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<b>set </b><font color="Maroon" title="c1">B</font> =  <a href="lattice3.html#K1" title="LATTICE3:func.1">BooleLatt</a> <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> ;<br/>
<b>consider </b><font color="Maroon" title="c2">b</font> being   <a href="monoid_0.html#NM1" title="MONOID_0:NM.1">BinOp</a> of <span class="p1">(<span class="default"><a href="lattice3.html#K1" title="LATTICE3:func.1">BooleLatt</a> <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> </span>)</span>;<br/>
<b>take </b>
 <a href="quantal1.html#G1" title="QUANTAL1:aggr.1">QuantaleStr</a>(# <font color="Maroon">H<sub>1</sub></font>( <a href="lattice3.html#K1" title="LATTICE3:func.1">BooleLatt</a> <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> ),<font color="Maroon">H<sub>2</sub></font>( <a href="lattice3.html#K1" title="LATTICE3:func.1">BooleLatt</a> <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> ),<font color="Maroon">H<sub>3</sub></font>( <a href="lattice3.html#K1" title="LATTICE3:func.1">BooleLatt</a> <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> ),<font color="Maroon" title="c2">b</font> #)
;<br/>

<b>thus </b><a NAME="E2:19_1_1"/>
(  <a href="quantal1.html#G1" title="QUANTAL1:aggr.1">QuantaleStr</a>(# <font color="Maroon">H<sub>1</sub></font>( <a href="lattice3.html#K1" title="LATTICE3:func.1">BooleLatt</a> <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> ),<font color="Maroon">H<sub>2</sub></font>( <a href="lattice3.html#K1" title="LATTICE3:func.1">BooleLatt</a> <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> ),<font color="Maroon">H<sub>3</sub></font>( <a href="lattice3.html#K1" title="LATTICE3:func.1">BooleLatt</a> <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> ),<font color="Maroon" title="c2">b</font> #) is <a href="group_1.html#V4" title="GROUP_1:attr.4">associative</a> &amp;  <a href="quantal1.html#G1" title="QUANTAL1:aggr.1">QuantaleStr</a>(# <font color="Maroon">H<sub>1</sub></font>( <a href="lattice3.html#K1" title="LATTICE3:func.1">BooleLatt</a> <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> ),<font color="Maroon">H<sub>2</sub></font>( <a href="lattice3.html#K1" title="LATTICE3:func.1">BooleLatt</a> <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> ),<font color="Maroon">H<sub>3</sub></font>( <a href="lattice3.html#K1" title="LATTICE3:func.1">BooleLatt</a> <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> ),<font color="Maroon" title="c2">b</font> #) is <a href="group_1.html#V7" title="GROUP_1:attr.7">commutative</a> &amp;  <a href="quantal1.html#G1" title="QUANTAL1:aggr.1">QuantaleStr</a>(# <font color="Maroon">H<sub>1</sub></font>( <a href="lattice3.html#K1" title="LATTICE3:func.1">BooleLatt</a> <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> ),<font color="Maroon">H<sub>2</sub></font>( <a href="lattice3.html#K1" title="LATTICE3:func.1">BooleLatt</a> <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> ),<font color="Maroon">H<sub>3</sub></font>( <a href="lattice3.html#K1" title="LATTICE3:func.1">BooleLatt</a> <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> ),<font color="Maroon" title="c2">b</font> #) is <a href="group_1.html#V2" title="GROUP_1:attr.2">unital</a> &amp;  <a href="quantal1.html#G1" title="QUANTAL1:aggr.1">QuantaleStr</a>(# <font color="Maroon">H<sub>1</sub></font>( <a href="lattice3.html#K1" title="LATTICE3:func.1">BooleLatt</a> <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> ),<font color="Maroon">H<sub>2</sub></font>( <a href="lattice3.html#K1" title="LATTICE3:func.1">BooleLatt</a> <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> ),<font color="Maroon">H<sub>3</sub></font>( <a href="lattice3.html#K1" title="LATTICE3:func.1">BooleLatt</a> <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> ),<font color="Maroon" title="c2">b</font> #) is <a href="quantal1.html#V6" title="QUANTAL1:attr.6">with_zero</a> &amp;  <a href="quantal1.html#G1" title="QUANTAL1:aggr.1">QuantaleStr</a>(# <font color="Maroon">H<sub>1</sub></font>( <a href="lattice3.html#K1" title="LATTICE3:func.1">BooleLatt</a> <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> ),<font color="Maroon">H<sub>2</sub></font>( <a href="lattice3.html#K1" title="LATTICE3:func.1">BooleLatt</a> <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> ),<font color="Maroon">H<sub>3</sub></font>( <a href="lattice3.html#K1" title="LATTICE3:func.1">BooleLatt</a> <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> ),<font color="Maroon" title="c2">b</font> #) is <a href="quantal1.html#V8" title="QUANTAL1:attr.8">left-distributive</a> &amp;  <a href="quantal1.html#G1" title="QUANTAL1:aggr.1">QuantaleStr</a>(# <font color="Maroon">H<sub>1</sub></font>( <a href="lattice3.html#K1" title="LATTICE3:func.1">BooleLatt</a> <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> ),<font color="Maroon">H<sub>2</sub></font>( <a href="lattice3.html#K1" title="LATTICE3:func.1">BooleLatt</a> <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> ),<font color="Maroon">H<sub>3</sub></font>( <a href="lattice3.html#K1" title="LATTICE3:func.1">BooleLatt</a> <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> ),<font color="Maroon" title="c2">b</font> #) is <a href="quantal1.html#V7" title="QUANTAL1:attr.7">right-distributive</a> &amp;  <a href="quantal1.html#G1" title="QUANTAL1:aggr.1">QuantaleStr</a>(# <font color="Maroon">H<sub>1</sub></font>( <a href="lattice3.html#K1" title="LATTICE3:func.1">BooleLatt</a> <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> ),<font color="Maroon">H<sub>2</sub></font>( <a href="lattice3.html#K1" title="LATTICE3:func.1">BooleLatt</a> <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> ),<font color="Maroon">H<sub>3</sub></font>( <a href="lattice3.html#K1" title="LATTICE3:func.1">BooleLatt</a> <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> ),<font color="Maroon" title="c2">b</font> #) is <a href="lattice3.html#V4" title="LATTICE3:attr.4">complete</a> &amp;  <a href="quantal1.html#G1" title="QUANTAL1:aggr.1">QuantaleStr</a>(# <font color="Maroon">H<sub>1</sub></font>( <a href="lattice3.html#K1" title="LATTICE3:func.1">BooleLatt</a> <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> ),<font color="Maroon">H<sub>2</sub></font>( <a href="lattice3.html#K1" title="LATTICE3:func.1">BooleLatt</a> <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> ),<font color="Maroon">H<sub>3</sub></font>( <a href="lattice3.html#K1" title="LATTICE3:func.1">BooleLatt</a> <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> ),<font color="Maroon" title="c2">b</font> #) is <a href="lattices.html#V10" title="LATTICES:attr.10">Lattice-like</a> )
 <b>by </b><i><a class="ref" href="quantal1.html#T4" target="_self" title="QUANTAL1:th.4">Th4</a></i>;<br/>


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