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<div>:: <span class="kw">deftheorem </span><span class="lab"><font color="Green" title="E3">asc</font></span>   defines <a href="ring_2.html#V1" title="RING_2:attr.1">ascending</a> <a onclick="hs(this)" href="javascript:()">RING_2:def 1 : <br/></a><span> for <font color="Olive" title="b1">X</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="ring_2.html#NM1" title="RING_2:NM.1">Chain</a> of <font color="Olive" title="b1">X</font> holds <br/> ( <font color="Olive" title="b2">C</font> is  <a href="ring_2.html#V1" title="RING_2:attr.1">ascending</a>  iff  for <font color="Olive" title="b3">i</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a> holds  <font color="Olive" title="b2">C</font> <a href="nat_1.html#K8" title="NAT_1:func.8">.</a> <font color="Olive" title="b3">i</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b2">C</font> <a href="nat_1.html#K8" title="NAT_1:func.8">.</a> <span class="p1">(<span class="default"><font color="Olive" title="b3">i</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> );<br/></span></div>
