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

<b>let </b><font color="Maroon">c<sub>1</sub></font> be   <a href="quantal1.html#NM5">Girard-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>thus </b><font color="Maroon">c<sub>2</sub></font> <a href="quantal1.html#K9" target="_self">delta</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="lattices.html#K4">"/\"</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> = 
 <a href="quantal1.html#K5" target="_self">Bottom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="quantal1.html#K5" target="_self">Bottom</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="monoid_0.html#NK3" target="_self">[*]</a> <span class="p2">(<span class="default"><a href="quantal1.html#K5" target="_self">Bottom</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="lattices.html#K4">"/\"</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span></span>)</span>

<br/>.= 
 <a href="quantal1.html#K5" target="_self">Bottom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="quantal1.html#K5" target="_self">Bottom</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="monoid_0.html#NK3" target="_self">[*]</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="quantal1.html#K5" target="_self">Bottom</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="lattices.html#K3">"\/"</a> <span class="p3">(<span class="default"><a href="quantal1.html#K5" target="_self">Bottom</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="quantal1.html#T26" target="_self">Th26</a></i>
<br/>.= 
 <a href="quantal1.html#K5" target="_self">Bottom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="quantal1.html#K5" target="_self">Bottom</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="monoid_0.html#NK3" target="_self">[*]</a> <span class="p3">(<span class="default"><a href="quantal1.html#K5" target="_self">Bottom</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span> <a href="lattices.html#K3">"\/"</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="quantal1.html#K5" target="_self">Bottom</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="monoid_0.html#NK3" target="_self">[*]</a> <span class="p3">(<span class="default"><a href="quantal1.html#K5" target="_self">Bottom</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="quantal1.html#T6" target="_self">Th6</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="quantal1.html#K5" target="_self">Bottom</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="quantal1.html#K5" target="_self">Bottom</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="monoid_0.html#NK3" target="_self">[*]</a> <span class="p3">(<span class="default"><a href="quantal1.html#K5" target="_self">Bottom</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span></span>)</span> <a href="lattices.html#K4">"/\"</a> <span class="p1">(<span class="default"><a href="quantal1.html#K5" target="_self">Bottom</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="quantal1.html#K5" target="_self">Bottom</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="monoid_0.html#NK3" target="_self">[*]</a> <span class="p3">(<span class="default"><a href="quantal1.html#K5" target="_self">Bottom</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="quantal1.html#T26" target="_self">Th26</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="quantal1.html#K9" target="_self">delta</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="lattices.html#K4">"/\"</a> <span class="p1">(<span class="default"><a href="quantal1.html#K5" target="_self">Bottom</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="quantal1.html#K5" target="_self">Bottom</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="monoid_0.html#NK3" target="_self">[*]</a> <span class="p3">(<span class="default"><a href="quantal1.html#K5" target="_self">Bottom</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span></span>)</span>

<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="quantal1.html#K9" target="_self">delta</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="lattices.html#K4">"/\"</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="quantal1.html#K9" target="_self">delta</a> <font color="Maroon">c<sub>4</sub></font></span>)</span>

;<br/>

<b>thus </b><span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="lattices.html#K4">"/\"</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="quantal1.html#K9" target="_self">delta</a> <font color="Maroon">c<sub>2</sub></font> = 
 <a href="quantal1.html#K5" target="_self">Bottom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="quantal1.html#K5" target="_self">Bottom</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="lattices.html#K4">"/\"</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span> <a href="monoid_0.html#NK3" target="_self">[*]</a> <span class="p2">(<span class="default"><a href="quantal1.html#K5" target="_self">Bottom</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span>

<br/>.= 
 <a href="quantal1.html#K5" target="_self">Bottom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="quantal1.html#K5" target="_self">Bottom</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="lattices.html#K3">"\/"</a> <span class="p3">(<span class="default"><a href="quantal1.html#K5" target="_self">Bottom</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span> <a href="monoid_0.html#NK3" target="_self">[*]</a> <span class="p2">(<span class="default"><a href="quantal1.html#K5" target="_self">Bottom</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="quantal1.html#T26" target="_self">Th26</a></i>
<br/>.= 
 <a href="quantal1.html#K5" target="_self">Bottom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="quantal1.html#K5" target="_self">Bottom</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="monoid_0.html#NK3" target="_self">[*]</a> <span class="p3">(<span class="default"><a href="quantal1.html#K5" target="_self">Bottom</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="lattices.html#K3">"\/"</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="quantal1.html#K5" target="_self">Bottom</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="monoid_0.html#NK3" target="_self">[*]</a> <span class="p3">(<span class="default"><a href="quantal1.html#K5" target="_self">Bottom</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="quantal1.html#T6" target="_self">Th6</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="quantal1.html#K5" target="_self">Bottom</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="quantal1.html#K5" target="_self">Bottom</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="monoid_0.html#NK3" target="_self">[*]</a> <span class="p3">(<span class="default"><a href="quantal1.html#K5" target="_self">Bottom</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span> <a href="lattices.html#K4">"/\"</a> <span class="p1">(<span class="default"><a href="quantal1.html#K5" target="_self">Bottom</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="quantal1.html#K5" target="_self">Bottom</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="monoid_0.html#NK3" target="_self">[*]</a> <span class="p3">(<span class="default"><a href="quantal1.html#K5" target="_self">Bottom</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="quantal1.html#T26" target="_self">Th26</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="quantal1.html#K9" target="_self">delta</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="lattices.html#K4">"/\"</a> <span class="p1">(<span class="default"><a href="quantal1.html#K5" target="_self">Bottom</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="quantal1.html#K5" target="_self">Bottom</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="monoid_0.html#NK3" target="_self">[*]</a> <span class="p3">(<span class="default"><a href="quantal1.html#K5" target="_self">Bottom</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span>

<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="quantal1.html#K9" target="_self">delta</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="lattices.html#K4">"/\"</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="quantal1.html#K9" target="_self">delta</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>

;<br/>


</div>
