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<div><span class="kw">theorem </span><a NAME="T3"><span class="comment"><font color="firebrick">:: RING_2:3</font></span><br/></a><div class="add"> 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#V1" title="RING_2:attr.1">ascending</a>  <a href="ring_2.html#NM1" title="RING_2:NM.1">Chain</a> of <font color="Olive" title="b1">X</font><br/>  for <font color="Olive" title="b3">i</font>, <font color="Olive" title="b4">j</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a>  st <font color="Olive" title="b3">i</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Olive" title="b4">j</font> holds <br/><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> <font color="Olive" title="b4">j</font> <span class="kw">by</span> <span class="lab"><a class="txt" href="ring_2.html#E5"><span class="lab"><font color="Green" title="E4">ch1</font></span></a></span>;<br/></div></div>
