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<div>:: <span class="kw">deftheorem </span>   defines <a href="stirl2_1.html#V2" title="STIRL2_1:attr.2">'increasing</a> <a onclick="hs(this)" href="javascript:()">STIRL2_1:def 3 : <br/></a><span> for <font color="Olive" title="b1">Ne</font>, <font color="Olive" title="b2">Ke</font> being   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <a href="numbers.html#NK1" title="NUMBERS:NK.1">NAT</a><br/>  for <font color="Olive" title="b3">f</font> being   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <font color="Olive" title="b1">Ne</font>,<font color="Olive" title="b2">Ke</font> holds <br/> ( <font color="Olive" title="b3">f</font> is  <a href="stirl2_1.html#V2" title="STIRL2_1:attr.2">'increasing</a>  iff  for <font color="Olive" title="b4">l</font>, <font color="Olive" title="b5">m</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a>  st <font color="Olive" title="b4">l</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="relset_1.html#K2" title="RELSET_1:func.2">rng</a> <font color="Olive" title="b3">f</font> &amp; <font color="Olive" title="b5">m</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="relset_1.html#K2" title="RELSET_1:func.2">rng</a> <font color="Olive" title="b3">f</font> &amp; <font color="Olive" title="b4">l</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Olive" title="b5">m</font> holds <br/> <a href="nat_1.html#K3" title="NAT_1:func.3">min*</a> <span class="p1">(<span class="default"><font color="Olive" title="b3">f</font> <a href="relset_1.html#K8" title="RELSET_1:func.8">"</a> <span class="p2"><a href="seq_4.html#K1" title="SEQ_4:func.1">{</a><span class="default"><font color="Olive" title="b4">l</font></span><a href="seq_4.html#K1" title="SEQ_4:func.1">}</a></span></span>)</span> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="nat_1.html#K3" title="NAT_1:func.3">min*</a> <span class="p1">(<span class="default"><font color="Olive" title="b3">f</font> <a href="relset_1.html#K8" title="RELSET_1:func.8">"</a> <span class="p2"><a href="seq_4.html#K1" title="SEQ_4:func.1">{</a><span class="default"><font color="Olive" title="b5">m</font></span><a href="seq_4.html#K1" title="SEQ_4:func.1">}</a></span></span>)</span> );<br/></span></div>
