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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E5">Th5</font></span>: <a NAME="T5"><span class="comment"><font color="firebrick">:: POLYNOM3:5</font></span><br/></a><div class="add"> 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" title="b2">p</font>, <font color="Olive" title="b3">q</font>, <font color="Olive" title="b4">r</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/> ( ( <font color="Olive" title="b2">p</font> <a href="polynom3.html#R1" title="POLYNOM3:pred.1">&lt;</a> <font color="Olive" title="b3">q</font> &amp; <font color="Olive" title="b3">q</font> <a href="polynom3.html#R1" title="POLYNOM3:pred.1">&lt;</a> <font color="Olive" title="b4">r</font> implies <font color="Olive" title="b2">p</font> <a href="polynom3.html#R1" title="POLYNOM3:pred.1">&lt;</a> <font color="Olive" title="b4">r</font> ) &amp; ( ( ( <font color="Olive" title="b2">p</font> <a href="polynom3.html#R1" title="POLYNOM3:pred.1">&lt;</a> <font color="Olive" title="b3">q</font> &amp; <font color="Olive" title="b3">q</font> <a href="polynom3.html#R2" title="POLYNOM3:pred.2">&lt;=</a> <font color="Olive" title="b4">r</font> ) or ( <font color="Olive" title="b2">p</font> <a href="polynom3.html#R2" title="POLYNOM3:pred.2">&lt;=</a> <font color="Olive" title="b3">q</font> &amp; <font color="Olive" title="b3">q</font> <a href="polynom3.html#R1" title="POLYNOM3:pred.1">&lt;</a> <font color="Olive" title="b4">r</font> ) or ( <font color="Olive" title="b2">p</font> <a href="polynom3.html#R2" title="POLYNOM3:pred.2">&lt;=</a> <font color="Olive" title="b3">q</font> &amp; <font color="Olive" title="b3">q</font> <a href="polynom3.html#R2" title="POLYNOM3:pred.2">&lt;=</a> <font color="Olive" title="b4">r</font> ) ) implies <font color="Olive" title="b2">p</font> <a href="polynom3.html#R2" title="POLYNOM3:pred.2">&lt;=</a> <font color="Olive" title="b4">r</font> ) )</div></div>
