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<div>:: <span class="kw">deftheorem </span><span class="lab"><font color="Green" title="E33">Def4</font></span>   defines <a href="cardfil4.html#K5" title="CARDFIL4:func.5">square-downarrow</a> <a onclick="hs(this)" href="javascript:()">CARDFIL4:def 5 : <br/></a><span> for <font color="Olive" title="b1">n</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a><br/>  for <font color="Olive">b<sub>2</sub></font> being   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><a href="numbers.html#NK1" title="NUMBERS:NK.1">NAT</a>,<a href="numbers.html#NK1" title="NUMBERS:NK.1">NAT</a></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span> holds <br/> ( <font color="Olive">b<sub>2</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cardfil4.html#K5" title="CARDFIL4:func.5">square-downarrow</a> <font color="Olive" title="b1">n</font> iff  for <font color="Olive" title="b3">x</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><a href="numbers.html#NK1" title="NUMBERS:NK.1">NAT</a>,<a href="numbers.html#NK1" title="NUMBERS:NK.1">NAT</a></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span> holds <br/> ( <font color="Olive" title="b3">x</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive">b<sub>2</sub></font> iff  ex <font color="Olive" title="b4">n1</font>, <font color="Olive" title="b5">n2</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a> st <br/>( <font color="Olive" title="b4">n1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b3">x</font> <a href="domain_1.html#K2" title="DOMAIN_1:func.2">`1</a>  &amp; <font color="Olive" title="b5">n2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b3">x</font> <a href="domain_1.html#K3" title="DOMAIN_1:func.3">`2</a>  &amp; <font color="Olive" title="b4">n1</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Olive" title="b1">n</font> &amp; <font color="Olive" title="b5">n2</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Olive" title="b1">n</font> ) ) );<br/></span></div>
