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<div><span class="kw">theorem </span><a NAME="T3"><span class="comment"><font color="firebrick">:: QUANTAL1:3</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">L</font> being   non  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>   <a href="lattices.html#L3" title="LATTICES:struct.3">LattStr</a> <br/>  for <font color="Olive" title="b2">X</font> being   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Olive" title="b1">L</font>  st <font color="Olive" title="b2">X</font> is  <a href="quantal1.html#V1" title="QUANTAL1:attr.1">directed</a>  holds <br/> not <font color="Olive" title="b2">X</font> is  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> </div></div>
