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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E54">Th52</font></span>: <a NAME="T52"><span class="comment"><font color="firebrick">:: DILWORTH:52</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">R</font> being   non  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>   <a href="orders_2.html#V4" title="ORDERS_2:attr.4">transitive</a>   <a href="orders_2.html#V5" title="ORDERS_2:attr.5">antisymmetric</a>   <a href="dilworth.html#V4" title="DILWORTH:attr.4">with_finite_stability#</a>   <a href="orders_2.html#L1" title="ORDERS_2:struct.1">RelStr</a>   ex <font color="Olive" title="b2">S</font> being   non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Olive" title="b1">R</font> st <br/>( <font color="Olive" title="b2">S</font> is  <a href="dilworth.html#V7" title="DILWORTH:attr.7">strong-chain</a>  &amp; (  for <font color="Olive" title="b3">D</font> being   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Olive" title="b1">R</font>  holds <br/>(  not <font color="Olive" title="b3">D</font> is  <a href="dilworth.html#V7" title="DILWORTH:attr.7">strong-chain</a>  or  not <font color="Olive" title="b2">S</font> <a href="xboole_0.html#R2" title="XBOOLE_0:pred.2">c&lt;</a> <font color="Olive" title="b3">D</font> ) ) )</div></div>
