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<div><span class="kw">theorem </span><a NAME="T11"><span class="comment"><font color="firebrick">:: PCS_0:11</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">I</font> being   non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>   <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a> <br/>  for <font color="Olive" title="b2">C</font> being  () <a href="pboole.html#NM1" title="PBOOLE:NM.1">ManySortedSet</a> of <font color="Olive" title="b1">I</font><br/>  for <font color="Olive" title="b3">p</font>, <font color="Olive" title="b4">q</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="pcs_0.html#K18" title="PCS_0:func.18">pcs-union</a> <font color="Olive" title="b2">C</font></span>)</span> holds <br/> ( <font color="Olive" title="b3">p</font> <a href="orders_2.html#R1" title="ORDERS_2:pred.1">&lt;=</a> <font color="Olive" title="b4">q</font> iff  ex <font color="Olive" title="b5">i</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Olive" title="b1">I</font> ex <font color="Olive" title="b6">p9</font>, <font color="Olive" title="b7">q9</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><font color="Olive" title="b2">C</font> <a href="pcs_0.html#K16" title="PCS_0:func.16">.</a> <font color="Olive" title="b5">i</font></span>)</span> st <br/>( <font color="Olive" title="b6">p9</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b3">p</font> &amp; <font color="Olive" title="b7">q9</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b4">q</font> &amp; <font color="Olive" title="b6">p9</font> <a href="orders_2.html#R1" title="ORDERS_2:pred.1">&lt;=</a> <font color="Olive" title="b7">q9</font> ) )</div></div>
