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<b>let </b><font color="Maroon" title="c1">Q</font> be   <a href="quantal1.html#NM5" title="QUANTAL1:NM.5">Girard-Quantale</a>;<br/><b>let </b><font color="Maroon" title="c2">a1</font>, <font color="Maroon" title="c3">b1</font>, <font color="Maroon" title="c4">a2</font>, <font color="Maroon" title="c5">b2</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">Q</font>;<br/>









<b>assume </b><a NAME="E1:70"/>
( <font color="Maroon" title="c2">a1</font> <a href="lattices.html#R3" title="LATTICES:pred.3">[=</a> <font color="Maroon" title="c3">b1</font> &amp; <font color="Maroon" title="c4">a2</font> <a href="lattices.html#R3" title="LATTICES:pred.3">[=</a> <font color="Maroon" title="c5">b2</font> )
 ;<br/>

<a NAME="E2:70"/><b>then </b>
(  <a href="quantal1.html#K5" title="QUANTAL1:func.5">Bottom</a> <font color="Maroon" title="c3">b1</font> <a href="lattices.html#R3" title="LATTICES:pred.3">[=</a>  <a href="quantal1.html#K5" title="QUANTAL1:func.5">Bottom</a> <font color="Maroon" title="c2">a1</font> &amp;  <a href="quantal1.html#K5" title="QUANTAL1:func.5">Bottom</a> <font color="Maroon" title="c5">b2</font> <a href="lattices.html#R3" title="LATTICES:pred.3">[=</a>  <a href="quantal1.html#K5" title="QUANTAL1:func.5">Bottom</a> <font color="Maroon" title="c4">a2</font> )
 
<b>by </b><i><a class="ref" href="quantal1.html#T23" target="_self" title="QUANTAL1:th.23">Th23</a></i>;<br/>
<a NAME="E3:70"/><b>then </b>
( <span class="p1">(<span class="default"><a href="quantal1.html#K5" title="QUANTAL1:func.5">Bottom</a> <font color="Maroon" title="c3">b1</font></span>)</span> <a href="monoid_0.html#NK3" title="MONOID_0:NK.3">[*]</a> <span class="p1">(<span class="default"><a href="quantal1.html#K5" title="QUANTAL1:func.5">Bottom</a> <font color="Maroon" title="c5">b2</font></span>)</span> <a href="lattices.html#R3" title="LATTICES:pred.3">[=</a> <span class="p1">(<span class="default"><a href="quantal1.html#K5" title="QUANTAL1:func.5">Bottom</a> <font color="Maroon" title="c2">a1</font></span>)</span> <a href="monoid_0.html#NK3" title="MONOID_0:NK.3">[*]</a> <span class="p1">(<span class="default"><a href="quantal1.html#K5" title="QUANTAL1:func.5">Bottom</a> <font color="Maroon" title="c4">a2</font></span>)</span> &amp; <font color="Maroon" title="c2">a1</font> <a href="quantal1.html#K9" title="QUANTAL1:func.9">delta</a> <font color="Maroon" title="c4">a2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="quantal1.html#K5" title="QUANTAL1:func.5">Bottom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="quantal1.html#K5" title="QUANTAL1:func.5">Bottom</a> <font color="Maroon" title="c2">a1</font></span>)</span> <a href="monoid_0.html#NK3" title="MONOID_0:NK.3">[*]</a> <span class="p2">(<span class="default"><a href="quantal1.html#K5" title="QUANTAL1:func.5">Bottom</a> <font color="Maroon" title="c4">a2</font></span>)</span></span>)</span> &amp; <font color="Maroon" title="c3">b1</font> <a href="quantal1.html#K9" title="QUANTAL1:func.9">delta</a> <font color="Maroon" title="c5">b2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="quantal1.html#K5" title="QUANTAL1:func.5">Bottom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="quantal1.html#K5" title="QUANTAL1:func.5">Bottom</a> <font color="Maroon" title="c3">b1</font></span>)</span> <a href="monoid_0.html#NK3" title="MONOID_0:NK.3">[*]</a> <span class="p2">(<span class="default"><a href="quantal1.html#K5" title="QUANTAL1:func.5">Bottom</a> <font color="Maroon" title="c5">b2</font></span>)</span></span>)</span> )
 
<b>by </b><i><a class="ref" href="quantal1.html#T9" target="_self" title="QUANTAL1:th.9">Th9</a></i>;<br/>
<b>hence </b><a NAME="E4:70"/>
<font color="Maroon" title="c2">a1</font> <a href="quantal1.html#K9" title="QUANTAL1:func.9">delta</a> <font color="Maroon" title="c4">a2</font> <a href="lattices.html#R3" title="LATTICES:pred.3">[=</a> <font color="Maroon" title="c3">b1</font> <a href="quantal1.html#K9" title="QUANTAL1:func.9">delta</a> <font color="Maroon" title="c5">b2</font>
 <b>by </b><i><a class="ref" href="quantal1.html#T23" target="_self" title="QUANTAL1:th.23">Th23</a></i>;<br/>


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