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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E25">Th10</font></span>: <a NAME="T10"><span class="comment"><font color="firebrick">:: E_TRANS2:10</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">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><br/>  for <font color="Olive" title="b2">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> holds <br/> ( <span class="p1">(<span class="default"><a href="e_trans2.html#K3" title="E_TRANS2:func.3">x.</a> (<font color="Olive" title="b1">k</font>,<font color="Olive" title="b2">p</font>)</span>)</span> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <span class="p1"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><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> <span class="p4">(<span class="default"><font color="Olive" title="b1">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span> <a href="binom.html#K2" title="BINOM:func.2">|^</a> <font color="Olive" title="b2">p</font></span>)</span></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="e_trans2.html#K3" title="E_TRANS2:func.3">x.</a> (<span class="p1">(<span class="default"><font color="Olive" title="b1">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span>,<font color="Olive" title="b2">p</font>) &amp;  <a href="group_4.html#K3" title="GROUP_4:func.3">Product</a> <span class="p1">(<span class="default"><a href="e_trans2.html#K3" title="E_TRANS2:func.3">x.</a> (<span class="p2">(<span class="default"><font color="Olive" title="b1">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span>,<font color="Olive" title="b2">p</font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="group_4.html#K3" title="GROUP_4:func.3">Product</a> <span class="p2">(<span class="default"><a href="e_trans2.html#K3" title="E_TRANS2:func.3">x.</a> (<font color="Olive" title="b1">k</font>,<font color="Olive" title="b2">p</font>)</span>)</span></span>)</span> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="e_trans2.html#K2" title="E_TRANS2:func.2">tau</a> <span class="p3">(<span class="default"><font color="Olive" title="b1">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span> <a href="binom.html#K2" title="BINOM:func.2">|^</a> <font color="Olive" title="b2">p</font></span>)</span> )</div></div>
