.html#E4"><i><font color="Green">Lemma15</font></i></a>, , </i>;<br/>
<b>hence </b><a NAME="E9:18_3_1"/>
( <font color="Maroon">GG</font> is <a href="lattices.html#V3" target="_self">strict</a> &amp; <font color="Maroon">GG</font> is <a href="lattices.html#V10" target="_self">Lattice-like</a> )
 <b>by </b><i/>;<br/>


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