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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E56">Th31146</font></span>: <a NAME="T55"><span class="comment"><font color="firebrick">:: LATTAD_1:55</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">L</font> being   <a href="lattad_1.html#NM2" title="LATTAD_1:NM.2">GAD_Lattice</a> holds <br/> ( <font color="Olive" title="b1">L</font> is  <a href="lattices.html#V4" title="LATTICES:attr.4">join-commutative</a>  iff  <a href="lattad_1.html#K4" title="LATTAD_1:func.4">ThetaOrder</a> <font color="Olive" title="b1">L</font> is  <a href="relat_2.html#V4" title="RELAT_2:attr.4">antisymmetric</a>  )</div></div>
