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<div><span class="kw">theorem </span><a NAME="T34"><span class="comment"><font color="firebrick">:: QUANTAL1:34</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">Q</font> being   <a href="quantal1.html#NM1" title="QUANTAL1:NM.1">Quantale</a><br/>  for <font color="Olive" title="b2">j</font> being   <a href="struct_0.html#NM14" title="STRUCT_0:NM.14">UnOp</a> of <font color="Olive" title="b1">Q</font>  st <font color="Olive" title="b2">j</font> is  <a href="quantal1.html#V14" title="QUANTAL1:attr.14">monotone</a>  &amp; <font color="Olive" title="b2">j</font> is  <a href="quantal1.html#V11" title="QUANTAL1:attr.11">idempotent</a>  &amp; <font color="Olive" title="b2">j</font> is  <a href="quantal1.html#V15" title="QUANTAL1:attr.15">\/-distributive</a>  holds <br/> ex <font color="Olive" title="b3">L</font> being   <a href="lattice3.html#V4" title="LATTICE3:attr.4">complete</a>  <a href="lattices.html#NM1" title="LATTICES:NM.1">Lattice</a> st <br/>(  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Olive" title="b3">L</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="relset_1.html#K2" title="RELSET_1:func.2">rng</a> <font color="Olive" title="b2">j</font> &amp; (  for <font color="Olive" title="b4">X</font> being   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Olive" title="b3">L</font> holds   <a href="lattice3.html#NK17" title="LATTICE3:NK.17">"\/"</a> <font color="Olive" title="b4">X</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">j</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><a href="lattice3.html#K15" title="LATTICE3:func.15">"\/"</a> (<font color="Olive" title="b4">X</font>,<font color="Olive" title="b1">Q</font>)</span>)</span> ) )</div></div>
