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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E18">Th14</font></span>: <a NAME="T14"><span class="comment"><font color="firebrick">:: LATTICE3:14</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">V</font> being   <a href="orders_2.html#V5" title="ORDERS_2:attr.5">antisymmetric</a>   <a href="lattice3.html#V1" title="LATTICE3:attr.1">with_suprema</a>   <a href="orders_2.html#L1" title="ORDERS_2:struct.1">RelStr</a> <br/>  for <font color="Olive" title="b2">u1</font>, <font color="Olive" title="b3">u2</font>, <font color="Olive" title="b4">u3</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Olive" title="b1">V</font>  st <font color="Olive" title="b1">V</font> is  <a href="orders_2.html#V4" title="ORDERS_2:attr.4">transitive</a>  holds <br/><span class="p1">(<span class="default"><font color="Olive" title="b2">u1</font> <a href="lattice3.html#K10" title="LATTICE3:func.10">"\/"</a> <font color="Olive" title="b3">u2</font></span>)</span> <a href="lattice3.html#K10" title="LATTICE3:func.10">"\/"</a> <font color="Olive" title="b4">u3</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">u1</font> <a href="lattice3.html#K10" title="LATTICE3:func.10">"\/"</a> <span class="p1">(<span class="default"><font color="Olive" title="b3">u2</font> <a href="lattice3.html#K10" title="LATTICE3:func.10">"\/"</a> <font color="Olive" title="b4">u3</font></span>)</span></div></div>
