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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E10">Th31</font></span>: <a NAME="T31"><span class="comment"><font color="firebrick">:: YELLOW14:31</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">M</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">i</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Olive" title="b1">M</font><br/>  for <font color="Olive" title="b3">J</font> being   <a href="waybel_3.html#V4" title="WAYBEL_3:attr.4">non-Empty</a>   <a href="waybel18.html#V1" title="WAYBEL18:attr.1">TopStruct-yielding</a>  <a href="pboole.html#NM1" title="PBOOLE:NM.1">ManySortedSet</a> of <font color="Olive" title="b1">M</font><br/>  for <font color="Olive" title="b4">x</font> being   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <span class="p1">(<span class="default"><a href="waybel18.html#K3" title="WAYBEL18:func.3">product</a> <font color="Olive" title="b3">J</font></span>)</span> holds   <a href="card_3.html#K5" title="CARD_3:func.5">pi</a> (<span class="p1">(<span class="default"><a href="pre_topc.html#K2" title="PRE_TOPC:func.2">Cl</a> <span class="p2"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Olive" title="b4">x</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span></span>)</span>,<font color="Olive" title="b2">i</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="pre_topc.html#K2" title="PRE_TOPC:func.2">Cl</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><span class="p2">(<span class="default"><font color="Olive" title="b4">x</font> <a href="waybel18.html#K5" title="WAYBEL18:func.5">.</a> <font color="Olive" title="b2">i</font></span>)</span></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span></div></div>
