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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E29">Th27</font></span>: <a NAME="T30"><span class="comment"><font color="firebrick">:: CHAIN_1:30</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">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="b2">l</font>, <font color="Olive" title="b3">r</font>, <font color="Olive" title="b4">l9</font>, <font color="Olive" title="b5">r9</font> being    <a href="finseq_2.html#M2" title="FINSEQ_2:mode.2">Element</a> of  <a href="euclid.html#K1" title="EUCLID:func.1">REAL</a> <font color="Olive" title="b1">d</font>  st (  for <font color="Olive" title="b6">i</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <font color="Olive" title="b1">d</font> holds  <font color="Olive" title="b2">l</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b6">i</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Olive" title="b3">r</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b6">i</font> ) &amp; (  for <font color="Olive" title="b6">i</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <font color="Olive" title="b1">d</font>  holds <font color="Olive" title="b5">r9</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b6">i</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Olive" title="b4">l9</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b6">i</font> ) holds <br/>(  <a href="chain_1.html#K3" title="CHAIN_1:func.3">cell</a> (<font color="Olive" title="b2">l</font>,<font color="Olive" title="b3">r</font>) <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="chain_1.html#K3" title="CHAIN_1:func.3">cell</a> (<font color="Olive" title="b4">l9</font>,<font color="Olive" title="b5">r9</font>) iff  ex <font color="Olive" title="b6">i</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <font color="Olive" title="b1">d</font> st <br/>( <font color="Olive" title="b3">r</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b6">i</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Olive" title="b5">r9</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b6">i</font> or <font color="Olive" title="b4">l9</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b6">i</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Olive" title="b2">l</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b6">i</font> ) )</div></div>
