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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E25">Th31</font></span>: <a NAME="T31"><span class="comment"><font color="firebrick">:: NUMBER16:31</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">n</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a> holds <br/> (  <a href="relset_1.html#K2" title="RELSET_1:func.2">rng</a> <span class="p1">(<span class="default"><a href="nat_3.html#K12" title="NAT_3:func.12">prime_exponents</a> <span class="p2">(<span class="default"><a href="wsierp_1.html#K2" title="WSIERP_1:func.2">Product</a> <span class="p3">(<span class="default"><a href="number13.html#K1" title="NUMBER13:func.1">primesFinS</a> <font color="Olive" title="b1">n</font></span>)</span></span>)</span></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,1</span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span> &amp;  <a href="card_1.html#K4" title="CARD_1:func.4">card</a> <span class="p1">(<span class="default"><a href="pre_poly.html#K22" title="PRE_POLY:func.22">support</a> <span class="p2">(<span class="default"><a href="nat_3.html#K12" title="NAT_3:func.12">prime_exponents</a> <span class="p3">(<span class="default"><a href="wsierp_1.html#K2" title="WSIERP_1:func.2">Product</a> <span class="p4">(<span class="default"><a href="number13.html#K1" title="NUMBER13:func.1">primesFinS</a> <font color="Olive" title="b1">n</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">n</font> )</div></div>
