<?xml version="1.0"?>
<div>:: <span class="kw">deftheorem </span><span class="lab"><font color="Green" title="E39">Def33</font></span>   defines <a href="qc_lang1.html#R1" title="QC_LANG1:pred.1">&lt;=</a> <a onclick="hs(this)" href="javascript:()">QC_LANG1:def 33 : <br/></a><span> for <font color="Olive" title="b1">A</font> being    <a href="qc_lang1.html#M1" title="QC_LANG1:mode.1">QC-alphabet</a> <br/>  for <font color="Olive" title="b2">s</font>, <font color="Olive" title="b3">t</font> being   <a href="qc_lang1.html#NM2" title="QC_LANG1:NM.2">QC-symbol</a> of <font color="Olive" title="b1">A</font> holds <br/> ( ( <font color="Olive" title="b2">s</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="numbers.html#NK1" title="NUMBERS:NK.1">NAT</a>  &amp; <font color="Olive" title="b3">t</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="numbers.html#NK1" title="NUMBERS:NK.1">NAT</a>  implies ( <font color="Olive" title="b2">s</font> <a href="qc_lang1.html#R1" title="QC_LANG1:pred.1">&lt;=</a> <font color="Olive" title="b3">t</font> iff  ex <font color="Olive" title="b4">n</font>, <font color="Olive" title="b5">m</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a> st <br/>( <font color="Olive" title="b4">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">s</font> &amp; <font color="Olive" title="b5">m</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b3">t</font> &amp; <font color="Olive" title="b4">n</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Olive" title="b5">m</font> ) ) ) &amp; (  not <font color="Olive" title="b2">s</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="numbers.html#NK1" title="NUMBERS:NK.1">NAT</a>  &amp;  not <font color="Olive" title="b3">t</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="numbers.html#NK1" title="NUMBERS:NK.1">NAT</a>  implies ( <font color="Olive" title="b2">s</font> <a href="qc_lang1.html#R1" title="QC_LANG1:pred.1">&lt;=</a> <font color="Olive" title="b3">t</font> iff <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Olive" title="b2">s</font>,<font color="Olive" title="b3">t</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  the    <a href="qc_lang1.html#M2" title="QC_LANG1:mode.2">Relation</a> of <font color="Olive" title="b1">A</font> ) ) &amp; ( (  not <font color="Olive" title="b2">s</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="numbers.html#NK1" title="NUMBERS:NK.1">NAT</a>  or  not <font color="Olive" title="b3">t</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="numbers.html#NK1" title="NUMBERS:NK.1">NAT</a>  ) &amp; ( <font color="Olive" title="b2">s</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="numbers.html#NK1" title="NUMBERS:NK.1">NAT</a>  or <font color="Olive" title="b3">t</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="numbers.html#NK1" title="NUMBERS:NK.1">NAT</a>  ) implies ( <font color="Olive" title="b2">s</font> <a href="qc_lang1.html#R1" title="QC_LANG1:pred.1">&lt;=</a> <font color="Olive" title="b3">t</font> iff <font color="Olive" title="b3">t</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="numbers.html#NK1" title="NUMBERS:NK.1">NAT</a>  ) ) );<br/></span></div>
