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<b>let </b><font color="Maroon" title="c1">Q</font> be   <a href="quantal1.html#NM2" title="QUANTAL1:NM.2">Quantale</a>;<br/><b>let </b><font color="Maroon" title="c2">a</font>, <font color="Maroon" title="c3">b</font>, <font color="Maroon" title="c4">c</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="E1:30"/><i><font color="Green" title="E10">A1</font></i>: 
<font color="Maroon" title="c2">a</font> <a href="lattices.html#R3" title="LATTICES:pred.3">[=</a> <font color="Maroon" title="c3">b</font>
 ;<br/>

<b>thus </b><span class="p1">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="monoid_0.html#NK3" title="MONOID_0:NK.3">[*]</a> <font color="Maroon" title="c4">c</font></span>)</span> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">b</font> <a href="monoid_0.html#NK3" title="MONOID_0:NK.3">[*]</a> <font color="Maroon" title="c4">c</font></span>)</span> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon" title="c3">b</font></span>)</span> <a href="monoid_0.html#NK3" title="MONOID_0:NK.3">[*]</a> <font color="Maroon" title="c4">c</font>
<b>by </b><i><a class="ref" href="quantal1.html#T6" target="_self" title="QUANTAL1:th.6">Th6</a></i>
<br/>.= 
<font color="Maroon" title="c3">b</font> <a href="monoid_0.html#NK3" title="MONOID_0:NK.3">[*]</a> <font color="Maroon" title="c4">c</font>
<b>by </b><i><a class="txt" href="quantal1.html#E1:30"><i><font color="Green" title="E10">A1</font></i></a>, <a class="ref" href="lattices.html#D3" title="LATTICES:def.3">LATTICES:def 3</a></i>
; <i><font color="Red">:: according to </font></i><a class="ref" href="lattices.html#D3" title="LATTICES:def.3">LATTICES:def 3</a><br/>

<b>thus </b><span class="p1">(<span class="default"><font color="Maroon" title="c4">c</font> <a href="monoid_0.html#NK3" title="MONOID_0:NK.3">[*]</a> <font color="Maroon" title="c2">a</font></span>)</span> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">c</font> <a href="monoid_0.html#NK3" title="MONOID_0:NK.3">[*]</a> <font color="Maroon" title="c3">b</font></span>)</span> = 
<font color="Maroon" title="c4">c</font> <a href="monoid_0.html#NK3" title="MONOID_0:NK.3">[*]</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon" title="c3">b</font></span>)</span>
<b>by </b><i><a class="ref" href="quantal1.html#T6" target="_self" title="QUANTAL1:th.6">Th6</a></i>
<br/>.= 
<font color="Maroon" title="c4">c</font> <a href="monoid_0.html#NK3" title="MONOID_0:NK.3">[*]</a> <font color="Maroon" title="c3">b</font>
<b>by </b><i><a class="txt" href="quantal1.html#E1:30"><i><font color="Green" title="E10">A1</font></i></a>, <a class="ref" href="lattices.html#D3" title="LATTICES:def.3">LATTICES:def 3</a></i>
; <i><font color="Red">:: according to </font></i><a class="ref" href="lattices.html#D3" title="LATTICES:def.3">LATTICES:def 3</a><br/>


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