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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E49">Th48</font></span>: <a NAME="T51"><span class="comment"><font color="firebrick">:: CHAIN_1:51</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">k</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a><br/>  for <font color="Olive" title="b2">d</font> being   non  <a href="ordinal1.html#V8" title="ORDINAL1:attr.8">zero</a>  <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a><br/>  for <font color="Olive" title="b3">G</font> being    <a href="chain_1.html#M1" title="CHAIN_1:mode.1">Grating</a> of <font color="Olive" title="b2">d</font><br/>  for <font color="Olive" title="b4">A</font> being   <a href="chain_1.html#NM3" title="CHAIN_1:NM.3">Cell</a> of <font color="Olive" title="b1">k</font>,<font color="Olive" title="b3">G</font><br/>  for <font color="Olive" title="b5">C</font> being   <a href="chain_1.html#NM4" title="CHAIN_1:NM.4">Chain</a> of <span class="p1">(<span class="default"><font color="Olive" title="b1">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span>,<font color="Olive" title="b3">G</font> holds <br/> ( <font color="Olive" title="b4">A</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="chain_1.html#K10" title="CHAIN_1:func.10">del</a> <font color="Olive" title="b5">C</font> iff ( <font color="Olive" title="b1">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Olive" title="b2">d</font> &amp;  <a href="card_1.html#K4" title="CARD_1:func.4">card</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="chain_1.html#K9" title="CHAIN_1:func.9">star</a> <font color="Olive" title="b4">A</font></span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <font color="Olive" title="b5">C</font></span>)</span> is  <a href="abian.html#NV2" title="ABIAN:NV.2">odd</a>  ) )</div></div>
