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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E12">Th15</font></span>: <a NAME="T15"><span class="comment"><font color="firebrick">:: LATSUM_1:15</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">R</font>, <font color="Olive" title="b2">S</font> being   non  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>   <a href="orders_2.html#L1" title="ORDERS_2:struct.1">RelStr</a> <br/>  for <font color="Olive" title="b3">a</font>, <font color="Olive" title="b4">b</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Olive" title="b1">R</font><br/>  for <font color="Olive" title="b5">c</font>, <font color="Olive" title="b6">d</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Olive" title="b2">S</font>  st <font color="Olive" title="b3">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b5">c</font> &amp; <font color="Olive" title="b4">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b6">d</font> &amp; <font color="Olive" title="b1">R</font> <a href="latsum_1.html#R1" title="LATSUM_1:pred.1">tolerates</a> <font color="Olive" title="b2">S</font> &amp; <font color="Olive" title="b1">R</font> is  <a href="orders_2.html#V4" title="ORDERS_2:attr.4">transitive</a>  &amp; <font color="Olive" title="b2">S</font> is  <a href="orders_2.html#V4" title="ORDERS_2:attr.4">transitive</a>  holds <br/>( <font color="Olive" title="b3">a</font> <a href="orders_2.html#R1" title="ORDERS_2:pred.1">&lt;=</a> <font color="Olive" title="b4">b</font> iff <font color="Olive" title="b5">c</font> <a href="orders_2.html#R1" title="ORDERS_2:pred.1">&lt;=</a> <font color="Olive" title="b6">d</font> )</div></div>
