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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E8">Th9</font></span>: <a NAME="T10"><span class="comment"><font color="firebrick">:: BAGORDER:10</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#L1" title="ORDERS_2:struct.1">RelStr</a> <br/>  for <font color="Olive" title="b2">s</font> being   <a href="struct_0.html#NM9" title="STRUCT_0:NM.9">sequence</a> of <font color="Olive" title="b1">R</font>  st <font color="Olive" title="b1">R</font> is  <a href="wellfnd1.html#V1" title="WELLFND1:attr.1">well_founded</a>  &amp; <font color="Olive" title="b2">s</font> is  <a href="bagorder.html#V1" title="BAGORDER:attr.1">non-increasing</a>  holds <br/> ex <font color="Olive" title="b3">p</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a> st <br/> for <font color="Olive" title="b4">r</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a>  st <font color="Olive" title="b3">p</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Olive" title="b4">r</font> holds <br/><font color="Olive" title="b2">s</font> <a href="nat_1.html#K8" title="NAT_1:func.8">.</a> <font color="Olive" title="b3">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">s</font> <a href="nat_1.html#K8" title="NAT_1:func.8">.</a> <font color="Olive" title="b4">r</font></div></div>
