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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>assume </b><a NAME="E1:30"/><i><font color="Green">E26</font></i>: 
<font color="Maroon">a</font> <a href="lattices.html#R3">[=</a> <font color="Maroon">b</font>
 ;<br/>

<b>thus </b><span class="p1">(<span class="default"><font color="Maroon">a</font> <a href="monoid_0.html#NK3" target="_self">[*]</a> <font color="Maroon">c</font></span>)</span> <a href="lattices.html#K3">"\/"</a> <span class="p1">(<span class="default"><font color="Maroon">b</font> <a href="monoid_0.html#NK3" target="_self">[*]</a> <font color="Maroon">c</font></span>)</span> = 
<span class="p1">(<span class="default"><font color="Maroon">a</font> <a href="lattices.html#K3">"\/"</a> <font color="Maroon">b</font></span>)</span> <a href="monoid_0.html#NK3" target="_self">[*]</a> <font color="Maroon">c</font>
<b>by </b><i/>
<br/>.= 
<font color="Maroon">b</font> <a href="monoid_0.html#NK3" target="_self">[*]</a> <font color="Maroon">c</font>
<b>by </b><i>, <a class="ref" href="lattices.html#D3">LATTICES:def 3</a></i>
; <i><font color="Red">:: according to </font></i><a class="ref" href="lattices.html#D3">LATTICES:def 3</a><br/>

<b>thus </b><span class="p1">(<span class="default"><font color="Maroon">c</font> <a href="monoid_0.html#NK3" target="_self">[*]</a> <font color="Maroon">a</font></span>)</span> <a href="lattices.html#K3">"\/"</a> <span class="p1">(<span class="default"><font color="Maroon">c</font> <a href="monoid_0.html#NK3" target="_self">[*]</a> <font color="Maroon">b</font></span>)</span> = 
<font color="Maroon">c</font> <a href="monoid_0.html#NK3" target="_self">[*]</a> <span class="p1">(<span class="default"><font color="Maroon">a</font> <a href="lattices.html#K3">"\/"</a> <font color="Maroon">b</font></span>)</span>
<b>by </b><i/>
<br/>.= 
<font color="Maroon">c</font> <a href="monoid_0.html#NK3" target="_self">[*]</a> <font color="Maroon">b</font>
<b>by </b><i>, <a class="ref" href="lattices.html#D3">LATTICES:def 3</a></i>
; <i><font color="Red">:: according to </font></i><a class="ref" href="lattices.html#D3">LATTICES:def 3</a><br/>


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