<?xml version="1.0"?>
<div class="add">

<b>let </b><font color="Maroon">c<sub>1</sub></font> be   <a href="quantal1.html#NM2">Quantale</a>;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font>, <font color="Maroon">c<sub>3</sub></font>, <font color="Maroon">c<sub>4</sub></font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>1</sub></font>;<br/>







<b>assume </b><a NAME="E1:30"/><i><font color="Green">E10</font></i>: 
<font color="Maroon">c<sub>2</sub></font> <a href="lattices.html#R3">[=</a> <font color="Maroon">c<sub>3</sub></font>
 ;<br/>

<b>thus </b><span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="monoid_0.html#NK3" target="_self">[*]</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="lattices.html#K3">"\/"</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="monoid_0.html#NK3" target="_self">[*]</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> = 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="lattices.html#K3">"\/"</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="monoid_0.html#NK3" target="_self">[*]</a> <font color="Maroon">c<sub>4</sub></font>
<b>by </b><i><a class="ref" href="quantal1.html#T6" target="_self">Th6</a></i>
<br/>.= 
<font color="Maroon">c<sub>3</sub></font> <a href="monoid_0.html#NK3" target="_self">[*]</a> <font color="Maroon">c<sub>4</sub></font>
<b>by </b><i><a class="txt" href="quantal1.html#E1:30"><i><font color="Green">E10</font></i></a>, <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<sub>4</sub></font> <a href="monoid_0.html#NK3" target="_self">[*]</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="lattices.html#K3">"\/"</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="monoid_0.html#NK3" target="_self">[*]</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> = 
<font color="Maroon">c<sub>4</sub></font> <a href="monoid_0.html#NK3" target="_self">[*]</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="lattices.html#K3">"\/"</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="quantal1.html#T6" target="_self">Th6</a></i>
<br/>.= 
<font color="Maroon">c<sub>4</sub></font> <a href="monoid_0.html#NK3" target="_self">[*]</a> <font color="Maroon">c<sub>3</sub></font>
<b>by </b><i><a class="txt" href="quantal1.html#E1:30"><i><font color="Green">E10</font></i></a>, <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/>


</div>
