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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E36">Th18</font></span>: <a NAME="T16"><span class="comment"><font color="firebrick">:: E_TRANS2:16</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">p</font> being   <a href="int_2.html#V1" title="INT_2:attr.1">prime</a>   <a href="abian.html#NV2" title="ABIAN:NV.2">odd</a>  <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a><br/>  for <font color="Olive" title="b2">m</font> being   <a href="xxreal_0.html#V2" title="XXREAL_0:attr.2">positive</a>  <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a><br/>  for <font color="Olive" title="b3">k</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a>  st  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Olive" title="b3">k</font> &amp; <font color="Olive" title="b3">k</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Olive" title="b1">p</font> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 1 holds <br/> for <font color="Olive" title="b4">i</font>, <font color="Olive" title="b5">j</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a>  st <font color="Olive" title="b4">i</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <span class="p1">(<span class="default"><font color="Olive" title="b3">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> holds <br/> <a href="e_trans2.html#K2" title="E_TRANS2:func.2">tau</a> <font color="Olive" title="b5">j</font> <a href="gcd_1.html#R2" title="GCD_1:pred.2">divides</a> <span class="p1">(<span class="default"><a href="ringder1.html#K4" title="RINGDER1:func.4">LBZ</a> (<span class="p2">(<span class="default"><a href="ringder1.html#K9" title="RINGDER1:func.9">Der1</a> <a href="int_3.html#K1" title="INT_3:func.1">INT.Ring</a></span>)</span>,<font color="Olive" title="b3">k</font>,<span class="p2">(<span class="default"><a href="group_4.html#K3" title="GROUP_4:func.3">Product</a> <span class="p3">(<span class="default"><a href="wsierp_1.html#K3" title="WSIERP_1:func.3">Del</a> (<span class="p4">(<span class="default"><a href="e_trans2.html#K4" title="E_TRANS2:func.4">ff_0</a> (<font color="Olive" title="b2">m</font>,<font color="Olive" title="b1">p</font>)</span>)</span>,<font color="Olive" title="b5">j</font>)</span>)</span></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="e_trans2.html#K2" title="E_TRANS2:func.2">tau</a> <font color="Olive" title="b5">j</font></span>)</span> <a href="binom.html#K2" title="BINOM:func.2">|^</a> <font color="Olive" title="b1">p</font></span>)</span>)</span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Olive" title="b4">i</font></div></div>
