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<div>:: <span class="kw">deftheorem </span><span class="lab"><font color="Green" title="E8">Def3</font></span>   defines <a href="polynom3.html#K5" title="POLYNOM3:func.5">TuplesOrder</a> <a onclick="hs(this)" href="javascript:()">POLYNOM3:def 3 : <br/></a><span> for <font color="Olive" title="b1">n</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#NK1" title="NUMBERS:NK.1">NAT</a> <br/>  for <font color="Olive">b<sub>2</sub></font> being   <a href="orders_1.html#NM4" title="ORDERS_1:NM.4">Order</a> of <span class="p1">(<span class="default"><font color="Olive" title="b1">n</font> <a href="finseq_2.html#K4" title="FINSEQ_2:func.4">-tuples_on</a> <a href="numbers.html#NK1" title="NUMBERS:NK.1">NAT</a></span>)</span> holds <br/> ( <font color="Olive">b<sub>2</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="polynom3.html#K5" title="POLYNOM3:func.5">TuplesOrder</a> <font color="Olive" title="b1">n</font> iff  for <font color="Olive" title="b3">p</font>, <font color="Olive" title="b4">q</font> being    <a href="finseq_2.html#M2" title="FINSEQ_2:mode.2">Element</a> of <font color="Olive" title="b1">n</font> <a href="finseq_2.html#K4" title="FINSEQ_2:func.4">-tuples_on</a> <a href="numbers.html#NK1" title="NUMBERS:NK.1">NAT</a> holds <br/> ( <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Olive" title="b3">p</font>,<font color="Olive" title="b4">q</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive">b<sub>2</sub></font> iff <font color="Olive" title="b3">p</font> <a href="polynom3.html#R2" title="POLYNOM3:pred.2">&lt;=</a> <font color="Olive" title="b4">q</font> ) );<br/></span></div>
