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<div><span class="kw">theorem </span><a NAME="T6"><span class="comment"><font color="firebrick">:: NUMBER16:6</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a>  st <font color="Olive" title="b1">a</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  &amp; <font color="Olive" title="b2">b</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  holds <br/> ex <font color="Olive" title="b3">N</font> being   <a href="finset_1.html#NV2" title="FINSET_1:NV.2">infinite</a>  <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> st <br/> for <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><br/>  for <font color="Olive" title="b6">p</font> being   <a href="int_2.html#NM1" title="INT_2:NM.1">Prime</a>  st <font color="Olive" title="b4">n</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b3">N</font> &amp; <font color="Olive" title="b5">m</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b3">N</font> holds <br/>( <font color="Olive" title="b6">p</font> <a href="nat_d.html#R1" title="NAT_D:pred.1">divides</a> <span class="p1">(<span class="default"><a href="number06.html#K1" title="NUMBER06:func.1">ArProg</a> (<font color="Olive" title="b2">b</font>,<font color="Olive" title="b1">a</font>)</span>)</span> <a href="recdef_1.html#K1" title="RECDEF_1:func.1">.</a> <font color="Olive" title="b4">n</font> iff <font color="Olive" title="b6">p</font> <a href="nat_d.html#R1" title="NAT_D:pred.1">divides</a> <span class="p1">(<span class="default"><a href="number06.html#K1" title="NUMBER06:func.1">ArProg</a> (<font color="Olive" title="b2">b</font>,<font color="Olive" title="b1">a</font>)</span>)</span> <a href="recdef_1.html#K1" title="RECDEF_1:func.1">.</a> <font color="Olive" title="b5">m</font> )</div></div>
