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<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> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>1</sub></font>;<br/>



<b>assume </b><a NAME="E1:46"/>
<font color="Maroon">c<sub>2</sub></font> is <a href="quantal1.html#V18" target="_self">cyclic</a>
 ;<br/>

<a NAME="E2:46"/><b>then </b><i><font color="Green">E21</font></i>: 
( <font color="Maroon">c<sub>3</sub></font> <a href="lattices.html#R3">[=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="quantal1.html#K1" target="_self">-r&gt;</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="quantal1.html#K1" target="_self">-r&gt;</a> <font color="Maroon">c<sub>2</sub></font> &amp; <font color="Maroon">c<sub>3</sub></font> <a href="quantal1.html#K1" target="_self">-r&gt;</a> <font color="Maroon">c<sub>2</sub></font> <a href="lattices.html#R3">[=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="quantal1.html#K1" target="_self">-r&gt;</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="quantal1.html#K1" target="_self">-r&gt;</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="quantal1.html#K1" target="_self">-r&gt;</a> <font color="Maroon">c<sub>2</sub></font> &amp; <font color="Maroon">c<sub>3</sub></font> <a href="lattices.html#R3">[=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="quantal1.html#K2" target="_self">-l&gt;</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="quantal1.html#K2" target="_self">-l&gt;</a> <font color="Maroon">c<sub>2</sub></font> &amp; <font color="Maroon">c<sub>3</sub></font> <a href="quantal1.html#K2" target="_self">-l&gt;</a> <font color="Maroon">c<sub>2</sub></font> <a href="lattices.html#R3">[=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="quantal1.html#K2" target="_self">-l&gt;</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="quantal1.html#K2" target="_self">-l&gt;</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="quantal1.html#K2" target="_self">-l&gt;</a> <font color="Maroon">c<sub>2</sub></font> )
 
<b>by </b><i><a class="ref" href="quantal1.html#T16" target="_self">Th16</a></i>;<br/>
<a NAME="E3:46"/><b>then </b>
( <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="quantal1.html#K1" target="_self">-r&gt;</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="quantal1.html#K1" target="_self">-r&gt;</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="quantal1.html#K1" target="_self">-r&gt;</a> <font color="Maroon">c<sub>2</sub></font> <a href="lattices.html#R3">[=</a> <font color="Maroon">c<sub>3</sub></font> <a href="quantal1.html#K1" target="_self">-r&gt;</a> <font color="Maroon">c<sub>2</sub></font> &amp; <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="quantal1.html#K2" target="_self">-l&gt;</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="quantal1.html#K2" target="_self">-l&gt;</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="quantal1.html#K2" target="_self">-l&gt;</a> <font color="Maroon">c<sub>2</sub></font> <a href="lattices.html#R3">[=</a> <font color="Maroon">c<sub>3</sub></font> <a href="quantal1.html#K2" target="_self">-l&gt;</a> <font color="Maroon">c<sub>2</sub></font> )
 
<b>by </b><i><a class="ref" href="quantal1.html#T13" target="_self">Th13</a></i>;<br/>
<b>hence </b><a NAME="E4:46"/>
( <font color="Maroon">c<sub>3</sub></font> <a href="quantal1.html#K1" target="_self">-r&gt;</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="quantal1.html#K1" target="_self">-r&gt;</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="quantal1.html#K1" target="_self">-r&gt;</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="quantal1.html#K1" target="_self">-r&gt;</a> <font color="Maroon">c<sub>2</sub></font> &amp; <font color="Maroon">c<sub>3</sub></font> <a href="quantal1.html#K2" target="_self">-l&gt;</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="quantal1.html#K2" target="_self">-l&gt;</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="quantal1.html#K2" target="_self">-l&gt;</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="quantal1.html#K2" target="_self">-l&gt;</a> <font color="Maroon">c<sub>2</sub></font> )
 <b>by </b><i><a class="txt" href="quantal1.html#E2:46"><i><font color="Green">E21</font></i></a>, <a class="ref" href="lattices.html#T26">LATTICES:26</a></i>;<br/>


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