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<b>let </b><font color="Maroon">Q</font> be   <a href="quantal1.html#NM2">Quantale</a>;<br/><b>let </b><font color="Maroon">a</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">Q</font>;<br/><b>let </b><font color="Maroon">b</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">Q</font>;<br/><b>let </b><font color="Maroon">c</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">Q</font>;<br/><b>let </b><font color="Maroon">d</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">Q</font>;<br/>









<b>assume </b><a NAME="E1:31"/>
( <font color="Maroon">a</font> <a href="lattices.html#R3">[=</a> <font color="Maroon">b</font> &amp; <font color="Maroon">c</font> <a href="lattices.html#R3">[=</a> <font color="Maroon">d</font> )
 ;<br/>

<a NAME="E2:31"/><b>then </b>
( <font color="Maroon">a</font> <a href="monoid_0.html#NK3" target="_self">[*]</a> <font color="Maroon">c</font> <a href="lattices.html#R3">[=</a> <font color="Maroon">b</font> <a href="monoid_0.html#NK3" target="_self">[*]</a> <font color="Maroon">c</font> &amp; <font color="Maroon">b</font> <a href="monoid_0.html#NK3" target="_self">[*]</a> <font color="Maroon">c</font> <a href="lattices.html#R3">[=</a> <font color="Maroon">b</font> <a href="monoid_0.html#NK3" target="_self">[*]</a> <font color="Maroon">d</font> &amp; <font color="Maroon">Q</font> is   <a href="lattices.html#NM1">Lattice</a> )
 
<b>by </b><i/>;<br/>
<b>hence </b><a NAME="E3:31"/>
<font color="Maroon">a</font> <a href="monoid_0.html#NK3" target="_self">[*]</a> <font color="Maroon">c</font> <a href="lattices.html#R3">[=</a> <font color="Maroon">b</font> <a href="monoid_0.html#NK3" target="_self">[*]</a> <font color="Maroon">d</font>
 <b>by </b><i><a class="ref" href="lattices.html#T25">LATTICES:25</a></i>;<br/>


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