<?xml version="1.0"?>
<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E42">Th24</font></span>: <a NAME="T21"><span class="comment"><font color="firebrick">:: E_TRANS2:21</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   non  <a href="ordinal1.html#V8" title="ORDINAL1:attr.8">zero</a>  <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a>  st <font color="Olive" title="b1">p</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Olive" title="b3">k</font> holds <br/> <a href="polynom4.html#K2" title="POLYNOM4:func.2">eval</a> (<span class="p1">(<span class="default"><a href="basel_2.html#K2" title="BASEL_2:func.2">~</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<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> <a href="vectsp11.html#K1" title="VECTSP11:func.1">|^</a> <font color="Olive" title="b3">k</font></span>)</span> <a href="ringder1.html#K8" title="RINGDER1:func.8">.</a> <span class="p3">(<span class="default"><a href="e_trans2.html#K5" title="E_TRANS2:func.5">f_0</a> (<font color="Olive" title="b2">m</font>,<font color="Olive" title="b1">p</font>)</span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <a href="int_3.html#K1" title="INT_3:func.1">INT.Ring</a></span>)</span>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Olive" title="b3">k</font> <a href="newton.html#K2" title="NEWTON:func.2">!</a></span>)</span> <a href="binom.html#K5" title="BINOM:func.5">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="basel_2.html#K2" title="BASEL_2:func.2">~</a> <span class="p3">(<span class="default"><a href="group_4.html#K3" title="GROUP_4:func.3">Product</a> <span class="p4">(<span class="default"><a href="e_trans2.html#K3" title="E_TRANS2:func.3">x.</a> (<font color="Olive" title="b2">m</font>,<font color="Olive" title="b1">p</font>)</span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K8" title="NAT_1:func.8">.</a> <span class="p2">(<span class="default"><font color="Olive" title="b3">k</font> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> <span class="p3">(<span class="default"><font color="Olive" title="b1">p</font> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> 1</span>)</span></span>)</span></span>)</span></div></div>
