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<b>let </b><font color="Maroon">Q</font> be  non <a href="struct_0.html#V3">empty</a> <a href="lattices.html#V10">Lattice-like</a> <a href="lattice3.html#V4">complete</a>  <a href="quantal1.html#L2" target="_self">QuasiNetStr</a> ;<br/>

<b>assume </b><a NAME="E1:25_1_1"/>
( <font color="Maroon">Q</font> is <a href="quantal1.html#V8" target="_self">left-distributive</a> &amp; <font color="Maroon">Q</font> is <a href="quantal1.html#V7" target="_self">right-distributive</a> )
 ;<br/>

<b>hence </b><a NAME="E2:25_1_1"/>
( ( for <font color="Olive">X</font>, <font color="Olive">Y</font> being  <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">Q</font>  st <font color="Olive">X</font> is <a href="quantal1.html#V1" target="_self">directed</a> &amp; <font color="Olive">Y</font> is <a href="quantal1.html#V1" target="_self">directed</a> holds <br/><span class="p1">(<span class="default"><a href="lattice3.html#K15">"\/"</a> <font color="Olive">X</font>,<font color="Maroon">Q</font></span>)</span> <a href="monoid_0.html#NK3" target="_self">[*]</a> <span class="p1">(<span class="default"><a href="lattice3.html#K15">"\/"</a> <font color="Olive">Y</font>,<font color="Maroon">Q</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="lattice3.html#K15">"\/"</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><font color="Olive">a</font> <a href="monoid_0.html#NK3" target="_self">[*]</a> <font color="Olive">b</font></span>)</span> where <font color="Olive">a</font> is   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">Q</font>, <font color="Olive">b</font> is   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">Q</font> : ( <font color="Olive">a</font> <a href="hidden.html#R2">in</a> <font color="Olive">X</font> &amp; <font color="Olive">b</font> <a href="hidden.html#R2">in</a> <font color="Olive">Y</font> ) </span>}</span> ,<font color="Maroon">Q</font> ) &amp; ( for <font color="Olive">a</font>, <font color="Olive">b</font>, <font color="Olive">c</font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">Q</font> holds <br/> ( <span class="p1">(<span class="default"><font color="Olive">a</font> <a href="lattices.html#K3">"\/"</a> <font color="Olive">b</font></span>)</span> <a href="monoid_0.html#NK3" target="_self">[*]</a> <font color="Olive">c</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Olive">a</font> <a href="monoid_0.html#NK3" target="_self">[*]</a> <font color="Olive">c</font></span>)</span> <a href="lattices.html#K3">"\/"</a> <span class="p1">(<span class="default"><font color="Olive">b</font> <a href="monoid_0.html#NK3" target="_self">[*]</a> <font color="Olive">c</font></span>)</span> &amp; <font color="Olive">c</font> <a href="monoid_0.html#NK3" target="_self">[*]</a> <span class="p1">(<span class="default"><font color="Olive">a</font> <a href="lattices.html#K3">"\/"</a> <font color="Olive">b</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Olive">c</font> <a href="monoid_0.html#NK3" target="_self">[*]</a> <font color="Olive">a</font></span>)</span> <a href="lattices.html#K3">"\/"</a> <span class="p1">(<span class="default"><font color="Olive">c</font> <a href="monoid_0.html#NK3" target="_self">[*]</a> <font color="Olive">b</font></span>)</span> ) ) )
 <b>by </b><i>, </i>; <i><font color="Red">:: according to </font></i><a class="ref" href="quantal1.html#D7" target="_self">QUANTAL1:def 7</a>,<a class="ref" href="quantal1.html#D8" target="_self">QUANTAL1:def 8</a><br/>


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